Realism, Nominalism, Modality

There is an important intersection between the 14th century debate about realism and nominalism and contemporary questions about the status of modality in logic that ought to be of interest to non-specialists. Both of these topics probably sound obscure to most people. At sound-byte level, the first is about the status of universals, and modality is something we implicitly presuppose any time we try to reach for something “more” than allegedly pure phenomena or mere appearance.

Both sides of the medieval debate often wanted to enlist the support of Aristotle, who took a remarkably even-handed approach to these questions we have yet to clarify. The debate was often invested with a great moral significance, and provoked a number of intemperate claims. But at the same time, both sides were able to use the technical vocabulary of the theory of “supposition” — along with shared familiarity with Aristotle — to discuss semantic issues of concrete meaning and word use in detail, in terms both sides could in large measure agree upon. This led to a very high quality and sophistication in many contributions to the debate on both sides.

On some slight acquaintance, many modern readers can easily sympathize with nominalist critiques of the premature and illegitimate use of universals. We may think of vulgar platonism, excessive abstraction, reification, alienation, and so on. On the other side though, there are premature and illegitimate claims that universals can be explained away entirely. But Hegel’s Frau Bauer could not even recognize her individually named cows, if there were no such thing as legitimately reusable reference, naming, and vocabulary. I think most people should be able to see that there are two sides to the coin here.

If we ask how legitimate repeatabilities in ordinary language are constituted and used, something like modality inevitably comes into play. It now occurs to me that Brandom’s emphasis on the priority of hypotheticals over alleged categoricals in real-world material inference — a point to which I am deeply sympathetic — really calls for something like the notion of modality that he develops.

Truth and Assertibility

Here we consider the second to last chapter of Brandom’s 1976 dissertation, which has proven to be quite an interesting document. On the one hand, he contrasts Dewey’s pragmatist notion of “warranted assertibility” with standard representationalist theories of truth. On the other, he argues that a thorough account of assertibility conditions entails an account of truth conditions, and that a thorough account of truth conditions entails an account of assertibility conditions. This chapter uses some formal logical machinery and a running series of examples, both of which I will downplay.

The very idea of examining the conditions that make something true is already quite sophisticated. One could almost forget its representationalist and foundationalist origins, because here we seem to be dealing with something more like reasons why. Truth conditions border on the territory of subjunctive robustness that Brandom develops in his later work. Truth in this sense is not just a static property that sentences abstractly and in a binary way have or do not have.

“The dominant tradition in contemporary philosophy of language, influenced by Frege, Russell, Wittgenstein of the Tractatus, Tarski, and Carnap, takes truth to be the basic concept in terms of which a theory of meaning, and hence a theory of language, is to be developed. According to this view, the essential feature of language is its capacity to represent the way things are. Understanding this function in detail is a matter of describing the conditions under which particular sentences truly represent the way things are. Formal semantics, the study of the truth conditions of sentences of various sorts of discourse, is the natural expression of this point of view.”

“On the other hand, there is a pragmatic approach to language shared by Dewey and the later Wittgenstein which attributes little or no importance to the notion of truth. According to this view, language, the medium of cognition, is best thought of as a set of social practices. In order to understand how language works, we must attend to the uses to which its sentences are put and the circumstances in which they are used. Dewey claimed that everything useful which could be said about language with the notion of truth could also be said with a more general and methodologically unproblematic notion of justified utterance or ‘warranted assertibility’ ” (p. 101).

The truth to which little or no importance is attributed is truth as representational correspondence. Even representational correspondence still has its uses though, as we will see from his remarks about Russell further below. But first he elaborates on Dewey’s concept.

“We want to associate with each sentence of the language the set of conditions under which it is appropriately uttered, or, as Dewey puts it, ‘warrantedly assertible’. We want, in other words, to associate with each sentence of the language some set, call it the assertibility conditions of the sentence such that our theory of the language gives us a uniform away of generating the regularities of usage a speaker must conform to for a given sentence, given only the ‘assertibility conditions’ assigned to that sentence” (p. 103).

