aristotle thesis antithesis synthesis

• Table of Contents
• Random Entry
• Chronological
• Editorial Information
• About the SEP
• Editorial Board
• How to Cite the SEP
• Special Characters
• Advanced Tools
• Support the SEP
• PDFs for SEP Friends
• Make a Donation
• SEPIA for Libraries
• Entry Contents

Bibliography

Academic tools.

• Friends PDF Preview
• Author and Citation Info
• Back to Top

Contradiction

Do I contradict myself? Very well, then, I contradict myself. (I am large, I contain multitudes.)    —Walt Whitman, “Song of Myself”

Vorrei e non vorrei.    —Zerlina, “Là ci darem la mano”, Don Giovanni

This entry outlines the role of the law of non-contradiction (LNC) as the foremost among the first (indemonstrable) principles of Aristotelian philosophy and its heirs, and depicts the relation between LNC and LEM (the law of excluded middle) in establishing the nature of contradictory and contrary opposition. §1 presents the classical treatment of LNC as an axiom in Aristotle's “First Philosophy” and reviews the status of contradictory and contrary opposition as schematized on the Square of Opposition. §2 explores in further detail the possible characterizations of LNC and LEM, including the relevance of future contingent statements in which LEM (but not LNC) is sometimes held to fail. §3 addresses the mismatch between the logical status of contradictory negation as a propositional operator and the diverse realizations of contradictory negation within natural language. §4 deals with several challenges to LNC within Western philosophy, including the paradoxes, and the relation between systems with truth-value gaps (violating LEM) and those with truth-value gluts (violating LNC). In §5, the tetralemma of Buddhist logic is discussed within the context of gaps and gluts; it is suggested that apparent violations of LNC in this tradition (and others) can be attributed to either differing viewpoints of evaluation, as foreseen by Aristotle, or to intervening modal and epistemic operators. §6 focuses on the problem of “borderline contradictions”: the range of acceptability judgments for apparently contradictory sentences with vague predicates as surveyed in empirical studies, and the theoretical implications of these studies. Finally, §7 surveys the ways of contradiction and its exploitation in literature and popular culture from Shakespeare to social media.

1. LNC as Indemonstrable

2. lem and lnc, 3. contradictory negation in term and propositional logic, 4. gaps and gluts: lnc and its discontents, 5. lnc and the buddhist tetralemma.

• 6. Vagueness and Borderline Contradictions
• 7. Contradiction in Everyday Life

Other Internet Resources

Related entries.

The twin foundations of Aristotle's logic are the law of non-contradiction (LNC) (also known as the law of contradiction, LC) and the law of excluded middle (LEM). In Metaphysics Book Γ, LNC—“the most certain of all principles”—is defined as follows:

It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect, and all other specifications that might be made, let them be added to meet local objections (1005b19–23).

It will be noted that this statement of the LNC is an explicitly modal claim about the incompatibility of opposed properties applying to the same object (with the appropriate provisos). Since Łukasiewicz (1910), this ontological version of the principle has been recognized as distinct from, and for Aristotle arguably prior to, the logical formulation (“The opinion that opposite assertions are not simultaneously true is the firmest of all”—Met. 1011b13–14) and the psychological formulation (“It is impossible for anyone to believe that the same thing is and is not, as some consider Heraclitus said”—Met. 1005b23–25) offered elsewhere in Book Γ; we return to Heraclitus below. Wedin (2004a), who argues for the primacy of the ontological version (see also Meyer 2008, Other Internet Resources), formalizes it as ¬◊(∃ x )( Fx ∧ ¬ Fx ). These three formulations of LNC differ in important respects, in particular as to whether the law is explicitly modal in character, whether it applies to propositions or to properties and objects, and whether it requires the invocation of a metalinguistic truth predicate. (See also the entry Aristotle on non-contradiction .)

For Aristotle, the status of LNC as a first, indemonstrable principle is obvious. Those who mulishly demand a proof of LNC clearly “lack education”: since “a demonstration of everything is impossible”, resulting in infinite regress. At least some principles must be taken as primitive axiomata rather than derived from other propositions—and what principle more merits this status than LNC? (1006a6–12). In first philosophy, as in mathematics, an axiom is both indemonstrable and indispensable; without LNC, Aristotle argues, “a is F ” and “a is not F ” are indistinguishable and no argumentation is possible. While Sophists and “even many physicists” may claim that it is possible for the same thing to be and not to be at the same time and in the same respect, such a position self-destructs “if only our opponent says something”, since as soon as he opens his mouth to make an assertion, any assertion, he must accept LNC. But what if he does not open his mouth? Against such an individual “it is ridiculous to seek an argument” for he is no more than a vegetable (1006a1–15).

The celebrated Arab commentator Avicenna (ibn Sīnā, 980–1037) confronts the LNC skeptic with a more severe outcome than Aristotle's vegetable reduction: “As for the obstinate, he must be plunged into fire, since fire and non-fire are identical. Let him be beaten, since suffering and not suffering are the same. Let him be deprived of food and drink, since eating and drinking are identical to abstaining” ( Metaphysics I.8, 53.13–15).

The role of LNC as the basic, indemonstrable “first principle” is affirmed by Leibniz, for whom LNC is taken as interdefinable with the Law of Identity that states that everything is identical to itself: “Nothing should be taken as first principles but experiences and the axiom of identity or (what is the same thing) contradiction, which is primitive, since otherwise there would be no difference between truth and falsehood, and all investigation would cease at once, if to say yes or no were a matter of indifference” (Leibniz 1696/Langley 1916: 13–14). For Leibniz, everybody—even “barbarians”—must tacitly assume LNC as part of innate knowledge implicitly called upon at every moment, thus demonstrating the insufficiency of Locke's empiricism (ibid., 77). [ 1 ]

In accounting for the incompatibility of truth and falsity, LNC lies at the heart of Aristotle's theory of opposition, governing both contradictories and contraries. (See traditional square of opposition .) Contradictory opposites (“She is sitting”/“She is not sitting”) are mutually exhaustive as well as mutually inconsistent; one member of the pair must be true and the other false, assuming with Aristotle that singular statements with vacuous subjects are always false. As it was put by the medievals, contradictory opposites divide the true and the false between them; for Aristotle, this is the primary form of opposition. [ 2 ] Contrary opposites (“He is happy”/“He is sad”) are mutually inconsistent but not necessarily exhaustive; they may be simultaneously false, though not simultaneously true. LNC applies to both forms of opposition in that neither contradictories nor contraries may belong to the same object at the same time and in the same respect ( Metaphysics 1011b17–19). What distinguishes the two forms of opposition is a second indemonstrable principle, the law of excluded middle (LEM): “Of any one subject, one thing must be either asserted or denied” ( Metaphysics 1011b24). Both laws pertain to contradictories, as in a paired affirmation (“ S is P ”) and denial (“ S isn't P ”): the negation is true whenever the affirmation is false, and the affirmation is true when the negation is false. Thus, a corresponding affirmation and negation cannot both be true , by LNC, but neither can they both be false , by LEM. But while LNC applies both to contradictory and contrary oppositions, LEM holds only for contradictories: “Nothing can exist between two contradictories, but something may exist between contraries” ( Metaphysics 1055b2): a dog cannot be both black and white, but it may be neither.

As Aristotle explains in the Categories, the opposition between contradictories—“statements opposed to each other as affirmation and negation”—is defined in two ways. First, unlike contrariety, contradiction is restricted to statements or propositions; terms are never related as contradictories. Second, “in this case, and in this case only, it is necessary for the one to be true and the other false” (13b2–3).

Opposition between terms cannot be contradictory in nature, both because only statements (subject-predicate combinations) can be true or false ( Categories 13b3–12) and because any two terms may simultaneously fail to apply to a given subject. [ 3 ] But two statements may be members of either a contradictory or a contrary opposition. Such statements may be simultaneously false, although (as with contradictories) they may not be simultaneously true. The most striking aspect of the exposition for a modern reader lies in Aristotle's selection of illustrative material. Rather than choosing an uncontroversial example involving mediate contraries, those allowing an unexcluded middle (e.g. “This dog is white”/“This dog is black”; “Socrates is good”/“Socrates is bad”), Aristotle offers a pair of sentences containing immediate contraries, “Socrates is sick”/“Socrates is well”. These propositions may both be false, even though every person is either ill or well: “For if Socrates exists, one will be true and the other false, but if he does not exist, both will be false; for neither ‘Socrates is sick’ nor ‘Socrates is well’ will be true, if Socrates does not exist at all” (13b17–19). But given a corresponding affirmation and negation, one will always be true and the other false; the negation “Socrates is not sick” is true whether the snub-nosed philosopher is healthy or non-existent: “for if he does not exist, ‘he is sick’ is false but ‘he is not sick’ true” (13b26–35).

Members of a canonical pair of contradictories are formally identical except for the negative particle:

An affirmation is a statement affirming something of something, a negation is a statement denying something of something…It is clear that for every affirmation there is an opposite negation, and for every negation there is an opposite affirmation…Let us call an affirmation and a negation which are opposite a contradiction ( De Interpretatione 17a25–35).

But this criterion, satisfied simply enough in the case of singular expressions, must be recast in the case of quantified expressions, both those which “signify universally” (“every cat”, “no cat”) and those which do not (“some cat”, “not every cat”).

For such cases, Aristotle shifts from a formal to a semantically based criterion of opposition (17b16–25). Members of an A / O pair (“Every man is white”/“Not every man is white”) or I / E pair (“Some man is white”/“No man is white”) are contradictories because in any state of affairs one member of each pair must be true and the other false. Members of an A / E pair—“Every man is just”/“No man is just”—constitute contraries, since these cannot both be true simultaneously but can both be false. The contradictories of these contraries (“Not every man is just”/“Some man is just”) can be simultaneously true with reference to the same subject (17b23–25). This last opposition of I and O statements, later to be dubbed subcontraries because they appear below the contraries on the traditional square, is a peculiar opposition indeed; Aristotle elsewhere ( Prior Analytics 63b21–30) sees I and O as “only verbally opposed”, given the consistency of the I statement, e.g. “Some Greeks are bald”, with the corresponding O statement, “Some Greeks aren't bald” (or “Not all Greeks are bald”, which doesn't necessarily amount to the same thing, given existential import; see traditional square of opposition ).

The same relations obtain for modal propositions, for propositions involving binary connectives like “and” and “or”, for quantificational adverbs, and for a range of other operators that can be mapped onto the square in analogous ways utilizing the same notions of contradictory and contrary opposition and with unilateral entailment definable on duals (see Horn 1989). Thus for example we have the modal square below, based on De Interpretatione 21b10ff. and Prior Analytics 32a18–28, where the box and diamond symbols denote necessity and possibility, respectively. As with universal affirmatives and universal negatives, necessity and impossibility constitute contraries: “A priest must marry” and “A priest can’t marry” can both be (and, on the Episcopalian reading, are) false but cannot both be true. “A priest can marry” and “A priest can (if he wants) not marry” are subcontraries; these can be simultaneously true but not simultaneously false. And necessity, as in “A priest must marry”, unilaterally entails its possibility dual counterpart, “A priest may marry”.

(1) Modal Square

In the twelfth century, Peter of Spain (1972: 7) offers a particularly elegant formulation in his Tractatus ; it will be seen that these apply to the modal propositions in (1) as well as to the quantificational statements in the original square:

• Each contradictory is equivalent to (entails and is entailed by) the negation of the other.
• Each contrary statement entails the negation of the other but not vice versa. [E.g. “I am happy” unilaterally entails “I am not unhappy”; “It is necessary that Φ” unilaterally entails “It is not impossible that Φ”.]
• The law of subcontraries is such that if one is false the other is true but not vice versa.

By these definitions, the three central species of opposition—contradiction, contrariety, and subcontrariety—are mutually inconsistent.

The law of excluded middle, LEM, is another of Aristotle's first principles, if perhaps not as first a principle as LNC. Just as Heraclitus's anti-LNC position, “that everything is and is not, seems to make everything true”, so too Anaxagoras's anti-LEM stance, “that an intermediate exists between two contradictories, makes everything false” ( Metaphysics 1012a25–29). Of any two contradictories p and ¬p, LNC entails that at most one be true while LEM entails that at least one be true. A logic validates LEM if p v ¬p is a theorem in that logic. LEM thus imposes a constraint on logical syntax and is distinct from the Principle of Bivalence, the purely semantic property dictating that any given proposition is either true or false. The latter principle is rejected in some multivalued and supervaluationist logics that validate LEM, a point to which we return in §6 (see also many-valued logics , Sorites Paradox , truth values ). Despite the logical distinction between these two principles, in practice they are often conflated.

For Aristotle, the status of LEM and bivalence comes down to the problem of future contingents. In a passage that has launched a thousand treatises, Aristotle ( De Interpretatione , Chapter 9) addresses the difficulties posed by apparently contradictory contingent statements about future events, e.g. (2a,b).

(2a) There will be a sea-battle tomorrow. (2b) There will not be a sea-battle tomorrow.

Clearly, (2a) and (2b) cannot both be true; LNC applies to future contingents as straightforwardly as to any other pair of contradictories. But what of LEM? Here is where the difficulties begin, culminating in the passage with which Aristotle concludes and (apparently) summarizes his account:

It is necessary for there to be or not to be a sea-battle tomorrow; but it not necessary for a sea-battle to take place tomorrow, nor for one not to take place—though it is necessary for one to take place or not to take place. So, since statements are true according to how the actual things are, it is clear that wherever these are such as to allow of contraries as chance has it, the same necessarily holds for the contradictories also. This happens with things that are not always so or are not always not so. With these it is necessary for one or the other of the contradictories to be true or false—not, however, this one or that one, but as chance has it; or for one to be true rather than the other, yet not already true or false. Clearly, then it is not necessary that of every affirmation and opposite negation one should be true and the other false. For what holds for things that are does not hold for things that are not but may possibly be or not be; with these it is as we have said. ( De Interpretatione 19a30-b4)

Unfortunately, given the systematic ambiguity and textual variations in the Greek text, the difficulty of telling when Aristotle is speaking with his own voice or characterizing an opponent's argument, and the lack of formal devices for the essential scopal distinctions at issue, it has never been clear exactly just what has been said here and in the chapter more generally. Some, including Boethius and Lukasiewicz, have seen in this text an argument for rejecting LEM for future contingent statements, which are therefore to be assigned a non-classical value (e.g. “Indeterminate”) or no truth-value at all. [ 4 ] Their reasoning is based in part on the premise that the alternative position seems to require the acceptance of determinism. Others, however, read Aristotle as rejecting not simple bivalence for future contingents but rather determinacy itself. This interpretive tradition, endorsed by al-Fārābi, Saint Thomas, and Ockham, is crystallized in this passage from Abelard's Dialectica (210–22) cited by Kneale and Kneale (1962: 214):

No proposition de contingenti futuro can be determinately true or determinately false…, but this is not to say that no such proposition can be true or false. On the contrary, any such proposition is true if the outcome is to be true as it states, even though this is unknown to us.

Even if we accept the view that Aristotle is uncomfortable with assigning truth (or falsity) to (2a) and (2b), their disjunction in (3a) is clearly seen as true, and indeed as necessarily true. But the modal operator must be taken to apply to the disjunction as a whole as in (3b) and not to each disjunct as in (3c).

(3a) Either there will be or there will not be a sea-battle tomorrow. (3b) □ (Φ ∨ ¬Φ) (3c) □ Φ ∨ □ ¬Φ

For Aristotle, LNC is understood primarily not as the principle that no proposition can be true simultaneously with its negation, but as a prima facie rejection of the possibility that any predicate F could both hold and not hold of a given subject (at the same time, and in the same respect). A full rendering of the version of LNC appearing at Metaphysics 1006b33–34—“It is not possible to truly say at the same time of a thing that it is a man and that it is not a man”—would require a representation involving operators for modality and truth and allowing quantification over times. [ 5 ] In the same way, LEM is not actually the principle that every statement is either true or has a true negation, but the law that for any predicate F and any entity x , x either is F or isn't F .

But these conceptualizations of LNC and LEM must be generalized, since the principle that it is impossible for a to be F and not to be F will not apply to statements of arbitrary complexity. We can translate the Aristotelian language, with some loss of faithfulness, into the standard modern propositional versions in (4) and (5) respectively, ignoring the understood modal and temporal modifications:

(4) LNC: ¬(Φ ∧ ¬Φ) (5) LEM: Φ ∨ ¬Φ

Taking LNC and LEM together, we obtain the result that exactly one proposition of the pair {Φ, ¬Φ} holds, where ¬ represents contradictory negation.

Not every natural language negation is a contradictory operator, or even a logical operator. A statement may be rejected as false, as unwarranted, or as inappropriate—misleading, badly pronounced, wrongly focused, likely to induce unwanted implicatures or presuppositions, overly or insufficiently formal in register. Only in the first of these cases, as a toggle between truth and falsity, is it clear that contradictory negation is involved (Horn 1989, Smiley 1993). Sainsbury (2004) takes truth-functional contradictory negation to be a special case of a generalized option negation as a deselection operator: If there are two mutually exhaustive and exclusive options A and B, to select A is to deselect B. But the relevant options may involve not truth, but some other aspect of utterance form or meaning as in the standard examples of metalinguistic negation (Horn 1989; see the entry on negation ). In such cases, a speaker uses negation metalinguistically or echoically to object to a previous utterance on any grounds whatsoever, including its phonetic or grammatical form, register, or associated presuppositions or implicatures: “That's not a car, it's a Volkswagen”, “Cancer selection is not a but the major force in the emergence of complex animal life”, “He's not your old man, he's your father”, “We didn't call the POlice, we called the poLICE”. In such cases, the relevant target for deselection is what the right thing is to say in a particular context, where “truth is not sufficient for being right, and may not even be necessary” (Sainsbury 2004: 87). Thus the apparent LNC violation (if it's a Volkswagen, it both is and isn't a car) is not a real one.

Given that not every apparent sentential negation is contradictory, is every contradictory negation sentential? Within propositional logic, contradictory negation is a self-annihilating operator: ¬(¬Φ) is equivalent to Φ. This is explicitly recognized in the proto-Fregean Stoic logic of Alexander of Aphrodisias: “‘Not: not: it is day’ differs from ‘it is day’ only in manner of speech” (Mates 1953: 126). The Stoics' apophatikon directly prefigures the iterating and self-cancelling propositional negation of Frege and Russell. As Frege puts it (1919: 130), “Wrapping up a thought in double negation does not alter its truth value.” The corresponding linguistic principle is expressed in the grammarians' bromide, “Duplex negatio affirmat.”

