Combining Philosophers

Ideas for William W. Tait, Chilo and Baron,S/Miller,K

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2 ideas

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C]
     Full Idea: The axiomatic conception of mathematics is the only viable one. ...But they are true because they are axioms, in contrast to the view advanced by Frege (to Hilbert) that to be a candidate for axiomhood a statement must be true.
     From: report of William W. Tait (Intro to 'Provenance of Pure Reason' [2005], p.4) by Charles Parsons - Review of Tait 'Provenance of Pure Reason' §2
     A reaction: This looks like the classic twentieth century shift in the attitude to axioms. The Greek idea is that they must be self-evident truths, but the Tait-style view is that they are just the first steps in establishing a logical structure. I prefer the Greeks.
5. Theory of Logic / L. Paradox / 7. Paradoxes of Time
A traveller takes a copy of a picture into the past, gives it the artist, who then creates the original! [Baron/Miller]
     Full Idea: Suppose an art critic travels back in time with a copy of an artist's masterpiece, gives the artist the copy, and the artist copies it. The copy of the copy turns out to be the original mastepiece. The artwork seems to come from nowhere.
     From: Baron,S/Miller,K (Intro to the Philosophy of Time [2019], 8.6)
     A reaction: Lovely thought. Is the example possible (even with time travel)? How would the critic possess the copy before making the time journey? What if the critic decided not to travel back in time? Can a picture exist if no one has imagined it first?