“Now it is clear that no regularity of appropriate utterance which a speaker learns to conform to and which is reconstructed by a hypothetical theory of assertibility conditions for a language can amount to requiring that all utterances be true. To require that each speaker report the presence of a deer when and only when a deer is present would make infallibility a prerequisite for learning the language. The most that can be codified in the conditions of appropriate utterance of such reports is that one report deer when and only when there are what pass in the community as good reasons for believing a deer to be present” (p. 104).

The important thing here from an ethical point of view is not vacuous “certainty” about presumed facts, but the goodness of reasons for believing this or that.

“The suggestion I will develop as to the proper role of truth in explaining language-use is that of Michael Dummett….’Epistemic justifiability’ is a part of what we have called the ‘assertibility conditions’ of an utterance…. What we want to know is indeed how a notion of truth can be ‘born out of’ the less specific mode of commendation which is assertibility. And Dummett’s suggestion is that it is sentential compounding that enforces such a distinction.”

Dummett offers philosophical arguments for the superiority of constructive or “intuitionist” logic over classical logic. Constructive logic does not accept any assertion as primitive. It requires assertions to be justified by concrete evidence, rather than derived from axioms or assumed truths. It thus identifies what is true with what is provable, and at the same time it constrains what qualifies as proof.

The sentential compounding that Dummett emphasizes is a syntactic way of characterizing the idea of logical self-reference. One clause of a compound sentence modifies and refers to another clause or clauses in the same sentence. This is how richer meanings are built up. The suggestion is that truth arises out of this elemental process of refining meanings and increasing their “robustness” by tying them to other meanings.

“The primary sort of compound sentence Dummett has in mind seems to be the conditional” (p. 106).

The if-then form of conditionals is one way of expressing the fundamental notion of logical consequence, or how something follows from something else. Logic is less about distinguishing the true from the false than it is about discerning what follows from what.

“We may take the suggestion, then, to be that truth is ‘born out of’ assertibility as an auxiliary notion introduced to explain the assertibility conditions of some kinds of compound sentences” (p. 107).

“The ideal case would be one in which each compounding operator were assertibility-explicable…. Thus Dummett, giving him his premises, would have shown that English is not uniformly assertibility-explicable…. ” (pp. 110-111). “There are, of course, languages which are assertibility explicable. Intuitionistic mathematics is formulated in such a way that the assertibility conditions of compounds depends only upon the assertibility conditions of the components” (p.111n).

No natural language is purely constructive. Next we come to Brandom’s point about the interdependence of truth conditions and assertibility conditions.

“In the context of the machinery just developed, one thing which we might take Dummett to be saying is that truth is to be defined functionally, as the auxiliary … which explicates a certain class of compounding devices, among which is the conditional. In order to generate in a uniform way the assertibility conditions of compound sentences we need to look not only at the assertibility conditions of the embedded sentences, but also at the truth conditions of those embedded sentences. Put slightly differently, there is a class of compounding devices which are not uniformly assertibility-explicable, and such that they are truth-inducing, in that whatever does explicate them is a truth-concept…. I will try to show that there is a class of compounding devices which ought to be taken to be Truth Inducing Sentential Contexts…. I will try, in other word, to exhibit truth as an auxiliary notion introduced in order to account for the assertibility conditions of certain kinds of compound sentences” (p. 112).

“For if (speaker) meaning is, plausibly, whatever it is that the speaker must be said to ‘know’ when he can use that sentence properly, then that meaning includes on our account not just the assertibility conditions of the sentence, but also the contribution the sentence makes to the assertibility conditions of compound sentences containing it. Identity of assertibility conditions is thus a necessary but not sufficient condition for identity of meaning. Indeed, in any language containing [truth inducing sentential contexts], truth conditions, as well as assertibility conditions, are part of the meaning of each sentence which can appear embedded in a [truth inducing sentential context]” (p. 113).

“According to our formal analysis, then, … English is not assertibility-explicable. So some auxiliary notion must be introduced to generate the assertibility conditions of compound sentences. Dummett’s suggestion, as we have reformulated it, is that there is a class of compounding devices in English such that the auxiliary notion we need to introduce to explicate them (in our technical sense) is truth. What set of compounding devices ought we to take as [truth inducing sentential contexts] in English, then? Presumably the conditional is one” (p. 114).