Not all systems of propositional logic accept a biconditional law of double negation (LDN), ¬(¬Φ) ≡ Φ. In particular, LDN, along with LEM, is not valid for the Intuitionists, who reject ¬(¬Φ) → Φ while accepting its converse, Φ → ¬(¬Φ). But the very possibility of applying negation to a negated statement presupposes the analysis of contradictory negation as an iterative operator (one capable of applying to its own output), or as a function whose range is identical to (or a subset of) its domain. Within the categorical term-based logic of Aristotle and his Peripatetic successors, every statement—whether singular or general—is of subject-predicate form. Contradictory negation is not a one-place operator taking propositions into propositions, but rather a mode of predication , a way of combining subjects with predicates: a given predicate can be either affirmed or denied of a given subject. Unlike the apophatikon or propositional negation connective introduced by the Stoics and formalized in Fregean and Russellian logic, Aristotelian predicate denial, while toggling truth and falsity and yielding the semantics of contradictory opposition, does not apply to its own output and hence does not syntactically iterate. In this respect, predicate denial both anticipates the form of negation in Montague Grammar (see the entry on Montague semantics ) and provides a more plausible representation of contradictory negation in natural language, whether Ancient Greek or English, where reflexes of the iterating one-place connective of the Stoics and Fregeans (“Not: not: the sun is shining”) are hard to find outside of artificial constructs like the “it is not the case” construction (Horn 1989, §7.2). In a given natural language, contradictory negation may be expressed as a particle associated with a copula or a verb, as an inflected auxiliary verb, as a verb of negation, or as a negative suffix or prefix.

In addition, there is a widespread pragmatically motivated tendency for a formal contradictory negation to be strengthened to a semantic or virtual contrary through such processes as litotes (“I don't like prunes” conveying that I dislike prunes) and so-called neg(ative) raising (“I don't think that Φ” conveying “I think that ¬Φ”). Similarly, the prefixal negation in such adjectives as “unhappy” or “unfair” is understood as a contrary rather than contradictory (not-Adj) of its base. These phenomena have been much discussed by rhetoricians, logicians, and linguists (see the entry on negation and Horn 1989: Chap. 5).

In addition to predicate denial, in which a predicate F is denied of a subject a , Aristotelian logic allows for narrow-scope predicate term negation , in which a negative predicate not-F is affirmed of a . The relations of predicate denial and predicate term negation to a simple affirmative proposition (and to each other) can be schematized on a generalized square of opposition for singular (non-quantified) expressions ( De Interpretatione 19b19–30, Prior Analytics Chapter 46):

(6) Negation Square

If Socrates doesn't exist, “Socrates is wise” ( A ) and its contrary “Socrates is not-wise” ( E ) are both automatically false (since nothing—positive or negative—can be truly affirmed of a non-existent subject), while their respective contradictories “Socrates is not wise” ( O ) and “Socrates is not not-wise” ( I ) are both true. Similarly, for any object x , either x is red or x is not red—but x may be neither red nor not-red; if, for instance, x is a unicorn or a prime number.

While Russell (1905) echoed (without acknowledgment) Aristotle's ambiguist analysis of negation as either contradictory (“external”) or contrary (“internal”), by virtue of the two logical forms assigned to “The king of France is not bald” (see descriptions ), such propositionalized accounts are bought at a cost of naturalness, as singular sentences of subject-predicate grammatical form are assigned the logical form of an existentially quantified conjunction and as names are transmuted into predicates.

The difference between denying P of S and affirming not-P of S is realized in Ancient Greek as a scopal distinction reflected in word order: S P [not is] (Socrates healthy not-is) vs. S [not P] is (Socrates not-healthy is) . As indicated in (6), for Aristotle only sentences can be in contradictory opposition. P and not-P both yield falsity when predicated of a non-existent subject but one or the other of the two terms is truthfully predicable of any existent subject in the relevant domain. P and not-P are “logical contraries” that exclude a true middle, an existent entity which is neither P nor not-P . But naturally occurring cases of prefixal adjectives, those marked by a ( n )- in Greek, may involve an unexcluded middle, as do polar contraries or antonym pairs. Modern grammatical discourse departs from Aristotle in allowing for contradictory terms: middle-allowing contrary adjectives ( white / black , happy / unhappy ) are distinguished from middle-excluding contradictory adjectives ( transitive / intransitive , alive / dead ).

Jespersen (1917: 144) describes the logical status of negatively prefixed adjectives in English:

The modification in sense brought about by the addition of the prefix [ un- ] is generally that of a simple negative: unworthy = ‘not worthy’, etc. The two terms [P, unP] are thus contradictory terms. But very often the prefix produces a “contrary” term…: unjust (and injustice ) generally imply the opposite of just ( justice ); unwise means more than not wise and approaches foolish , unhappy is not far from miserable, etc.

Like Aristotle, Jespersen predicts that the negation of true contraries like unhappy , unjust , or unwise will be semantically distinct from their positive bases. Thus, not unhappy fails to reduce to happy by virtue of allowing an unexcluded middle: one can be neither happy nor unhappy but just blaah, in the same way that something can be neither black nor white but one of the fifty-plus shades of gray. At the same time, even those adjectives that are semantic contradictories, e.g. impossible , may be coerced under negation into virtual contraries. While technically any action or event must be either possible or impossible, to assess something as not impossible is often to portray its occurrence as a more remote possibility than to assess it as possible simpliciter, as reflected in attestations of “It’s possible, or at least not impossible”. Similar instances of virtual contrariety are readily attested with negated verb phrases (“I don’t NOT love the dog” ≠ I love the dog) or predicate nominals (“We’re not NOT friends” ≠ We’re friends); see Horn 2017.

Drawing on an epistemic theory of vagueness, Krifka (2007) argues that prefixal negation always yields semantic contradictories. On this view, unhappy is literally just ‘not happy’, with the characteristic stronger understanding derived pragmatically. The incomplete cancellation of the two negators in not unhappy is taken to be a purely pragmatic phenomenon, conflating this case with that of not impossible . But the classical theory has its advantages. On that approach, un-Adj antonyms (like their morphologically simplex classmates, sad or bad ) are lexical items that can constitute contraries vis-à-vis the corresponding positive. By virtue of their lexical status, they are candidates to undergo further semantic drift, unlike not Adj sequences (or non-Adj forms), as evidenced in the semantic and phonological opacity of infamous or impious . Note too that many un - and in - adjectives ( unkempt , inchoate , incorrigible ) lack corresponding simple bases. Furthermore, the prefix non- yields staunch contradictories (typically with objective and/or technical senses) often contrasting minimally with un-Adj or iN-Adj contraries favoring gradable and evaluative contexts:

• non-American vs. un-American; non-professional vs. unprofessional
• non-Christian vs. un-Christian; non-rational vs. irrational
• non-moral vs. immoral; non-realistic vs. unrealistic
• non-natural vs. unnatural; non-scientific vs. unscientific

Even more problematically for a unified treatment, the treatment of all negatively prefixed adjectives as semantic contradictories would seem naturally to extend from unhappy or unwise to simplex antonymic pairs like happy / sad or wise / foolish , where the evidence for semantic contrariety appears to be incontrovertible. While Krifka (2007: 174) supports the analysis of e.g. happy and unhappy as “literally contradictories that receive their interpretations as contraries only via pragmatic strengthening”, Horn (2017) argues that a traditional (neo-Aristotelian) approach invoking parallel but distinct semantic and pragmatic strengthening processes is on sounder empirical footing.

In addition to the future contingent statements discussed in §2, vacuous subjects like those in (7a,b) have sometimes been taken to yield a violation of LEM through the emergence of a truth-value gap.

(7a) {The present king of France/King Louis} is bald. (7b) {The present king of France/King Louis} isn't bald.

While Aristotle would see a republican France as rendering (7a) false and (7b) automatically true, Frege (1892) and Strawson (1950) reject the notion that either of these sentences can be used to make a true or false assertion. Instead, both statements presuppose the existence of a referent for the singular term; if the presupposition fails, so does the possibility of classical truth assignment. Note, however, that such analyses present a challenge to LEM only if (7b) is taken as the true contradictory of (7a), an assumption not universally shared. Russell, for example, allows for one reading of (7b) on which it is, like (7a), false in the absence of a referent or denotatum for the subject term; on that reading, on which the description has primary occurrence, the two sentences are not contradictories. In this way, Russell (1905: 485) seeks to guide the French monarch out of the apparent trap without recourse to wigs or truth value gaps:

By the law of the excluded middle, either ‘A is B’ or ‘A is not B’ must be true. Hence either ‘the present king of France is bald’ or ‘the present king of France is not bald’ must be true. Yet if we enumerated the things that are bald and the things that are not bald, we should not find the king of France on either list. Hegelians, who love a synthesis, will probably conclude that he wears a wig.

In those systems that do embrace truth value gaps (Strawson, arguably Frege) or non-classically-valued systems (Łukasiewicz, Bochvar, Kleene), some sentences or statements are not assigned a (classical) truth value; in Strawson's famous dictum, the question of the truth value of “The king of France is wise”, in a world in which France is a republic, simply fails to arise. The negative form of such vacuous statements, e.g. “The king of France is not wise”, is similarly neither true nor false. This amounts to a rejection of LEM, as noted by Russell 1905. In addition to vacuous singular expressions, gap-based analyses have been proposed for future contingents (following one reading of Aristotle's exposition of the sea-battle; cf. §2 above) and category mistakes (e.g. “The number 7 likes/doesn't like to dance”).

While LNC has traditionally remained more sacrosanct, reflecting its position as the primus inter pares of the indemonstrables, transgressing this final taboo has become increasingly alluring in recent years. The move here involves embracing not gaps but truth value gluts , cases in which a given sentence and its negation are taken to be both true, or alternatively cases in which a sentence may be assigned more than one (classical) truth value, i.e. both True and False. Parsons (1990) observes that the two non-classical theories are provably logically equivalent, as gluts arise within one class of theories precisely where gaps do in the other; others, however, have argued that gaps (as in Intuitionist non-bivalent logics) are easier to swallow than gluts (see papers in the Priest et al. 2004 collection for further debate). Dialetheists reject the charge of incoherence by noting that to accept some contradictions is not to accept them all; in particular, they seek to defuse the threat of logical armageddon or “explosion” posed by Ex Contradictione Quodlibet, the inference in (8):

(8) p , ¬ p     _____     ∴ q

Far from reduced to the silence of a vegetable, as Aristotle ordained, the proponents of true contradictions, including self-avowed dialetheists following the lead of Sylvan (né Routley) and Priest have been eloquent.

Is the status of Aristotle's “first principle” as obvious as he believed? Adherents of the dialetheist view that there are true contradictories (Priest 1987, 1998, 2002; see also the entries on dialetheism and paraconsistent logic ) would answer firmly in the negative. [ 6 ] In the Western tradition, the countenancing of true contradictions is typically—although not exclusively—motivated on the basis of such classic logical paradoxes as “This sentence is not true” and its analogues; such a statement is evidently true if and only if it is not true. The Liar, or really the family of Liar’s paradoxes (see Liar Paradox ), and Russell’s paradox, its set-theoretic analogue (a set that is not a member of itself both is and is not a member of itself—see the entry on Russell’s Paradox ), would no longer constitute immediate threats to logical coherence in the absence of LNC (see papers in Priest et al. for extended discussion). If we are indeed prepared to jettison LNC, we can regard “This sentence is not true” (or “This statement is false”) as simultaneously true and not true without deriving the resultant absurdity taken by Aristotle and his heirs to result from such a contradiction. As Smiley (1993: 19) has remarked, “Dialetheism stands to the classical idea of negation like special relativity to Newtonian mechanics: they agree in the familiar areas but diverge at the margins (notably the paradoxes).”

Related to the classic paradoxes of logic and set theory is the Paradox of the Stone. One begins by granting the basic dilemma, as an evident instance of LEM: either God is omnipotent or God is not omnipotent. With omnipotence, He can do anything, and in particular He can create a stone, call it s , that is so heavy even He cannot lift it. But then there is something He cannot do, viz. (ex hypothesi) lift s . But this is a violation of LNC: God can lift s and God cannot lift s . This paradox, and the potential challenge it offers to either LNC or the possibility of omnipotence, has been recognized since Aquinas, who opted for retaining the Aristotelian law by understanding omnipotence as the capacity to do only what is not logically impossible. (Others, including Augustine and Maimonides, have noted that in any case God is “unable” to do what is inconsistent with His nature, e.g. commit sin.) For Descartes, on the other hand, an omnipotent God is by definition capable of any task, even those yielding contradictions. Mavrodes (1963), Kenny, and others have sided with St. Thomas in taking omnipotence to extend only to those powers it is possible to possess; Frankfurt (1964), on the other hand, essentially adopts the Cartesian line: Yes, of course God can indeed construct a stone such that He cannot lift it—and what's more, He can lift it! (See also Savage 1967 for a related solution.)

As we have seen, the target of Aristotle's psychological (doxastic) version of LNC was Heraclitus: “It is impossible for anyone to believe that the same thing is and is not, as some consider Heraclitus said—for it is not necessary that the things one says one also believes” (Met. 1005b23–26). But as Aristotle acknowledges here (even if he is less politic elsewhere), there is considerable uncertainty over exactly what Heraclitus said and what he believed. Heraclitus could not have literally rejected LNC, as he is often accused of (or praised for) doing, as his writings preceded the statement of that principle in Metaphysics Γ by well over a century. But the question remains: do his words, as represented in the extant fragments, anticipate the Dialetheists and other rejectionists? Yes and no. To be sure, Heraclitus was proud to wear the mantle of “paradoxographer” (Barnes 1982: 80) and enjoyed nothing more than to épater les bourgeois of his day. But the key fragments supporting his proclamation of the Unity of Opposites can be taken in more than one way. He points out that sea water is salutary (if you're a fish) and unhealthy (if you're a human), just as garbage is preferable to gold (for a donkey) but then again it isn't (for a person). And given the inevitability of flux (as Heraclitus memorably illustrated by his river into which one cannot step twice), what is true (today) is also false (tomorrow). But these astute observations do not so much refute the LNC as much as demonstrate (through what Barnes calls the Fallacy of the Dropped Qualification) the need for Aristotle's crucial codicil: sea water, for example, cannot be both healthful and unhealthful for the same experiencer at the same time and in the same respect. (In a similar way, “It is raining” may of course be deemed true at this moment in Seattle and false in Palo Alto; we need admit no contradiction here, whether we deal with the issue by endorsing unarticulated constituents or in some other manner; cf. Recanati 2002 inter alia.) Ultimately, whether one follows Kirk (Heraclitus [1954]) in charging Aristotle with misrepresenting Heraclitus as an LNC-denier or sides with Barnes (1982) and Wedin (2004b) in sustaining Aristotle's accusation, it is hard to see in what respect the evidence presented by Heraclitus, however subtle a guide he may be for our travels on that path on which up and down is one and the same, threatens the viability of LNC. (See also Heraclitus .)

Within the modern philosophical canon, Hegel has often been seen as the echt LNC-skeptic, well before his reputed deathbed lament, “Only one man ever understood me, and he didn't understand me.” Hegel saw himself as picking up where Heraclitus left off—“There is no proposition of Heraclitus which I have not adopted in my logic” (Barnes 1982: 57)—and indeed the Heraclitean view of a world shaped by the unity of opposites through strife and resolution does seem to foreshadow Hegelian dialectic. In fact, however, an unresolved contradiction was a sign of error for Hegel. The contradiction between thesis and antithesis results in the dialectical resolution or superseding of the contradiction between opposites as a higher-level synthesis through the process of Aufhebung (from aufheben, a verb simultaneously interpretable as 'preserve, cancel, lift up'). Rather than repudiating LNC, Hegel's dialectic rests upon it. In Marxist theory, too, contradictories do not simply cancel out but are dynamically resolved ( aufgehoben ) at a higher level in a way that both preserves and supersedes the contradiction, motivating the historical dialectic. (See Horn 1989: §1.3.2.)

For Freud, there is a realm in which LNC is not so much superseded but dissolved. On the primary, infantile level, reflected in dreams and neuroses, there is no not : “‘No’ seems not to exist as far as dreams are concerned. Anything in a dream can mean its contrary” (Freud 1910: 155). When the analysand insists of a dream character “It's not my mother”, the analyst knowingly translates, “So it is his mother!” Freud sought to ground this pre-logical, LNC-free (and negation-free) realm not just in the primal realm of the dreamer's unconscious but also in the phenomenon of Gegensinn , words (especially Urworte , primal words) with two opposed meanings purported attested widely in ancient and modern languages. The empirical basis for this latter claim, however, has been widely discredited; see Benveniste 1956.

Given Aristotle's observation ( Metaphysics 1006a2) that “even some physicists” deny LNC and affirm that it is indeed possible for the same thing to be and not to be at the same time and in the same respect, he might not have been surprised to learn that quantum mechanics has brought such challenges once more into play. Thus, we have Schrödinger's celebrated imaginary cat, placed (within the context of a thought experiment) inside a sealed box along with radioactive material and a vial of poison gas that will be released if and only if that material decays. Given quantum uncertainty, an atom potentially inhabits both states—decayed and non-—simultaneously, seeming to render the cat (in the absence of an observer outside the system) both alive and dead. But most physicists would argue that while quantum mechanics may challenge some aspects of classical logic it does not threaten LNC. If we could in fact observe a cat, or a particle, as A and not-A at the same time, then there would be a violation of the Law of Non-Contradiction; the mere potential for an entity to be in either of two mutually inconsistent states does not in itself violate the LNC. 

As we have seen, Aristotle himself anticipated many of the challenges that have since been raised against LNC. One more such challenge is posed by the ubiquity of doxastic inconsistency. Take the desires of Oedipus, for example. In seeking Jocasta as his mate, did he wish to marry his mother? Certainly he did on the de re reading: Oedipus's mother (Jocasta) is such that he wanted to marry her, although he would not have assented to the claim that he wanted to marry his mother. In a sense, then, “Oedipus wanted to marry his mother” is true (de re) and false (de dicto), but no violation of LNC is incurred, since these represent different propositions, the semantic distinction neutralized within the sentential form. But what of the de dicto reading itself: it is really false? After all, as a young boy Oedipus can be assumed (by some) to have exhibited the eponymous complex, according to which the falsity of the (de dicto) proposition that he wanted to marry his mother on a conscious level belies the truth of this proposition on an unconscious level. But this does not entail that he both wished and did not wish to “marry” his mother at the same time and in the same respect . Whether it concerns the unacknowledged incestuous conflict of the Theban king, the indecision of Zerlina's “Vorrei e non vorrei” response to Don Giovanni's invitation, or the unspecified ambivalence of the respondent in Strawson's exchange (1952: 7)

—Were you pleased? —Well, I was and I wasn't.

we have ample opportunity to reflect on the foresight of Aristotle's rider: “a is F ” and “a is not F ” cannot both hold in the same sense, at the same time, and in the same respect .

Beyond the Western canon, the brunt of the battle over LNC has been largely borne by the Buddhists, particularly in the exposition by Nāgārjuna of the catuṣkoṭi or tetralemma (c. 200 A.D.; cf. Bochenski 1961: Part VI, Raju 1954, Garfield 1995, Tillemans 1999, Garfield & Priest 2002), also known as the four-cornered or fourfold negation. Consider the following four possible truth outcomes for any statement and its (apparent) contradictory:

(9)   (i) S is P (ii) S is not P (iii) S is both P and not- P (iv) S is neither P nor not- P

For instances of the positive tetralemma, on Nāgārjuna's account, all four statement types can or must be accepted:

Everything is real and not real. Both real and not real. Neither real nor not real. That is Lord Buddha's teaching.    — Mūla-madhyamaka-kārikā 18:8, quoted in Garfield (1995: 102)

Such cases arise only when we are beyond the realm to which ordinary logic applies, when “the sphere of thought has ceased.” On the other hand, more use is made of the negative tetralemma, in which all four of the statements in (9) can or must be rejected, and thus one cannot assert either Φ, ¬Φ, both Φ and ¬Φ, or neither Φ nor ¬Φ. Is this tantamount, as it appears, to the renunciation of LEM and LNC, the countenancing of both gaps and gluts, and thus—in Aristotle's view—the overthrow of all bounds of rational argument?

