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factualist and conventionalist positions associated with a priori accounts of logic, associated with irrealist positions about logic.
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Note: to hold that there are no known facts determining the truth of logical principles is not to hold that there are no such facts at all. The conventionalist position entails no ontological position either way. Like most irrealist102 positions it presupposes that truth is epistemically constrained (particularly in the case where truth determines meaning); this means that when speakers do not have cognitive access to the relevant truth conditions then they cannot be said to play a role in the attribution of meaning (Wright, 1987). In the case where realists defend the “objectivity” of meaning, they are arguing that there are objective “facts” about meaning. Objective facts here simply means the sorts of “facts” which
Boghossian makes a case for (see sections 1 and 2, above); they are of “the world” and are not
“language dependent”. As already explained, they are “antecedent” (Hale and Wright, 2003) to language construction and are what we measure the truth of our sentences against. But when we have no
cognitive access to such objective facts about our sentences’ truth then it seems very difficult to tell how we are supposed to understand their meaning.
The purpose of a semantic theory is to explain how it is that terms and sentences obtain their meaning.
In order to explain how terms and sentences obtain their meaning, a semantic theory also needs to include an account of how it is that we grasp or know those meanings (Dummett, 2006, p. 15). In other words, semantic theories will always require a supporting epistemology. This is so because there is no way to explain how we know what a term or sentence means without explaining how or what it is that speaker’s grasp when they understand what a term and sentence means. This much is true, in principle, even for endorsers of a truth-conditional account of meaning. For instance, is what speakers grasp an obtaining fact (i.e. as in factualism) or simply a stipulation of meaning (i.e. as in conventionalism)?
If it is our wish to be able to offer a semantic theory without making any prior assumptions about the existence or non-existence of meaning facts then we must offer the required explanations of how meaning is fixed without presupposing the existence or non-existence of any facts about meaning (Dummett, 2006, pp. 14, 15).103
What then can be said about the meaning of logical terms and the analyticity of the sentences expressing logical principles without making ontological assumptions? Implicit definition is part of a
102 More about the relationship between irrealism and conventionalism in section 5 to come. In this section I shall look more closely at the semantic anti-realism espoused by Dummett and Wright. But ‘irrealism’ is the preferred term for now because it is used by Hale in his critique of Boghossian and others.
103 It is, of course, not possible that any theory, without empirical support settles the question about the existence of anything. So, not even the prior holding of a very plausible semantic theory, postulating the need for the existence of meaning facts, will settle whether there are indeed such facts. The relationship between semantic theories and metaphysical theories can at best be something like theoretical consistency or inconsistency.
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semantic theory because it offers an explanation of how certain terms obtain their meaning. Implicit definition holds that the truth of logical principles is arbitrarily stipulated. Boghossian concurs and also holds that “the facts” make a sentence true. It is also therefore such facts which bear on what a sentence means.
Until now I have used ‘fact’ as used by Boghossian. So, I have used ‘fact’ in sections 1 and 2 to indicate Boghossian’s use of “the facts” to be something like “the world”. Since Boghossian has made it clear that the truth conditions for any sentence cannot be determined by the sentence or language to which the sentence belongs (i.e. the thesis of conventionalism) “facts” is something outside of language; language- independent.
I am happy to continue using fact in this manner since it will make engagement with Boghossian easier, but I think the following should be pointed out: Dummett considers the question about what ‘facts’ are.
He first offers metaphysical considerations of what a fact might be.104 Metaphysical considerations form part of a description of ‘facts’ and might also imply something about their ontological status. Dummett decides that there is not much use in offering a metaphysical account of facts. There simply is no way of telling what a ‘fact’ is without further specifications of the use of the term, and we evidently use the term in different ways. He reminds us of the two ways in which we speak about ‘facts’; facts obtain or facts are expressed. Depending on how the term is used in a sentence this would indicate a very different sort of entity corresponding to ‘fact’. If ‘facts’ obtain then, if they exist, they are part of ‘the world’ in Boghossian’s sense. If they are expressed or stated then they are probably more in line with what Wittgenstein, in a constructivist mood, meant when he said “The world is probably the totality of facts, not of things” (Dummett, 2006, p. 3). Then a fact which is expressed is taken to be something like a true claim. A fact which obtains is part of “the world” and is presumably not dependent on us for its existence (unless otherwise, by some radical idealism or constructivism). Boghossian uses the term indicating mind-independent existence.
