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The Geometrical Method in Spinoza's Ethics

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Laura Byrne; The Geometrical Method in Spinoza's Ethics . Poetics Today 1 September 2007; 28 (3): 443–474. doi: https://doi.org/10.1215/03335372-2007-004

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While the goal of Spinoza's Ethics has strong affinities with the Aristotelian goal of eudaimonia , structurally the text itself is modeled on Euclid's Elements . Does Spinoza think that the precision and certainty of mathematics can be extended to moral philosophy? To answer this question, I discuss the relation between the geometrical method of the Ethics and its content and goal. Arguing that the deductive structure of the Ethics mirrors the causal necessity by which all of nature follows from God, I conclude that Spinoza applies the geometrical method to ethics because nothing, including human life and well-being, is exempt from this causal necessity. Furthermore, I discuss the role the geometrical method plays in an aspect of the argument of the Ethics which can best be described as dialectical, in the Aristotelian sense of the word: Spinoza hoped to persuade the members of his circle of theologically radical yet devout friends, and others intellectually similar to them, of the truth of his philosophy by beginning with Cartesian principles they would accept. Finally, I argue that certain nongeometrical portions of the Ethics are directed at the emotions of these readers.

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Spinoza’s Philosophy: Unity, Truth, and the Geometrical Method

Table of Contents

Have you ever pondered how the mathematical precision of shapes and equations could unravel the mysteries of existence? Enter the world of Spinoza , a philosopher who dared to seek truth through a lens that merged mathematics with metaphysical inquiry. His approach, known as the geometrical method , was not merely a tool for understanding the physical world but a key to exploring the vast landscape of human existence and the divine. Let’s embark on a journey through Spinoza’s unique philosophical vision, where every deduction is a step closer to understanding the unity of all things.

Spinoza’s Quest for Truth

Baruch Spinoza was a thinker who wasn’t content with fragmented knowledge. He envisioned a world where all knowledge was interconnected, stemming from a singular divine essence. But what does it mean to start from the divine? For Spinoza, it meant that the nature of reality itself could be logically deduced, much like a mathematician deduces the properties of a geometric figure. By starting with the nature of God, or the absolute substance , Spinoza sought to logically derive the nature of everything that exists.

The Geometrical Method Explained

What exactly is the geometrical method? Inspired by Euclid ’s works, Spinoza applied the same rigorous structure of definitions, axioms, propositions, and proofs to philosophy. Just as Euclid would define a point and a line before proving theorems about triangles, Spinoza began with the definition of substance and proceeded to deduce the nature of mind, matter, and morality. This method promised a coherent and objective structure to philosophical arguments, seeking to remove the ambiguity and inconsistency that often plagued metaphysical discussions.

Imagination, Reason, and Intuition

Spinoza’s method wasn’t cold or devoid of human experience. On the contrary, he recognized the roles of imagination , reason , and intuition in attaining knowledge. These cognitive faculties represented different levels of understanding reality. Imagination allowed us to perceive individual things; reason connected these perceptions to universal truths; and intuition, the highest form of knowledge, gave us a direct grasp of the divine essence and its manifestations. This tripartite scheme of knowledge reflects Spinoza’s belief in a structured path to enlightenment.

Applying Mathematics to Metaphysics

Applying mathematics to metaphysics might seem like an attempt to quantify the unquantifiable. However, Spinoza’s intention was not to reduce reality to numbers but to ensure that philosophical claims had the same certainty and clarity as mathematical truths. The geometrical method allowed Spinoza to present his philosophy in a form that was as irrefutable as a mathematical proof. This approach aimed to cut through the complexities and confusions of philosophy by presenting ideas as clear-cut as a geometrical diagram.

The Coherence of Ideas

Why did Spinoza believe coherence was so crucial? Coherent ideas mirror the interconnectedness of the universe. Spinoza’s philosophy was not just a collection of isolated insights but a grand tapestry where every thread was essential to the integrity of the whole. The geometrical method ensured that each idea logically followed from another, just as in the natural world, every effect has a cause. This coherence was not just an intellectual exercise; it had profound implications for ethics and politics, as it suggested that understanding the logical structure of the universe could lead to a more harmonious society.