It should first be noted that the axiomatic status of LNC and LEM is as well-established within the logical traditions of India as it is for the Greeks and their epigones. [ 7 ] Garfield (1995) and Tillemans (1999) convincingly refute the claim that Nāgārjuna was simply an “irrationalist”. [ 8 ] In the first place, if Nāgārjuna simply rejected LNC, there would be no possibility of reductio arguments, which hinge on the establishment of untenable contradictions, yet such arguments are standardly employed in his logic. In fact, he explicitly prohibits virodha (contradiction). Crucially, it is only in the realm of the Absolute or Transcendent, where we are contemplating the nature of the ultimate, that contradictions are embraced; in the realm of ordinary reality, LNC operates and classical logic holds. (Recall Freud's dichotomy between the LNC-observant conscious mind and the LNC-free unconscious.) In this sense, the logic of Nāgārjuna and of the Buddhist tradition more generally can be seen not as inconsistent but paraconsistent. Indeed, just as Aristotle ridiculed LNC-skeptical sophists as no better than vegetables (see §1), the Buddhists dismissed the arch-skeptic Sanjaya and his followers, who refused to commit themselves to a definite position on any issue, as “eel-wrigglers” (amarāvikkhepa) . Sanjaya himself was notorious for his periodic lapses into the extended silence Aristotle described as the last refuge of the LNC-skeptic (see Raju 1954).

One aspect of the apparent paradox is precisely parallel to that arising with some of the potential counterexamples to the LNC arising in Western thought. In various Buddhist and Jainist systems of thought, the apparent endorsement of Fa & ¬ Fa (or, in propositional terms, Φ ∧ ¬Φ) is upon closer examination qualified in precisely the way foreseen by the codicils in Aristotle's statement of the law: From a certain viewpoint, Φ (e.g. Nirvana exists); from a certain viewpoint, ¬Φ (e.g. Nirvana does not exist). (Compare the observation of Jainists two millennia ago that “ S is P ” and “ S is not P ” can both be true from different standpoints; cf. Raju 1954: 698–701; Balcerowicz 2003.)

To further explore the status of truth-value gluts, in which both classical values are simultaneously assigned to a given proposition (e.g. “ x is real”), let us consider the analogous cases involving gaps. Recall, for example, the case of future contingents as in (2a,b) above: we need not maintain that “Iraq will become a secular democracy” is neither true nor false when uttered today, but only that neither this statement nor its contradictory “Iraq will not become a secular democracy” is assertable today in the absence of foreknowledge. Similarly for past unknowables, such as (to adapt an example from Quine) the proposition that the number of blades of grass on the Old Campus lawn during the 2005 Yale commencement exercises was odd. This is again more plausibly viewed as unassertable than as truth-valueless, even though its truth-value will never be known. To take a third example, we can argue, with Grice (1989: 80ff.), that a negation outside the scope of a conditional is generally intended as a refusal (or hesitation) to assert “if p then q ” rather than as the contradictory negation of a conditional, whose truth value is determined in accord with the standard material equivalence:

(10) ¬( p → q ) ≡ ( p & ¬ q )

Thus, in denying your conditional “If you give her penicillin, she will get better”, I am allowing for the possibility that giving her penicillin might have no effect on her, but I am not predicting that you will administer the penicillin and she will fail to recover. Nor does denying the apothegm (typically though inaccurately attributed to Dostoyevsky or Nietzsche) that if God is dead everything is permitted commit one to the conjoined proposition that God is dead and something is forbidden. As Dummett (1973: 328–30) puts the point, we must distinguish negation outside the scope of a Fregean assertion operator, not (⊢ p ), from the assertion of a negative proposition, ⊢(not p ). The former interpretation “might be taken to be a means of expressing an unwillingness to assert” p , in particular when p is a conditional:

(11)    X : If it rains, the match will be canceled. Y : That's not so. ( or, I don't think that's the case.)

Y 's contribution here does not constitute a negation of X 's content; rather, we can paraphrase Y as conveying (11′a) or (11′b):

(11′a) If it rains, the match won't necessarily be canceled. (11′b) It may [ epistemic ] happen that it rains and yet the match is not canceled.

Dummett observes, “We have no negation of the conditional of natural language, that is, no negation of its sense: we have only a form for expressing refusal to assent to its assertion.”

Similarly with disjunction. Consider the exchange in (12) preceding the 2000 election, updated from an example of Grice:

(12)    X : Bush or Gore will be elected. Y : That's not so: Bush or Gore or Nader will be elected.

Y 's rejoinder cannot be a contradictory of the content of X 's claim, since the (de jure) election of Bush rendered both X 's and Y 's statements true. Rather, Y objects on the grounds that X is not in an epistemic position to assert the binary disjunction.

Unassertability can be read as the key to the apparent paradox of the catuṣkoṭi as well. The venerable text in Majjhima-nikāya 72, relating the teachings of the historical Buddha, offers a precursor for Nāgārjuna's doctrine of the negative tetralemma. Gotama is responding to a monk's question concerning the doctrine of rebirth (quoted in Robinson 1967: 54):

Gotama, where is the monk reborn whose mind is thus freed?    Vaccha, it is not true to say that he is reborn. Then, Gotama, he is not reborn.    Vaccha, it is not true to say that he is not reborn. Then, Gotama, he is both reborn and not reborn.    Vaccha, it is not true to say that he is both reborn and not reborn. Then, Gotama, he is neither reborn nor not reborn.    Vaccha, it is not true to say that he is neither reborn nor not reborn.

Note the form of the translation here, or similarly that of the standard rendering of the negative catuṣkoṭi that “it profits not” to assert Φ, to assert ¬Φ, to assert both Φ and ¬Φ, or to assert neither Φ nor ¬Φ: the relevant negation can be taken to operate over an implicit modal, in particular an epistemic or assertability operator. If so, neither LEM nor LNC is directly at stake in the tetralemma: you can have your Aristotle and Buddha too.

We tend to recalibrate apparent violations of LNC as conforming to a version of the law that incorporates the Aristotelian qualifications: a sincere defense of “ p and not- p ” plausibly involves a change in the context of evaluation or a shift in viewpoint, or alternatively a suppression of modal or epistemic operators. This practice can be seen as an instance of a general methodological principle associated with Davidson and Quine that has come to be called the principle of charity (or, alternately, the principle of rational accommodation ): when it is unclear how to interpret another's argument, interpret it in a way that makes the most sense. At the same time, this procedure evokes the standard Gricean mode of explanation (Grice 1989; see the entry on implicature ): granted the operation of the Cooperative Principle and, more broadly, the shared premise of rationality, we reinterpret apparent violations of valid principles or maxims so as to conserve the assumption that one's interlocutor is a rational and cooperative agent. And as Aristotle would remind us, no principle is more worthy of conservation than the Law of Non-Contradiction.

6. Vagueness and borderline contradictions

We have seen that two of the more significant threats to the unchallengeable status of LNC tend to dissolve under closer scrutiny. Heraclitus-type contradictions (Sea water is healthy and sea water is not healthy) are rendered LNC-compatible by the Aristotelian rider designed for that purpose (“a is F ” and “a is not F ” cannot both hold in the same sense, at the same time, and in the same respect ) once the “dropped qualification” or contextual specification is restored (§4). Buddhist-type contradictions (Nirvana exists and Nirvana does not exist) can be understood as modalized, embedded under an epistemic modal or assertability operator.

We are left with two significant challenges for LNC: (i) the case of the Liar and related paradoxes of self-reference as touched on in §3 and work cited therein (see the entries on Liar Paradox, Russell’s Paradox, Dialetheism, Paraconsistent Logic) and (ii) the case of vagueness and its implications for borderline truth, discussed in this section. As we have seen, the admission of truth-value gaps (exceptions to LEM) is mirrored by the admission of truth-value gluts (exceptions to LNC). As intellectual heirs of the Hegelian tradition, Marxists have willing to accept paradox, and indeed the pre-Revolutionary theorist Plekanov (1909) suggests that Sorites (in the form of the bald man; see sorites entry) can be resolved by rejecting LNC. Hyde (1997) traces the history of vagueness-based arguments for paraconsistency from Plekhanov through Jaśkowski, McGill, and Parry in the 1940s to the dialetheist logics of today. Pointing out the parallels between treatments of vagueness via truth-value gap theories (including the supervaluation theory of van Fraassen 1969) and their truth-value glut counterparts, Hyde laments the unwarranted neglect of the latter option: “The thought that an adequate response might require the recognition of cases of overdetermination and and truth-value gluts has few supporters” (Hyde 1997: 641). In the two decades since the publication of his important paper, that neglect has been largely rectified, especially with the accretion of empirical support for glut-oriented approaches endorsing the acceptability of a range of true contradictions of the form a is P and a is not P, in particular when P is a vague predicate like tall , vague , or red .

Supervaluation theory utilizes the concept of admissible sharpening or precisification of vague predication (see the entry on vagueness ). I may be unable to assert truthfully of a given color chip in the red-orange range that it is red, while also being unable to assert that it is not red. Once the notion of red is sharpened or precisified to a particular interval of wave-lengths, I am in a position to assert either the positive proposition “a is red” or its negation “a is not red”, but which one depends on the details of the sharpening. A sentence S is supertrue iff it is true on every sharpening and superfalse if it is false on every sharpening; if is true on some sharpenings and false on others, it is neither supertrue nor superfalse, thus corresponding to a truth-value gap. One salutary result of this approach is that LEM can be retained: P or not P is supertrue since it is true on every sharpening. Hyde (1997) draws on the dual status of gaps and gluts to define a paraconsistent “subvaluation” theory: S is subtrue iff is true on at least one sharpening, subfalse iff it is false on at least one sharpening, and neither subtrue nor subfalse if it is true on some sharpenings and false on others. Given the status of supervaluation and subvaluation as duals, each is equally defensible and applicable to the semantics of vagueness. Crucially, it is the notion of supertruth, or subtruth as the case may be, that tracks our natural language intuitions of truth, and similarly for falsity. In this sense, the logic of supervaluation is paracomplete (allowing for violations of LEM) and the logic of subvaluation paraconsistent (allowing for violations of LNC). In the tradition of paraconsistent logics, Hyde stresses the need for “quarantining the gluts” to avoid the explosive consequences of ex contradictione quodlibet (see §4).

Where supervaluation theory allows a is not tall or a is not bald to be neither (super)true nor (super)false if a represents a borderline instance of tallness, subvaluation theory would characterize such an assessment as both (sub)true and (sub)false. But since tautologies are preserved if validity is defined in terms of truth and not subtruth (or supertruth)—an assumption that some might challenge— a is tall and a is not tall can never be true, even when a is tall and a is not tall are both true:

A vague sentence ‘ A ’ and its negation might both be true (since they each have some true disambiguation—i.e. the sentence ‘ A ’ itself as some true and some false disambiguation—but their conjunction can never be. ‘ A & ¬A ’ has only false disambiguations; LNC is retained. (Hyde 1997: 654)

For Akiba (1999), however, paraconsistent subvaluation theories, like paracomplete supervaluation theories, should be recast in a modal light, by supplying an epistemic possibility operator Pos in the former case (reminiscent of the modalized accounts of the tetralemma explored in §5) and its dual, an abstract modal concept Akiba defines as Def (corresponding to necessary truth) in the latter. Thus, while P & ¬P remains a full-fledged contradiction, its modalized counterpart Pos(P) & Pos(¬P) is coherent, and while P v ¬P is a valid instance of LEM, Def(P) v Def(¬P) is not: “Super- and subvaluation systems can be considered not really alternatives to classical logic but in fact just modal extensions of it.” Akiba’s key departure from Hyde’s approach is in rejecting the move to identify truth simpliciter with subtruth (or supertruth).

Confronted with the task of applying semantically vague predicates like tall and red to borderline cases, the intuitions of respondents in psycholinguistic studies often tend to become uncertain. Subjects produce varying responses for the crucial data, and the framers of the studies have produces varying explanations for the data. In one of the earlier studies, Bonini et al. point to the asymmetries in judgments of truth and falsity for borderline cases of a is red/tall and ultimately reject truth-gap and truth-glut accounts in favor of an LEM- and LNC-compatible epistemic theory of “vagueness as ignorance”. That is, the subject S “mentally represents vague predicates in the same way as other predicates with sharp true/false boundaries of whose location S is uncertain” (Bonini et al. 1999: 387).

Kyburg (2000) offers a pragmatic explanation for why a is tall might be judged neither true nor false in a case of borderline tallness, or why a is tall and a is not tall might be judged true in the same circumstance. Without conceding gaps or gluts, she points to a disconnect between truth-value intuitions and assertability intuitions for a cooperative speaker aiming to be maximally informative. Of course, in some cases, the felicity of a is tall and a isn’t tall might simply reflect the awareness that different cut-off points apply depending on the relevant comparative class of entities (children vs. adults, male adults vs. male professional basketball players, etc.)—the instances foreseen by the Aristotelian rider. But in other cases, such a statement would indeed convey that a possesses a borderline degree of tallness, while simply affirming or denying the vague predicate— a is tall or a is not tall— would communicate too high or too low a degree. Just as speakers might a sentence might refrain from uttering, or classifying as true, a perfectly and “sharply” true sentence whose use would mislead the hearer— Snow is white or snow is purple— so too the assertion of a conjunction of opposites in borderline cases— a is tall and he’s not tall— might be preferred, despite its contradictory nature, to the misleading assertion of either a is tall or a is not tall in the same circumstance.

For Sorensen (2001), an individual’s acceptance of the truth of certain false claims, including those necessarily false claims of the form a is tall and a is not tall, reflect not the inadequacy of our semantic and logical analyses but the tendency for speakers to be wrong, confused, or ignorant about the truth conditions of given sentences or about their own beliefs, especially those involving vagueness, similarly to the way in which perceptions can mislead in the case of visual illusions.

The vagueness-as-ignorance theory of Bonini et al. (1999), the modal theory of Akiba (1999), the assertability theory of Kyburg (2000), and the error theory of Sorensen (2001) are all semantically classical in their preservation of LNC (along with LEM and bivalence). In essence, each of these approaches to the assessment of vague predications reflects a wariness about jettisoning the classical account of truth and contradiction in favor of an approach endorsing either supervaluations (and gaps) or subvaluations (and gluts). Despite the difficulties posed by vagueness, these theorists would thus adopt the philosophical corollary to the familiar legal adage: “Hard cases make bad laws.”

In two recent papers the reconciliatory approach is rejected in favor of defenses of paraconsistency, although not precisely along the lines laid out by Hyde. On Hyde’s account, a is tall and a is not tall can both be true when a is borderline tall (say, 5′11″) while the full or reduced conjunction of these statements, a is tall and (a is) not tall, will be false, given the standard supervaluationist approach. Alxatib & Pelletier, however, find the opposite judgments among a majority of the subjects of their study, who accept the conjunction while rejecting the individual ascriptions of truth. In addition to reinforcing the view of gappy and glutty theories as mirror images, Alxatib & Pelletier present their results as evidence against the neo-classical vagueness-as-ignorance position of Bonini et al. (1999), a position which also has difficulty accounting for the paucity of subjects choosing the “can’t tell” option in the surveys. Like the assertability-based pragmatic theory of borderline contradictions proposed by Kyburg, Alxatib & Pelletier (2011: 321) offer a Gricean explanation for subjects’ endorsement of the truth of apparent contradictory statements— a is tall and not tall when a is just short of 6 feet tall—which yields (in just this case) a subvaluationary interpretation on which the speaker is taken to convey the borderline status of a ’s height. Their central finding (2011: 298–9) is that theories admitting truth-value gaps like that of Hyde (1997) or the paraconsistent logic of Priest 2006 fare better in accounting for the full range of interesting data presented in their experiments—and those of Ripley 2011.

Like Alxatib & Pelletier, Ripley (2011: §2) conducts his own survey of reactions to apparent contradictions involving vague predications (e.g., “The circle is both is and isn’t near the square”; “The circle neither is nor isn’t near the square”). He leverages the results of his study to argue against error (or epistemic) theories on which borderline contradictions are always false even when believed true; he also refutes fuzzy theories of vagueness, which fail to predict why subjects are so willing to accept the truth of borderline contradictions rather than assigning them an intermediate acceptability ranking. Ripley also finds pragmatic or contextualist theories not insufficiently fleshed out to yield the correct predictions. He adopts a dialetheist account that enables him to line up with a majority of his subjects in finding both “ a is F and a is not F ” and “ a is neither F nor not F ” true for borderline applications of F . Supporting this view, he notes (2011: 186–7) that there may be variation with respect to the “cultural aversion to contradictions”; there is evidence tending to suggest that Asian subjects are less likely than Westerners (specifically, as it happens, Canadians) to object to contradictions like “It’s raining and it’s not raining.” But as Ripley concedes, more research is needed on this point.

7. Contradiction in everyday life

The logical incoherence of contradictions is the ground both for indecision (as with Zerlina’s ambivalent Vorrei e non vorrei in our epigraph) and for the pragmatic exploitation of apparent contradictions for communicative ends. One locus is the oxymoron, a phrasal contradiction recognized for millennia as a figure of speech. The dramatic effect of yoking contradictories is as old as the classical festina lente (‘make haste slowly’, adopted as a motto by Augustine and the Medicis. The German counterpart, deployed by Goethe and others, adds rhyme: Eile mit Weile .

The use of actual or apparent contradiction to generate meanings via reconstrual may convey advice to seek the middle way, reminiscent of the function of borderline contradictions surveyed in §6, or may, in the case of an apparently incoherent phrasal structure, serve as a signal that the modifier constrains the denotation of the head. Thus bittersweet is not taken as self-contradictory property, while a tragicomedy is a work or production that spans the two normally opposed genres—recall Walt Whitman’s “I am large; I contain multitudes”. Classic oxymorons include cruel kindness, living death, and true lies; jocular ones are regularly proposed, from military intelligence and congressional ethics to airplane food and open secrets . A particularly transparent form is offered by those promoting undesign design or the non-concept concept.

