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Supposedly Euclid employed analysis (conclusions→principles) and not synthesis (principles→conclusions) when he devised his definitions/postulates/axioms in his Elements.

How did Aristotle discover his logic? By analysis or synthesis?

This question was prompted by the passage about Aristotle in Stephen Wolfram, What Is ChatGPT Doing … and Why Does It Work?, § "What Really Lets ChatGPT Work?"

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2 Answers 2

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Bocheński, O.P., History of Formal Logic pp. 41-44 notes that although "We have no extrinsic criteria to help us establish the chronological sequence of the different parts of the Organon", there are intrinsic criteria (ibid. p. 42):

The presence or absence of:

  1. the syllogism
  2. variables
  3. a "technical level of the thought"
  4. modal vs. assertoric logic
    Modal logic is more consonant with his hylemorphism than the assertoric logic that appeared in Plato's dialogues; thus, assertoric logic in Aristotle is an indicator the Aristotelian work is youthful, while modal logic would indicate a more mature work.

Bocheński concludes (ibid. p. 44):

It is only certain that the Topics and Sophistic Refutations contain a different and earlier logic than the Analytics, and that the Hermeneia exhibits an intermediate stage. For the rest we have well-founded hypotheses which can lay claim at least to great probability.

Bocheński, O.P., Ancient Formal Logic pp. 23-24:

4 E. Survey of the evolution

In the fight of the above chronology the evolution of Aristotle’s formal logic may be stated in the following way:

  1. He first elaborated the Platonic λόγους (Top., Met. Γ, De Int.), considerably developing and explicitly stating the rules or laws on which they are based. By doing so he stated a wealth of interesting logical principles of which, however, none is an analytic syllogism. This period may coincide with that of travels (348/7—335/4).
  2. Later on he made his two great discoveries: that of the analytical syllogism and that of the variable. He then declared that the other (non-analytic) laws and rules are of lesser importance and concentrated on syllogism, first assertoric, then modal.
  3. By analyzing the axiomatic system of the former (he did not have time, as it seems, to do so with the latter) he discovered several metalogical rules and even some laws of the logic of propositions. These last discoveries were, however, not systematized by him.

The process he followed is thus analytic or inductive.

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While Bocheński's analysis of Aristotle's formal logic evolution provides an interesting perspective, there are aspects of his argument that could be scrutinized further.

Firstly, his classification of Aristotle's work into periods based on the presence or absence of certain logical tools (like the syllogism, variables, a "technical level of thought", and the difference between modal and assertoric logic) might oversimplify the evolution of Aristotle's thought. Aristotle's works are multifaceted and rich in nuanced arguments, and their development may not be as linear or as binary as Bocheński's criteria suggest.

Secondly, the claim that the presence of modal logic over assertoric logic in Aristotle's work indicates maturity could be challenged. The preference for one type of logic over another might be more reflective of the subject matter or the specific argument Aristotle was making at the time, rather than a marker of his philosophical maturity.

Finally, Bocheński's assertion that Aristotle's process was "analytic or inductive" could be seen as reductive. Aristotle's method incorporated both inductive and deductive reasoning, and his philosophical inquiries often transcended the boundaries of formal logic. It is thus crucial to consider the full breadth of Aristotle's intellectual approach when examining his formal logic's evolution.

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  • "Bocheński's assertion that Aristotle's process was 'analytic or inductive'" That's not Bocheński's, but my interpretation/summary of Bocheński.
    – Geremia
    Jul 26, 2023 at 18:21

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