The Rationalist Approach to Existence

Spinoza was a rationalist at heart. He believed that through the power of reason, humans could transcend their immediate sensory experiences and comprehend the underlying principles that govern all of existence. This rationalist perspective was in contrast to the empiricists of his time, who argued that knowledge comes primarily from sensory experience. Spinoza’s approach posited that through the meticulous application of reason, much like in mathematics, one could arrive at truths that were universal and necessary.

Spinoza’s Influence and Legacy

The echoes of Spinoza’s geometrical method can be felt throughout the centuries. His ideas influenced a broad range of areas, from psychology and ethics to political theory and literature. His rationalist pursuit of truth through a methodical and structured approach has inspired countless thinkers to seek clarity in their own philosophical endeavors. It’s a testament to the lasting impact of Spinoza’s vision that his geometrical method, while deeply rooted in the intellectual context of the 17th century, continues to provoke thought and discussion in the modern era.

Spinoza’s geometrical method is more than a historical curiosity; it’s a compelling vision of a universe where everything is connected in a coherent, logical structure. By exploring his approach, we not only gain insights into Spinoza’s philosophy but also encounter a unique way of understanding the world around us. In a landscape often clouded by uncertainty and relativism, Spinoza’s quest for truth and certainty offers a refreshing clarity that still resonates with seekers of knowledge today.

What do you think? Can the application of mathematical principles to philosophical inquiry enrich our understanding of the world? Is there a place for Spinoza’s rationalist approach in today’s society? Share your thoughts and let’s continue the conversation about the relevance of Spinoza’s geometrical method in our quest for truth.

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Research Methodology

1 Introduction to Research in General

• Research in General
• Research Circle
• Tools of Research
• Methods: Quantitative or Qualitative
• The Product: Research Report or Papers

2 Original Unity of Philosophy and Science

• Myth Philosophy and Science: Original Unity
• The Myth: A Spiritual Metaphor
• Myth Philosophy and Science
• The Greek Quest for Unity
• The Ionian School
• Towards a Grand Unification Theory or Theory of Everything
• Einstein’s Perennial Quest for Unity

3 Evolution of the Distinct Methods of Science

• Definition of Scientific Method
• The Evolution of Scientific Methods
• Theory-Dependence of Observation
• Scope of Science and Scientific Methods
• Prevalent Mistakes in Applying the Scientific Method

4 Relation of Scientific and Philosophical Methods

• Definitions of Scientific and Philosophical method
• Philosophical method
• Scientific method
• The relation
• The Importance of Philosophical and scientific methods

5 Dialectical Method

• Introduction and a Brief Survey of the Method
• Types of Dialectics
• Dialectics in Classical Philosophy
• Dialectics in Modern Philosophy
• Critique of Dialectical Method

6 Rational Method

• Understanding Rationalism
• Rational Method of Investigation
• Descartes’ Rational Method
• Leibniz’ Aim of Philosophy
• Spinoza’ Aim of Philosophy

7 Empirical Method

• Common Features of Philosophical Method
• Empirical Method
• Exposition of Empiricism
• Locke’s Empirical Method
• Berkeley’s Empirical Method
• David Hume’s Empirical Method

8 Critical Method

• Basic Features of Critical Theory
• On Instrumental Reason
• Conception of Society
• Human History as Dialectic of Enlightenment
• Substantive Reason
• Habermasian Critical Theory
• Habermas’ Theory of Society
• Habermas’ Critique of Scientism
• Theory of Communicative Action
• Discourse Ethics of Habermas

9 Phenomenological Method (Western and Indian)

• Phenomenology in Philosophy
• Phenomenology as a Method
• Phenomenological Analysis of Knowledge
• Phenomenological Reduction
• Husserl’s Triad: Ego Cogito Cogitata
• Intentionality
• Understanding ‘Consciousness’
• Phenomenological Method in Indian Tradition
• Phenomenological Method in Religion

10 Analytical Method (Western and Indian)

• Analysis in History of Philosophy
• Conceptual Analysis
• Analysis as a Method
• Analysis in Logical Atomism and Logical Positivism
• Analytic Method in Ethics
• Language Analysis
• Quine’s Analytical Method
• Analysis in Indian Traditions

11 Hermeneutical Method (Western and Indian)

• The Power (Sakti) to Convey Meaning
• Three Meanings
• Pre-understanding
• The Semantic Autonomy of the Text
• Towards a Fusion of Horizons
• The Hermeneutical Circle
• The True Scandal of the Text
• Literary Forms