When ‘meaning is use’ (i.e. linguistic use) this indicates to Dummett (2006, pp. 14 - 28) that to first settle the metaphysical question and then the semantic one is misguided. Whether or not we gain any ground in deciding whether there are things such as facts and what they are will depend on what it is that we are looking for. If meaning facts obtain then we look to ‘the world’ for them, as in the case of
104 His strategy of first considering the metaphysical question of what facts are is to illustrate how, in the end, we cannot settle this issue until we decide what we are going to take ‘fact’ to mean. So it is part of his defence for why semantic considerations precede metaphysical ones. This should be clearer as I continue in this section.
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Boghossian; if they are stated or expressed then we obviously have no hope to find them in the same place as a fact which obtains. Semantic theories therefore precede metaphysical theories.
Our metaphysics is therefore determined by our semantic theory. In any semantic theory, linguistic items of some particular kind will be treated by the theory as its basic units. These will necessarily be types of sentences, whether of a natural language or of such a language regimented by having its sentences put into a standardized form suitable for logical manipulation […] Sentences, for the purposes of any basic given semantic theory, will be whatever that theory selects as its basic units. (Dummett, 2006, p. 15)
The ‘non-factualism’ which Carnap adopts when being a proponent of implicit definition involves an explanation for how it is possible that we seem to understand the meanings of many sentences even though there are no known ‘facts’ to correspond to these. It is this problem for semantic theory, that there sometimes are terms and sentences which have meaning despite not having any known truth conditions in “the world” which leads Frege to distinguish between the sense and reference of a term.105 Carnap also identifies this problem for semantics, hence delineating intensional from extensional contexts for determining meaning.106 The difference, of course, between Frege’s sense-reference distinction and Carnap’s intension-extension distinction is that Frege holds that senses are objectively real, whereas Carnap holds that intensions are a function of conventional or constructed linguistic frameworks. In other words, they are language dependent and certainly not objective if ‘objective’ is what Frege says it is.
Both Frege and Carnap’s semantic distinctions result from the inadequacy of truth-conditional accounts of meaning when truth conditions run into the following two problems: 1. When truth is cashed out in terms of correspondence to the world despite our having no cognitive access to the relevant truth conditions. And, 2. When two terms mean distinct things despite having the same truth conditions (or referents in “the world”). So, when there are no known truth conditions to fix meaning, as in (1), or when it is obviously something other than the truth conditions which fix the meanings, as in (2), the standard view of the truth-conditional account of meaning fails. Contrary to what Boghossian argues, examples of such cases are the sentences which express logical principles; (1) there are no known objective or language-independent facts about logic, and (2) since, for instance, there are many
different types of logic proposing different rules for entailment there are many different uses for ‘entail’.
A semantic theory should be able to give an account of such sentences.
105 See Part 1, sections 2.1, 2.2, 2.3 for a discussion of sense and reference.
106 See Part 1, section 3.4 for a discussion of intension and extension
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The problem for factualists about meaning is that they are required, like everyone else, to give an epistemology to support their factualism. In the case of the sentences expressing logical principles the factualist is therefore required to give evidence of the facts which are available to speakers (in this case the users of logic) to enable them to know the truth and meaning of the sentences expressing those principles. The implications of not being able to do so, is that factualists about meaning fail to give a working semantic theory for the relevant sentences.
