We contend that in the Kritik A70-76 (B95-101) Kant attempted to give what in modern terms would be a formal definition of the syntax of his logic (i.e. an inductive definition of judgment).
The question we wish to ask is, given such an analysis of Kant's logic, is the said logic sufficiently expressive (with regards to multiple generality) to formulate Kant's own analogies of experience ?
The original version of the second analogy in A was: for everything that happens there is something which succeeds it, according to a rule. Alles, was geschiet (anhebt zu sein) setzt etwas voraus, worauf es nach einer Regel folgt.
for all x. (if Happens(x) then there exists y such that Follows_by_a_rule(x,y))
We think this question might interest researchers who are interested in how multiple generality might have been dealt with in ancient and medieval logic.
I plan to write a survey article discussing Bobzien and Shogry's paper Stoic Logic and Multiple Generality. These authors argue that the Stoics 'had all the elements' to develop a variable-free version of quantifier logic, even if there is no direct evidence that the Stoics actually carried out such an enterprise. One of the reason sthis interests me is because of my own project involving combinatory (variable-free) intensional logics.
1. Kant said in the First Critique that syllogistic logic was the last word on the subject.
2. A sentence featuring stacked quantifiers such as "for everything that happens there is something which succeeds it according to a rule" is not expressible in syllogistic logic.
3. Therefore ...
Arnold Cusmariu I object to premise 1.
In B98 / A73 Kant clearly includes Stoic propositional logic as part of "logic". This includes judgments such as (in Kant's own example) "if perfect justice exists then the obstinately wicked are punished". This type of judgment is not part of syllogistic logic in the strict Aristotelic sense. Therefore we cannot conflate Kant's concept of logic with such syllogistic logic. And my question stands.
The standard treatment of logic in Kant's days probably included so-called 'relational' or 'hypothetical' syllogisms. These correspond not only to Stoic propositional calculus but to the following kind of syllogism discussed in Galen:
If x is double of y then y is half of x.
4 is double of 2.
Therefore 2 is half of 4.
forall x, y. Double(x,y) => Half(y,x)
Double(4,2)
Therefore Half(2,4)
"If perfect justice exists then the obstinately wicked are punished" is easily paraphrased as an A-proposition (try it).
Arnold Cusmariu By A-proposition I assume you mean a sentence of the form
forall x. A(x) => B(x)
For example, "all men are mortal". What you propose amounts to the claim that natural language propositional implications p => q can always be put into this form. If we supply an ontology and semantics then I agree with you. For Kant's conditional this might be something like:
forall x. (x is a possible world in which perfect justice exists) => (x is a possible world in which the obstinately wicked are punished).
But I doubt that conditionals were read this way in Kant's time.
In Kritik A70-76 (B95-101) Kant appears to be saying that:
If J is a judgment, then (not J) is also a judgment.
If J1 and J2 are judgments then (J1 => J2) is a judgment.
Hence (not (J1 => J2)) is also a judgment. Thus, to deal with this, Kant must have accepted the axioms and rules of Stoic propositional logic as (not (J1 => J2)) is not equivalent to any judgment of the form J'_1 => J'_2 used in the strict Aristotelic syllogism (even assuming the equivalence between conditional sentences and A-propositions).
Gerardo Ó. Matía Cubillo I am planning a paper dedicated specifically to investigating formally the nature of Kant's logic in the CPR and whether it is sufficient to express his 'transcendental analytic' and 'transcendental dialectic'. I have some improvements to make regarding what I wrote above...
Gerardo Ó. Matía Cubillo
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