12 Deconstructive Method

• The Seminal Idea of Deconstruction in Heidegger
• Deconstruction in Derrida
• Structuralism and Post-structuralism
• Sign Signifier and Signified
• Writing and Trace
• Deconstruction as a Strategic Reading
• The Logic of Supplement
• No Outside-text

13 Method of Bibliography

• Preparing to Write
• Writing a Paper
• The Main Divisions of a Paper
• Writing Bibliography in Turabian and APA
• Sample Bibliography

14 Method of Footnotes

• Citations and Notes
• General Hints for Footnotes
• Writing Footnotes
• Examples of Footnote or Endnote
• Example of a Research Article

15 Method of Notes Taking

• Methods of Note-taking
• Note Book Style
• Note taking in a Computer
• Types of Note-taking
• Notes from Field Research
• Errors to be Avoided

16 Method of Thesis Proposal and Presentation

• Preliminary Section
• Presenting the Problem of the Thesis
• Design of the Study
• Main Body of the Thesis
• Conclusion Summary and Recommendations
• Reference Material

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Geometrical Method

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• Errol E. Harris 2  

Part of the book series: Archives Internationales D’Histoire des Idees International Archives of the History of Ideas ((ARCH,volume 59))

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The ultimate concern of Spinoza’s philosophy, as we have seen, is not simply a theoretical interest in ethics but a deep practical desire to discover the best way to live. Spinoza was no mere theorist; he put his philosophy into practice and lived the kind of life he found on theoretical grounds to be the most satisfactory. And he did so only when and because he was rationally convinced. Though experience taught him that the pursuit of mundane advantages was frustrating and unsatisfying, he was not content to accept experience as the final arbiter of the truth and to rest his convictions upon it. That experience was real and bitter. The Synagogue, in which his learning and great intellectual powers might have qualified him for distinction, rejected him with the most awesome curses and expelled him from the Jewish community. His own sister attempted to exclude him from his heritage, so that he had to resort to the law to establish his rights (which he then voluntarily relinquished). In trade he found men all too ready to swindle and defraud; and, if Lucas’ report is to be trusted, an attempt was made upon his life for no stronger reason than that his opinions and neglect of religious observance displeased the Jewish authorities. With reason he was able to write that experience had taught him that all things usually encountered in common life were futile and vain.

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Cf. Ethics II, vii and H. H. Joachim, Study of the Ethics of Spinoza (Oxford, 1901, New York, 1964), Introduction. Hereafter abbreviated Study .

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Cf. John Caird, Spinoza (London, 1910), Ch. VI. Also H. G. Hubbeling, Spinoza’s Methodology , (Assen, 1967), p. 10 and passim.

Cf. Joachim, Spinoza’s Tractatus de Intellectus Emendatione (Oxford, 1940), Ch. II, § 6, Ch. III, Excursus, Ch. IV, § 21 and passim. (Hereafter abbreviated as Spinoza’s Tractatus ).

For the contrary view see, Stuart Hampshire, Spinoza (London, 1956), pp. 89–91; R. McKeon, The Philosophy of Spinoza , (New York, 1928 ).

For the contrary view see, Stuart Hampshire, Spinoza (London, 1956), pp. 89–91; R. McKeon, The Philosophy of Spinoza , (New York, 1928).

Cf. P. F. Strawson, Introduction to Logical Theory , (London, 1952), pp. 58ff.

Cf. Hubbeling, Spinoza , (Baarn 1966), p. 44.

Cf. A. J. Ayer, The Problem of Knowledge , (Harmondsworth, 1956), p. 29, for instance

Cf. A. Eddington, The Expanding Universe (Cambridge, 1993), pp. 104-5 and 120; D. W. Sciama, The Unity of the Universe (New York, 1961);L de Broglie. The Revolution in Physics (London, 1954),, p. 205 “The fundamental postulates are justified by the possibility of founding on them a coherent theory, compatible with all the experimental fact” W. Heisenberg, Physics and Philosophy (London, 1959),p. 69, and Philosophical Problems of Nuclear Science (London, 1952), p. 105.

