A Fregean Solution to the Logocentric Predicament

04/07/2022

What, however, if beings were even found whose laws of thought directly contradicted ours, so that their application often led to opposite results? … I would say: here we have a hitherto unknown kind of madness.

— Gottlob Frege, Basic Laws of Arithmetic, pp. 11–12

In his amodalist interpretation of Frege found in Necessity Lost, Sanford Shieh holds that, for Frege, “nothing external to the thought that is a primitive truth of logic is require to ground that justification of that thought, and nothing more than a grasp of that thought is needed to acknowledge its truth” (Shieh, Necessity Lost, p. 209). What Shieh has just said sounds extremely similar, if not identical to BonJour and McGrew’s theories of rational insight and analytic a priori intuition respectively. The foundationalist character of this interpretation of Frege is clear. That there is a hint of internalism is also evident. It is interesting that Shieh essentially makes the classic division that classical foundationalism itself makes in Figure 5.1 (see below):

What Shieh’s Frege really holds is that “primitive logical truths are justificationally self-sufficient … that, in a sense, primitive logical truths are self-justifying” (Shieh, Necessity Lost, p. 209). Shieh, once again, clarifies, “The grounds of their [primitive logical truths] justification lies in the thoughts that they are, and, nothing more than a grasp of these thoughts is required to acknowledge their truth” (Shieh, Necessity Lost, p. 210). Again, this sounds almost, if not completely identical to what many theorists of rational insight have put forward (specifically, Laurence BonJour, the McGrews, and C.I. Lewis have all put forward a similar notion).

Now, just like rational insight, this Fregean account runs into the question of meta-justification and circularity. To be clear, the claim Shieh is putting forward is that “[p]rimitive logical truths are justificationally self-sufficient” (Shieh, Necessity Lost, p. 210). Now, it is clear that Shieh is aware of the logocentric predicament. He even says, “it seems that any attempt to justify a law of logic is going to run into a circle or an infinite regress” (Shieh, Necessity Lost, p. 219). I must, however, that the way Shieh goes about dealing with the epistemic autonomoy of primitive logical truths is poorly done in that it is an almost rule-circular justification. Shieh argues that because “the justification grounds for any instance of this form of inference [modus ponens] to be truth-preserving are not external to the thoughts that constitute this instance. Hence this form of inference is justificationlly self-sufficient and so logically primitive” (Shieh, Necessity Lost, p. 225). The issue is that this really doesn’t demonstrate anything other than a fact of, I want to say, circularity. It seems no actual non-circular metajustification is given. Furthermore, it seems that Shieh is committing the common fallacy of equivocating grounding and justification. Eventually, Shieh even admits that “we have an infinite regress … on [both] the ontological … [and] the epistemological side” (Shieh, Necessity Lost, p. 228). We are off to a very weak start, but let us not fret though, for many other Fregeans have attempted to address the logocentric predicament.

In his essay “When Logic Gives Out,” Walter B. Pedriali asks “how can deduction be justified,” so we are immediately on the right track (Pedriali, “When Logic Gives Out,” p. 1). Pedriali says that “[a]ccording to Frege, the Urproblem of arithmetic is the question of how we apprehend logical objects,” which to a certain extent is definitely true, but I propose that the Urproblem of philosophy, of thought itself, is the question of how we justify deduction, i.e., how we solve the logocentric predicament (Pedriali, “When Logic Gives Out,” p. 1).

Pedriali suggests three routes to answering my Urproblem: 1. “the logical laws are constitutive of thought and hance that they are given to us through the activity of thinking and judging” 2. “that their authority over us flows from their being self-evident (we cognise them through some sort of rational insight, and their self-evidence entails that they are self-justifying as well)” 3. “that BLL [basic logical laws] are apprehended via grasp of their constituent sense — they are true-in-virtue-of-content, and it is sense-understanding (via grasp of compositionally determined structure) that grounds their apprehension while also providing appropriate justification for our holding them to be logically true” (Pedriali, “When Logic Gives Out,” pp. 1–2). Let us note here that Pedriali does not fall into the common error of fallaciously equivocating between grounding and justification.

