A response to Edward Feser

Edward Feser has a new blog post, 'The Problem of Hume's Problem of Induction'. Given my previous response to Eugene Earnshaw, I think it's appropriate to cover Feser's two arguments, one which we can call an argument for self-refutation and the second a burden-shifting argument. 

I will begin with the argument for self-refutation, show that it proves too much, then, assuming Feser's argument that Hume's Fork is self-refuting, end with the burden-shifting argument. In short, the burden-shifting argument is an argumentative tactic closer to a forced perspective: from a certain angle the argument looks large and impressive (the inductive sceptic is now on the defensive!), but once we are able to move freely, we see from a different angle it is in fact quite small and oddly-shaped in order to give it a certain desirable appearance (the inductive sceptic would be on the defensive, if we make the following controversial assumptions).

1. Hume's Fork

Hume's Fork is as follows--there are two sorts of justifiers for sentences: either a sentence is justified in terms of 'relations of ideas' or justified in terms of 'matters of fact'. Furthermore, a sentence may either assert the existence of non-abstract entities or not assert the existence of non-abstract entities.

For example, the sentence, 'Triangles have three sides' does not assert the existence of non-abstract entities, for the truth of the sentence is discoverable, in Hume's words, 'without dependence on what is anywhere existent in the universe', for 'though there never were a circle or triangle in nature, the truths, demonstrated by Euclid, would forever retain their certainty and evidence'; it is, as Hume calls it, 'intuitively certain',  or 'demonstrably' certain: the truth of the sentence is self-evident.

The sentence, 'Yield signs are yellow', however, is a 'matter of fact': it is not 'demonstrably certain', and its negation could hold true, that is, as Hume says, 'the contrary of every matter of fact is still possible, because it can never imply a contradiction'; furthermore, it asserts the existence of non-abstract entities, namely yield signs.

Georges Dicker in Hume's Epistemology and Metaphysics: An Introduction (1998, 38-40) covers another type of sentence, that is, statements that are 'matters of fact' but do not assert the existence of non-abstract entities, such as Hume's 'causal principle'. Whatever principle of induction were presented, it would not assert the existence of non-abstract entities; rather, it would be a bridge principle not unlike a causal principle. For Hume, however, no statement expressing a 'matter of fact' is self-evident.

We now face the first horn of the Fork: is a principle of induction justified in terms of 'relations of ideas' in the same way that all bachelors are unmarried is? A principle of induction does not seem like it falls within the modern taxonomic categories of necessary truths, analytic sentences, or sentences knowable a priori. Feser acknowledges this difficulty: 'it is at least conceivable that bread could fail to nourish us, in a way it is not conceivable that a bachelor could be unmarried'.

In more modern parlance, is there some possible world in which 'bread nourishes us' is false? Yes, therefore it is not necessary. Is the sentence 'bread nourishes us' true by meaning of the constituent terms? No, therefore it is not analytic. Is the sentence knowable without engaging in empirical inquiry? No, therefore it is not a priori. (Note: some defenders of an inductive principle disagree with this assessment, but their defence of this position will not be addressed here).

Consequently, these results exclude a principle of induction being some combination of the categories, such as a synthetic a priori truth or analytic a posteriori truth; nor could a principle of induction be an a posteriori necessity similar to Saul Kripke's famous examples, 'Hesperus is Phosphorus' or 'Water is H₂0'. Ergo a principle of induction cannot satisfy the first horn.

Now for the second horn of the Fork: following from Feser, 'The proposition that many bachelors go to singles bars is true... because it simply happens to be a contingent empirical fact that many bachelors do this'. Similarly, for a principle of induction to be justified by 'matters of fact', a principle of induction fits more within modern categories of contingent truths, synthetic sentences or sentences knowable a posteriori.

An inductive principle must be a reliable form of reasoning about 'matters of fact', akin to Hume's causal principle. For a principle of induction to be accepted as a reliable form of reasoning, there must be grounds for accepting its reliability in the future. The only available grounds are empirical, i.e. its demonstrated reliability in the past; however, this is a form of circular reasoning, justifying the principle of induction  by appealing to an inductive inference about its past reliability. Thus a principle of induction cannot satisfy the second horn.