The oxymoron, and in particular the catalogue of oxymorons, may signal the breakdown of logical coherence, given the explosive effect of ex contradictione quodlibet . In Romeo and Juliet, we ascend from the former’s risible inventory of battling binaries to the latter’s ardent valediction on her balcony:

Why, then, O brawling love! O loving hate! O anything, of nothing first create! O heavy lightness! Serious vanity! Misshapen chaos of well-seeming forms! Feather of lead, bright smoke, cold fire, sick health!    — Romeo and Juliet , I.i Good night, good night. Parting is such sweet sorrow That I should say good night till it be morrow.    — Romeo and Juliet , II.ii

Expanding from the phrasal to the sentential level, we find self-contradictory propositions, whether in full or elliptical form, functioning in forums from high culture to social media to generate a variety of implicatures. In her recent study of the phenomenology of ambivalence, Razinsky takes the affirmation of conjoined contradictories “a is v and a is not v ” for a given value judgment v, or the affirmation of “a is v and a is v´ ” where v, v´ are contraries (e.g. a is good and a is bad ), to be “central to the logic of value and of value judgment” (2017: 229). Some apparent instances of ambivalence (and of any underlying violation of LNC) can be explained away. Citing Mill, Razinsky (2017: 201) accepts that there are instances in which a is just and a is unjust reflects only an apparent opposition, to be understood essentially as a is just in some respects and a is unjust in other respects . Such cases illustrate the prescience of the Aristotelian rider: “a is F ” and “a is not F ” cannot both hold in the same sense, at the same time, and in the same respect . Similarly, the imposition of the edict a ought to F and a ought not to F results in difficulty for the unfortunate a , to be sure, but not necessarily in an LNC violation, given the availability of distinct sources of obligation. But other cases involve true ambivalence: “Meaningful contradictions are moored in the possibility of conceptual ambivalence” (Razinsky 2017: 44). The analysis of such cases must preserve the dynamic tension in affirming that a is v and a is not-v and at the same time acknowledge the speaker’s awareness of the violation of LNC, not an easy task: “Do people believe contradictions when it comes to value? I do not think there is a good answer to give here” (Razinsky 2017: 228)—they believe them and do not believe them.

Perhaps as a reflection of this tension, the A-not-A meme has widely proliferated in popular entertainment, advertisements, and social media. “Sorry not sorry” has become a standard device for a sarcastic or insincere apology (also known as a “non-apology apology”), while #SorryNotSorry is a trending Twitter hashtag as well as a Demi Lovato song title (see Carey 2014 in Other Internet Resources). A related meme is “I’m not saying, I’m just saying”, a now notorious “get out of jail free” discourse ploy showing up in hundreds of google hits, as the subject of an urbandictionary entry and several online commentaries by linguists, and as the title of a 2012 flash fiction paperback by Matthew Salesses. The category of “Christmas-not-Christmas movies” makes its perennial appearance on the web during holiday season, and the #worknotwork has been adopted as the house meme of Samsonite luggage. #GuiltyNotGuilty is another popular hashtag as well as a theme for Gucci ads.

A relatively new means for expressing ambivalence in colloquial U.S. and Australian English is the “Yeah no” (or, less frequently, “No yeah”) response, which has been analyzed as conveying a variety of possible discourse functions (see Burridge & Florey 2002, Lee-Goldman 2011, and Liberman 2008 in Other Internet Resources).

The conjunction of contradictory predicates of the form not A and/but not NOT A is used to indicate the borderline status of an entity with respect to a category and its complement:

• They not brown but they not NOT brown . [Saturday Night Live (faux commercial Levi’s Wokes ), Nov. 30, 2017]
• Karl Mitze, Geoff Manyin, Nick Montopoli, and Zachariah Matteson redefine what it means to be a string quartet. Described as “ not classical…but not not classical ”, bowed and fretted Invoke continues to successfully dodge even the most valiant attempts at genre classification. [ youtube.com ]
• Not punk enough to be punk but not not punk enough to be not punk . [ skyblock forums ]
• Strayed and I are heading out for a stroll in Portland, Oregon, in the kind of weather for which that city is famous: not raining, but not not-raining . [Schulz 2014, Other Internet Resources]
• Mozzarella sticks are one of my favorite appetizers…The thing is, are they healthy? No. Are they even in the middle, like not healthy but not not healthy ? No. [ Creme de la Crumb recipe column ]

While these appear fully contradictory, that diagnosis relies on the status of S is not not P as an instance of ¬(¬(S is P)) within a logic employing a robust Law of Double Negation. Arguably, however, in each of these attestations, the inner negation— not brown, not punk, not healthy, and even not-raining— can be viewed as a coerced or virtual contrary, in which case the two negations do not fully cancel out. Thus, just as not impossible fails to reduce to possible, not not classical is distinct from classical, and no actual violation of LNC is ultimately condoned. But, as on Grice’s (1989) analysis of irony and tautology, it is the recognition of the apparent contradiction that the speaker exploits to generate the higher-order coherence of the message.

A less, or perhaps differently, mediated case of coherence in apparent contradictories involves prosody. In this case, the hearer/reader seems to have to reconcile LNC with the joint predication of A and not A rather than the more complex not A and not not A . But on closer examination, the task is less daunting than it appears, as it’s really a matter of affirming A while rejecting A , or of metalinguistically rejecting A in favor of A :

• After playing a staggering 40,000 minutes (in just 11 seasons) and carrying four straight Finals teams, LeBron [James] might be battling the long-term effects of a historically ridiculous two-way burden. He’s still great, but he’s not GREAT . [Simmons 2014, Other Internet Resources]
• I’m short. Not SHORT, but short . I'm 5′8″ (on a good day) with a 30″ inseam. [ Total Motorcycle Forum posting , May 31, 2007]
• “Rita”, he whispered. “I’m tired.” And the way he said the word, she understood. He wasn’t tired, he was tired , a condition of the mind as well as the body. A state of the soul. [Lisa Gardner, 2008, Say Goodbye , p. 151]
• But – I can tell you this, and maybe I'm stating the obvious here but – Vegas is a DESERT. In other words, it’s hot. No, it’s not hot… it’s HOT . REALLY HOT. People drop like flies during the day from *walking* too much. [ Skate Log Forum posting , Nov. 5, 2007]

The prosodic focus in such cases serves to invoke a scalar contrast in degrees or qualities of A-ness; the result is analogous to instances in which a descriptor is contrasted with a clone or contrastive focus reduplication instance of the same descriptor, yielding variants of the true borderline contradictions discussed in §6:

• Average American man is 5′9″. You’re tall, but not TALL tall … if that makes sense. [ https://www.girlsaskguys.com/other/q1740369-is-6-1-1-85m-tall-for-a-guy ]
• ( So he’s dead but not dead -dead . Get it?) [ https://tinyurl.com/y8656rqy , of Jon Snow on Game of Thrones]

Finally, it is worth noting the role contradiction plays as a lively source of ironic humor, especially for the highbrow reader. In one New Yorker cartoon (Benjamin Schwartz, March 30, 2015), a veterinarian comes into the waiting room, places a comforting arm on the worried man’s shoulder, and breaks the news: “About your cat, Mr. Schrödinger—I have good news and bad news.” (See §4 above for more on the poor cat’s indeterminate prognosis.) In another (J. B. Handelsman, March 9, 1987), a mutton-chopped publisher, seated at his Victorian office desk and riffling through an immense manuscript, explains to the dejected bearded author, “I wish you would make up your mind, Mr. Dickens. Was it the best of times or was it the worst of times? It could scarcely have both.” .

We end by borrowing the last words of Samuel Beckett’s The Unnamable (1954)—“I can’t go on, I’ll go on”—as my valedictory, since in fact I can’t go on.

• Akiba, Ken, 1999. “On super- and subvaluation: a classicist's reply to Hyde,” Mind , 108: 727–32.
• Alxatib, Sam and Francis Jeffry Pelletier, 2011. “The psychology of vagueness: Borderline cases and contradictions,” Mind & Language , 26(3): 287–326.
• Aristotle. Categories and De Interpretatione , J. N. Ackrill (ed.), Oxford: Clarendon, 1963.
• Aristotle. Metaphysics , Hippocrates Apostle (ed.), Bloomington: Indiana University Press, 1966.
• Aristotle. Metaphysics Books Γ, Δ, and E , Christopher Kirwan (ed.), 2nd edition, Oxford: Clarendon, 1993.
• Aristotle. Prior and Posterior Analytics , W. D. Ross (ed.), Oxford: Clarendon, 1957.
• Avicenna. La Métaphysique du Shifā Livres I à V , Georges Anawati (ed.), Paris: Vrin, 1978.
• Balcerowicz, Piotr, 2003. “Some remarks on the Naya method,” in Essays in Jaina Philosophy and Religion. Warsaw Indological Studies (Volume 2), Delhi: Motilal Banarsidass Publishers, pp. 37–68.
• Barnes, Jonathan, 1969. “The law of contradiction,” Philosophical Quarterly , 19: 302–309.
• Barnes, Jonathan, 1982. The Presocratic Philosophers , London: Routledge & Kegan Paul.
• Benveniste, Émile, 1956. “Remarks on the function of language in Freudian theory,” reprinted in Problems in General Linguistics , M. E. Meek (trans.), Coral Gables: University of Miami Press, 1971, pp. 65–75.
• Bochenski, Joseph M., 1961. A History of Formal Logic , Ivo Thomas (ed. and trans.), Notre Dame: University of Notre Dame Press.
• Bonini, Nicolao, Daniel Osherson, Riccardo Viale, and Timothy Williamson, 1999. “On the psychology of vague predicates,” Mind & Language , 14: 377–93.
• Dummett, Michael, 1973. Frege: philosophy of language , London: Duckworth.
• Fine, Kit, 1975. “Vagueness, truth, and logic,” Synthese , 30: 265–300.
• van Fraassen, Bas, 1969. “Presuppositions, super-valuations, and free logic,” in K. Lambert (ed.), The Logical Way of Doing Things , New Haven: Yale University Press, pp. 67–91.
• Frankfurt, Harry, 1964. “The logic of omnipotence,” Philosophical Review , 73: 262–63.
• Frege, Gottlob, 1892. “On sense and reference”, in Translations from the Philosophical Writings of Gottlob Frege , P. Geach and M. Black (eds.), Oxford: Blackwell, 1952, pp. 56–78.
• Frege, Gottlob, 1919. “Negation,” in Translations from the Philosophical Writings of Gottlob Frege , P. Geach and M. Black (eds.), Oxford: Blackwell, 1952, pp. 117–35.
• Freud, Sigmund, 1910. “The antithetical sense of primal words,” in J. Strachey (ed.), The Standard Edition of the Complete Psychological Works of Sigmund Freud (Volume 11), London: Hogarth Press, 1957, pp. 155–61.
• Garfield, Jay, 1995. The fundamental wisdom of the middle way: Nāgārjuna's Mūlamadhyamakakārikā , Jay L. Garfield (trans., commentary), New York: Oxford University Press.
• Garfield, Jay and Graham Priest, 2002. “Nāgārjuna and the limits of thought,” in Priest 2002, pp. 249–70.
• Geach, P. T., 1972. Logic Matters , reprinted Berkeley: University of California Press, 1980.
• Grice, H. P., 1989. Studies in the Way of Words , Cambridge: Harvard University Press.
• Heraclitus. Heraclitus: The Cosmic Fragments , G. S. Kirk (ed.), Cambridge: Cambridge University Press, 1954.
• Horn, Laurence, 1989. A Natural History of Negation , Chicago: University of Chicago Press; reissue edition, Stanford: CSLI, Publications, 2001.
• Horn, Laurence, 2017. “Lie-toe-tease: double negatives and excluded middles,” Philosophical Studies , 174: 79–103.
• Hyde, Dominic, 1997. “From heaps and gaps to heaps of gluts,” Mind , 106: 641–660.
• Jespersen, Otto, 1962. Negation in English and Other Languages , Copenhagen: A. F. Høst.
• Kneale, William and Martha Kneale, 1962. The Development of Logic , Oxford: Clarendon.
• Kumārila Bhaṭṭa, The Mīmāmsā-śloka-vārtika , R. Talainga (ed.), Benares: Freeman & Co., 1899.
• Kyburg, Alice, 2000. “When vague sentences inform,” Synthese , 124: 175–91.
• Lear, Jonathan, 1980. Aristotle and Logical Theory , Cambridge: Cambridge U. Press.
• Leibniz, Wilhelm Gottfried von, 1696. New Essays Concerning Human Understanding by Gottfried Wilhelm Leibniz , A. G. Langley (ed. and trans.), 2nd edition, Chicago: Open Court, 1916.
• Lee-Goldman, Russell, 2011. “ No as a discourse marker,” Journal of Pragmatics , 43: 2627–49.
• Łukasiewicz, Jan, 1910. “On the principle of contradiction in Aristotle”, V. Wedin (trans.), Review of Metaphysics , 24 (1971): 485–509.
• Mates, Benson, 1953. Stoic Logic , Berkeley and Los Angeles: University of California Press.
• Mavrodes, George, 1963. “Some puzzles concerning omnipotence,” Philosophical Review , 72: 221–23.
• Parsons, Terence, 1990. “True Contradictions,” Canadian Journal Philosophy , 20: 335–53.
• Peter of Spain, Tractatus, called afterwards Summulae Logicales , L. M. de Rijk (ed.), Assen: van Gorcum, 1972.
• Plekhanov, Gyorgii, 1909. Fundamental Problems of Marxism , D. Ryazanov (ed.), New York: International Publishers, 1929.
• Priest, Graham, 1987. In Contradiction , Dordrecht: M. Nijhoff.
• –––, 1998. “To be and not to be—that is the answer. On Aristotle on the law of non-contradiction,” Philosophiegeschichte und logische Analyse , 1: 91–130.
• –––, 2002. Beyond the Limits of Thought , Oxford: Oxford University Press.
• –––, 2006. In Contradiction: A Study of the Transconsistent , The Hague: M. Nijhoff.
• Priest, Graham, J. C. Beall, and Bradley Armour-Garb (eds.), 2004. The Law of Non-Contradiction: New Philosophical Essays , Oxford: Clarendon.
• Raju, P. T., 1954. “The principle of four-cornered negation in Indian philosophy,” Review of Metaphysics , 7: 694–713.
• Razinsky, Hili, 2017. Ambivalence: A Philosophical Exploration , London: Rowman & Littlefield.
• Recanati, François, 2002. “Unarticulated constituents,” Linguistics and Philosophy , 25: 299–345.
• Ripley, David, 2011. “Contradiction at the borders,” in R. Nouwen, R. van Rooij, U. Sauerland, and H.-C. Schmitz (eds.), Vagueness in Communication , Dordrecht: Springer, pp. 169–88.
• Robinson, Richard, 1967. Early Mâdhyamika in India and China , Madison: University of Wisconsin Press.
• Russell, Bertrand, 1905. “On descriptions”, Mind , 14: 479–93.
• Sainsbury, R. M., 2004. “Option negation and dialetheias,” in Priest et al. (eds.) 2004, 85–92.
• Savage, C. Wade, 1967. “The paradox of the stone,” Philosophical Review , 76: 74–79.
• Smiley, Timothy, 1993. “Can contradictions be true?,” Proceedings of the Aristotelian Society (Supplementary Volume), 67: 17–33.
• Sorensen, Roy, 2001. Vagueness and Contradiction , Oxford: Oxford University Press.
• Strawson, P. F., 1952. Introduction to Logical Theory , London: Methuen.
• Tillemans, Tom, 1999. “Is Buddhist Logic non-classical or deviant?,” Scripture, Logic, Language (Chapter 9) Boston: Wisdom Publications.
• Wedin, Michael V., 2004a. “Aristotle on the firmness of the principle of non-contradiction,” Phronesis , 49: 226-65.
• –––, 2004b. “On the use and abuse of non-contradiction: Aristotle's critique of Protagoras and Heraclitus in Metaphysics Gamma 5,” Oxford Studies in Ancient Philosophy , 26: 213–39.

How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

• Carey, Stan (2014). “ Sorry not sorry: The many names for non-apologies ,” LexiconValley blogpost, Slate , Nov. 20, 2014.
• Liberman, Mark (2008). “ Yeah-no mailbag ,” Language Log blog post, April 3, 2008.
• Meyer, Matthew (2008). “ Non-contradiction as an ontological principle: An interpretation of Aristotle's Metaphysics IV.3-4 ,” unpublished manuscript, Boston University.
• Saturday Night Live (2017). Levi’s Wokes , non-gender-conforming style-free jeans introduced in faux commercial, Nov. 30, 2017.
• Schulz, Kathryn (2014). “ The walking cure: Talking to Cheryl Strayed about what made Wild work ,” Vulture , Dec. 3, 2014.
• Simmons, Bill (2014). Grantland column , Dec. 19, 2014.

Aristotle, General Topics: logic | Aristotle, General Topics: metaphysics | Aristotle, Special Topics: on non-contradiction | dialetheism | fatalism | Heraclitus | liar paradox | logic: many-valued | negation | Russell’s paradox | Sorites paradox | square of opposition | truth values | vagueness

Acknowledgments

I thank an anonymous reader and Professor Piotr Balcerowicz for very helpful comments on the original version of this entry. I am especially grateful to an anonymous referee for comments on the 2018 update.

Copyright © 2018 by Laurence R. Horn < laurence . horn @ yale . edu >

• Accessibility

Support SEP

Mirror sites.

View this site from another server:

• Info about mirror sites

The Stanford Encyclopedia of Philosophy is copyright © 2023 by The Metaphysics Research Lab , Department of Philosophy, Stanford University

Library of Congress Catalog Data: ISSN 1095-5054

• Scholarly Community Encyclopedia
• Log in/Sign up

Video Upload Options

• MDPI and ACS Style
• Chicago Style

In philosophy, the triad of thesis, antithesis, synthesis (German: These, Antithese, Synthese; originally: Thesis, Antithesis, Synthesis) is a progression of three ideas or propositions. The first idea, the thesis, is a formal statement illustrating a point; it is followed by the second idea, the antithesis, that contradicts or negates the first; and lastly, the third idea, the synthesis, resolves the conflict between the thesis and antithesis. It is often used to explain the dialectical method of German philosopher Georg Wilhelm Friedrich Hegel, but Hegel never used the terms himself; instead his triad was concrete, abstract, absolute. The thesis, antithesis, synthesis triad actually originated with Johann Fichte.

1. History of the Idea

Thomas McFarland (2002), in his Prolegomena to Coleridge's Opus Maximum , [ 1 ] identifies Immanuel Kant's Critique of Pure Reason (1781) as the genesis of the thesis/antithesis dyad. Kant concretises his ideas into:

• Thesis: "The world has a beginning in time, and is limited with regard to space."
• Antithesis: "The world has no beginning and no limits in space, but is infinite, in respect to both time and space."

Inasmuch as conjectures like these can be said to be resolvable, Fichte's Grundlage der gesamten Wissenschaftslehre ( Foundations of the Science of Knowledge , 1794) resolved Kant's dyad by synthesis, posing the question thus: [ 1 ]

• No synthesis is possible without a preceding antithesis. As little as antithesis without synthesis, or synthesis without antithesis, is possible; just as little possible are both without thesis.

Fichte employed the triadic idea "thesis–antithesis–synthesis" as a formula for the explanation of change. [ 2 ] Fichte was the first to use the trilogy of words together, [ 3 ] in his Grundriss des Eigentümlichen der Wissenschaftslehre, in Rücksicht auf das theoretische Vermögen (1795, Outline of the Distinctive Character of the Wissenschaftslehre with respect to the Theoretical Faculty ): "Die jetzt aufgezeigte Handlung ist thetisch, antithetisch und synthetisch zugleich." ["The action here described is simultaneously thetic, antithetic, and synthetic." [ 4 ] ]

Still according to McFarland, Schelling then, in his Vom Ich als Prinzip der Philosophie (1795), arranged the terms schematically in pyramidal form.

According to Walter Kaufmann (1966), although the triad is often thought to form part of an analysis of historical and philosophical progress called the Hegelian dialectic, the assumption is erroneous: [ 5 ]

Whoever looks for the stereotype of the allegedly Hegelian dialectic in Hegel's Phenomenology will not find it. What one does find on looking at the table of contents is a very decided preference for triadic arrangements. ... But these many triads are not presented or deduced by Hegel as so many theses, antitheses, and syntheses. It is not by means of any dialectic of that sort that his thought moves up the ladder to absolute knowledge.

