Ripheus23

Transcendental inferences can be critiqued or defended as circular or recursive: if an interlocutor does not accept the "explained" (transexplained!) premises themselves, then the explanatory axioms will fail to convince on the same level. Now so far, the notion of explanation has been referred to in a self-explanatory way. However, given the role of the relevant kind of argument in stopping epistemic regression, another characterization is possible: if an argument is a sequence of inferences, and if inferences hold between sentential forms, a transcendental inference can be defined as a piece of erotetic logic. That is, some questions (erotetic functions), concerning the forms of kinds of knowledge, entail or imply some assertions (assertoric functions). A transcendental inference is from a question to an answer. Since the fundamental premise in this argument would be a question, it does not admit of circularity as far as its inferential value goes. Asking the question at all commits the interlocutor to accepting the given answer.

To illustrate: consider the problem of ethical rationality in general. This is often parsed as, "Why should I do the right thing?" Setting aside the ethical force attendant upon the word "should," I would suggest that the substantial answer to the question is that asking "why" of activity in the first place commits the interlocutor to acting on reasons "why." There is, in other words, no reason to ask, "Why do x?" unless one intends to do x just in case one knows why. The very question, "Why do x?" contains the motive of ethical activity in general.* [*Axiomatically and recursively, the variable "do x" can be taken for the activity of asking "why" in itself, so that the function becomes, "Why ask 'why'?" And it is exactly this question that entails the assertoric function, "Because there is no reason to ask why unless one intends to do what there is a reason "why," to do, in the first place." Asking the question commits the interlocutor to the ethical outlook transcendentally.]

An illustration of the erotetic transinference, here, would be Kant's distinction between analytic and synthetic knowledge. To put the distinction in mathematical parlance, an analytic truth is one resulting from an epistemic function taking itself as an input; synthetic knowledge is knowledge from epistemic functions that take self-distinct inputs (the function being synthesized with external information-values). But an epistemic function is erotetic: answers to questions that can be known by assigning the semantic value of the constants to the variables are known by analysis as such, and answers to questions that can be known only by assignment of external semantic constants to the variables are known by synthesizing the information-value of the question with external such values.*

*[This description immediately applies only to so-called "wh"-term questions (also known as "open questions") [add citation]. However, "yes/no"-questions can be converted into "wh"-term ones. Take, for instance, "Is Sarah in South Africa?" being recast as, "Where is Sarah?" "Yes," to the first question can be known by analysis or synthesis if and only if, "South Africa," could be known by analysis or synthesis of the information-value of "Sarah" in the "wh"-term case.]

[The existence of free will is a matter of transcendental argument owing to the unity of the erotetic and prescriptive functions of the mind. Although questions are not absolutely reducible to epistemic prescriptions, the epistemic-imperative model of erotetic logic does testify to the fundamental relationship between the two classes of mental object [ac]. Empirically, all languages are recognized to express sentential syntax in erotetic, prescriptive, and assertoric forms [ac] [phrase in terms of illocutionary force?].

Accordingly, the principle ought-implies-can is the keystone of our modal knowledge in concreto. That is, noncontradictory description is possible description simpliciter, but to know what in particular is possible requires more than bare conceivability or imaginability, and it is the deontic transit that gives us this. In other words, ought-implies-can is the principle of specific knowledge par excellence. But if this is so, physical determinism is unnecessary as a belief because the opposite belief is in fact necessary.

... What mathematics describe the action of the will? On the face of it, probabilities---and the difference between the chancy and the random [ac]---apply to this question. However, from the Kantian vantage, the existence of free will pertains to the antinomian problem of reason, which depends on the limits of infinite representative synthesis. Now, in Cantor's paradise, the antinomian sequences can all be collapsed into the problem of the absolutely infinite aleph-number ("omega"). Free will, mathematically, therefore must be expressed in the form of the aleph-numbers and their pure order.]