Truth viewed in this way can be thought of as a kind of identity property that emerges out of the details of how things follow from other things.

In a note he quotes Quine, Roots of Reference (1970), “Two-valued logic is a theoretical development that is learned, like any other theory, in indirect ways upon which we can only speculate”, and adds, “The present chapter presents just such a detailed speculation” (ibid).

“The present suggestion is that we take truth as the auxiliary notion introduced … to explicate a certain class of compounds…. This is as yet only the form of a definition, for all we know so far of the class of compounds which would need to be specified is that it contains the devices used in our examples. Assuming that we had some independent characterization of the desired class of compounding devices, then, we could define the truth concept of any particular theory of a language to be that notion which in that theory explicates the hypothesized class. Some theories would be better than others in accounting for language-use, for all of the mundane reasons applicable anywhere else in science — ease of coupling with other theories, power, elegance, intuitive acceptability, exhibition of general principles, and so on. A fortiori, then, some truth-concepts would be better than others, for the language in question. We seek a definition of what it is to be a truth-concept (what role a notion must play in a theory of a language to be functioning as the truth-concept of the language according to that theory) which will allow us to be somewhat precise about the point of truth-theories before the entire details of the ‘best’ theory of any language are known. It is a striking fact that, as Dummett led us to see, we have pretty good intuitions concerning the role of truth in explicating the assertibility conditions of compounds even though we know nothing about such crucial details as what sort of thing the elements of sets of assertibility conditions are best taken to be, and even though we can exhibit no single concrete example of a sentence for which we can write down assertibility conditions” (pp. 116-117).

“Representationalists like Russel, arguing for a language-transcendent notion of truth, have claimed against truth-as-assertibility theorists like Dewey that the very notion of truth lies in the contrast it enables and enforces between how things are and how they are thought to be, believed to be, or desired to be by any person or group of people. If you have this distinction, you have a notion of truth; fail to make this distinction and you are simply talking about something else…. [W]e have seized on just that distinction which according to the representationalists generates the notion of truth. For on our account it is precisely the explication of compounds which systematically discriminate between the content of an utterance (how it says things are) and any state of the utterer (belief, desire, or what have you) which may be associated with it which requires the notion of truth as an auxiliary notion” (pp. 121-122).

My late father, who wrote his dissertation on Pierce, attributed to Pierce an aphorism to the effect that “the mark of reality is the sheriff’s hand on your shoulder”. In other words, reality can be distinguished as whatever constrains us in some way. In an earlier chapter, Brandom in passing situates Pierce as dealing with a recognizably Cartesian problem of how we can know an “external” reality that is what it is independent of us. My own distaste for Descartes notwithstanding, this does seem like an important point.

“In languages with sentential compounding devices, the speaker-meaning of a sentence (what the speaker must ‘know’ in order to be able to use the sentence) must be taken to consist not just of the assertibility conditions of that sentence, but also the contribution that a sentence makes to the assertibility conditions of sentences of which it is a component” (p. 122).

“Semantics as such never considers the final step of generating assertibility conditions given the truth conditions of components. For some sorts of compounding device — the conditional, negation, tensing, modal operators, and some others — it happens to be possible to generate the truth conditions of their components in relatively simple ways, as formal semantics has shown us. For other sorts of compounds, notoriously for analogues of ‘Waldo believes that…’ it appears that not only the truth conditions of components are needed, but also the assertibility conditions. If so, then the theory of truth conditions will not be able to insulate itself as a self-contained part ” (p. 123).

The point about belief here has to do with the need to distinguish something other than mere appearance. If I say I believe something, it has to be possible to ask whether I am justified or not in believing it, and that is different from simply asking what it was that I said I believed.