Cf. A. Eddington, The Expanding Universe (Cambridge, 1993), pp. 104-5 and 120; D. W. Sciama, The Unity of the Universe (New York, 1961);L. de Broglie. The Revolution in Physics (London, 1954),, p. 205 “The fundamental postulates are justified by the possibility of founding on them a coherent theory, compatible with all the experimental fact” W. Heisenberg, Physics and Philosophy (London, 1959),p. 69, and Philosophical Problems of Nuclear Science (London, 1952), p. 105.

Cf. L. Roth, Spinoza (London, 1945), p. 37, and Descartes, Spinoza and Maimo-nides ( Oxford, 1924 ), Ch. II.

Cf. L. Roth, Spinoza (London, 1945), p. 37, and Descartes, Spinoza and Maimo-nides (Oxford, 1924), Ch. II.

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Harris, E.E. (1973). Geometrical Method. In: Salvation from Despair. Archives Internationales D’Histoire des Idees International Archives of the History of Ideas, vol 59. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2495-2_2

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Behind the Geometrical Method

A reading of spinoza's ethics.

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• Keywords: Thought ; Ethics ; Philosophy ; Treatise ; Reason ; God ; Explanation ; Materialism ; Theory ; Thomas Hobbes ; Baruch Spinoza ; Philosopher ; Principle ; Monism ; Dualism (philosophy of mind) ; Good and evil ; Sadness ; Inference ; De Cive ; Leo Strauss ; Pity ; Concept ; Hypothesis ; Causality ; Contradiction ; Conatus ; René Descartes ; Spinozism ; Lecture ; Omniscience ; Conceptions of God ; Teleology ; Prima facie ; Self-interest ; Criticism ; Psychology ; Scholasticism ; Physicalism ; Existence ; Disposition ; Intelligibility (philosophy) ; Indication (medicine) ; Writing ; Stuart Hampshire ; Quantity ; Awareness ; Calculation ; Critical thinking ; Existence of God ; Pineal gland ; Self-preservation ; Omnipresence ; Principles of Philosophy ; Subjectivism ; Self-consciousness ; Counterexample ; Absurdity ; Self-love ; Theory of mind ; D. Reidel ; Immutability (theology) ; Analogy ; Morality ; Phenomenon ; Science ; Abbreviation ; Aristotelianism ; Natura naturata ; Individuation ; Aristotle
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Spinoza's Ethics: An Introduction

Steven Nadler, Spinoza's Ethics: An Introduction , Cambridge University Press, 2006, 313pp., $27.99 (pbk), ISBN 0521544793.

Reviewed by Michael LeBuffe, Texas A&M University

Spinoza's Ethics is a recent addition to Cambridge's Introductions to Key Philosophical Texts, a series developed for the purpose of helping readers with no specific background knowledge to begin the study of important works of Western philosophy. Steven Nadler accomplishes that aim admirably. He covers nearly every major position in the Ethics , including very difficult topics that are often neglected in the literature but which often interest or puzzle readers of Spinoza, such as the distinction between mediate and infinite modes in Part 1 of the Ethics or the account of the eternal part of the mind in Part 5. He does so, moreover, using a number of different tools likely to make the book of interest to a variety of readers. The book includes a clear, concise biography of Spinoza. Nadler makes numerous comparisons to Descartes, who was Spinoza's most important influence as well as a figure that may be more familiar to many readers. Where it is appropriate, he also introduces other important influences on Spinoza, including Cicero, Maimonides, and Hobbes. He compares discussions in the Ethics to parallel discussions in Spinoza's other works, making especially good use of Spinoza's letters, which enlivens debate and allows Nadler to raise in the voice of Spinoza's correspondents questions that readers are likely to have themselves. And, in the course of discussing the issues that have been of greatest interest to Spinoza's critics, Nadler refers readers to some of the most important recent work on Spinoza by philosophers, historians. and political theorists. So readers with specific interests in metaphysics, the philosophy of mind, ethics, religion, politics, or history will find some hook here to draw them into the Ethics . Nadler's book is comprehensive, engaging, and bright. It is sure to answer the questions that will strike a new reader of Spinoza and to raise new questions and productive lines of inquiry.