2. The self-refuting argument

Feser claims the Fork is 'overrated', for it is 'notoriously self-refuting': the Fork is neither justified in terms of 'relations of ideas' nor justified by 'matters of fact'. Since the Fork belongs to neither category, it is unjustified. It is, in Feser's words, 'highly problematic at best and demonstrably false at worst'.

The argument for the Fork's self-refutation is, in Dicker's words, when phrased against a modernised fork (MV) (1998, 49), 'MV: All knowable propositions are either analytic a priori or synthetic a posteriori. ... Suppose that we ask the following question: is MV itself analytic a priori or synthetic a posteriori?If it is neither, the ... argument is ruined. The upshot is that if MV of Hume's Fork is true, then it is unknowable!'

Since accepting Hume's Fork is a necessary premise for Hume's argument against the possibility of justifying induction and Hume's Fork is self-refuting, the rationality of inductive inference is (presumably) saved. The dilemma for the inductivist dissipates.

Feser says,

'Nor can the Humean plausibly salvage the argument by softening Hume's fork so as to avoid the self-refutation problem. For the softening can take one of three forms. The Humean could liberalize the principle by admitting that there is after all a third category in addition to "relations of ideas" and "matters of fact"; or he could maintain this dichotomy while liberalizing the "relations of ideas" in such a way that Hume's Fork itself will come out true by virtue of the relations of ideas; or he could maintain the dichotomy while liberalizing the notion of "matters of fact" in such a way that Hume's Fork will come out true by virtue of matters of fact'. 

Feser concludes, 'Until one of these strategies is actually developed, we don't really have a Humean "problem of induction"'.

Feser neglects a fourth option, and this neglect can be shown in a (slightly) roundabout way by addressing the following question: does Feser's argument prove too much? It may apply equally to any demarcation criteria that do not fall squarely into any domain circumscribed by the criteria, viz. the same argument may be run against distinctions between more modernised post-Kantian taxonomy: the necessary and contingent, a priori and a posteriori and analytic and synthetic. 

2.1 Carnap's criterion

Consider for the moment that Feser may find the argument so convincing because he has learned of the analogous charge made against the logical empiricists, with A.J. Ayer in particular. Does this analogy hold? Dicker disagrees (1998, 53-89) with this comparison, since Hume's definition of 'matters of fact' is strictly weaker than syntheticity, but assume that the analogy does hold. Personally, I find this objection against Ayer to be ill-conceived, but in order to give some idea as to why I think the argument for self-refutation does not succeed against the logical empiricists, it is better to look at a stronger case: Rudolf Carnap's criterion.

For Carnap, empirically meaningful terms and predicates in a language L are empirically meaningful if they belong to sentences that are either confirmable or disconfirmable (that is, in Carnap's words, 'partially confirmable'); other sentences in L may be analytic (for Carnap, tautologies) or self-contradictory. It is not disputed that Carnap's criterion of confirmation does not satisfy his own criterion, for it is not confirmable or disconfirmable in L, nor is it analytic (or, for that matter, obviously self-contradictory) in L. Is Carnap's criterion therefore self-refuting on the same grounds as Hume's Fork?

One reason to defend Carnap's criterion from the charge of self-refutation (and, by extension, defend Hume's Fork from the same charge), is as follows: this form of reasoning is simply too easy to be get at. Any potential bugbear is killed off from a distance--it is trivial to refute Carnap without having to read anything in Carnap's writings other than his criterion. It is so easy a child could refute Carnap. 

Any argument that appears so easy as to dismiss Carnap without having read Carnap must, I believe, have been anticipated in some form by Carnap, and would not have escaped the attention of Carnap's critics. However, this self-refuting argument is not thought within philosophical orthodoxy to have been the knockdown argument for Carnap's criterion. Therefore we have prima facie grounds to believe this form of argument just isn't strong enough on its own to do away with Carnap's criterion (and, by extension, do away with Hume's Fork).

In fact, if one cares to read anything of Carnap outside his criterion, Carnap has a great deal to say explaining why he thinks his criterion functions as an appropriate criterion with which to disambiguate our different forms of linguistic discourse (and, implicitly, is not self-refuting).