To hold that a class of statements may be fully intelligible to us although resolving their truth-values may defeat our cognitive powers (even when idealized) may naturally be described as believing in the objectivity of truth. (Wright in Miller, 1998, p. 290)
The meaning of a statement is a real constraint, to which we are bound, as it were, by contract, and to which verdicts about its truth-value may objectively conform, quite independently of our considered opinion on the matter. (Wright in Miller, 1998, p. 290)
The objectivity of meaning is a manifest implication of the objectivity of truth. If statements of certain sorts can be undetectably true, then we have no alternative but to think of their meanings as, so to speak, reaching into regions where we cannot follow: there is already a verdict about the truth-value of such a statement which – if it is intelligible to suppose that our cognitive powers could be appropriately extended – our present understanding of its constituents and syntax would oblige us to give once we had investigated matters properly. (Wright in Miller, 1998, p. 291)
The positive programme of this thesis issues as a case for adopting conventionalism about the meaning of logical principles and all other types of analytic sentences, where standard truth-conditional accounts of meaning clearly have no role to play. To be a conventionalist about the meaning of logical principles is to say that the sentences which express them are true by virtue of linguistic conventions which we have adopted for pragmatic reasons and not for reasons which depend on the way “the world” is. Put another way; to be a conventionalist about any statement or sentence is to say that its truth and meaning is known without the need further empirical investigation.
But the question is how to elicit a respectable notion of convention […] The obvious proposal is simply that the connection between the occurrence of a particular ostensively explained type of state of affairs and a particular statement, S, is one of conventional support if and only if we would consider it acceptable in certain circumstances to assert S on the basis of knowledge of such a state of affairs; and we would not require, in order for someone to be credited with a full understanding both of S and what type of state of affairs had been ostensively explained, that he knows what it would be empirically to investigate whether
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occurrences of that type of state of affairs really did provide reason for believing S and to find that they did not. (Wright, 1987, p. 252)
Boghossian, however, would be the first to claim that he is not suggesting that factualism about logic demands empirical substantiation - he does, after all, endorse the a priori knowledge of the analytical truth of logical principles. So here perhaps it is not so easy to attribute a failed semantic account to him.
He does, after all, say that we know the ‘truth conditions’ for the sentences of logic a priori. So, has his epistemology failed and has, therefore, his semantics failed? Yes, they have.
Boghossian’s position amounts to the endorsement of non-trivial truths being knowable a priori. I think he would be happy to concede this point. He evidently does not think the sentences expressing logical principles, which he takes to be analytic, are not factual – he has argued for factualism about logic. This means that Boghossian offers us a view of “Analyticity” which renders it non-trivial. By Carnap’s
account107 analytic truth, what it means to be an analytic sentence is, partially, informed by that sentence being non-factual. Consequently, by Carnap’s account of what it means to be an analytic sentence, Boghossian’s implicitly defined logical principles are not analytic.
Since Carnap’s account of analytic truth is the one I endorse, I maintain that Boghossian has made logical principles synthetic. And, since he makes a case for logic being a priori, the upshot of his arguments is that logic, on the whole, is synthetic a priori. This is not a position Boghossian has argued for, but it is entailed by his arguments against conventionalism and non-factualism about logic.
I have not here offered an argument against the synthetic a priori (although I have already taken myself to have made some arguments for this in previous sections). So, my claim against Boghossian might only hold sway for those already convinced, like me, that non-trivial truths must be justified empirically or a posteriori. For now, Boghossian is certainly endorsing logical principles as analytic and as non-trivial. He is certainly also endorsing them as a priori. We leave it at that for now.
More to the point is that whether “the facts” are, in principle, knowable a priori or not; in actuality they seem to be beyond our cognitive ‘reach’ either a priori or empirically. This means that they cannot support a semantic theory about how it is that we actually do understand the sentences expressing logical principles.
107 As shown in Part 1, sections 3.
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But the classical truth-conditional conception of meaning breaks faith with this thought wherever it construes the kind of state of affairs that would render a particular statement true as something that can impinge only indirectly, or in part, on the faculties of one who understands the statement. (Hale, 2006, p.