The book begins with an account of Spinoza's life. Nadler is the author of the best biography of Spinoza, Spinoza: A Life (Cambridge University Press, 1999), and this essay summarizes his account there. Chapter 2, a discussion of Spinoza's geometric method, includes a discussion of the formal apparatus of the Ethics . The highlight of Chapter 2 is an extended discussion of Spinoza's theory of definition in the course of which Nadler argues that Spinoza's definitions in the Ethics ought to be understood as real rather than stipulative definitions. All of the subsequent chapters follow the order of argument of the Ethics . Chapter 3, "On God: substance" describes the argument to substance monism at 1p14 (that is, Part 1, Proposition 14) and Spinoza's identification of God with nature. Chapter 4 concerns necessity and determinism. It includes a helpful discussion of the relation of Spinoza's "God" to traditional religious conceptions of God, something that does not interest many philosophical critics of Spinoza but which does continue, three centuries later, to raise eyebrows among undergraduate readers. In Chapter 5, after a brief discussion of Spinoza's parallelism -- the view that the order and connection of ideas is the same as the order and connection of extended things -- Nadler describes Spinoza's account of the human being and, in particular, the mind/body relation that Spinoza draws out of this central doctrine. Nadler makes extensive and apt use there of a comparison to Descartes. Chapter 6, following along the structure of Part 2 of the Ethics , focuses on epistemological themes: Spinoza's theory of ideas, his account of the three kinds of cognition at 2p40s2, and his identification of will and intellect at 2p49. Chapter 7 summarizes Spinoza's accounts of desire and the passions. It emphasizes Spinoza's naturalism about human psychology and what Nadler characterizes as Spinoza's egoism. Here the main comparison is to Hobbes, whom Nadler also takes to be an egoist. Chapter 8 is an account of some of the central themes of Spinoza's moral theory. One might emphasize any number of near equivalent concepts that Spinoza uses in Part 4 of the Ethics (the good, what reason commands, what is useful, what conduces to self-preservation). Nadler chooses to emphasize virtue and, what he rightly regards as a different kind of concept, Spinoza's model of human nature, the "free man." The chapter also features a brief discussion of Spinoza's political philosophy. Chapter 9 concerns, principally, Part 5 of the Ethics and Spinoza's use there of some of the terms of traditional eschatology, "eternity" and "blessedness." Drawing upon, especially, the medieval Jewish tradition, Nadler offers an interpretation of Spinoza as denying personal immortality.

Nadler takes few strong interpretative positions in his introduction to the Ethics . On topics of debate among Spinoza scholars, he typically refers readers to other sources rather than entering into argument himself. For example, on the question of whether Spinoza's account of the free man amounts to an argument that everybody ought to try to live like the free man, Nadler (pp. 237-238) merely mentions the dispute and refers to papers by Edwin Curley and Don Garrett, which he takes to offer different views on the issue.

Nevertheless, Nadler does, in a few places, defend particular interpretative views, and these parts of the book are likely to be of particular interest to specialists in the history of early modern philosophy. In his introduction (p. 58) of Spinoza's notion of attribute, which Spinoza defines at 1d4 as what the intellect perceives as constituting the essence of substance, Nadler mentions an important dispute concerning whether attributes are to be understood subjectively, as a way in which what is real is perceived, or objectively, as themselves real features of the world. Later (pp. 129-130), after his discussion of parallelism, which gives the reader more detailed knowledge of two attributes, Nadler argues for an objectivist reading, on the grounds that: first, outside of the appearance of Spinoza's initial accounts of attributes, considered in isolation, there is little evidence for a subjectivist reading; and, second, Spinoza clearly argues (1p9) that the more reality a thing has the more attributes belong to it. The second point is one that Martial Gueroult also emphasizes, a debt that Nadler clearly acknowledges. This is a compact, efficient argument that, at the very least, puts the burden of evidence on a defender of the subjectivist interpretation to show how it is that, on Spinoza's view, just from being able to be perceived in a variety of different ways, one thing can be considered to be more real than another.

