Posts Tagged ‘ Logic ’

First thoughts on relativity in the Peri Ideon

After seeing me talk about relatives (ta pros ti) in Aristotle’s Categories 7, James Warren suggested that I look again at the so-called ‘relativity argument’ in Alexander’s testimony on the lost treatise Peri Ideon. Many of you will know the argument from Owen’s classic 1957 paper A Proof in the Peri Ideon and the industrial-scale debate it generated. But here, I’m just going to offer one preliminary idea.

Alexander (In Met. 82, 11-83,16) reports Aristotle’s (type of) argument that reconstructs a Platonic argument for Forms. Most doubt Alexander quotes the Peri Ideon verbatim, but scholars take Alexander to be a good witness to Aristotle’s argument. But I wonder whether Alexander (and others) have misunderstood Aristotle’s intentions with the argument, even if Alexander’s report is accurate.

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Transformative induction in Prior Analytics B21

Since this is my first post after the Blogistikon hiatus, I’d like to thank Dhananjay for asking me to contribute. I’m really excited to be able to get some ideas out and hopefully readers will enjoy it too. I expect I will post mainly on epistemology and logic in Plato and Aristotle because my current work looks at how logic gets used in different contexts: dialectical encounters, analysis, epistemology and so on. I got interested in the puzzle I address in this post because Prior Analytics B21 is a bit of a quirky text where Aristotle relates logic to epistemology.

Sometimes we fail to know logical consequences of our knowledge or to believe logical consequences of our beliefs. I can know the axioms of arithmetic and set-theory, for example, but not know whether the Goldbach conjecture is true. B21 asks why this is. Aristotle compares his answer to ‘the argument in the Meno’ (cf. A. Po. A 1 71a17-b8) then says something puzzling:

For it never turns out that someone knows the individual (to kath’hekaston) in advance, but she gets knowledge of the particular  (ton kata meros) at the same time, by induction, just like those who are reminded. For sometimes we know directly, for example that <such-and-such> has two right-angles if we see that <such-and-such> is a triangle (Pr. An. B 21 67a21-26).

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