Ludwig Wittgenstein is quite the theorist. There is a possibility that he may have been the last theorist.[1] In determining Wittgenstein’s relation to us, we must first see what he has to give in regards to the logocentric predicament.
Robert Hanna in The Fate of Philosophy says, “A deduction, by contrast to a single proposition, is a seqeunce of propositons that are related by ‘laws of inference,’ such that the last proposition in the sequence (the conclusion) is a logical consequence of the other propositions in the sequence (the premises), according to those laws” (69). Hanna first reframes the logocentric predicament as an issue of justifying deduction. Is this fair? He quotes Wittgenstein from his “Notes On Logic,” “Deductions only proceed according ot the laws of deduction but these laws cannot justify deduction” (qtd. in Hanna 68). I would argue that the reframing of the logocentric predicament in the context of deduction is not at all unfair and in fact is not a reframing but rather a rewording of the logocentric predicament. Per Hanna’s definition of deduction (see above), “the problem of justifying deduction,” as Hanna calls it, is exactly Sheffer’s logocentric predicament in that the justification of deduction would be a justification of those laws of inference which it supposes and employs in its operation, as well as the necessity of a relation of consequence between premises and its conclusion, and this necessary relation of consequence is logic itself (Hanna 68). Therefore, the justification of deduction would be the justification of logic and inference (reasoning [therefore, reason (too[?])]). So let’s see what Wiggy does to get around the logocentric predicament.[2]
Wiggy argues that “the conclusion of every such deduction is ‘internally related’ to the complex proposition which is the true conjunction of all its premises & thus ‘contained’ in that complex proposition” (Hanna 69). Hanna rewords this as, “in deduction the conditions under which all the premises are true will suffice for the truth of the conclusion” (Hanna 69). Now, I would reword this as follows, the deduction of a consequence, x, from premise(s), y, is not dependent on an external law of inference such as modus ponens, but rather the deduction, which is to say, the premise(s) and the conclusion in relation to one another contain the inference internally. Therefore, we do not have to do deal with any idea of inferential laws needing to be justified in that, contra Caroll, inferential laws are not actually laws in that they do not regulate the deduction externally (from above), but are rather found within the deduction itself. There is no supposition of inferential laws, for they do not exist. Let me quote Wiggy himself from the Tractatus Logico-Philosophicus,
If the truth of one proposition follows from the truth of others, this expresses itself in relations in which the forms of these propositions stand to one another, and we do not need to put them in these relations first by connecting them with one another in a proposition; for these relations are internal, and exist as soon as, and by the very fact that, the propositions exist. (5.131)
That modus ponens does not exist as some external law of inference is certainly the case once we realize that the relation itself (which, in regards to logic, is going to be the necessary consequence of relation) does not exist without the propositions. That p is the necessary condition of q and that p also is and therefore q also is cannot be expressed as a law of inference without p and q, which is to say, modus ponens cannot exist independent of that deduction whose constituent’s (the premise[s] and the conclusion) relation already internally contains the law within itself. Wiggy furthers this point, HE, in fact, DOUBLES DOWN (which is good, the Wiggy of the Tractatus had the gusto), when he says,
If p follows from q, I can conclude from q to p; infer p from q. The method of inference is to be understood from the two propositions alone. Only they themselves can justify the inference. Laws of inference, which — as in Frege and Russel — are to justify the conclusions, are senseless and would be superfluous. (5.132)
All inference takes place a priori. (5.133)
In this sense, extrapolating a law of inference from, as Wiggy says in the Tractatus, “the structure of the proposition” would be superfluous because the structure of the proposition is itself the inference which is justified by the very fact that its constituents are relating in some way (5.13). In other words, “[t]he world is everything that is the case” (TLP 1).