In the philosophy of mind, Nadler defends (171-173) a particular account of what it is, on Spinoza's view, for a mind to be conscious. Traditionally, critics have either despaired of giving an account of consciousness in the Ethics or defended one of two interpretations. On the first option, which Nadler takes to have its principal source in Curley, Spinoza does not take ideas of body to be conscious, which is good if he can thereby save himself from making ordinary objects such as tennis balls, which have both mental and physical aspects, conscious. Spinoza does, however, on the first reading take ideas of ideas to be conscious. If it were true, on Spinoza's view, that only those things that we want to show to be conscious contained ideas of ideas, then the first option might be promising. Nadler argues, however, that Spinoza takes there to be an idea of every mode in every attribute. So, for a tennis ball, just as there is an idea corresponding to the extended tennis ball, so there is also an idea corresponding to the idea of the tennis ball. The first option, therefore, does not find consciousness precisely where we would like it to be. Nadler instead endorses the second option, which was entertained and rejected by Margaret Wilson and which Garrett recently has also entertained. On this option, it is the complexity of a mind that makes it conscious. Nadler helpfully defends the view that the human mind is complex, on Spinoza's account, by referring to the great complexity Spinoza finds in its extended counterpart, the human body. Then he concludes that, as the human body is extremely complex, so the mind is conscious.

The second option ought to be presented as one according to which some things are relatively more conscious than others, rather than in terms of what is or is not conscious, since anything, even a tennis ball, has some degree of complexity. So, according to this option, Spinoza is not saved entirely from attributing consciousness to tennis balls; he attributes to them a very confused and rudimentary kind of consciousness. This, of course, is a weakness of the view, and the grounds upon which Wilson rejects it. However, as Garrett has noted, it is also a strength for Spinoza insofar as it jibes well with Spinoza's naturalism in making the difference between human beings and tennis balls a difference in degree rather than in kind.

Nadler also takes an interesting position on the interpretation of Spinoza's remarks about the eternal part of the mind in Part 5, following 5p20. It is, as I have mentioned, a great strength of Nadler's book that he discusses those portions of the Ethics that many other commentators, because of their own lack of interest, do not. This will be a service to curious students of the Ethics who are regularly struck by Spinoza's claims about God, blessedness, and eternity. Another notable strength of the book, which I have not mentioned, is Nadler's ability to handle even very difficult and obscure parts of the book in a way that makes them accessible and invites readers to test interpretations where they might otherwise just be struck numb. Both of these strengths are evident at the end of the book, in Nadler's discussion of eternity. He rejects interpretations of Spinoza's account of the eternity of part of the mind as a kind of doctrine of personal immortality, arguing that neither consciousness nor memory survive the death of the body. Instead, Nadler sides with a line of interpretation on which Spinoza takes the eternal part of the mind to be a body of knowledge.

A strength of the discussion is Nadler's account of Spinoza's strategy in defending this conception of eternity. Instead of taking Spinoza to offer an alternative account of eternal life -- as if the eternity of one's knowledge without consciousness or memory to enjoy it could be enticing -- Nadler (p. 271) presents Spinoza as engaged in an attempt to show why a life of freedom and reason is preferable to a life guided by passions. Traditional accounts of immortality, on this interpretation of Spinoza's view, depend upon hope and fear as motives for submission to ecclesiastic authority. In demonstrating that genuine eternal existence is not personal immortality, Spinoza, on Nadler's account, attempts to weaken the harmful influence of these passions.

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Spinoza's Ethics: A Guide

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This guide has an introduction and five chapters, one for each of the parts of Spinoza’s Ethics . The Introduction includes background material necessary for productive study of the Ethics : advice for working with Spinoza’s geometrical method, a biographical sketch of Spinoza, and accounts of important predecessors: Aristotle, Maimonides, and Descartes. The chapters that follow trace the Ethics in detail, including accounts of most of the elements in Spinoza’s book and raising questions for further research. Chapter 1, “One Infinite Substance,” covers central arguments of Spinoza’s substance monism. Chapter 2, “The Idea of the Human Body,” follows Spinoza’s detailed metaphysics of ordinary objects, his theory of mind, and his epistemology. Chapter 3, “Striving, Joy, and Sadness,” works from Spinoza’s broad theory of finite activity in the striving to persevere in being to his detailed accounts of human action and passion. Chapter 4, “Bondage to Passion,” emphasizes Spinoza’s formal theory of value, his intellectualism in ethics, and particular claims about value that follow from these commitments. Chapter 5, “The Power of the Intellect,” begins with Spinoza’s criticism of Descartes’s account of our ability to control passion and moves to Spinoza’s own theory, which emphasizes reason, the eternal part of the mind, and human blessedness.

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Behind the geometrical method : a reading of Spinoza's Ethics

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