Is Wittgen Justified?

Previous posts have argued that all reasoning can be recreated by means of explicit rules that themselves are expressed in terms of a simple intrinsic rule. One possible form for the intrinsic rule is expressed by the Wittgen language. This will be referred to henceforth as the Association Intrinsic Rule (AIR).

The AIR can be expressed as the simple assertion that you can assign a label or definition to some string of symbols and then that label is assigned to those symbols. For example, you can define "A" as the word "table". Thereafter "A" is assigned to "table". You can ask "what is "A"?" and the answer will be "table". Of course you can try and reject AIR and ask: "How do I know that "A" is assigned to "table"? Perhaps it is "chair" instead." The only response is that nothing at all is coherent in any sense if you don't accept this basic operation of assigning and retrieving the assignment.

One could define a computer, in the abstract or empirically, as specified by the Wittgen language, which is an expression of the AIR. If you program assignments into that computer it will generate new assignments by running AIR. You can always object and say, how do I know that the computer will implement AIR. Perhaps it will break. By what criteria can I compare it to an ideal of AIR in order to determine that it has malfunctioned or not. No answer is provided to that objection. The only response is that, if I assign "table" to the label "A" and I don't know whether with the label "A", I will retrieve "table" or "chair", then nothing, absolutely nothing, in coherent. Nevertheless, the point stands, the objection has not been answered.

You can express all other rules, logic in all its forms, mathematics, empirical reasoning etc. explicitly in terms of the AIR but the AIR itself must be assumed. It is used not only as the base for reasoning but also as the means for generating outputs using the rules as well as determining that the rules are indeed being followed.

Some would say that AIR is true, self-evidently, analytically or by definition. Others would argue that AIR remains unjustified. There seems no way to resolve this conflict. Therefore, both options are considered. The implications of each option will be discussed. Additionally, even if no justification can be brought for AIR, some reasons for recommending its use nevertheless, are suggested.

If AIR is true, then one can say that it is true that some theorems follow from specific premises, where "follows from" is defined by explicit rules expressed using AIR. It is true that, specific procedures expressed using AIR do indeed produce specific new assignments. It is true that, given a matching procedure expressed using AIR, the assignments thus generated match other assignments that we choose to classify as "observation statements". This would not mean that the explicit rules such as, say, matching, variable substitution procedures, Modus Ponens, other basic axioms of logic or any theory of science so capable of generating matching procedures, could be labelled true. This list, is just what it is, a set of explicit rules that pay for their board by generating statements that match other statements we want matched. Thus following Quine's (1951) suggestion, all assertions (and procedures) get judged together as a whole regardless of analytic/synthetic divisions.

If AIR is true, why not extend it? Why not accept that string matching is true, that the premises of logic is true, that there are analytic truths etc.? After all, whatever reasoning might lead to saying that AIR is true, might hold equally for this list. A number responses may be offered as a reason for a minimization strategy that restricts the realm of truth only to AIR. To give just one argument as an example, it may not be necessary to expand the field. If a reasonably workable account of our rational framework can be given by accepting only the truth of AIR, why stick one's neck out and claim reflection-free truth status for more?

For now, no more will be said of the option that AIR is true. The question is what can be said, if there is no justification for AIR.

First of all, if it undecidable whether  AIR is true, it is not possible to make an argument such as "if AIR is true, then.." and develop the "then" branch always knowing that there is an "otherwise" branch. The reason is that and "If... then.." arguments assumes at least the truth of AIR.

One can read Wittgenstein's (1953) famous §201 as arguing exactly this undecidability of AIR when he says: "This was our paradox: no course of action could be determined by a rule, because every course of action can be made out to accord with the rule."

AIR may be unjustifiable, but what choice is there but to use it? What sense can be made of the questions themselves or anything written here, without the ability to assign one symbol to another? The only alternative to accepting AIR and moving forward under its aegis, is to fall silent. Nevertheless, even if there is no choice but to move forward, this is not a justification for AIR. It is an acceptance of the use of AIR, while realizing that no validation has been provided. This lack of capability to live with an alternative is not an ontological argument for absolute facts. There is no argument for AIR, there is just no alternative.

