The idea that the holding of certain sentences “true by convention” might somehow provide a foundation for a priori knowledge generally has been regarded with suspicion ever since Quine’s “Truth by
Convention”, while “Two Dogmas of Empiricism” sowed the seed for a widespread scepticism, persisting to this day, not just about analyticity and the a priori but about the very notion of meaning which Carnap and the other early friends of implicit definition thought such definitions might determine. (Hale and Wright, 2003, p. 2)
Boghossian holds that the sentences which express logical principles are “arbitrarily stipulated” as true despite the fact that there might yet be facts about their truth and meaning.112 In doing so the meanings of logical terms are determined (Boghossian, 2006, p. 349). This makes him an endorser of implicit definition for the meanings of logical terms (i.e. logical constants). I have already argued that to hold
112 I have explained, in the introduction to Part 3 above, the what it is I understand Boghossian saying when he endorses the ‘arbitrary’ stipulation of the truth of logical principles despite arguing in favour of the existence of Frege-analyticities and facts about the truth of logical principles. I have, of course, argued against being able to consistently holding both these positions.
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that logical terms are implicitly defined is part of a semantic theory about logical terms and the principles of which they form part. But can a semantic theory which incorporates implicit definition perhaps not also be factualist and non-conventionalist? My answer is, no.
If taking Carnap’s account of analytic truth to be correct, there is no type of analytic sentence about which a realist semantic view could be correct. The reason is simply that semantic realism advocates the existence of “mind-independent” (Boghossian, 2006, p. 360) as well as language independent meaning facts or “meanings” (Boghossian, 2006, p. 360). Yet there is no analytically true sentence, according to Carnap, which has factual content. Sentences with factual content are contingently true and, therefore, synthetic. Furthermore, given that the a priori knowledge of a truth must entail that that truth is not factual truth, to hold that, for instance, logical principles are knowable a priori, is also to hold that they have no factual content. This then precludes realism (which incorporates both factualism and non- conventionalism) about, for instance, logical principles. This much has already been discussed.
I now argue further reasons why Boghossian’s realism is inconsistent with his endorsement of implicit definition as well as his endorsement of logic as a priori. I do so without assuming Carnap is correct.
Boghossian argues that it is possible to endorse both the a priori knowledge of logic as well as the implicit definition of logical terms, without succumbing to the conventionalism and non-factualism usually associated with endorsing implicit definition. He does this by making a moderate claim; that implicit definition of logical terms does not entail a further commitment to non-factualism and
conventionalism about meaning (Boghossian, 2006, p. 350). He does this, but does so explicitly stating his commitment to meaning realism (Boghossian, 2006, p. 331) whilst acknowledging that to defend meaning realism would require a very particular sort of justification; one which exceeds what arguments about the consistency or inconsistencies of “meaning constituting rules” or stipulations can secure (Boghossian, 2006, pp. 359 - 360).
In reading the following quote note that what Boghossian means by “meaningful” is that there are objective facts (in the case of logic there are “logical objects”) which determine the correct meaning of a statement (Boghossian, 2006, pp. 358, 359). “Meaning-constituting rules” are simply stipulations of meaning like implicit definitions for logical terms:
How might it turn out that a set of constitutive rules for a term t fails to determine a meaning for it? I can think of two ways. First, the meaning-constituting role specified for t may impose inconsistent demands on it, thus making it impossible for there to be a meaning that makes true all of its meaning-constituting
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sentences. A second worry might arise simply against the background of a robust propositionalism, without exploiting worries about inconsistency. For according to a robust propositionalism, meanings are radically mind-independent entities whose existence no amount of defining could ensure. Hence, there may well not be a meaning answering to all the demands placed upon a term by a set of stipulations […]
For both these reasons, then, we cannot immediately conclude from the fact that t is governed by a set of meaning-constituting rules, that t is meaningful. (Boghossian, 2006, pp. 359, 560)
The point being made by Boghossian is that whether or not all the stipulations for the use of a term are consistent with each other, or whether some are inconsistent with each other, does not prove that there either are or are not facts about the meaning of that term. He is, of course, completely right about this. Ontological claims need other sorts of justification – I think it should be empirical. So do Wright and Hale (I quote again):113
Let us call arrogant any stipulation of sentence, “#f” whose truth, such as the antecedent meaning of “#_”
and the syntactic type of “f”, cannot be justifiably be affirmed without collateral (a posteriori) epistemic work. (Hale and Wright, 2003, p. 14)
So, for Hale and Wright, when the truth is settled by stipulation, as is the case in implicit definitions, the truth cannot also be dependent on having to do further epistemic work – which would have to be the case when there are meaning facts weighing in on the truth and meaning of the supposed stipulation.