“In conclusion I would like to say something about the notion of truth that results from this way of looking at things. According to the usual understanding, the notion of truth is generated initially by the consideration of sentences in their categorical uses. According to this almost universally held view, a sentence like ‘Snow is white’, is either true or not true as a free-standing utterance. The employment of the notion of truth (in the form of truth conditions) in compounds of which the sentence is a part, e.g., conditionals, is a secondary, derivative matter. On the view which I have been urging in this chapter, however, it is the hypothetical use of sentences to which the notion of truth is primarily applicable, and its application to sentences in their categorical use is derivative. For according to our account, a free-standing utterance is truth-criticizable only in virtue of the possibility of taking it as the antecedent of a conditional” (pp. 125-126).

This is a fundamental point that in his later work Brandom attributes to Kant. Simple “categorical” judgments are always derivative. It is hypothetical judgments — that something follows from something else — that are more originary.

“Thus truth is primarily a predicate applicable to sentences used hypothetically, as antecedents of conditionals and similar constructions” (p. 126).

That is to say that rather than being an inexplicable property of categorical assertions, truth has do primarily with what is or is not a good inference.

“Thus the notion of truth is appropriately applied to free-standing, categorical utterances just insofar as they are involved in a social discourse in which conclusions may be based upon them according to inferential practices codified in conditionals with those sentences as antecedents” (p. 128).

“In order to see how the formal notion of truth invoked by the technical linguistic discipline we have considered is connected to the ordinary use of the truth predicate within the language, … one must consider the relations of the hypothetical use of a sentence as an antecedent of a conditional to the apparently categorical use of that sentence which is implicitly conditionalized by its utterance in the social context of argument, with inferential schemes parallel to conditionals” (ibid).

This is another important point. The fact that the surface grammar of an assertion is simple and categorical does not require that what is meant by it is categorical. When a superficially categorical assertion is cited in support of some other assertion, that pragmatic context makes it effectively a conditional.

Next in this series: Convention, Novelty, and Truth in Language

McDowell on the Space of Reasons

John McDowell’s paper “Sellars and the Space of Reasons” (2018) provides a useful discussion of this concept. Unlike Brandom, who aims to complete Sellars’ break with empiricism, McDowell ultimately wants to defend “a non-traditional empiricism, uncontaminated by the Myth of the Given” (p. 1).

McDowell begins by quoting Sellars: “in characterizing an episode or a state as that of knowing, we are not giving an empirical description of that episode or state; we are placing it in the logical space of reasons, of justifying and being able to justify what one says” (ibid; emphasis added).

For Sellars, to speak of states of knowing is to talk about “epistemic facts”. A bit later, McDowell says that Sellars’ epistemic facts also include judgments and uses of concepts that might not be considered knowledge. Not only beliefs but also desires end up as a kind of epistemic facts. McDowell uses this to argue that the space of reasons is a version of the concept of knowledge as justified true belief. I want to resist this last claim.

McDowell points out that knowledge for Sellars has a normative character. Sellars also regards the foundationalist claim that epistemic facts can be explained entirely in terms of non-epistemic facts (physiology of perception and so on) as of a piece with the naturalistic fallacy in ethics.

McDowell cites Donald Davidson’s contrast between space-of-reasons intelligibility and the kind of regularity-based intelligibility that applies to a discipline like physics, but does not want to assume there is a single model for all non-space-of-reasons intelligibility.

He notes that Sellars contrasts placing something in the space of reasons with empirical description, but wants to weaken that distinction, allowing epistemic facts to be grounded in experience, and to be themselves subject to empirical description. “Epistemic facts are facts too” (p. 5). I prefer going the other direction, and saying empirical descriptions are judgments too.

The space of reasons is only occupied by speakers. Sellars is quoted saying, “all awareness of sorts, resemblances, facts, etc., in short all awareness of abstract entities — indeed, all awareness even of particulars — is a linguistic affair” (p. 7, emphasis in original). “And when Sellars connects being appropriately positioned in the space of reasons with being able to justify what one says, that is not just a matter of singling out a particularly striking instance of having a justified belief, as if that idea could apply equally well to beings that cannot give linguistic expression to what they know” (ibid).

