18 June 2013

Ow My Butt

20 minute workout 5:30 AM: 159 supine pullups, 150 steps (interrupted at 100 owing to tiredness and pain, but completed). Intense pain this morning reduced by breakout medication and paying attention to position.

    Kant Study

    Writing the commentary on pp 201-266 of Guyer/Wood (Analytic of Concepts). Note that you have to go “thru” sensation and intuition to get to the concept if we consider that Kant has constructed a directed graph. This infects the concept with dependency on sensation, so Kant doesn’t mean that the concept isn’t connected at all with sensation.

    kana’s philosophy of mathematics: is 7+5=12 synthetic a priori because there are multiple ways of summing to 12? Analytically, 5+7=12 if 7+5=12. But 7+5=12 doesn’t seem to analytically imply that 11+1=12.

    Russell tried to refute Kant by inferring Peano arithmetic from logic since from the former you can infer all of math. But it was collectively discovered that you need synthetic a priori existence propositions for this to work.

    Indeed, Kant gets the last laugh two ways.

    From the standpoint of a reductionist metaphysics that would reduce to zero the number of synthetical or existential which is to say metaphysical assumptions needed to get started with math, Kant believed that ordinary arithmetic such as 7+5=12 consisted of synthetic a priori assertions: that quite ordinary propositions were synthetic apriori and that school kids are metaphysicians.. He apparently and to the best of my very limited knowledge would not deny that in the case of symbol manipulation shared with logic,

    isAnalyticAprioriThat(7+5 = 12)(12 = 5+7)

    But, lacking in self-confidence in math, Kant never showed us how to distinguish analytic transformations from synthetic whereas Frege and Russell went wild with pure analyticity until they hit the wall of the paradoxes.

    Metaphysics if minimal crept back into math after the negative if purely analytic discoveries of Godel. Quine showed us fifty years ago how metaphysical existence assumptions such as “there is at least one thing” were required, if memory serves me, to get his program in Set Theory and Its Logic jump-started. I studied this way back as an undergraduate but not longer have the book to hand: I will check this reference when I get access to a text.

    A negative metaphysics with an implicit Kantian seal of approval would be that of Brouwer, Heyting and the intuitionists. As Kant believed, Hume’s negativity as regards metaphysical enthusiasm was a closed system from which there was no facile escape. Therefore, I believe Kant, once apprised of the crisis in foundations of mathematics that started with Russell’s discovery of the paradoxes and continued with Godel would be approval of the Intuitionist ban on real infinities and use of the excluded middle. Kant sought a finite model in his short path from sensation to intuition to thinking to concept to minimize, not eliminate, existential (metaphysical) presumption while at the same time seeking key assumptions out for an honorable position.

    Change Record

    20 June 2013: added info re intuitionism and 20th century “minimal mathematical metaphysics”

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