Boghossian acknowledges that a defence of realism about meaning constituting facts would require something else, “This full-blown justification can be had only by knowing the relevant facts about meaning” (Boghossian, 2006, p. 358).
Of course, where Boghossian makes this particular point he is mostly concerned with explicating the difference between “entitlement” and “justification” with the particular aim of telling his reader that no
“subject” (quoting Tyler Burge) needs to know the relevant facts in order to be entitled to believe in the elementary truths of logic (Boghossian, 2006, pp. 357, 358). So, speakers are “entitled” to believe in (but are not “justified” in believing) the elementary truths of logic despite not having access to the facts which support them.
I here argue that the correct use of logical terms indicates full comprehension of their meaning. We have no other available option to explain the understanding we have of logic. The implication of holding
113 I discuss Hale and Wright’s position about epistemic arrogance in Part 2, section 4.
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this position is that meaning does not ‘outrun’ use, but is fully explicated by correct use. And here
‘correct’ is simply following the rules (implicit or/and explicit rules).
The arguments to follow rely on this one point already made in Part 2, sections 3.2 and briefly reiterated in different terminology, directly above; Boghossian’s view is that whether there are conventions determining our use of terms or not, or whether conceptual role semantics is plausible or not, neither prove or disprove the existence of language-independent meaning facts. The question that remains to be answered is whether it is indeed possible for factualism to be theoretically consistent (which is Boghossian’s moderate claim) with holding that logic is a priori and that logical terms are defined implicitly.
Like Boghossian, following Tyler Burge (Boghossian, 2006, pp. 357, 358), I hold that it seems to be the case that “subjects” do not have comprehension of the purported ‘realist’ facts. Unlike Boghossian, following Tyler Burge, I argue that this means that if there are such meaning facts, they are evidently irrelevant to the comprehension of logical principles and our justification in using logic. My argument rests on the assumption that there are different sorts of truth; factual and logical. Accepting the non- factually true nature of logical principles is the only account we can give of our seeming full
comprehension of their meaning. Boghossian’s arguments do not accommodate the distinction between these two ways in which sentences might be true.
Hale maintains that Boghossian is “committed to the intelligibility of a thick (that is, more than mere deflationary) notion of truth” (Hale, 2006, p. 378). By this Hale means that Boghossian is committed to a notion of truth where the truth conditions are always ‘facts’. And by ‘facts’ Hale means, with
Boghossian, facts which obtain in the world. Hale, on the other hand, maintains that there are different sorts of truth. To make explicit this difference he distinguishes between ‘true’ and ‘correct’. ‘True’ he uses to signify substantial truth; the sort of truth based on language-independent facts. He also calls this
‘inflated truth’. And ‘correct’ is used to signify when a statement114 is only minimally true. What Hale means by ‘minimally true’ is that the statement is used consistently with a set of accepted linguistic rules with no additional requirements to correspond with ‘the world’.
Meanwhile, I shall reserve the term ‘true’ for whatever more substantial notion might be taken to in play, and employ ‘correct’ for the minimal sense. (Hale, 2006, p. 375)
114 I use ‘statement’ here instead of sentence, since this is Hale’s convention. I do not necessarily think the terms can be used interchangeably. And I am sure Hale does not either. He is evidently happy to speak about the truth of a ‘statement’ and the truth of a ‘sentence’, so I follow him in this regard.
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To be clear; sentences which are ‘correct’ are still true, but only minimally so. Hale introduces the true- correct distinction to emphasise this.115 Going with Hale’s terminology, to adopt ‘non-factualism’ about a statement or type of statement means that one takes that statement not to be capable of “truth” but just of “correctness” (Hale, 2006, pp. 377, 378). Other statements might be true in the inflated sense that Boghossian wants the principles of logic to be. Hale also uses the distinction between a ‘thick’ and a ‘thin’ notion of truth (Hale, 2006, p. 378). According to a thick notion of truth, when a sentence is
“true”, it is “substantially” true. Any sentence which is substantially true is “factual” (Hale, 2006, p. 378).
