1

I was thinking of Kant's discourse on the form of the law and the law of formality as reciprocal (in the Critique of Practical Reason), where he seems to talk about a regress from specific maxims to the pure CI:

It is therefore the moral law, of which we become directly conscious (as soon as we trace for ourselves maxims of the will), that first presents itself to us... We can become conscious of pure practical laws just as we are conscious of pure theoretical principles, by attending to the necessity with which reason prescribes them and to the elimination of all empirical conditions, which it directs. The concept of a pure will arises out of the former, as that of a pure understanding arises out of the latter... [The CI], however, is not a precept to do something by which some desired effect can be attained (for then the will would depend on physical conditions), but a rule that determines the will a priori only so far as regards the forms of its maxims; and thus it is at least not impossible to conceive that a law, which only applies to the subjective form of principles, yet serves as a principle of determination by means of the objective form of law in general. We may call the consciousness of this fundamental law a fact of reason, because we cannot reason it out from antecedent data of reason...

Now I also recall somewhere in my set-theory studies that Frege was at least somewhat at odds with the idea of "abstraction," instead advocating proceeding (if possible) from the domain of what we otherwise supposedly "abstract to" when starting with concrete representations. But so then is the process of abstracting to generalities from particulars a kind of regress-of-reasoning, and if so, is it the only such regression? Note that we need not hold that the general/particular distinction is strictly binary, but can speak of levels of abstraction, for example.

Kristian Berry
  • 9,561
  • 1
  • 12
  • 33
  • 1
    Maybe something worthwhile in section 3.1 https://plato.stanford.edu/entries/tropes/. "it seems that there are resemblance tropes holding between the members of the pairs F and G, G and H, and F and H… Let us call the resemblance tropes in question R1, R2, and R3…each of these resemblance tropes in turn exactly resemble each other. Therefore, certain resemblance tropes hold between these tropes…we are launched on a regress... – J Kusin Jul 12 '23 at 03:56
  • 1
    ...no matter how many resemblances we regressively generate, ultimately they all depend for their existence on the existence of the resembling tropes, which resemble each other because of their individual nature." Tropes kind of straddle particularity and generality, they are technically neither though I suppose. – J Kusin Jul 12 '23 at 03:56
  • @JKusin with respect to order theory in general (as a mathematical subdiscipline), I think we can speak of terms that are equally general and particular, as well as terms which have incommensurable amounts of generality/particularity. So perhaps tropes are among such terms (one characterization of them is "abstract particulars," which has a ring of equivalence, but per the "weirdness" of some tropes, perhaps incommensuration). More than that, though, then, they might well play a special role in the regress of generalization. – Kristian Berry Jul 12 '23 at 06:12
  • You tread where few can keep up! – J Kusin Jul 12 '23 at 15:08

0 Answers0