“‘Inner’ episodes with conceptual content are to be understood on the model of overt performances in which people, for instance, say that things are thus and so” (p. 8). “What Sellars proposes is that the concept of, for instance, perceptual awareness that things are thus and so should be understood on the model of the concept of, for instance, saying that things are thus and so” (p. 10). All good so far.

To be in the space of reasons, “the subject would need to be able to step back from the fact that it is inclined in a certain direction by the circumstance. It would need to be able to raise the question whether it should be so inclined” (pp. 10-11, emphasis in original). But McDowell says — and I agree — that this is without prejudice as to whether there is still a kind of kinship between taking reasons as reasons, on the one hand, and the purposeful behaviors of animals, on the other.

McDowell acknowledges that the idea that epistemic facts can only be justified by other epistemic facts is easy to apply to inferential knowledge, but rather harder to apply to the “observational knowledge” that he claims should also be included in the space of reasons. For McDowell, observational knowledge is subject to a kind of justification by other facts.

McDowell and Brandom both recognize something called “observational knowledge”, but Brandom thinks that it necessarily involves appeal to claimed non-epistemic facts, whereas McDowell wants to broaden the concept of epistemic facts enough to be able to say that observational knowledge can be justified by appealing only to epistemic facts. I would prefer to say, observational judgments are subject to a kind of tentative justification by other judgments.

McDowell says that acquiring knowledge noninferentially is also an exercise of conceptual capacities. This clearly implies a noninferential conception of the conceptual, and seems to me to presuppose a representationalist one instead. This has huge consequences.

He says that the space of reasons must include noninferential relations of justification, which work by appeal to additional facts rather by inference. But where did those facts come from? In light of Kant, I would say that we rational animals never have direct access to facts that just are what they are. Rather, if we are being careful, we should recognize that we can only consider claims and judgments of fact, which may be relatively well-founded or not. But appeal to claims of fact for justification is just passing the buck. Claims of any sort always require justification of their own.

As an example, McDowell discusses claims to know that something is green in color. As non-inferential justification in this context, he says one might say that “This is a good light for telling the colours of things by looking” (p. 18). That is fine as a criterion for relatively well-founded belief, but that is all it is.

A bit later, he adds, “I can tell a green thing when I see one, at least in a good light, viewed head-on, and so forth. A serviceable gloss on that remark is to say that if I claim, in suitable circumstances, that something is green, then it is” (p. 19).

This is to explicitly endorse self-certification of one’s authority. It is therefore ultimately to allow the claim, it’s true because I said so. I think it was a rejection on principle of this kind of self-certification that led Plato to sharply distinguish knowledge from belief.

As Aristotle pointed out in discussing the relation between what he respectively called “demonstration” and “dialectic”, we can apply the same kinds of inference both to things we take as true and to things we are examining hypothetically. We can make only hypothetical inferences (if A, then B) from claims or judgments of A; we can only legitimately make categorical inferences (A, therefore B) from full-fledged knowledge of A — which, to be such, must at minimum not beg the question or pass the buck of justification.

The great majority of our real-world reasoning is ultimately hypothetical rather than categorical, even though we routinely act as if it were categorical. One of Kant’s great contributions was to point out that — contrary to scholastic and early modern tradition — hypothetical judgement is a much better model of judgment in general than categorical judgment is. The general form of judgment is conditional, and not absolute.

I think it’s fine to include beliefs, opinions, and judgments in the space of reasons as McDowell wants to do, provided we recognize their ultimately hypothetical and tentative character. But once we recognize the hypothetical and tentative character of beliefs, I think it follows that all relations within the space of reasons can be construed as inferential.

I don’t think contemporary science has much to do with so-called observational knowledge of the “it is green” variety, either. Rather, it has to do partly with applications of mathematics, and partly with well-controlled experiments, in which the detailed conditions of the controls are far more decisive than the observational component. The prejudice that simple categorical judgments like “it is green” have anything to do with science is a holdover from old foundationalist theories of sense data.

I would also contend that all putative non-space-of-reasons intelligibility ultimately depends on space-of-reasons intelligibility. (See also What We Saw.)