Hale explains that Boghossian is under the impression that a non-factualist is committed, in every situation, to be a non-factualist. In other words, that sentences are sometimes true in a minimal sense and at other times true in a factual or inflated or substantial sense is not plausible, according to Boghossian. Boghossian cannot see how such a distinction can be drawn. So, since “irrealism” (Hale, 2006, pp. 375 - 377)116 about meaning maintains that there is such a thing as minimal truth (i.e. truth which is dependent on conditions which are not part of the world; ‘conditions’ such as conventions) the irrealist is committed, according to Boghossian, to holding that their distinction between types of truth is also only minimally true.
Boghossian believes that the non-factualist has not merely to make room for a thick (or as he says
‘robust’) notion of truth, but that he must choose between that and a merely deflationary one.
Here Hale quotes Boghossian directly:
It is an assumption of the present paper that truth is univocal … We should not confuse the fact that it is now an open question whether truth is robust or deflationary for the claim that it can be both. There is no discernible plausibility in the suggestion that the concept of a correspondence between language and the world and the concept of a language-bound operator of semantic ascent might both be versions of the same idea. (Hale, 2006, p. 378)
What Boghossian means is that ‘truth’ cannot be explicated as both ‘correspondence to the world’
(factual) and ‘conventional agreement’ (non-factual). Hale goes on to say about Boghossian’s comment that “Clearly so crucial an assumption stands very much in need of supporting argument; surprisingly
115 I do not adopt Hale’s terminology elsewhere, for my own purposes, even though I agree with his conceptual distinction. Mostly I shall use Carnap’s terminology of factual-logical truth, which seems to me more accurate and more helpful. In the introduction and section 3, however, I give a detailed explanation of Wright’s notion of minimalism, which is the same as Hale’s. But, evidently, in principle I agree with Hale and Wright (and Carnap) about the fact that there are different ways in which sentences or propositions are true.
116 Hale uses “irrealism” to refer to a theoretical position endorsing conventionalism about truth and non- factualism about meaning.
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Boghossian provides none…” (Hale, 2006, p. 378). Hale disagrees with Boghossian; he says that the distinctions between types of truth are established by what he calls “metalinguistic attributions” (Hale, 2006, p. 378), in this case, of truth, falsity, correctness and incorrectness. And he argues that it is plausible to hold that such attributions are never true or false in themselves, even if other types of sentences are.
And so long as both notions are available, why can’t the non-factualist hold with perfect consistency, that metalinguistic attributions of truth, falsity, correctness and incorrectness are all alike, at most correct and never true? (Hale, 2006, p. 378)
This position is not dissimilar to the Carnapian idea that the rules for distinguishing between analytic and synthetic sentences are situated within a metalanguage but that the rules themselves are never factually true. In other words, there are no facts to substantiate these distinctions. We adopt metalanguages for pragmatically determined purposes.117 And so we also choose to adopt these metalinguistic attributions for particular reasons. While factualism, of the type that Boghossian would like to defend, might be necessary for certain types of sentences (in Hale’s, like in Carnap’s world, these would be empirical sentences) they are not necessary for the truth of, what Hale calls, metalinguistic distinctions, such as that between factual and logical truth. Nor, of course, are they required for the truth of logical principles themselves, according to Hale.
To see whether it is theoretically consistent to endorse implicit definition and to be a factualist about meaning let me look at exactly how implicit definition works when applied to a logical principle.
The following sentence is an example of a ‘sentence of logic’. It is the rule of implication in SD (derivational system of sentential logic):
A: “If P then Q implies not P or Q.”
What parts of sentence A is given meaning by the arbitrary stipulation of its truth? The arbitrary
stipulation of truth does not yield the meanings of the two variables, P and Q, in the case of sentence A.
By saying that ‘A’ expresses a true principle, we determine the meanings of the logical terms, ‘if’, ‘then’
‘implies’, ‘not, and ‘or’. Only the logical terms (or ‘constants’) of sentence ‘A’ can be implicitly defined.
117 In the case of adopting a metalanguage which distinguishes between analytic and synthetic sentences in the object language the reason, for Carnap, is to ensure that no sentences which have not been justified empirically are taken to be factually true. It was a metalinguistic distinction aimed at rejecting synthetic a priori propositions.
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Here are the two steps: 1. It is by stipulating the sentence to be a true logical principle that we
understand the meaning of ‘If …then’ in the first part of the implication: We understand that when (i.e.