Lining out how we are at “the limit of enquiry,” Pedriali holds that “logic has got to give out” because “[l]ogic … regulates thought-transitions, but there is no transition to BLL over which logic could legislate” (Pedriali, “When Logic Gives Out,” p. 2). Now, instead of immediately giving up on reason as many do when faced with the logocentric predicament, Pedriali understands that while logic does not regulate that which comes before it “[s]ome other form of rational constraint must be in place there” (Pedriali, “When Logic Gives Out,” p. 2). Again, the question we have to answer is “[b]ut of what kind [is this rational constraint]?” (Pedriali, “When Logic Gives Out,” p. 2).

The first argument Pedriali lines out which he dubs “the architectural argument” is just the regress problem argument for foundationism, i.e., “if there is to be any knowledge at all, there have to be, on pain of regress, some truths which are not derived from other truths which are not derived from other truths … On the plausible assumption that we do have knowledge of logical facts (e.g. entailments and so forth), the argument concludes that we have (and must be credited as having) knowledge of basic (i.e., underived) logical truths” (Pedriali, “When Logic Gives Out,” p. 3). The clear issue with this is that it already supposes we have justified true belief in entailments which is exactly the subject trying to be true. Hence, this argument is circular with respect to what we are trying to get from it.

So, where does that leave us? Certainly, not a point where we give up on answering my Urproblem. On the contrary, “[T]o parry [our] worry, we need to show that even without proof on their side BLL can still enjoy some kind of rational justification, indeed, enough justification to get the justification game going” (Pedriali, “When Logic Gives Out,” p. 5). Yeah! The justification game has to get going! But, the only way to get it moving is to solve the logocentric predicament. So, we return to answering the original question once more.

Pedriali sees that “either … there can be no such thing as a thought-transition to BLL or … the transition, although still subject to some sort of normative constraint, is not one that logic can regiment … Call these transitions, of either kind, BLL-entry points. They are, in effect, the entry points of rationality” (Pedriali, “When Logic Gives Out,” pp. 5–6).[1] If we go with the first option which sees that there is no thought-transition to BLL at all, then “cognitive access to BLL would be radically immediate, perhaps in a manner analogous to perception — that BLL are true is something that we can see” (Perdriali, “When Logic Gives Out,” p. 6). This sounds similar to rational insight. Obviously, Perdriali’s use of “see” is metaphorical but useful and informative. Now, what is extremely interesting to me is if we go with the second option, because “[u]nder the second option, access to BLL is not immediate, but the transition to them is not inferentially mediated either” (Perdriali, “When Logic Gives Out,” p. 6). So, with either option, we still have non-inferential justification, and therefore do not, at least in terms of first-order justification (we will have to see about second-order or meta- justification later), fall into the mad circle that the logocentric predicament is. Do note, that there is a third option offered by Perdriali that, like the first option, doesn’t see any transition to BLL, but, unlike both the first and second option, also doesn’t see that “there could be such a thing as an entry point to rationality” (Perdriali, “When Logic Gives Out,” p. 6).

Perdriali sees that, for Frege, “the (objective) self-evidence of BLL manifests itself through the transparency of compositionally determined sense” (Perdriali, “When Logic Gives Out,” p. 9). Perdriali further explains this, “we grasp the sense of the whole by compositionally computing the sense of its constituent parts. … In the case of BLL, then, the computation of their sense from its constituent sense brings forth the judgement that the truth condition thereby determined is necessarily satisfied. And that this is so immediately evident to anyone who properly and fully grasps that sense. …full understanding of sense is equivalent to taking the step to the judgement regarding truth value, and indeed to the acknowledgement that BLL name the True in all conceivable cases” (Perdriali, “When Logic Gives Out,” p. 10). Now, while this is an interesting solution, it worries me. This “process” of sense-computation seems to require justification. Why does it confer such a thing. Sure, there is no inference, so it is not circular on the level of using logic in a certain sense, but, once the demand for metajustification arises, things get worrisome. Furthermore, my worries become partly confirmed when Perdriali says, “We can then say that BLL-justification is logic-involving but non-circular” (Perdriali, “When Logic Gives Out,” p. 10).[2][3] It seems that Perdriali gets only a part of the way because “sense cannot be the sole vehicle of grasp of validity (it cannot bear the required epistemic weight all by itself)” (Perdriali, “When Logic Gives Out,” p. 13).