The continuation of Wittgenstein's §201 can be read as endorsing this view: "It can be seen that there is a misunderstanding here.... What this shews is that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call 'obeying the rule' and 'going against it' in actual cases." We can use AIR; we cannot philosophize about it.

It is inaccurate to call the foregoing an argument for AIR, because it is does not provide the justification that is implied by the strict sense of an argument. It would be better to call it a recommendation.

If AIR cannot be justified, does it have to be so minimal? If we follow AIR for lack of choice, why not extend the argument to the basics of logic or maths? One can answer that once one moves beyond AIR, it is no longer possible to argue that there is no choice. One can imagine affirming the consequent or even some novel axiom of logic that produces seemingly absurd results. There is a difference between having no alternative and having a strong intuition that only one alternative is true.

Consider for example, Kripke's (1982) argument that if you have never added a number greater than 57 before, when presented with the problem "68+57", there is no way to decide against answering "5" on the basis of an interpretation of addition as meaning an operation whose output is 5, whenever either of the arguments is greater that 57, based on past experience with addition. However, within a syntactic system that assumes AIR, the argument does not get off the ground. Addition is specified as a procedure operating on strings of digits. The skepticism applies to the intrinsic rule and only by extension to examples such as these; which is probably Kripke's point anyway.

There are other angles from which one can create a recommendation for AIR. One could argue that a system that assumes AIR is just what we call reasoning. Justified or not, the process of reasoning itself is the procedure of symbol manipulation under some intrinsic rule. The basic form of reasoning that we are familiar with is the one that assumes AIR. Thus a system that implements AIR is what we choose to call a "reasoning system" - not meaning to imply anything about its truth or justification.

Again, one can ask why not extend the intrinsic base to include more of what we automatically consider reasoning, such as, again, logic or mathematics. The answer here is less clear than in the "no choice" argument. One could argue that false reasoning is still reasoning, whereas there is still some minimum below which there is no reasoning. Alternately, one can accept any non-minimal intrinsic rule, but see the current project as an attempt to systematize what we call reasoning, justified or not, in terms of some core that itself is required for the systematization project.

A third recommendation for AIR is that, like it or not, everyone, or almost everyone, works within its framework. The problem with this recommendation is that it assumes a far wider ontological base. Nevertheless, this strategy has the advantage that it might be usable for justifying the normative aspects expected from epistemology. Arguing for minimization is easier using this method of recommendation because clearly, if the goal is to include as wide a demographic of thinkers as possible, it is best to aim for as minimal a core as possible.

There are other intrinsic rules that might be suggested as alternatives to AIR.

For example, the basic register operations of a standard computer system might serve as an intrinsic rule in terms of which all other reasoning is explicitly implemented (programmed). AIR can be implemented in terms of these register operations on the one hand, and on the other, the same basic register operations can be explicitly implemented in terms of AIR. Nothing said here suggests that AIR is the only alternative for an intrinsic rule system. However, one could argue that even the first step of defining a register and its contents is already a symbolic assignment. In other words, AIR will be assumed, however the register system is developed. AIR is still the core.

Another alternative intrinsic rule might be the basic substitution and matching system that is taught to any student of logic. This teaching process, from a perspective of the procedures implementing logic, (a perspective usually not made explicit in classic presentations of logic,) is simply teaching the student how to become an intuitive interpreter (in the Computer Science sense of the word) for a logic language. However, again, substitution and matching, when presented carefully, will include AIR as its core.

Is summary, AIR, may be seen as justified and true, or may be taken as inherently unjustified but nevertheless for extra-philosophical reasons, to be assumed anyway. The point is that it is not necessary to resolve this point. Either way, one moves forward with AIR. For the believer, its justification carries forward justification into further stages of the analysis. For the skeptic, justification, abandoned at this starting point, cannot be revived magically at later stages. Either way, it is valuable to focus on the existence of a core intrinsic rule and build analysis of the practice of rationality on the basis of a bounded kernel one can keep in sight.

References

Kripke, S., 1982, Wittgenstein on Rules and Private Language, Oxford: Blackwell.

Quine, W.V., 1951, “Two Dogmas of Empiricism”, Philosophical Review, 60: 20–43.

Wittgenstein, L., 1953, Philosophical Investigations, translated by G. E. M. Anscombe, Oxford: Blackwell, 3rd edition, 1967.