‘if’) the variable, in this case P, is the case, that it also (i.e. ‘then’) has to be the case that the second variable being referred to, Q, also has to be the case. Assuming the entailment to be a true expression of the relationship between P and Q results in us knowing the meanings of ‘if’ and ‘then’. And, 2. We understand that Q has to be the case when P is the case, and that we understand that we cannot also have it that P is not the case and Q is the case. In this way the constants are meaningless if the sentence is not true, because this leads to inconsistent meanings of the logical terms. We, therefore, understand we cannot have both P not being the case and Q being the case, when it is the case that there is the following relationship between the two; P entailing Q. So given the truth of the principle, we understand what the constants mean.
This shows that assuming the truth of a sentence, that is accepting it is true because it is stipulated to be so, is a necessary condition for the implicit definition of its ingredient terms.
So a thinker who is party to a stipulative acceptance of a satisfactory implicit definition is in a position to recognise both that the sentences involved are true – precisely because stipulated to be so – and what they say. (Hale and Wright, 2003, p. 26).
But to assume the truth of any sentence without further appeal to empirical matters of facts seems to fly in the face of everything that one sensibly believes about truth; surely truth must have something to do with the world? Yet, the grounds for implicit definitions seem not to demand any such word- to- world connection. The way around this problem is to say that they are true in a different sort of what to what a word to world connection establishes. They are true relative to a language system or linguistic framework.118
Let us say that realists say there is consensus about meaning and then there is correct consensus. 119
‘Correct consensus’ needs facts which will determine whether the, mere, ‘consensus’ reached about some linguistic convention is correct. In other words, conventions need truth conditions for consensus to be correct. Correct consensus is consensus which has been reached because there is a
correspondence with language to the world, or the facts, which makes our linguistic conventions true. In
118 I argue further for this point in Part 2, section 4, where I look at the non-inferential a priori knowledge of linguistic conventions.
119 Recall, I use ‘realism’ to refer to a rejection of conventionalism about truth and an adoption of factualism about meaning. There is therefore two aspects to ‘realism’ in the present context. I do not use ‘realism’ and ‘factualism’
interchangeably – even though they mostly seem to form part of the same view about truth and meaning.
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fact, not seeking out a word-to-world connection for linguistic conventions is to allow a slide into “the incredible and self-defeating conclusion that, all language is meaningless” (Hale, 2006, p. 376).120 McDowell claims that consensus alone, without it being measured against objective standards of correctness (i.e. factual truth), leads to meaning skepticism.
A linguistic convention is a principle or norm which has been adopted by a person or linguistic community about how to use, and therefore what the meaning is, of a specific term. The worry, for realists, about standard conventionalism (i.e. non-factualist conventionalism) is that there are no standards of truth or falsity against which our conventions and stipulations can be measured.
Boghossian and other theorists endorsing meaning realism, such as McDowell (Hale, 2006, p. 376), take standard conventionalism to imply meaning skepticism. They hold that objective facts about meaning are a way to determine whether the convention adopted is correct and are not simply a product of agreement or consensus among a linguistic community.
Before I continue, here is an important clarification: ‘Correctness’ is used in two (rather confusing) ways in what follows. Hale uses ‘correctness’ to draw a distinction with ‘truth’. He means by ‘correctness’
what I have already explained above; a sentence is used correctly when it meets minimal standards of
‘truth’, such as being grammatically correct and consistent with further linguistic conventions belonging to the same linguistic framework. So, in Hale’s case, ‘correctness’ is used in support of irrealism (Hale, 2006). Wright uses ‘correctness’ in a nearly opposite way to Hale, but he says very much what Hale says in the end (according to Hale). Wright uses ‘correct’ to draw a distinction between ‘consensus’ and
‘correctness’. He uses ‘correctness’ to mean something like objective correctness, in line with what realism wants for both truth and meaning. In other words, a sentence is ‘correct’, according to Wright’s realist, when it is true by correspondence to the facts and its meaning is determined by objective (i.e.
language-independent) meaning facts, such as those postulated by Boghossian. This is contrasted, by Wright, with ‘consensus’ which means that truth is determined by stipulation and meaning is a function of such stipulations, as explained above. Truth here is minimal in an irrealist sense (Hale, 2006; Miller, 1998). I shall indicate where I use ‘correctness’ in what way, in what follows.
If we want to distinguish between when we simply have agreement which leads somehow to a stipulation of truth and when the truth is more than that, i.e. based on a true reflection of the world, then there must be something to show us that we have more than this. There must be some
120 Here Hale quotes McDowell, quoting Kripke.