Okay, so we have solved this whole issue of having to justify laws of inference using inference being absolutely circular in that we do not make the inference with experience, rather the inference is done a priori (by the propositions themselves[?] or by us[?]) (I love this!). Now, there have been objections to this. For example in the Encyclopedia of Research Design, specifically the section “Inference: Deductive and Inductive,” it is said that “[i]mplication is a logical relationship; inference is a cognitive act. Statements imply; people infer” (594). Is this the case? If inference takes place a priori then no. Statements do not imply something to be inferred but infer themselves, no? Or, if we speak of us as that which infers and not the statement itself which seems to be more in line with point 5.132 then we can say that because the justification for the inference is contained within the relation of the propositions that is (supposedly) its implication, the implication entails its own inference. Wait, so if we infer from an implication is there not a problem here? Do we not also have to infer that there is an implication in the first place? Not at all because this inference takes places a priori through the propositions themselves that justifies (and propels) both this fundamental inference of the implication and the structural relation that is the implication itself. In this sense, the inference and implication come at the same time through the propositions themselves, and in occurring at the same time, they become indifferentiable in that since we did not create the implication, then the inference that infers the implication (which actually seems to be done by the propositions themselves) can also only come from the propositions creating the structural relation that is the implication itself; therefore, we have a case in which implication is inference and inference is implication, again, due to the fact that the propositions implicate inference and infer implication, therefore the structural relation of the propositions contains both implicaiton and inference, which is why all inference is a priori: the inference was already contained in the propositions itself.[3]
So, we must ask, what are the presuppositions of Wiggy’s latter assertion of the apriority of inference itself? It does not, and this why semiotic nihilism has never had too much of a purchase on my beliefs,[4] suppose that the composition of words and those words contained within the compositions itself mean anything in that the signified does not have to be understood for the semantically intended content (by semantically intended content I just mean that content which the signified was “supposed” to signify) to be just that content. That Wiggy’s points 5.13–5.132 within the Tractatus mean what Wiggy intends them to mean will always be the case, but that the subjectivity of signification will be gotten around does not have to be the case for that semantically intended content to contain the idea that inferences are a priori, for example, and, even then, that semantically intended content is there, whether one wants to acknowledge it or not. This helps us solve this issue of deduction supposing some “laws of deduction,” for the deduction itself is justified by the propositions themselves. In this sense, the only thing we have left to address is logic itself, for inference being contained within the propositions themselves a priori is the case, according to Wiggy, because “it is the propositions, or rather their behaviour, which gave us the rule. Modus ponens, modus tollens, and the like become merely names for forms of inference. If we mention them, then we have indicated what form of inference we have used, i.e., the particular aspects of certain propositional configurations which are of present interest” (Zwicky in “Wittgenstein and the Logic of Inference” 675). What justifies that modus ponens is the form of inference occurring? Simple: “the propositions and the relations in which they stand to one another” (Zwicky 675). With laws of inference and thus laws of deduction disposed with, and there just being deduction and inference, as we have stated, we then must go back to that which allows the inferences to be confirmed or denied: logic.
How does this help us solve the issue of the logocentric predicament? [I have realized that there may be irreconcilable issues with Wiggy’s theories which purport to solve the logocentric predicament. Further comment may be added]
Notes
[1]: Some say that the Tractatus completed philosophy.
[2]: The usage of Wiggy to refer to Wittgenstein is nothing more than a reference to a “cult paper” (in the sense of a cult film or a cult classic film as they are called) for a few of mine friends, e.g., Kevin and Haseeb, and I by Roderick Long titled “Wittgenstein, Austrian Economics, and the Logic of Action: Praxeological Investigations” which has the url of “praxeology.net/wiggy-draft.pdf.”
[3]: Here was the failed attempt to express what I have better expressed in this sentence; it may be of some use to some of you, so I’ll include it here: In this sense, we have a case of inference and implication being the same in that the inference of there being an implication is justified by the propositions themselves a priori, the inference of the implication and the implication are one in the same in that the propositions themselves propel them in a single movement (meaning that there can’t be two movements of both implication and inference).
[4]: Semiotic nihilism, as I have dubbed it, is just the position that language can never be justified in that one must use language to justify language, but semiotic nihilism supposes logic, which is exactly why it has little bearing on my mind.