First, we must make the distinction between internal questions and external questions for L, for questions about linguistic frameworks have both internal and external questions. Internal questions must be raised within and answered within a linguistic framework; external questions are addressed from outside the framework. 

The internal/external distinction can be understood as analogous to a toy example: consider a microbiologist examining different cells on a slide under a microscope. The microbiologist notes that different cells fall into distinct two types, with readily identifiable attributes and behaviours: red blood cells and white blood cells. Questions about the behaviour of the red and white blood cells refer to what occurs on the slide, not what occurs outside the slide; questions about the microbiologist (such as, for example, their criteria for when a blood cell is red or white) refers to what occurs outside the slide, not occurs within the slide.

Questions external to a linguistic framework can be about the consequences of adopting the framework, but to Carnap it would not make sense to speak of whether answers outside the framework are true or false, or can be judged from within the framework. It would be, as Carnap called it in the Aufbau (1929), 'mixing of spheres' ('Sphärenvermengung'), not unlike asking whether the microbiologist's criterion for red and white blood cells is a red blood cell or a white blood cell.

Similarly, these sorts of questions that inquire as to whether criteria that demarcate between different linguistic frameworks are true or false (or, in our case, itself subject to its own criteria) 'mix the spheres', or engage in, as Gilbert Ryle calls it, a category-mistake.

Perhaps Feser takes this form of reasoning not to exculpate Hume's Fork, but condemn Carnap's criterion as well, and consequently believes that Hume's Fork and Carnap's criterion are self-refuting. However, there are a large number of examples of criteria that are not self-applicable (and therefore self-refuting, by Feser's lights).

Specifically, we must be careful that Feser's argument does not result in the dismantling of the traditional borders between analytic and synthetic sentences, between the necessary and contingent, the a priori and a posteriori, and so on, all in an attempt to get at Hume's Fork.

Consider the following question: is the sentence, 'All meaningful sentences are either analytic (true in virtue of a sentence's linguistic meaning) or synthetic (true in virtue of some correspondence between the linguistic meaning of the sentence and some external fact)' itself analytic or synthetic?

The sentence isn't analytic, but is it synthetic? This is a bizarre question to ask, since it seems that we must first assume some sort of analytic/synthetic distinction in order to categorise sentences, for any instance of a purported correspondence relation would presuppose the analytic/synthetic distinction. That is, naturally, question-begging. Therefore, it is not synthetic. If it is neither analytic nor synthetic, is the sentence, 'All meaningful sentences are analytic or synthetic', self-refuting on the grounds that by its own lights it is meaningless (but also obviously meaningful)?

If Feser's argument for self-refutation is allowed to run its course, the baby is not just thrown out with the bathwater, but also the entirety of the bathroom. However, it is not obvious how Feser's criticism of the Fork doesn't dismantle too much. This companion in guilt argument is, I think, fairly strong, and is not addressed by Feser.

We are left with a choice: either this fourth option is accepted--we maintain our traditional categories of the analytic/synthetic, necessary/contingent a priori/a posteriori, 'relations of ideas'/'matters of fact', and note that a case of apparent self-refutation isn't sufficient grounds for abandoning a taxonomic system or criterion--or it is not. Is Feser willing to bite the bullet? I think not. Note that this approach does not 'soften' the Fork in the way Feser claims, nor does a principle of induction obviously enter through the window once the door is closed. The inductivist must make the further argument that questions about an inductive principle are external to L.

3. The burden-shifting argument

Assume Feser is able to get around this companion in guilt argument. Only Hume's Fork is genuinely self-refuting and all other examples are not. If so, are there any other possible issues with Feser's argument? I believe there is, specifically his subtle argument from burden-shifting.

(N.B. We have contravening evidence that bread is not always nourishing: ergot poisoning and coeliac disease. Mentioning the existence of ergot poisoning and coeliac disease is, I think, not an instance of a person's intellect not attaining 'a sufficiently penetrating grasp of the natures of bread and of the body'. But assume that Feser includes suitable ceteris paribus clauses in whatever inductive principle he accepts to rule out these cases.)