Gustav E. Mueller (1958) concurs that Hegel was not a proponent of thesis, antithesis, and synthesis, and clarifies what the concept of dialectic might have meant in Hegel's thought. [ 6 ]

"Dialectic" does not for Hegel mean "thesis, antithesis, and synthesis." Dialectic means that any "ism" – which has a polar opposite, or is a special viewpoint leaving "the rest" to itself – must be criticized by the logic of philosophical thought, whose problem is reality as such, the "World-itself".

According to Mueller, the attribution of this tripartite dialectic to Hegel is the result of "inept reading" and simplistic translations which do not take into account the genesis of Hegel's terms:

Hegel's greatness is as indisputable as his obscurity. The matter is due to his peculiar terminology and style; they are undoubtedly involved and complicated, and seem excessively abstract. These linguistic troubles, in turn, have given rise to legends which are like perverse and magic spectacles – once you wear them, the text simply vanishes. Theodor Haering's monumental and standard work has for the first time cleared up the linguistic problem. By carefully analyzing every sentence from his early writings, which were published only in this century, he has shown how Hegel's terminology evolved – though it was complete when he began to publish. Hegel's contemporaries were immediately baffled, because what was clear to him was not clear to his readers, who were not initiated into the genesis of his terms. An example of how a legend can grow on inept reading is this: Translate "Begriff" by "concept," "Vernunft" by "reason" and "Wissenschaft" by "science" – and they are all good dictionary translations – and you have transformed the great critic of rationalism and irrationalism into a ridiculous champion of an absurd pan-logistic rationalism and scientism. The most vexing and devastating Hegel legend is that everything is thought in "thesis, antithesis, and synthesis." [ 7 ]

Karl Marx (1818–1883) and Friedrich Engels (1820–1895) adopted and extended the triad, especially in Marx's The Poverty of Philosophy (1847). Here, in Chapter 2, Marx is obsessed by the word "thesis"; [ 8 ] it forms an important part of the basis for the Marxist theory of history. [ 9 ]

2. Writing Pedagogy

In modern times, the dialectic of thesis, antithesis, and synthesis has been implemented across the world as a strategy for organizing expositional writing. For example, this technique is taught as a basic organizing principle in French schools: [ 10 ]

The French learn to value and practice eloquence from a young age. Almost from day one, students are taught to produce plans for their compositions, and are graded on them. The structures change with fashions. Youngsters were once taught to express a progression of ideas. Now they follow a dialectic model of thesis-antithesis-synthesis. If you listen carefully to the French arguing about any topic they all follow this model closely: they present an idea, explain possible objections to it, and then sum up their conclusions. ... This analytical mode of reasoning is integrated into the entire school corpus.

Thesis, Antithesis, and Synthesis has also been used as a basic scheme to organize writing in the English language. For example, the website WikiPreMed.com advocates the use of this scheme in writing timed essays for the MCAT standardized test: [ 11 ]

For the purposes of writing MCAT essays, the dialectic describes the progression of ideas in a critical thought process that is the force driving your argument. A good dialectical progression propels your arguments in a way that is satisfying to the reader. The thesis is an intellectual proposition. The antithesis is a critical perspective on the thesis. The synthesis solves the conflict between the thesis and antithesis by reconciling their common truths, and forming a new proposition.

• Samuel Taylor Coleridge: Opus Maximum. Princeton University Press, 2002, p. 89.
• Harry Ritter, Dictionary of Concepts in History. Greenwood Publishing Group (1986), p.114
• Williams, Robert R. (1992). Recognition: Fichte and Hegel on the Other. SUNY Press. p. 46, note 37. 
• Fichte, Johann Gottlieb; Breazeale, Daniel (1993). Fichte: Early Philosophical Writings. Cornell University Press. p. 249. 
• Walter Kaufmann (1966). "§ 37". Hegel: A Reinterpretation. Anchor Books. ISBN 978-0-268-01068-3. OCLC 3168016. https://archive.org/details/hegelreinterpret00kauf. 
• Mueller, Gustav (1958). "The Hegel Legend of "Thesis-Antithesis-Synthesis"". Journal of the History of Ideas 19 (4): 411–414. doi:10.2307/2708045.  https://dx.doi.org/10.2307%2F2708045
• Mueller 1958, p. 411.
• marxists.org: Chapter 2 of "The Poverty of Philosophy", by Karl Marx https://www.marxists.org/archive/marx/works/1847/poverty-philosophy/ch02.htm
• Shrimp, Kaleb (2009). "The Validity of Karl Marx's Theory of Historical Materialism". Major Themes in Economics 11 (1): 35–56. https://scholarworks.uni.edu/mtie/vol11/iss1/5/. Retrieved 13 September 2018. 
• Nadeau, Jean-Benoit; Barlow, Julie (2003). Sixty Million Frenchmen Can't Be Wrong: Why We Love France But Not The French. Sourcebooks, Inc.. p. 62. https://archive.org/details/sixtymillionfren00nade_041. 
• "The MCAT writing assignment.". Wisebridge Learning Systems, LLC. http://www.wikipremed.com/mcat_essay.php. Retrieved 1 November 2015. 

• Terms and Conditions
• Privacy Policy
• Advisory Board

Newest Articles

• The Critique of Pure Reason by Immanuel Kant: A Comprehensive Overview
• Exploring the Interplay between Religious Experience and Faith
• Exploring the Ethical Theory of Utilitarianism
• Existentialism: An Introduction
• Metaphysics
• Theory of Forms
• Epistemology
• Materialism
• Moral relativism
• Utilitarianism
• Virtue ethics
• Normative ethics
• Applied ethics
• Moral Psychology
• Philosophy of art
• Philosophy of language
• Philosophy of beauty
• Nature of Art
• Philosophy of Film
• Philosophy of Music
• Deductive reasoning
• Inductive reasoning
• Justification
• Perception and Knowledge
• Beliefs and Truth
• Modern philosophy
• Romanticism
• Analytic philosophy
• Enlightenment philosophy
• Existentialism
• Enlightenment
• Ancient philosophy
• Classical Greek philosophy
• Renaissance philosophy
• Medieval philosophy
• Pre-Socratic philosophy
• Hellenistic philosophy
• Presocratic philosophy
• Rationalism
• Scholasticism
• Jewish philosophy
• Early Islamic philosophy
• Reasoning and Argumentation
• Seeking Justice After a Tractor-Trailer Accident: Why You Need an Experienced Lawyer
• Critical Thinking
• Fallacies and logical errors
• Skepticism and doubt
• Creative Thinking
• Lateral thinking
• Thought experiments
• Argumentation and Logic
• Syllogisms and Deductive Reasoning
• Fallacies and Rebuttals
• Inductive Reasoning and Analogy
• Reasoning and Problem-Solving
• Critical Thinking and Decision Making
• Creative Thinking and Problem Solving
• Analytical Thinking and Reasoning
• Philosophical Writing and Analysis
• Argumentative Writing and Analysis
• Interpreting Philosophical Texts
• Writing Essays and Articles on Philosophy
• Philosophical Research Methods
• Qualitative Research Methods in Philosophy
• Quantitative Research Methods in Philosophy
• Research Design and Methodology
• Ethics and Morality
• Aesthetics and Beauty
• Metaphysical terms
• Ontological argument
• Ethical terms
• Aesthetic terms
• Metaphysical theories
• Kant's Categorical Imperative
• Aristotle's Four Causes
• Plato's Theory of Forms
• Hegel's Dialectic
• Ethical theories
• Aesthetic theories
• John Dewey's aesthetic theory
• Immanuel Kant's aesthetic theory
• Modern philosophical texts
• Foucault's The Order of Things
• Descartes' Meditations
• Nietzsche's Beyond Good and Evil
• Wittgenstein's Tractatus Logico-Philosophicus
• Ancient philosophical texts
• Kant's Critique of Pure Reason
• Hegel's Phenomenology of Spirit
• Aristotle's Nicomachean Ethics
• Plato's Republic
• Ancient philosophers
• Modern philosophers
• Modern philosophical schools
• German Idealism
• British Empiricism
• Ancient philosophical schools
• The Skeptic school
• The Cynic school
• The Stoic school
• The Epicurean school
• The Socratic school
• Philosophy of Language
• Semantics and Pragmatics of Language Usage
• Analytic-Synthetic Distinction
• Meaning of Words and Phrases
• Philosophy of Science
• Scientific Realism and Rationalism
• Induction and the Hypothetico-Deductive Model
• Theory-Ladenness and Underdetermination
• Philosophy of Mind
• Mind-Body Dualism and Emergentism
• Materialism and Physicalism
• Identity Theory and Personal Identity
• Philosophy of Religion
• Religious Pluralism and Exclusivism
• The Problem of Evil and Suffering
• Religious Experience and Faith
• Metaphysical Theories
• Idealism and Realism
• Determinism, Fatalism, and Libertarianism
• Phenomenalism and Nominalism
• Epistemological Theories
• Intuitionism, Skepticism, and Agnosticism
• Rationalism and Empiricism
• Foundationalism and Coherentism
• Aesthetic Theories
• Formalist Aesthetics, Emotional Aesthetics, Experiential Aesthetics
• Relational Aesthetics, Sociological Aesthetics, Historical Aesthetics
• Naturalistic Aesthetics, Immanent Aesthetics, Transcendental Aesthetics
• Ethical Theories
• Virtue Ethics, Utilitarianism, Deontology
• Subjectivism, Egoism, Hedonism
• Social Contract Theory, Natural Law Theory, Care Ethics
• Metaphysical Terms
• Cause, Necessity, Possibility, Impossibility
• Identity, Persistence, Time, Space
• Substance, Attribute, Essence, Accident
• Logic and Argumentation Terms
• Analogy, Syllogism, Deduction, Induction
• Inference, Validity, Soundness, Refutation
• Premise, Conclusion, Entailment, Contradiction
• Epistemological Terms
• Perception and Knowledge Claims
• Infallibility, Verifiability, Coherence Theory of Truth
• Justification, Beliefs and Truths
• Ethical Terms
• Modern Texts
• A Vindication of the Rights of Woman by Mary Wollstonecraft
• Thus Spoke Zarathustra by Friedrich Nietzsche
• The Critique of Pure Reason by Immanuel Kant
• Medieval Texts
• The Guide for the Perplexed by Moses Maimonides
• The Summa Theologiae by Thomas Aquinas
• The Incoherence of the Incoherence by Averroes
• Ancient Texts
• The Nicomachean Ethics by Aristotle
• The Art of Rhetoric by Cicero
• The Republic by Plato
• Hegel's Dialectic: A Comprehensive Overview
• Philosophical theories

Georg Wilhelm Friedrich Hegel's dialectic is one of the most influential philosophical theories of the modern era. It has been studied and debated for centuries, and its influence can be seen in many aspects of modern thought. Hegel's dialectic has been used to explain a wide range of topics from politics to art, from science to religion. In this comprehensive overview, we will explore the major tenets of Hegel's dialectic and its implications for our understanding of the world. Hegel's dialectic is based on the premise that all things have an inherent contradiction between their opposites.

It follows that any idea or concept can be understood through a synthesis of the two opposing forces. This synthesis creates a new and higher understanding, which then leads to further progress and development. Hegel's dialectic has been used in many different fields, from philosophy to economics, and it provides an important framework for understanding how our world works. In this article, we will explore the historical origins and development of Hegel's dialectic. We will also examine its application in various fields, from politics to art, from science to religion.

Finally, we will consider the implications of Hegel's dialectic for our understanding of the world today. Hegel's dialectic is a philosophical theory developed by German philosopher Georg Wilhelm Friedrich Hegel in the early 19th century. It is based on the concept of thesis, antithesis and synthesis , which are steps in the process of progress. The thesis is an idea or statement that is the starting point of an argument. The antithesis is a statement that contradicts or negates the thesis.

The synthesis is a combination of the two opposing ideas, which produces a new idea or statement. This process can be repeated multiple times, leading to an evolution of ideas. Hegel's dialectic has been used in many fields, such as politics and economics . It has been used to explain how ideas progress through debate and discussion.

In politics, it has been used to explain how different points of view can lead to compromise or resolution. In economics, it has been used to explain how different economic theories can lead to new solutions and strategies. Hegel's dialectic can also be applied to everyday life. For example, it can be used to resolve conflicts between people or groups.

Thesis, Antithesis and Synthesis

Thesis and antithesis are two conflicting ideas, while synthesis is the result of their interaction. The dialectic process is a way of understanding how the world works, as it helps to explain the constant flux of ideas and events. It also helps to explain how change and progress are possible. Thesis and antithesis can be thought of as two sides of a coin. One side represents an idea or opinion, while the other side represents its opposite.

When the two sides come together, they create a synthesis that incorporates both sides. This synthesis can then be used to create new ideas or opinions. The dialectic process can be applied in various contexts, such as politics and economics. In politics, it can be used to explain how different factions come together to create policies that are beneficial to all parties. In economics, it can be used to explain how supply and demand interact to create a stable market. Hegel's dialectic can also be used in everyday life.

Applications of Hegel's Dialectic

For example, in the political sphere, it can be used to explore how different ideologies can be reconciled or how compromises can be reached. In economics, Hegel's dialectic has been used to explain the process of economic growth and development. It can be seen as a way of understanding how different economic systems interact with each other and how different economic actors are affected by changes in the marketplace. For example, it can help to explain how different economic policies can lead to different outcomes. Hegel's dialectic has also been applied to other social sciences, such as sociology and anthropology. In particular, it has been used to explore how different social systems interact with each other and how different social groups are affected by changes in their environment.

Using Hegel's Dialectic in Everyday Life

This process can be used to explain how various aspects of life, such as career or relationships, evolve over time. Thesis represents an idea or concept, while antithesis represents the opposite of that idea or concept. Synthesis is the resolution between the two opposing forces. This process is repeated until a conclusion is reached.

For example, in a career conflict between two people, one might present an idea while the other presents the opposite idea. Through discussion and negotiation, the two parties can come to a synthesis that meets both their needs. Hegel's dialectic can also be used to resolve conflicts between groups of people. It involves each party presenting their ideas and opinions, then engaging in dialogue to reach a compromise or agreement.

This process can be applied to any area of life, from politics and economics to relationships and personal growth. It helps to create understanding and respect between different perspectives, allowing everyone to come together in a meaningful way. By understanding and applying Hegel's dialectic in everyday life, we can better navigate our relationships and interactions with others. Through dialogue, negotiation, and compromise we can work towards resolutions that benefit all parties involved.

In economics, it has been used to explain how market forces interact with each other and how different economic theories can be used to explain the same phenomenon. The dialectic has also been used in other fields such as philosophy, science, and psychology. In philosophy, it has been used to explain the relationship between theory and practice and how theories evolve over time. In science, it has been used to explain the relationship between empirical evidence and logical reasoning.

This theory can be applied to any area of life, from career to relationships. The core of Hegel's dialectic involves the concept of thesis, antithesis, and synthesis, which is a way of understanding how ideas evolve over time. In this way, the dialectic helps to identify contradictions in a situation and find a resolution through synthesis. In terms of its application to everyday life, the dialectic can be used to find common ground between two opposing sides. For example, if two people are in disagreement, the dialectic can help them identify the underlying issues and then work to resolve them.

Additionally, it can help individuals and groups identify areas where they have common interests, which can lead to more productive conversations and outcomes. The dialectic is also useful in understanding how different perspectives can lead to different solutions. By recognizing different points of view, individuals and groups can gain insight into why certain solutions may not work for everyone involved. This can help to create a more productive environment for collaboration. Finally, the dialectic can be used as a tool for self-reflection. By understanding how different ideas evolve over time and how different perspectives interact, individuals can gain insight into their own views and values.

For example, it can be used to explain the development of a new policy proposal or a new form of government. In economics, Hegel's dialectic can be used to explain the dynamics of supply and demand, or the emergence of a new economic system. In addition, Hegel's dialectic has been applied in other areas, such as education and religion. In education, this theory can be used to explain the process of learning and understanding new concepts. In religion, it can be used to explain the evolution of religious beliefs and practices over time.

This is followed by a synthesis of the two, which creates a new, higher form of understanding. This new understanding then forms the basis for further analysis, which can lead to further synthesis and resolution. Hegel's dialectic can be applied to any area of life, such as career or relationships. For example, if two people have different approaches to a problem, they can use the dialectic to work together to find a solution that works for both of them.

This could involve identifying their respective points of view and then looking for common ground where they can agree. As the synthesis forms, it can provide a basis for further discussion, which may eventually lead to a resolution. The same process can be used to resolve conflicts between groups, such as political parties or countries. By recognizing each side's point of view and then looking for common ground, it is possible to find ways to bridge the divide between them.

This can help create an atmosphere of mutual understanding and respect, which can lead to constructive dialogue and positive outcomes. Hegel's dialectic is a valuable tool for helping people and groups come to agreement and harmony despite their differences. By recognizing both sides' points of view and then looking for common ground, it is possible to create a synthesis that can provide a basis for further discussion and resolution. Hegel's dialectic is a powerful philosophical tool that helps to explain how ideas evolve over time. Through the concept of thesis, antithesis and synthesis, it provides a framework for understanding how opposing forces interact and ultimately create new ideas and solutions.

This theory has been applied to many areas, such as politics and economics, and can be used in everyday life. The article has provided a comprehensive overview of Hegel's dialectic and its various applications.