276)
The solution for conventionalists is to be non-factualists about analytic sentences when providing a semantic theory requires them to be – not because they know there are no facts about meaning which might settle the truth of analytic sentences. To be a ‘non-factualist’ in such a case is therefore not to assume the non-existence of the truth conditions for, for example, the sentences of logic. To be a non- factualist about logical principles is to hold that somehow these sentences must have meaning despite there being no knowledge of the sorts of facts of the matter which usually act as truth conditions for sentences.
Here is the correct construal of conventionalism about logical principles: 1. Conventionalism is non- factualist because it denies that it is possible to give a semantic account of analytic sentences when truth conditions are supposed to fix meaning, but where they are not known and therefore cannot reasonably be thought to do so. So, let us call the ‘ontological’ attitude here, ontological agnosticism about meaning facts. There might yet be such meaning facts, and if there are, their existence is evidently irrelevant to the meaning of the actual sentences in question. Conventionalism is therefore, not a metaphysical position at all. It is at best a semantic and epistemological position.
2. Even though the purported inconsistency between conventionalism and non-factualism is not of primary concern to Boghossian, I argue that it is his view of truth (as only one sort of thing) which leads him to see this purported inconsistency, but has further, far more important, implications for his overall arguments. Thus I argue as follows: the truth which conventionalism attributes to analytic sentences and, specifically, logical sentences can therefore not be of the factual kind and Boghossian need not worry, therefore, that conventionalism and non-factualism seem to be at odds with each other. Given that conventionalism proposes that logical principles are true and that their truth is conventionally, and not factually, determined, conventionalists must mean something different when speaking about ‘truth’.
They cannot mean what Boghossian means. And, indeed, they do not. They mean what Carnap means by logical truth; that it is trivial and a product of a constructed language system. There is therefore no chance of meaning determining the world. Boghossian does not take into account the distinctions
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between different types of truth (Hale, 2006)108 when he, 1. flags up the purported inconsistency with being a conventionalist and non-factualist and when he, 2. deems the positivists’ account of truth by virtue of linguistic meaning indefensible because it supposedly suggests that in attributing the meaning of a sentence it is made true (about the world).
The distributive laws of logic tell us that P ᴧ (Q V R) is logically equivalent to (P ᴧ Q) V (P ᴧ R) (Barwise and Etchemendy, 1993, p. 82). There are no known meaning facts of the type Boghossian hopes for which can justify logical principles in the way Boghossian claims they do. The only facts known here are
‘facts’ (for want of a better word) established by convention. The difference between these two types of facts (‘facts’ by convention and ‘facts’ by the world) is related to the difference between two types of truth; the distinction between ‘logical’ and ‘factual’ truth. When a truth has no factual content Carnap means that it says nothing informative about “the world”. And by this he means the extra-linguistic and language independent world.
Therefore, using some of Tarski’s results, I defined L-truth in semantics as an explication of the familiar concept of logical truth and related concepts such as L-implication and L-equivalence. In this way, the distinction between logical and factual truth, which had always been regarded in discussion in the Vienna Circle as important and fundamental, was at last vindicated....Our solution based on Wittgenstein’s conception, consisted in asserting the thesis of empiricism only for factual truth. By contrast the truths in logic and mathematics are not in need of confirmation by observation, because they do not state anything about the world of facts. (Carnap, 1963, p. 64)
Had Boghossian’s arguments proceeded in conjunction with making the required accession to the positivists’ distinction between logical and factual truth, he would not have had the grounds for arguing that ‘truth by virtue of linguistic meaning’ is indefensible. Nor would he necessarily have seen the need to revert to factualism for analytic sentences in order to warrant our knowledge thereof. A priori knowledge is perfectly positioned, we have seen in the previous chapter, for explaining our knowledge of non-factual truths. Logical truth not only not require ‘the facts’ when they are part of ‘the world’, the claim is a stronger one: for a sentence to be logically true it must be true without assistance from facts which are part of the ‘the world’, whether there happen to be such facts or not.
108 Hale distinguishes between ‘minimal truth’ and ‘substantial truth’. Carnap would have used the terms ‘factual truth’ and ‘logical/trivial truth’.