Feser may object to the premises in Hume's argument for inductive scepticism. That is uncontested. This is true, naturally, of many arguments: premises are contested. If the premises are contested, all this gets is that there exists philosophical disagreement. An appropriate conclusion to be drawn would be to refrain from belief either way, either for the denial or affirmation of an inductive principle until the dispute has been resolved. But this is tantamount to inductive scepticism. I hasten to note that inductive scepticism is not the denial of the possibility of an inductive principle; rather, it is the strictly weaker claim that no inductive principle has yet been provided that surmounts well-known objections, such as Hume's Fork.

This disagreement does not get us to the desired conclusion that a principle of inductive inference is on par with necessary truths, pace Feser's claim, 'Perhaps if we had a complete grasp of the nature of bread and the nature of the human body, we would see that it is not in fact possible for bread to fail to be nourishing to us'. Perhaps, but the consequences are not dire for the inductive sceptic, as Dicker notes (1998, 77-80).

The fact that we may be mistaken about analytic sentences, such as 'the sum of the angles a Euclidean triangle add up to 180 degrees', does not make it obvious that we are similarly mistaken about having failed to identify some presently unknown essential nature of bread, such as the sentence, 'bread is essentially nourishing to us'. Is the sentence similar to an analytic sentence? It isn't obviously so, especially given the troubles Goodman-like predicates present.

To throw Feser's claim of 'Perhaps...' back at him, perhaps if we had a complete grasp of the essential nature of bread and the essential nature of the human body, we would see that bread behaves differently after a certain date, or in a different spatio-temporal region. It is, as far as we know, not impossible.

The mere possibility that a purported synthetic sentence is in fact a suitably hidden analytic sentence is not a sufficient reason to treat the sentence as on par with sentences known to be analytic. Feser must provide an additional reason to believe we can arrive at the hidden nature of bread such that part of its essence is nourishing. It does not appear that such a conclusion can be done by way of justification by 'relations of ideas', for it is not an analytic sentence, nor has it been justified by 'matters of fact', for it would be begging the question. Hence Hume's Fork survives intact. Feser may posit 'That bread will nourish the body could be a necessary truth even if we can know that it is true... only by empirical investigation', but Feser must do more than posit it to address the inductive sceptic's arguments.

3.1 The relevance of internal and external questions

In short, the two sentences are prima facie too dissimilar. What can explain this apparent dissimilarity? A proposal: their dissimilarity is best described by maintaining Hume's distinction between 'relations of ideas' and 'matters of fact', or by maintaining more recent categories of analytic/synthetic, a priori/a posteriori or necessary/contingent.

To use William James' term, we can easily talk about the cash-value of these categories, and their cash-value is shown by the fact that they help explain the apparent general dissimilarity between types of sentences; Carnap, similarly, would note that these conceptual categories provide an explication of our intuitive concepts.

These external questions about apparent distinctions between sentences are answered satisfactorily by adopting these conceptual categories, but to do away with these categories would require articulating some further explanation for their failure and a suitable replacement, or at minimum explain why such an activity would be unnecessary, impossible or undesirable.

3.2 The attempted burden-shift

What Feser has done here is fairly ingenious, but not new in philosophy: it involves the shifting of the burden on to the sceptic to argue for some other unrelated claim, to the effect that paradigmatic sentences justified by 'matters of fact' cannot be surreptitiously justified by 'relations of ideas'. If the sceptic cannot present a compelling argument, Feser claims victory.

The problem Feser presents is either intractable or quite difficult, for it is itself a sceptical argument that puts the inductive sceptic on his or her heels. Can we really know that an apparently synthetic sentence is not in fact analytic (or vice versa)? The inductive sceptic, however, need not reel at Feser's attempt at burden-shifting; instead, they need only ask for the evidence that sentences like 'bread nourishes the body' are suitably similar to 'the angles of a Euclidean triangle add up to 180 degrees'. This amounts to saying, as previously, the inductivist must show the inductive sceptic that there is no real 'cash-value' to these conceptual categories. Feser's sceptical reply is benign until he provides the next step in his critique of inductive scepticism.

In sum, while I thank Feser for providing a limpid introduction to Aristotelian-Thomist philosophy, as well as some other interesting and insightful articles, I can only conclude Feser's argument for self-refutation and burden-shifting argument do not stand up to scrutiny.

10/4/17