Top Articles

• Philosophy of Art: Exploring Aesthetics and Beauty

• Exploring Plato's Republic

• Understanding Inductive Reasoning and Analogy

• Exploring Expression: A Philosophical and Aesthetic Overview
• Exploring the Theory of Forms: A Comprehensive Overview
• Exploring Moral Relativism: A Comprehensive Overview
• Exploring the Philosophy of Art

Classical Greek Philosophy: A Comprehensive Overview

• Understanding Utilitarianism: A Guide
• Exploring Pragmatism: A Modern Philosophy
• Analytic Philosophy: A Comprehensive Overview

Medieval Philosophy: An Overview

• Epistemology: Understanding the Nature of Knowledge
• Exploring the Ideas of Enlightenment Philosophy
• Exploring Idealism: The History and Concepts of a Modern Philosophy
• Exploring Pre-Socratic Philosophy: An Overview
• Exploring Ontology: A Comprehensive Overview
• Understanding Inference: A Comprehensive Overview

Philosophy of Language: Exploring the Ways We Communicate

• Understanding Fallacies and Logical Errors
• Exploring the Philosophy of Beauty
• Understanding Inductive Reasoning
• Understanding Deontology: Ethics and Principles
• Lateral Thinking: An Overview
• Thought Experiments: Exploring Creative and Philosophical Thinking
• Exploring Skepticism and Doubt: A Philosophical and Critical Thinking Perspective
• Exploring Hellenistic Philosophy: An Introduction
• Exploring Deductive Reasoning
• A Comprehensive Look at Causality
• Exploring the Ontological Argument
• Exploring Egoism: What It Is and What It Means
• Exploring Aristotle's Four Causes
• Exploring Plato's Theory of Forms
• Deontology: An Introduction to an Ethical Theory
• Exploring Virtue Ethics: The Philosophical Theory
• Descartes' Meditations: An Introduction for None
• Aristotle: A Comprehensive Overview
• Exploring Hegel's Phenomenology of Spirit
• Exploring Noumenon: A Philosophical and Metaphysical Overview
• Exploring the Life and Legacy of Cicero: An Introduction
• Exploring Taste: A Philosophical and Aesthetic Guide
• Exploring Nietzsche's Beyond Good and Evil
• Exploring Wittgenstein's Tractatus Logico-Philosophicus
• Descartes: A Comprehensive Overview
• Sublime: An Introduction to Aesthetic and Philosophical Terms
• Understanding Existentialism: A Brief Introduction
• Exploring Friedrich Nietzsche: An Introduction to the Major Modern Philosopher
• Exploring Pragmatism: A Modern Philosophical School
• Exploring the Life and Work of Georg Wilhelm Friedrich Hegel
• German Idealism: A Comprehensive Overview
• Explore The Epicurean School of Ancient Philosophy
• Analytic Philosophy: A Primer
• Exploring Jewish Philosophy
• Exploring the Philosophy of Immanuel Kant
• Exploring British Empiricism
• Justification: A Comprehensive Overview
• Exploring the History and Impact of Empiricism
• Enlightenment: A History of Philosophy
• Perception and Knowledge: An Overview
• Understanding Fallacies and Rebuttals
• Exploring Applied Ethics
• Exploring Critical Thinking and Decision Making
• Exploring Theology: A Comprehensive Overview
• Exploring the Rationalism of Renaissance Philosophy
• Exploring Moral Psychology: A Closer Look
• Exploring Identity Theory and Personal Identity
• Exploring Quantitative Research Methods in Philosophy
• Exploring the Analytic-Synthetic Distinction in Philosophy of Language
• Exploring the Role of Research Design and Methodology
• Understanding the Meaning of Words and Phrases
• The Problem of Evil and Suffering: A Philosophical Exploration
• Exploring the Concepts of Cause, Necessity, Possibility, and Impossibility
• Comparing Analogy, Syllogism, Deduction and Induction
• Exploring Aesthetic Theories: Formalism, Emotionalism and Experientialism
• Understanding Inference, Validity, Soundness, and Refutation
• Exploring Relational Aesthetics, Sociological Aesthetics, and Historical Aesthetics
• Exploring Naturalistic, Immanent and Transcendental Aesthetics
• Exploring Rationalism and Empiricism
• Understanding Determinism, Fatalism, and Libertarianism
• Exploring Identity, Persistence, Time, and Space
• Understanding Virtue Ethics, Utilitarianism and Deontology
• Exploring Phenomenalism and Nominalism
• Ethical Theories: Virtue Ethics, Utilitarianism, and Deontology
• Exploring Justification, Beliefs and Truths
• Foundationalism and Coherentism: An Overview
• Exploring Social Contract Theory, Natural Law Theory, and Care Ethics
• An Overview of Friedrich Nietzsche's Thus Spoke Zarathustra
• Exploring Subjectivism, Egoism and Hedonism
• The Art of Rhetoric by Cicero: A Comprehensive Overview

New Articles

Which cookies do you want to accept?

Hegel-by-HyperText Resources

Excerpt from Hegel for Beginners

Source : Hegel for Beginners , by Llyod Spencer and Andrzej Krauze, Published by Icon Books, 14 of 175 pages reproduced here, minus the abundant illustrations.

"Classical reasoning assumes the principle of logical identity: A = A or A is not non-A".

"But in writing that book I became aware of employing a new and unprecedented way of thinking".

Dialectical Thinking

Aufhebung or sublation, a grammar of thinking.

"I liken my study of logic to the study of grammar. You only really see the rewards when you later come to observe language in use and you grasp what it is that makes the language of poetry so evocative".

Three Kinds of Contradiction

• The three divisions of the Science of Logic involve three different kinds of contradiction. In the first division Being the opposed pair of concepts at first seem flatly opposed, as if they would have nothing at all to do with one another: Being Nothing / Quantity Quality. Only be means of analysis or deduction can they be shown to be intimately interrelated.
• In the second division Essence the opposed pairs immediately imply one another. The Inner and the Outer, for example: to define one is at the same time to define the other.
• In the third division the Concept [ Notion ] we reach an altogether more sophisticated level of contradiction. Here we have concepts such as identity whose component parts, Universality and Particularity, are conceptually interrelated.

Triadic Structure

• The analytic logic of understanding which focuses the data of sense-experience to yield knowledge of the natural phenomenal world.
• The dialectical logic of understanding which operates independently of sense-experience and erroneously professes to give knowledge of the transcendent noumena ("things in themselves" or also the "infinite" or the "whole")
• Analytic understanding is only adequate for natural science and practical everyday life, not for philosophy.
• Dialectic reason s not concerned with Kant's "transcendent", nor with the abstract "mutilated" parts of reality, but with reality as a totality , and therefore gives true knowledge.

What is Knowing?

"the whole of philosophy resembles a circle of circles".

Further Reading: Introduction to Shorter Logic | Meaning of Hegel's Logic

—  Hegel-by-HyperText Home Page @ marxists.org  —

On Aristotle's dialectical method

• Brendan Montague

Creative Commons 4.0

Dialectic is a process of discovery and pedagogy that takes place between two individuals using logical argument, according to Aristotle. To an extent, this is the same as the familiar “thesis, antithesis, synthesis” to which Aristotle’s dialectic is often reduced, but that formulation actually originated with Johann Fichte (1762 - 1814). 

Dialectic is the same as rhetoric in that it is an intellectual activity aimed at changing minds, and is the same as logic in that it relies on reasoning to validate (or invalidate) arguments. It differs from rhetoric in that only logic should be deployed to persuade, and that it is aimed at a particular individual rather than a group, or a crowd. It differs from logic in that it is not concerned with the pursuit of absolute truth, or first principles, but in convincing a person of an argument. 

Read 'The nature of Aristotle's dialectic' here. 

Dr Evans explains that while dialectic is concerned with the individual and her perspective, logic is not: “Pure logic is not concerned with the vagaries of the individual's reaction, and indeed in its search for objectivity it is positively prohibited from considering the individual as such.” (75) He adds later: “Aristotle is aware that the conditions of the exercise of dialectical skill are such that, although the dialectician is indeed required to argue his case purely by logical means, he must at the same time not ignore the various ways in which circumstances which are external to his argument can affect its character.” (92) 

So what is the method of dialectic? Dialectic involves a dialogue between two people. These individuals do need an understanding of the logical method of reasoning - set out more fully here - and need to be seriously and genuinely engaged in the process. The concern is validating arguments on both sides. Dialectic is not a method for bad actors or the resolution of primarily emotional disputes. 

Aristotle asserts that dialectic does use logic to advance knowledge through the validation of arguments and through deductive reasoning through inference. “[W]e need to distinguish how many kinds of dialectical argument there are,” he writes in Topics. “One kind is induction, another is deduction. Here we discuss deduction, which is the essence of logic. 

The aim of both logic and dialectic is to validate the definition of things (indeed, everything from abstract concepts to physical objects). Logic seeks a true, absolute definition. Dialectic aims to validate or invalidate definitions presented in argument.

The beginning of any process of definition (of demonstration, and of argument) is actually very simple: we start with “this is the same is that,” and “this is different to that”: the human is the same as the bonobo in this way; the human is different to the bonono in this way. Dr Evans states: [T]here are certain things - same, other etc. - with which the dialectician is characteristically concerned...” (38). This is because ‘same’ and ‘different’ are the foundations of definition (of cognition and categorisation), which is how we come to recognise and define the things around us.

In both dialectic and logic, any one thing can only be defined by its relation to other things. The basic structure of a proposition includes a subject (the thing being defined) and an object (the thing it is defined in relation to) is. A proposition can be used as a premise in an argument, and through argument we can infer a new proposition, which is the conclusion. 

Definition 

Dialectic and logic both arrive at definitions by identifying the unique properties that belong to the subject - the properties that really make it what it is as opposed to superfluous detail, which Aristotle calls the accidents.

For example, in a definition humans we would want to include language, but not necessarily fingernails. It is the use of language that differentiates humans from other apes. Both humans and apes have fingernails. Language is a unique property in this instance, fingernails are accidents. 

Dialectic, like logic, is concerned with propositions that include a subject and a predicate, and the relationship between the two. The subject is the thing that is defined in any proposition. The predicate is the object and the relation to that object that defines the subject. An example of such a statement is, “all humans are animals”.

Here, the human is the subject and animal the predicate. We know that those properties that are universal to animals (for example, the property of needing to eat to survive) will also be true for us humans. The object of the sentence - the animal - is used to describe the subject - the human. Both unique properties and accidents are predicates, but only the former is useful in establishing a higher level definition. 

To define something skillfully, we need to understand the wider class of things to which our subject belongs. This, in Aristotle’s terminology, is its genus. A genus is a class or category of things that share the same property. The genus ‘vehicle’ will include modes of transport including busses, cars and bicycles.

We then need to establish what properties distinguish it from the other things in its genus. These properties Aristotle calls differentia. The subject that is differentiated within a genus is the species (from specific). The bus is a public mode of transport used by many, the car a private use of transport used by a few.

The mode of ownership and use differentiates the specific car, and specific bus, which are both in the genus, or category, vehicle. Dr Evans states: “Aristotle argues that only if the definition contains the genus and the differentia, can it indicate the essence of the subject” (114). We define our subject by placing it into the correct place in a wider system of categories. 

A true definition of any subject states its essence: the essence is those properties that allow us to categorise it in its genus, and then differentiate it from other members of that genus. We arrive at the essence of any thing through this double-sided process of classification. This is why for Aristotle the pursuit of the essence of things is primary and paramount. As Dr Evans writes: “[T]he requirement that the definition indicate the essence is an unargued premiss to the discussion in Topics...elsewhere in Aristotle’s work the axiomatic character of this requirement can be seen.” (107). 

We can see here the influence of Aristotle’s interest in biology, and the natural world provides a useful range of things that can give us concrete examples of what we mean. Let’s begin with what is most familiar: ourselves.

Humans are a species. The species human belongs to the genus of ape. One of the many differences between humans and other animals is that we have a complex language. Therefore, through this double process of establishing our genus (the general group that we belong to) and our differentia (that which is specific to our species) we are able to develop a definition of human: an ape with language. This definition describes the essence of what it means to be human. 

The process of defining a thing through its genus and species is derived from, but not limited to, the practice of biology. We can use the same process to define concepts, such as “true” and “false”. These terms appear to be entirely the opposite of each other. However, both are concerned with the validity of whatever they happen to describe.

They belong to the genus of statements about validity. Yet the differentia is one is positive and one is negative. The definition of “true” is therefore “a positive statement about validity”. This provides us with the essence of what we mean by true. 

In dialectics, and in logic, when we define any object we are not required to fix the genus and the species. The choice we make depends on what exactly we are trying to define and - in dialectic - for whom.

For example, we can also say that all humans are systems. Here, we may be concerned about universal claims about all systems. These claims would logically be true of humans. The terms we chose in our propositions depend very much on what we are hoping to establish. With dialectics (but not logic) it also depends on the premises that we can agree with our interlocutor.

This process of establishing definitions and validating arguments is enhanced through the use of the syllogism. (A longer definition of syllogism is provided in this Endoxa article). In short, a syllogism is a method of arriving at (or inferring) a valid conclusion from two valid premises.

There is - Aristotle establishes - a particularly useful from of syllogism where the first premise states the general (or universal); the second states the specific (the individual) and the third the relationship between the two (the particular). The classic syllogism would look like this:

All humans are animals

Eve is a human

Eve is an animal

If we agree that the premise that “all humans are animals” and also that “Eve is a human” then we can infer that the statement “Eve is an animal” is valid. This is the basis of formal logic. Dialectic uses the syllogism because it is compelling: it is highly likely to convince the person you are in conversation with, whereas logic utilises the same technique for slightly different purposes - the pursuit of absolute truth.

A sortie - a long chain of syllogisms - is the aim of rational thought. Aristotle argues in Topics: “[F]or it is impossible to demonstrate something if one does not start from the special foundations and link one's reasoning in a chain until one reaches what is at the end” (34/35).

This begs the question. What are these “special foundations”. For the syllogism, we need premises. Dialectic begins with “the securing of premises”. As we can see above, valid premises should provide us with valid conclusions, an invalid premise can conversely result in an invalid conclusion.

The house we build is only as sound as the foundations on which it sits. The securing of premises - according to Aristotle - includes 1. The detection of ambiguity; 2. The discovery of differences, and 3. The consideration of similarities. This follows tidily from our exploration of definition, above.

In this article I have attempted to give a brief definition and overview of Aristotle’s dialectic, setting out its aims, scope and method. Now that we have a working understanding of dialectic I want to follow Dr Evans in developing a dialectical definition of dialectic itself. This involves establishing the genus, or category, to which it belongs and setting out what properties define all the members of this category. Then I want to discuss how it is different to the other members of the category - it’s differentia. This will focus on the difference between dialectic and logic. 

The difference between dialectic and logic can be briefly and broadly explained by the fact logic (such as pure logic, formal logic) seeks absolute truth developed from true premises and sound argument, where dialectic seeks to persuade and calibrate arguments from the foundation of common sense.

Dialectic is therefore concerned with what people already understand, what is absolutely understandable, and how a person can guide her interlocutor from the first to the second position.

In the next article I will establish the essence of Aristotle’s dialectic.

This Author 

Brendan Montague is editor of  The Ecologist.  This article is part of the  Endoxa.review  project. 

Donate to The Ecologist and support high impact environmental journalism and analysis.

The nature of Aristotle's dialectic

Freedom begins in the workplace

A dialectical definition of Aristotle's dialectic - Pt II

More from this author.

History, repeating

The DNA of successful campaigns

‘What kind of American are you?’

• Editors’ Picks
• Ecologist Writers' Fund
• Biodiversity
• Climate Breakdown
• Economics and policy
• Food and Farming
• Yasmin Dahnoun
• Catherine Early
• Simon Pirani
• Gareth Dale
• Marianne Brown
• Resurgence & Ecologist
• Ecologist recycled
• Megamorphosis

Kant’s Cosmology pp 149–207 Cite as

The Antinomy of Pure Reason

• Brigitte Falkenburg 25  
• First Online: 19 December 2020

161 Accesses

Part of the book series: European Studies in Philosophy of Science ((ESPS,volume 12))

Chapter 5 analyzes the general structure of the antinomy of pure reason and the specific structures of its four versions, including a detailed logical reconstruction of all thesis and antithesis proofs. To understand the logical structure and epistemological significance of the antinomy, it is crucial to distinguish carefully between the pre-cretical views which correspond to the standpoint of transcendental realism on which the proofs are based, and the critical point of view, which is the key to Kant’s resolution of the antinomy. Kant was well aware that the proofs are defective. His critical diagnosis is that they seem conclusive from the point of view of transcendental realism, whereas transcendental idealism reveals that they derive from a self-contradictory cosmological concept. Our reconstruction shows that the proofs employ rationalist, empiricist, or verificationist arguments, including Kant’s own pre-critical conception of the infinite, but do not depend fatally on claims of transcendental idealism; and that the proof results are due to the logical fallacy of an ambiguous middle term in the proofs derive from semantic equivocations inherent to the cosmological concept of the spatio-temporal world, which Kant considered to be inevitable in particular in the case of the “mathematical” antinomy.

The second class of sophistical inference is applied in general to the transcendental concept of absolute totality in the series of conditions for a given appearance; and from the fact that I always have a self-contradictory concept of the unconditioned synthetic unity in the series on one side, I infer the correctness of the opposite unity, even though I also have no concept of it. (CPR, A 340/B 398)

This is a preview of subscription content, log in via an institution .

Buying options

• Available as PDF
• Read on any device
• Instant download
• Own it forever
• Available as EPUB and PDF
• Compact, lightweight edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info
• Durable hardcover edition

Tax calculation will be finalised at checkout

Purchases are for personal use only

The analysis of Grier ( 2001 , 172–229) is complementary to my approach, which I first presented in Falkenburg ( 2000 , 177–254). Grier focuses on the origin of the four antinomies in Kant’s theory of transcendental illusion; I focus on disentangling their logical, semantic, and epistemic aspects.

“Es dürfte kaum jemals […] mehr zur Diskreditierung der menschlichen Vernunft und ihrer Fähigkeiten geschehen sein, als mit diesem Abschnitt der ‘kritischen Transzendentalphilosophie’. Ich werde gelegentlich zeigen, daß es diesem Autor nur durch einen vagen, distinktionslosen Gebrauch des Unendlichkeitsbegriffs […] gelungen ist, seinen Antinomien Geltung zu verschaffen, und dies auch nur bei denen, die gleich ihm einer gründlichen mathematischen Behandlung solcher Fragen gern ausweichen.” My translation.

“Nicht um eine Widerlegung oder Ablehnung des Unendlichkeits begriffes handelte es sich hier bei Kant, sondern um seine Anwendung auf das Weltganze , um die Tatsache, daß die menschliche Vernunft sich durch ihre innere Natur ebenso gedrängt findet, die Welt als begrenzt wie als unbegrenzt, als endlich wie als unendlich anzunehmen—eine Tatsache, die weder durch mathematische Theorien wie die Cantorsche Mengenlehre noch durch seine wohl nicht sehr tiefgreifende Polemik aus der Welt geschafft werden kann.” Zermelo’s note [ 1 ] to Cantor’s text; my translation.

See Hinske 1971 . In contrast, the term ‘antithetic’ originates from Protestant controversial theology; see Hinske 1972 .

See the Ethics lectures Brauer (Menzer 1924 , 59), Collins (27:280), and Mongrovius (27:1431) from the mid 1770s.

According to Malzkorn ( 1999 , 38–53), Kant’s ideas of reason are defined as follows (my translations): they are concepts (I) “of the form of cognition” (ibid., 38), (II) “of the form of the relation between cognition of the understanding (judgments)” (ibid., 39), (III) “of the unity of all cognition of the understanding” (ibid., 45), and (IV) “of ‘unconditioned conditions’ of a uniform system of all empirical cognition” (ibid., 47). According to this determination, ideas are not concepts of empirical objects, but “meta-concepts of empirical science” (p. 45); the world as the “sum total of appearances […] is not an object that could fall under such a meta-concept” (ibid., 76). Accordingly, he states that the world as the sum total of appearances for Kant is no possible object of an idea of reason (i.e., it lacks real possibility): “It only appears as such if one conflates the realm of appearances with the realm of cognition about them” (ibid., 77). However, he disregards that Kant locates the origin of the cosmological antinomy exactly in this problem. For Kant, the sensible world lacks not only real possibility, but also logical possibility as an object of an idea of reason. Malzkorn ( 1999 , 77), however, criticizes Kant as follows: “A description of the world should not be conflated with the world itself. Such mistaken identity would make the world appear to be the object of a concept of reason, but it represented an illegitimate conflation of two distinct realms. Indeed, traces of such conflation can be found […] in Kant’s doctrine of the antinomy”; and he concludes: “Kant’s theory of reason may […] be coherently reconstructable and be an important part of his epistemology; however, it cannot convincingly present the world as an object of natural and inevitable speculation of reason”. Indeed Kant himself attributes the inevitability of the antinomy precisely to an immanent tendency of reason to commit those logical fallacies of which today’s interpreters would accuse him. For a comprehensive interpretation of Kant’s theory of reason and the rationality of its natural disposition toward metaphysics, see Willaschek ( 2018 ).