The pragmatic Fregean foundationalism proposed by Perdriali in no way does anything to get around the logocentric predicament because of the fact that “[t]he fruitfulness … of our BLL is … something that is verified experimentally, and a posteriori” which means that a standard for verification is supposed which begs the question for its justification which an answer is attempted lapses back into meta-regression (Perdriali, “When Logic Gives Out,” p. 21). Now, Perdriali then recognizes the Sheffer’s logocentric predicament explicitly, but, opting to not give up, he tries to salvage his pragmatic foundationalism. In doing so, he turns to externalism, which, while such a turn is certainly interesting, it is also only further worrying. Perdriali tries to argue, following his logic, which we will accept for the sake of argument, the pragmatic evaluation is “the only way in which that part of content is made available to any thinker … [and] it is the only way in which that part of the content comes into being” (Perdriali, “When Logic Gives Out,” p. 24). Ultimately, the conclusion Perdriali is trying to achieve is that “since the operational character of BLL is not justified by logic but rather by the acts it licenses, by something that logic determines but does not wholly constitute,” then we can say there is no circularity and we have solved the logocentric predicament (Perdriali, “When Logic Gives Out,” p. 26). This seems satisfying to some, but once one realizes the issue of metajustification arises, any satisfaction is taken by the spectre of skepticism. While, for the sake of argument alone, we agree that the pragmatic foundationalist account that Perdriali put forward could possibly answer his Urproblem of “how logical objects are given to us,” it does not answer my Urproblem which is how can we justify deduction (Perdriali, “When Logic Gives Out,” p. 28)? To try and answer the demand for metajustification, Perdriali argues, “we justify them [rules] first by their exemplification in acts of reasoning, and secondly by demonstrating that, so exemplified, they generate the appropriate class of consequences” (Perdriali, “When Logic Gives Out,” p. 25). Not only does demonstration in a certain sense necessitate inference, therefore rendering Perdriali’s account not non-inferential and therefore within a categorical error in the sense that only a non-inferential account rather than an inferential account can solve the logocentric predicament without circularity, but, this is only the tip of the iceberg. Simply, we could ask why these provide justification, and, if they are employed then circularity arises, hence why one must have a method of justification that isn’t intentionally or propositionally employed (or something of that manner). A certain epistemic libertarian, in the sense that one questions epistemic force that powers thought-transitions just as political libertarians question the force that the government employs, mindset helps us see that when Perdriali says, “It is BLL qua exemplified rules that power the transition to BLL qua propositions,” he really has said nothing in regard to justification, much less metajustification (Perdriali, “When Logic Gives Out,” p. 31). He can abductively infer that the power given to the transition is some sort of epistemic entitlement/justification, however, he can not and has not justified this. That what I have said is the case is evident due to the fact he said earlier in the essay, “[those movements that logic is] only come into existence once BLL qua rules are exemplified by reasoners,” while still not going through why the interpellation of BLL by way of reasoners provides epistemic justification (Perdriali, “When Logic Gives Out,” p. 25). It seems Perdriali either gets ahead of himself or simply just missed the thought of having to provide metajustification. Though, he does say that the reasoners and their exemplification of BLL qua rules provide justification to BLL because they are “epistemically stronger” but why they are epistemically stronger would require justification (Perdriali, “When Logic Gives Out,” p. 26).

Notes

[1]: I think if we describe rational insights in the way BonJour does, that is, as autonomous atoms of a priori justification, I don’t think it would be too far off to describe these atoms as BLL-entry points. Are they not, according to BonJour, the entry points of rationality?

[2]: If rational insight doesn’t need a faculty and is immediate, then this demand for the metajustification of the process ceases.

[3]: I do want to make a note that post facto explanation really is valid and not question begging. When I first started getting into this whole discussion of the logocentric predicament, any paper, book, essay, video, etc. that used inference in their explanation of their solution, I immediately discounted. This was an error however. Inference in explanation can be allowed, and we saw that I realized this with the early innovation of my concept of post facto explanation, yet I always deferred the explanation of its validity. So, I will note here that if one is solely explaining the solution then one is not trying to garner justification. For example, let’s say I am explaining rational insight, I use inference in various parts of my explanation. My explanation does not afford me the justification, but the rational insight itself. To elaborate, let me say that the reason “post facto” is a part of post facto explanation is that it is done after the fact of the non-inferential justification of logical and inferential principles.

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Evan Jack

How sweet terror is, not a single line, or a ray of morning sunlight fails to contain the sweetness of anguish. - Georges Bataille