For the precise relationship between the amphiboly chapter and the antinomy, see Grier ( 2001 ).

The parallels and differences between Kant’s antinomy and the antinomies of set theory have been considered in particular by Zermelo (in Cantor 1932 , 177) and Martin ( 1955 , 55); for a detailed, critical discussion see Hallett ( 1984 , 223–239).

Here, Kant differentiates as follows between ‘world’ and ‘nature’. The world is “the mathematical whole of all appearances and the totality of their synthesis in the great as well as in the small”, whereas nature is the world “insofar as it is considered as a dynamic whole and one does not look at the aggregation in space or time” ( CPR , A 418–419/B 446–447). In a corresponding footnote, Kant explains that here he means the concept of nature “taken substantively (materialiter) ”, in contradistinction to the concept of nature “taken adjectivally (formaliter) ” (ibid.).

See Sect. 5.4.1 and my discussion of Allison ( 1983 ) vs. Allison ( 2004 ), Grier ( 2001 ) below in n. 21.

Al Azm ( 1972 ) correctly observes that the arguments do not exactly correspond to rationalist and empiricist positions. Against the background of the Leibniz–Clarke debate, he then associates the thesis positions with Newton’s views and the antithesis positions with Leibniz’s views, overlooking that both Newton (or Clarke) as well as Leibniz themselves put forth rationalist as well as empiricist (or phenomenological) arguments, despite all their differences. See also the references to Bayle and Crusius in Heimsoeth ( 1960 , 260), and the detailed discussion in Grier ( 2001 , 182–229).

I attempted to give some hints as to its relevance for current science and its metaphysical generalization in Falkenburg ( 2000 , 341–350), and Falkenburg ( 2004 , 2005 ). See also Wind ( 1934 ).

See for example Kreimendahl ( 1990 , 424–430). Schmucker ( 1990 , 116–117), too, claims that Kant already takes the critical position when he relates the cosmological ideas to sensory perception. In my opinion, he conflates Kant’s critical conception of the phenomena with the common sensualistic concept of experience of the seventeenth/eighteenth-century schools. Guyer ( 1987 , 386–387) accuses Kant of either reducing truth to empirical confirmability, or rendering the argument in favour of transcendental idealism circular. His analysis of the proofs (ibid., 405–412) suffers from not distinguishing between the point of view of transcendental realism, which underlies the thesis and antithesis proofs, and the critical point of view, which gives rise to the resolution of the antinomy.

Malzkorn ( 1999 ) reconstructs the semantic aspects of the antinomy as far as possible by syntactic tools, including temporal logic and existential statements. Guided by a “principle of charity” (ibid., 118–119) he overlooks the fact that each kind of antinomy emerges from a crucial semantic equivocation which Kant wants to reveal.

A thoroughly syntactic reconstruction of the semantic claim cannot capture these features. It has to violate the proof principles of consistency. Not all of Kant’s proof premises can be consistent with one another. As regards Kant’s concerns for a “dialectical” logic of transcendental illusion it is sufficient that the premises seem to be satisfied from the point of view of transcendental realism. Uncovering the transcendental illusion shows that indeed they are not . The syntactic reconstructions of Malzkorn admit of this insight only for the dynamical antinomy; see Malzkorn ( 1999 , 199–200 and 221).

Malzkorn ( 1999 , 128) uses a predicate ‘non-F’ in order to preserve the contrary relation of thesis and antithesis.

According to Allison ( 2004 , 367–371), this is an assumption of transcendental realism, which presumes that the spatio-temporal world is a totum syntheticum and contradicts the definition (I) of infinity. My reconstruction of the thesis proof essentially agrees with Allison’s interpretation; see also his refutation of the objections raised by Russell ( 1903 ), Moore ( 1953 ), Strawson ( 1966 ), and Bennett ( 1974 ).

Malzkorn ( 1999 , 257) concedes this interpretation as admittable, in contrast to Strawson ( 1966 , 176), Mittelstaedt and Strohmeyer ( 1990 , 156), and Schmucker ( 1990 , 115–116). However, he thinks that the proof of the thesis in this case fatally depends on a transcendental philosophical premise: namely on (4a) “When a series has elapsed, then it can be completely synthesized successively” (Malzkorn 1999 , 257; my translation). According to my interpretation, this premise is not needed, given that “elapsed” for an infinite time series would mean that this time series was actually or cardinally infinite, in contradiction to the very concept of a series. The thesis proof confounds two concepts of the infinite which are incompatible regarding their real possibility; see below.

In contrast, van Benthem ( 1983 , 33) assumes that both concepts are logically rather than semantically incompatible. In Kant’s view, in the face of the resolution of the antinomy, this is just a consequence of the logical fallacy of taking the middle term of the cosmological syllogism in different meanings, which is what gives rise to the antinomy.

Malzkorn ( 1999 , 118–119 and 130–141) neglects this crucial point. To avoid the diagnosis of a non sequitur , he employs a syntactic “principle of charity” and reconstructs a logically valid proof.

Allison ( 1983 , 49) also emphasizes that the proof result depends decisively on Leibniz’s principle of indiscernibles, and interprets this in the sense of a verificationist position. In the revised edition, Allison ( 2004 , 373) no longer accepts this view, but argues that “the argument takes an epistemological turn, which is not to be confused with verificationism”; in the corresponding note he claims that it “is a confusion because it (falsely) implies that the assumption of an absolute beginning is meaningless rather than simply false” (ibid., 504, n. 33). I am puzzled about this claim; it fits in with the critical resolution of the antinomy, but not with the point of view of transcendental realism taken in the proof. Against the background of Kant’s 1755 and 1758 arguments (see Sect. 3.3.1 ), the verificationist interpretation seems plausible to me; whereas I do not share the view that Kant employs verificationist arguments in all four antinomies (Allison 1983 , 61 and 312): he only does so in the first antinomy, as far as I can see. In his revision, Allison ( 2004 ) seems to take into account the criticism of Grier ( 2001 , 190); she suggests an interpretation of the proof in terms of real relations, according to which “an empty time would lack any ‘distinguishing condition of existence’ (A 428/B 456)”, i.e., any real (ontic) ground of the world. However, the claim in step (4) that “the relation of the world to empty space would be a relation of the world to no object ” may well be understood as a claim about a meaningless concept (given that relations are usually understood as two-place predicates), and hence as a verificationist argument.

For a much more comprehensive analysis of the second antinomy, its historical background, its genesis, and its relation to Kant’s theory of cognition, see Engelhard ( 2005 ).

For the axioms which the relation <  of mereology obeys, see e.g., Simons ( 1987 ). The following reconstruction does not depend on specific mereological axioms.

The following reconstruction is basically identical to the one suggested in Falkenburg ( 2000 ), but differs from the one in Falkenburg ( 1995 ). My current definition of the predicate P agrees with that of Malzkorn ( 1999 , 172).

According to (A 440–442/B 468–470), the thesis does not directly refer to Leibniz’s monads, but to real monads, see Engelhard ( 2005 , 176–177). Kant’s own explanation of the thesis proposition in terms of “transcendental atomistic ” or “the dialectical principle of monadology ” (A 442/B 470) does not really contribute to clarifying this question. However, see also below.

The axiom SF5 of Simons ( 1987 , 42) is equivalent to ( H ), his SF3 to ( T2 ), and his SF4 to ( A2 2 ).

In Falkenburg ( 1995 , 15), I still did so.

However, the issue is not completely clear; see n. 25 above.

Malzkorn ( 1999 , 279, n. 96), in contrast, neglects the traditional metaphysical concept of a substance and defends the view that Kant does not employ an analytical argument.

See Russell ( 1903 , 460): “It is indeed obvious that the proposition, true or false, is concerned purely with whole and part, and has no special relation to space and time. Instead of a complex substance, we might consider the numbers between 1 and 2, or any other definable collection. And with this extension, the proof of the proposition must, I think, be admitted; only that terms or concepts should be substituted for substances , and that, instead of the argument that relations between substances are accidental ( zufällig ), we should content ourselves with saying that relations imply terms, and complexity implies relations.” Vogel ( 1975 , 299; my translation) charges the proof with circularity: “That the argument of the removal of all composition can indeed only apply to an object which already presupposes what is to be proved, we have already commented upon as against the proof in the Monadologia physica […].’

Engelhard ( 2005 , 175) challenges this claim, pointing to Kant’s third and fourth arguments against the discursive character of space in the Transcendental Aesthetic (B 39–40). However, Kant’s theory of mathematics does not admit of the abstract concept of a set, or a logical multiplicity, given that from 1770 on he considers the objects of mathematics to be generated in concreto in pure intuition.

The extent of the multiplicity, or the number of individuals that form a concrete composite, remains open. The proof does not claim that a composite has finitely or countably infinitely many simple parts. The thesis here does not imply a position of finitism; in contrast to the Prolegomena (§52c, 4:342), where Kant states the thesis and antithesis claims as follows: “[…] that bodies in themselves consist of infinitely many parts or of a finite number of simple parts.”

My reconstruction sets aside all details concerning the cosmological concept of freedom.

One could also express this claim by a predicate N with the meaning ‘obeys a law of nature’, or within second-order logic by a proposition of the form ∀ x ∃ N Nx , where N stands for the law of nature. Malzkorn ( 1999 , 194) defines two predicates ‘causality according to the laws of nature’ and ‘causality through freedom’, which he formalizes as three-place relations of two events x , y at a time t . This approach makes it possible to distinguish the absence of a cause (indeterminism or contingency) explicitly from causality out of freedom. In his approach, contradictory claims are also only obtained if the middle term ‘world’ of the cosmological syllogism is used equivocally (Malzkorn 1999 , 199–200).

In contrast, in his reconstruction Malzkorn ( 1999 , 231–234) uses a modal operator of contingency, which is defined by ♢ Px  ∨♢¬ Px .

The cosmological antinomy has this aspect in common with the paralogism of pure reason. The paralogism is based on a fallacious categorical syllogism in which the middle term ‘I’ is used equivocally in an empirical or intelligible sense. The antinomy, on the other hand, is based on a fallacious hypothetical syllogism in which the complete series of empirical conditions is conflated with an intelligible unconditioned; see the distinction between paralogism and antinomy (A 407/B 433–434) as well as the diagnosis that the antinomy is based on a sophisma figurae dictionis (A 499/B 527–528, and Logic §90, 9:135). See also Malzkorn ( 1999 , 110). Seifert ( 1989 ) concludes from this equivocation that Kant’s argument is inconclusive, similar to Malzkorn ( 1999 ), who does so for the third and fourth antinomy. Kant, however, only has the burden of showing that the proof seems conclusive from a dogmatic metaphysical point of view. He himself was convinced that they are not .

Allison, Henry E. 1983. Kant’s Transcendental Idealism: An Interpretation and Defence . New Haven: Yale University Press.

Google Scholar  

Allison, Henry E. 2004. Kant’s Transcendental Idealism: An Interpretation and Defence . Revised and Enlarged Edition. New Haven: Yale University Press.

Book   Google Scholar  

Al Azm, Sadik J. 1972. The Origin of Kant’s Arguments in the Antinomies . Oxford: Clarendon Press.

Bennett, Jonathan. 1974. Kant’s Dialectic . Cambridge: Cambridge University Press.

Baumgarten, Alexander Gottlieb. 1757. Metaphysica . Halle: Hemmerde. Quoted after Kants gesammelte Schriften , vol. 17.

Boscovich, Roger. 1758. Theoria philosophiae naturalis. A Theory of Natural Philosophy , ed. J.M. Child. Chicago and London: Open Court Publishing Company 1922. https://archive.org/details/theoryofnaturalp00boscrich .

Cantor, Georg. 1932. Gesammelte Abhandlungen mathematischen und philosophischen Inhalts , ed. Ernst Zermelo. Berlin: Springer.

Engelhard, Kristina. 2005. Das Einfache und die Materie. Untersuchungen zu Kants Antinomie der Teilung . Kantstudien-Ergänzungshefte 148. Berlin: de Gruyter.

Falkenburg, Brigitte. 1995. Kants zweite Antinomie und die Physik. Kant-Studien 86: 4–25.

Article   Google Scholar  

Falkenburg, Brigitte. 2000. Kants Kosmologie . Frankfurt a. M.: Klostermann.

Falkenburg, Brigitte. 2004. Experience and Completeness in Physical Knowledge: Variations on a Kantian Theme. In Philosophiegeschichte und Logische Analyse, Schwerpunkt: Geschichte der Naturphilosophie , ed. U. Meixner and A. Newen, 153–176. Paderborn: Mentis.

Falkenburg, Brigitte. 2005. Some remarks on cosmology and scientific realism. Kairos 26: 229–246.

Friedman, Michael. 1992. Kant and the Exact Sciences . Cambridge: Harvard University Press.

Grier, Michelle. 2001. Kant’s Doctrine of Transcendental Illusion . New York: Cambridge University Press.

Guyer, Paul. 1987. Kant and the Claims of Knowledge . Cambridge: Cambridge University Press.

Guyer, Paul, and Allen W. Wood. ed. 1998. The Critique of Pure Reason . Cambridge: Cambridge University Press.

Hallett, Michael. 1984. Cantorian Set Theory and Limitation of Size . Oxford: Clarendon Press.

Hegel, Georg Friedrich Wilhelm. 1832. Wissenschaft der Logik . Repr. in: Gesammelte Werke , Hamburg: Meiner (quoted here: Vol. 21, 1985). Engl.: The Science of Logic . Translated and edited by George Di Giovanni. Cambridge University Press 2010.

Heimsoeth, Heinz. 1960. Atom, Seele, Monade . Verlag der Akademie der Wissenschaften: Mainz und Franz Steiner Verlag: Wiesbaden.

Hinske, Norbert. 1971. “Antinomie”. In Historisches Wörterbuch der Philosophie , ed. Joachim Ritter, vol. I, Darmstadt, col. 393–396.

Hinske, Norbert. 1972. Kants Begriff der Antithetik und seine Herkunft aus der protestantischen Kontroverstheologie des 17. und 18. Jahrhunderts. Über eine unbemerkt gebliebene Quelle der Kantischen Antinomienlehre. Archiv für Begriffsgeschichte 16: 48–59.

Kreimendahl, Lothar. 1990. Kant—der Durchbruch von 1769 . Köln: Dinter.

Malzkorn, Wolfgang. 1999. Kants Kosmologie-Kritik. Kant-Studien Erg.-Hefte 134 . Berlin: de Gruyter.

Martin, Gottfried. 1955. Kant’s Metaphysics and Theory of Science . Manchester University Press. Transl. of: Immanuel Kant: Ontologie und Wissenschaftstheorie (Köln: Universitätsverlag 1951).

Menzer, Paul, ed. 1924. Eine Vorlesung Kants über Ethik . Im Auftrag der Kantgesellschaft herausgegeben von Paul Menzer. (Philosophia practica universalis). Second ed. 1925, Berlin-Charlottenburg: Pan Verlag Rolf Heise, Berlin-Charlottenburg.

Mittelstaedt, Peter, and Ingeborg Strohmeyer. 1990. Die kosmologischen Antinomien in der Kritik der reinen Vernunft und die moderne physikalische Kosmologie. Kant-Studien 81: 145–169.

Moore, Gerald E. 1953. Some Main Problems of Philosophy . London: Allen & Unwin.

Newton, Isaac. 1730. Opticks . With a preface by I.B. Cohen, based on the 4th ed., New York. 4th ed., London 1930. With a Preface by I.B. Cohen, Dover 1979.

Russell, Bertrand. 1903. The Principles of Mathematics . New York: W.W.Norton & Company Inc.

Schmucker, Josef. 1990. Das Weltproblem in Kants Kritik der reinen Vernunft . Bonn: Bouvier.

Seifert, Josef. 1989. Das Antinomienproblem als ein Grundproblem aller Metaphysik: Kritik der “Kritik der reinen Vernunft”. Prima Philosophia 2: 143–168.

Simons, Peter. 1987. Parts. A Study in Ontology . Oxford: Clarendon Press.

Strawson, Peter F. 1952. Introduction to Logical Theory . London: Methuen.

Strawson, Peter F. 1966. The Bounds of Sense. An Essay on Kant’s Critique of Pure Reason . London: Methuen.

van Benthem, Johan. 1983. The Logic of Time: a modal-theoretic investigation into the varieties of temporal ontology and temporal discourse . Dordrecht: Reidel.

Vogel, Karl. 1975. Kant und die Paradoxien der Vielheit . Meisenheim am Glan: Hain.

Willaschek, Marcus. 2018. Kant on the Sources of Metaphysics. The Dialectic of Pure Reason . New York: Cambridge University Press.

Wind, Edgar. 1934. Das Experiment und die Metaphysik . Tübingen: Mohr. Repr.: B. Buschendorf (ed.), with an introduction by B. Falkenburg, Frankfurt am Main: Suhrkamp 2000. Engl. transl. by C. Edwards: Experiment and Metaphysics. Towards a Resolution of the Cosmological Antinomies . Oxford: Legenda 2001.

Wolff, Michael. 2017. Der Begriff des Widerspruchs. Eine Studie zur Dialektik Kants und Hegels , 3rd ed. Berlin: Owl of Minerva Press.

Download references

Author information

Authors and affiliations.

Department of Philosophy and Political Science, Faculty of Human Sciences and Theology, TU Dortmund, Dortmund, Germany

Brigitte Falkenburg

You can also search for this author in PubMed   Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Cite this chapter.

Falkenburg, B. (2020). The Antinomy of Pure Reason. In: Kant’s Cosmology . European Studies in Philosophy of Science, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-030-52290-2_5

Download citation

DOI : https://doi.org/10.1007/978-3-030-52290-2_5

Published : 19 December 2020

Publisher Name : Springer, Cham

Print ISBN : 978-3-030-52289-6

Online ISBN : 978-3-030-52290-2

eBook Packages : Religion and Philosophy Philosophy and Religion (R0)

Share this chapter

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Publish with us

Policies and ethics

• Find a journal
• Track your research

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons
• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

8.2: Plato and Aristotle

• Last updated
• Save as PDF
• Page ID 67192

• Jim Marteney
• Los Angeles Valley College via ASCCC Open Educational Resources Initiative (OERI)

For a quick look back at the key origins of a clear argumentation process we need to travel back to ancient Greece and the influences of Plato and Aristotle. Plato felt that a discussion was the most productive way to solve a conflict. He called these discussions, a dialogue which worked best when conducted by the " all-knowing, great minds " of Greece, which he called the Philosopher Kings. Plato appreciated discussions as an unlimited number of positions could be examined and reflected on through the process of question and answer. Plato called this process the Dialectic Approach .

Plato’s discussions were very focused.

“Plato's dialectic is a purposeful conversation, a dialogue that addresses ideas and arguments, encourages contradiction and counter-arguments, and stresses analysis and synthesis as the primary means for discovering knowledge. The capacity of the dialectic for self-examination and self-instruction sets it apart from other kinds of discourse .” 1

According to Plato, the dialectic is the art of being able to pose questions and provide answers. They start with a hypothesis, or as we would call it a claim, and through the discussion add knowledge to test if the soundness of the hypothesis.

The Dialectic Approach involved developing an opening thesis or position and an antithesis or opposite position. These positions were fully developed and discussed. The goal of this dialogue was to arrive at synthesis, which Plato said could be considered the absolute Truth. Synthesis could be thesis, antithesis, or a new position developed during the dialogue process. To Plato, synthesis equaled the Truth and no further discussion was needed.

Aristotle's approach to argumentation focused more on persuading others. His philosophy of argument is embodied in his Rhetorical Approach . Aristotle’s book, THE RHETORIC , is generally considered the most important single work in the literature of the Speech discipline. Book I of The Rhetoric opens with this definition: " Rhetoric is the counterpart of Dialectic ." 2 The Rhetorical Approach may be described as a process for discovering all of the available means of "artistic" persuasion on any subject. This is opposed to “inartistic” forms of persuasion like torture or even being threatened with an “F” for not doing your homework.

• Kimball, Jack. Plato's Communicative Utility in Japan. 1995. 12 June 2017. http://www.fauxpress.com/kimball/res/plato.html (Accessed November 15, 2019)
• Aristotle and C.D.C.Reeve, Aristotle's The Rhetoric, (Indianapolis: Hackett Publishing Company Inc. 2018)

Your complimentary articles

You’ve read one of your four complimentary articles for this month.

You can read four articles free per month. To have complete access to the thousands of philosophy articles on this site, please

Hegel and the Trinity

Peter benson explains why hegel was obsessed with the number three..

One of the best known popularizers of philosophy in Britain is Bryan Magee. Many people will fondly recall his illuminating series of interviews with philosophers for radio and television. So his lavishly illustrated book The Story of Philosophy (Dorling Kindersley, 2001) will attract many readers eager to learn more about the subject. Nor will they be disappointed, for it contains a wealth of information and useful summaries of philosophical ideas.

Nevertheless, I want to draw attention to a significant error in his chapter on Hegel (admittedly a notoriously difficult philosopher). The error is important because it represents a widespread misunderstanding of Hegel’s thought. Quite rightly, Magee emphasizes that, for Hegel, “everything — ideas, religion, the arts, the sciences, the economy, institutions, society itself — is always changing.” But he then goes on to say that Hegel “produced a vocabulary to describe [this process]. The process as a whole he called the dialectical process, or just the dialectic, and he analysed it as made up of three main stages .... thesis, antithesis, synthesis.”

This supposed ‘fact’ about Hegel’s philosophy continues to be frequently repeated in text-books and popular accounts of his ideas. Yet Hegel himself never used the words ‘thesis, antithesis, synthesis’ to characterize the dialectical process. It’s true that the word ‘antithesis’ occasionally appears in his writings. But I have never found any passage anywhere in his voluminous works where the third stage of a dialectic is referred to as a ‘synthesis’.

The use of these three words originates in a book about Hegel published shortly after his death (when he was no longer around to criticize it). The terminology was used again, greatly increasing its influence, in an 1847 book by a young philosopher named Karl Marx (I wonder whatever happened to him?)

If read carefully, Marx’s account of Hegel’s philosophy is fairly accurate. But his use of the word ‘synthesis’ has subsequently led to grave misunderstandings. Magee typifies this erroneous view when he writes, “because the synthesis is a new situation it contains new conflicts, and therefore becomes the beginning of a new triad of thesis, antithesis, synthesis.” Not surprisingly, statements like this have puzzled people and contributed to the exaggerated air of mystery surrounding Hegel’s thought. Are these new conflicts supposed to exist within the synthesis? (And if so, why are they different from the original conflicts out of which it was formed?) Or does the synthesis constitute a new thesis, over against which its equal and opposite antithesis must be formed? Both interpretations suggest a process which would carry on indefinitely, a waltz rhythm of:

If this is, indeed, a false and misleading interpretation of Hegel, how can we get a better idea of what he meant by ‘dialectic’, so that we can assess his philosophy more accurately?

Triads and Pyramids

First of all, it can’t be denied that Hegel was obsessed with dividing everything into threes. You don’t even need actually to read his books to recognize this — you only need to look at their contents pages. Each is divided into three sections, and each of those sections is further divided into three subsections, which themselves are often divided into three sub-sub-sections. Even individual paragraphs (sometimes even individual sentences ) frequently have three distinct parts. Why this obsession with the number 3? Did Hegel believe (as many people have) that there is a mystic meaning to this numeral?

Hegel wasn’t in fact a mystic (at least, not in that sense). He didn’t believe in mysteries at all. On the contrary, he thought that absolutely everything, ultimately, could be explained. And his own philosophy would provide the groundwork for this complete explanation (which he called ‘Absolute Knowledge’). This is an ambition somewhat similar to the ‘theories of everything’ sought by modern physicists. It doesn’t mean that one knows absolutely everything, only that one has a general underlying framework for all such knowledge.

Hegel set out his philosophy most fully in his Encyclopaedia of the Philosophical Sciences which, needless to say, has 3 volumes. The first is on Logic; the second is on Nature; and the third is on Spirit (which includes everything to do with human life). The whole work is constructed in Hegel’s dialectical manner, subdivided into smaller and smaller triads. And this demonstrates that Hegel’s dialectic is not an endless waltz. It is not formed like this:

Instead, Hegel’s dialectic is formed like this:

The dialectic forms a pyramid. The various sub-categories can be sub-divided further and further and further. But at the top everything converges on a single A (standing here for ‘Absolute Knowledge’). This Absolute Knowledge divides into its three aspects: I Logic; II Nature; III Spirit. And each of these is divided into further triads of sub-categories.

Of course none of us, not even Hegel, start our investigations from a position of Absolute Knowledge. That is, rather, where we hope to end up. Each little area of knowledge has to be slowly acquired over the course of our lives, and over the long laborious course of human history. According to Hegel, history also has a dialectical structure. Essentially, it is the process of starting way down on the pyramid, and making our way, with plodding effort, towards the top. History is not just a random succession of events. Its pattern arises partly because we can learn from the past, preventing ourselves from repeating it. Our growing knowledge is not just an aggregate accumulation of separate facts. At certain crucial turning points, our insight can rise to a new level of awareness, taking a step up the pyramid. This doesn’t happen by synthesizing everything we know, but rather by exhausting all of the possibilities at one level, so that we are forced to seek a completely new perspective. Having tried every available avenue, and found them all wanting, we are compelled into forming a new view of our world, to get us out of the maze we have been trapped in. Of course, after a brief period of euphoria, we find we are only in a new, and perhaps even darker maze. It is no wonder that Hegel calls the process “a highway of despair”. Only desperation and failure push our feet further forward.

The place where each of us starts on this journey depends on the historical period into which we happen to be born. Hegel himself was born in 1770, the same year as William Wordsworth. Both, in their youth, experienced the great excitement generated throughout Europe by the events of the French Revolution. “Bliss was it in that dawn to be alive,” wrote Wordsworth. But it was a bliss that didn’t last. Hegel wrote about the French Revolution in his Phenomenology of Spirit in a chapter with the striking title ‘Absolute Freedom and Terror’. It was not enough, for Hegel, to bemoan the way that things had gone wrong, as if they might have followed a preferable path. In retrospect, it became possible to see such a descent into Terror as an inevitable consequence of the breakdown in stable social structures occasioned by the Revolution. Nevertheless, that breakdown itself was a necessary effect of the conflicts within the previous state of French society. The freedom that briefly erupted was not completely illusory, but new social structures would be needed to accommodate the legitimate demands of freedom. It should be obvious, however, that the next step could hardly be a synthesis of Freedom and Terror (containing, presumably, the ‘best’ parts of each)!

In fact, the next step in this historical dialectic took an unexpected turn. Paradoxically, individual freedom was best consolidated and developed (at this particular historical juncture) under a dictatorship (that of Napoleon). Such paradoxical results of historical dilemmas are the frequent focus of Hegel’s reflections.

Following this journey through Freedom, Terror, and Dictatorship, Europe entered a completely new phase of history, one dominated by the political philosophy of Liberalism and the pursuit of the Universal Rights of Man as first declared by the Revolutionaries in France. Liberal societies are marked by a striking and continuing conflict between the demand for individual rights and the need for social cohesion. “This collision, this problem is that with which history is now occupied,” wrote Hegel (in his Lectures on the Philosophy of History ), “and whose solution it has to work out in the future.”

So he did not believe that liberalism was a final ‘end of history’ (a view often wrongly attributed to him by more recent thinkers such as Kojève and Fukuyama). More significantly, from Hegel’s viewpoint, liberalism allowed for the dissemination of a new form of ethical thinking which placed individual choice at its centre. At a higher level of Hegel’s system from that of the sequential events of political history, there is a slow transition between different forms of ethical thought. And this whole level (of ethics) forms only one component of the even higher level which he calls Geist (‘Spirit’).

Hegel’s account of the twists and turns of history, set out most eloquently in his Lectures on the Philosophy of History , has proved endlessly fascinating to subsequent thinkers. But this has sometimes led to the mistaken belief that all of his thought is fundamentally a philosophy of history. It would be more true to say that this is only one aspect or, rather, one perspective view of the vast multi-levelled edifice of Hegel’s philosophy.

Triangles and the Trinity

It is possible to view Hegel’s system of thought from (at least) two directions. On the one hand, we can follow the process whereby, via alternating error and insight, the slow progress of humanity ascends towards Absolute Knowledge. This is the story Hegel tells in his Phenomenology of Spirit . On the other hand, we could start from the complete totality of everything, the Absolute itself, and show how this can be divided up into smaller and smaller aspects, until every different domain of the world, and of human life, reveals its place within the whole. This is the system as set out in Hegel’s Encyclopaedia of the Philosophical Sciences .

The first journey (the upward progress) is only propelled forward because, at each stage, dissatisfied humanity finds it has not arrived at the complete, coherent and consistent truth. For Hegel, complete truth can only be found in the whole, not the part, and in the way that each part has its assigned place within this whole. The ‘whole’ (which we might also call ‘Totality’ or ‘Absolute’) contains not only all substance (all ‘things’) but also subjectivity, which is equally a part of reality. And this ‘whole’ is, for Hegel, a unity. It is in fact (as Hegel states on many occasions) God, as the self-consciousness of the universe.

Hegel’s view of God is somewhat unorthodox, and his view of the relation of the individual human being to God is even more unorthodox. Nevertheless, he persistently insisted that he was a Christian, and that, among all the religions that have evolved historically on earth, Christianity was the most complete expression of truth. Out of all the various dogmas of the Christian Church, however, there is only one that figures prominently in Hegel’s discussions: the dogma of the Trinity — i.e. that there are three persons (Father, Son, and Spirit) within the single being of God.

So, if we look at Hegel’s system from the top downwards, starting with the totality and seeing how everything is contained within it, we can see more clearly the source of the tripartite divisions into which it repeatedly divides. The original triad, from which all the others can be derived, is formed by the three persons of one God. To get a grasp on Hegel’s dialectic, it is far more helpful to think in terms of Father, Son and Spirit, than to worry about the quasi-logical terms Thesis, Antithesis, Synthesis.

Does this mean that Hegel’s system ultimately has its foundation in Christian faith, and is of no relevance to unbelievers? Not at all. Hegel thought that his philosophy would replace faith with knowledge. The trinitarian structure of God was not to be taken on trust, but was revealed by the triadic structure of the world and of experience. Hegel’s dialectic is not the repeated application of a logical formula (Thesis; Negation of Thesis; Negation of the Negation; etc.). On the contrary, each of the triads that appears in Hegel’s work is discovered anew, through the specificities of each situation, following no path known in advance. But gradually they reveal a congruence with the three aspects of God as elucidated in Christian theology.

The doctrine of the Trinity was first expounded at length by St Augustine in his treatise De Trinitate , written around 400 A.D. This has been the basis for all subsequent discussions of the topic. (Thomas Aquinas, for example, relies heavily on Augustine.) Anticipating Hegel, Augustine found 22 different examples of triads in the cosmos and within the human being, which are analogous to the divine Trinity. The most important of these, in the human realm, is Mind, Knowledge, and Love.

This closely parallels Hegel’s principal division of his system into Logic, Nature, and Spirit. Hegel’s Logic is not (and was never intended to be) a set of principles of deductive reasoning like those of Aristotle. It is, rather, a systematic array of concepts, before those concepts are instantiated by particular things. As Hegel put it, only half-metaphorically, the content of his Logic is “the exposition of God as he is in his eternal essence before the creation of nature and a finite mind.” Logic can therefore be aligned with God the Father: the ‘creative principle’, according to Augustine.

Nature is the created world, of which we can have knowledge. It is the world in which, in the famous words of St John’s Gospel, the Word (i.e. the concept) becomes flesh (i.e. concrete and particular). In the incarnation of Christ the universal (God) becomes particular (a single human being). Similarly, Hegel’s Philosophy of Nature shows how the array of universal concepts from the Logic guide (without determining) the scientific search for specific knowledge of facts.

The third part of Hegel’s system is the Philosophy of Spirit. The word ‘Spirit’ ( Geist in German) is used by Hegel in a very specific sense which is at the core of his philosophy. Spirit, for Hegel, always involves relation. An isolated individual might be a consciousness, but only in relating with others can the level of Spirit (higher than that of mere consciousness) be reached. This is the level which includes all the phenomena of art, religion, and society.

The parallel with Augustine’s exposition of the Trinity is particularly striking here. In Book 15 of his treatise, Augustine writes “If the love whereby the Father loves the Son, and the Son the Father, reveals in an ineffable manner the union between both, what more fitting than that He, who is the Spirit, common to both, should be properly called love?” So the Holy Spirit is not so much a separate being (that vague and symbolic dove that appears in Renaissance paintings) but the embodiment of the love between the Father and the Son. There is the Father, the Son, and also the relation (of love) between them, which is Spirit (exactly as Hegel understands the word).

I can only give a very brief indication of the relevance of all this to Hegel’s philosophy as a whole. But it is worth considering the very first chapter of The Phenomenology of Spirit , one of the most widely discussed and persistently relevant sections of Hegel’s work, in which he gives a critique of empiricist attempts to ground truth in the unquestionability of sense data. The details of his discussion are well worth reading because the ideas he is criticizing remain widely influential today. But it is also worth looking at the structure of the chapter as a whole. First (paras. 94-99) Hegel considers the view that we have immediate knowledge of the object of our sense perceptions. Then (paras. 100-102), when this proves to be delusory, he considers the possibility that at least we have certainty of ourselves as the subjects of experience. Finally (paras. 103-110) he considers the view that the relation between subject and object must be an undoubted certainty.

At a pinch, we could call these three Positions the thesis, antithesis and synthesis. But the third position is not a combination of the first two, but a focus on the relation between them. It is therefore (at a lowly level) analogous to the Hegelian relational category of ‘Spirit’. And, far from resolving the conflict, the ‘synthesis’ proves just as unsatisfactory as the previous approaches, forcing the thinker to reconsider the whole way of posing the problem, using a new set of concepts which will move the discussion to a higher level and create the second triad in the book’s structured progress. And the third term of the first triad is not the first term of the second triad, which is already posed within the new conceptual schema.

As the Phenomenology ascends through a bewildering and fascinating maze of themes, involving philosophy, history and literature, it is easy to lose one’s bearings. Remembering that the Christian Trinity provides the underlying model for the Hegelian dialectic will help us to find our way through its notoriously convoluted twists and turns.

© Peter Benson 2003

Peter Benson has been a participant for several years in the seminars on Hegel run by Pamela Jencks at Birkbeck College, London.

This site uses cookies to recognize users and allow us to analyse site usage. By continuing to browse the site with cookies enabled in your browser, you consent to the use of cookies in accordance with our privacy policy . X

Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to  upgrade your browser .

Enter the email address you signed up with and we'll email you a reset link.

• We're Hiring!
• Help Center

Leibniz as the synthesis to Plato's thesis and Aristotle's antithesis

Related Papers

Ephraim-Stephen Essien

Saad Al Otaibi

Sreekumar Nellickappilly

A Brief Overview of some important contributions in European Thought

Ricky Sialagan

Nikos Telan

Roisin Lally

The question concerning technology lies at the heart of human existence. As such it must take a central place in philosophy today. This importance, however, is veiled by a historical interpretation of technology as instrumental. This instrumentalism is the result of an ambiguity in the Aristotelian legacy that arises from an understanding of reality rooted in a theory of the categories, on the one hand, and a theory of causality on the other. This has left us with an ambiguous understanding of human making split by the twofold structure of artistic and representational thinking. The former is characteristic of empirical knowledge, the latter epistemological knowledge. This thesis follows Heidegger in arguing that an integral understanding of technology can only be achieved through a creative retrieval of Aristotle's ontology that interweaves the question of causality and the question of the categories, which we have outlined below as the interplay between potentiality and actuality, between being and non-being, and between truth and untruth. While indebted to Aristotle, this involves an important re-thinking of the nature of ontology, for it is made possible by exposing the limits of Aristotle’s theory of time, which understands time as a succession of present instants, and moving towards the Heideggerian understanding of presencing as the opening of a horizon in which things perdure. Consequently, this is an ontology in which technology is tied to our notion of time just as much as to our notion of being. After establishing this temporal ontology as the basis for an understanding of technology, in a unique way we apply it to the particular case of 3D printing and come to see that this technology is indeed more than an instrument; it is an interweaving of the epistemic and the poetic, the rational and the artistic. Thus I accept the consensus in contemporary philosophy of technology that questions of technology must be understood in terms of their political and social implications. However, unlike many thinkers in this field I also argue that they can be fruitfully understood in terms of a temporal ontology. I call this temporal ontology of technology, hyperology.

ganesh varma

history of western philosophy

María Laprea

Tarja Kallio-tamminen

Amdouni Sabrine

RELATED PAPERS

Linda Pickard

Dede Suleman

Olivier De Almeida

Dental Materials

2014 IEEE International Conference on Robotics and Automation (ICRA)

Angel Pascual del Pobil Ferré

Peter Riisager

Bioorganic &amp; Medicinal Chemistry Letters

Brian Fulton

Michelle Carstensen

Scandinavian Journal of Information Systems

Mike Martin

Journal of Acquired Immune Deficiency Syndromes

Lucia Jorge

Review of Scientific Instruments

Maria Dienerowitz

Lyn Phillipson

Journal of Orofacial Research

Gautam Maurya

IJNS - Indonesian Journal on Networking and Security

Edhi Prayitno

Camila Salinas

Anais do XVII Congresso Latino-Americano de Software Livre e Tecnologias Abertas (Latinoware 2020)

Leonardo Castillo

Spin Observables in Proton-Nucleus Scattering. Lecture Courses. Chapter One. Spin-Orbit Interactions at Proton Scattering in Nonrelativistic and Relativistic Models

Anatoli Plavko

Escola Anna Nery

Ruth Irmgard Bärtschi Gabatz

Etudes finno-ougriennes

Johanna Domokos

ania citraresmini

Journal of Communication and Information Systems

André L. F. de Almeida

Janine Leschke

Ecological Indicators

Hugues B Massicotte

Stanley Nattel

Innovation in Aging

Israel Doron

•   We're Hiring!
•   Help Center
• Find new research papers in:
• Health Sciences
• Earth Sciences
• Cognitive Science
• Mathematics
• Computer Science
• Academia ©2024

--> Read more » -->