Introduction
Boghossian (2006) argues that the constants of logical sentences are implicitly defined. However, though it is more usual for proponents of implicit definition to adopt a type of irrealism about meaning facts (Boghossian, 2006; Hale, B and Wright, C. 2003), Boghossian (2006) rejects both non-factualism and conventionalism. 98 He provides an account of analytic truth, which he believes renders it
compatible with Frege-analyticity, i.e. that analytic truth is logical truth, yet he argues that this position is consistent with realism about meaning. Furthermore, Boghossian argues, since realism about meaning facts for logical sentences is correct they are not factually contentless.
A quick reminder that the difference between an implicit and explicit definition is as follows: An explicit definition offers a definiens for a term which is equivalent in meaning (i.e. semantically equivalent) to the definiendum. Whereas an implicit definition establishes the meaning of a term, or definiendum, by placing constraints on how it can be used in a particular sentence.
My focus here is particularly on the meanings of logical constants. Examples of logical constants are, translated into natural language, terms such as ‘if’, ‘then, ‘therefore’, ‘and’ or ‘or’. For this I look at Boghossian’s (2006) account of the meaning of logical constants. I have already explained (Part 2, section 2) that, standardly, a term is implicitly defined when the sentence in which it occurs is
“arbitrarily” stipulated as true. “Arbitrarily” is taken to mean what most endorsers of implicit definition mean by it; truth is established, for all intents and purposes, only by saying that it is true (Boghossian, 2006, p. 348; Hale and Wright, 2003).
The above thesis of implicit definition is one which is consistent with conventionalism about truth and non-factualism about meaning. This is why it is considered to be standard; because
conventionalism and non-factualism are usually presupposed by defenders of implicit definition.
Boghossian here cites Wittgenstein and Carnap. It, therefore, seems fair to say that this is not exactly what Boghossian’s thesis about implicit definition is. At least, it should not be since his present arguments (2006) argue directly and explicitly against conventionalism and non-factualism. He does, however, not explicitly offer another thesis of implicit definition; one which would be consistent with
98 I take ‘irrealism’ to be a blanket term for these two theoretical positions.
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a ‘non-conventionalist’ position about truth and ‘factualist’ position about meaning. One which he would, consequently, endorse. And since it is the conventionalism and non-factualism of implicit definition which imports the ‘arbitrariness’ of the stipulation, one would expect Boghossian’s thesis of implicit definition to not contain the term ‘arbitrary’ since he argues against conventionalism and non-factualism.
How to continue then? What exactly does Boghossian mean by implicit definition? Because if the explicitly stated thesis of implicit definition above is, in fact, the one Boghossian follows then there is, of course, immediately an inconsistency in his overall position; he cannot argue for factualism and non-conventionalism and hold that the stipulation is arbitrary. However, if he means something else by ‘implicit definition’, something which does not include the concept of ‘arbitrary’, then this would at least stand a better chance of being consistent with the rest of what he argues. But would a thesis of ‘implicit definition’ which does not include ‘arbitrary’ even look like anything any other defender of implicit definition might recognise as such? Is there then even a coherent discussion to be had about implicit definition once ‘arbitrary’ is left out of the statement of its thesis?
I continue as follows: The standard view, according to Boghossian, is that terms which are defined implicitly are the constituent terms arbitrary stipulations. And he offers such a thesis of it (quoted above). Boghossian, however, wants to argue a very particular point:
What I dispute is that it follows from the fact that a given sentence Q is being used to implicitly define one of its ingredient terms, that Q is not a factual sentence, not a sentence that “tells us anything that is the case.” These two claims seem to me entirely independent of each other. (Boghossian, 2006, p. 350)
To me it seems clear that Boghossian is happy to endorse the above formulation of the thesis of implicit definition, including the use of the term ‘arbitrary’. His point is much more nuanced than out rightly rejecting the cardinal feature of arbitrariness from a definition of ‘implicit definition’. He is simply holding that even if it seems to us that there are no facts about logic, facts about what is the case about logic, and that we therefore seem to be arbitrarily stipulating the truth of logical principles, it does not “follow” that there are, in fact, no facts about logic. Furthermore, it does not follow, for Boghossian, that a seeming arbitrary stipulation settles the dispute about facts about logic. I, therefore, continue my arguments assuming that the above articulation of the thesis of implicit definition is indeed the one that Boghossian endorses; with the inclusion of arbitrariness in the workings of implicit definition.
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The standard view (i.e. the view endorsed by Carnap, and Hale and Wright) is that the implicit definition of terms presupposes that there are no “antecedent” (Hale and Wright, 2003), objective facts about the meanings of such terms. The meanings of implicitly defined terms are established entirely by their conventionally attributed truth. This means that the standard view of implicit definition presupposes ‘non-factualism’ and ‘conventionalism’ about meaning.
By logical non-factualism Boghossian means “the view that the sentences of logic that implicitly define the logical primitives do not express factual claims and, hence, are not capable of genuine truth or falsity.” (Boghossian, 2006, p. 348)
By logical conventionalism Boghossian means “the view that, although the sentences of logic are factual – although they can express truths – their truth values are not objective, but are, rather, determined by our conventions.” (Boghossian, 2006, p. 349)
Boghossian departs from this view; he rejects non-factualism and conventionalism about the meaning of implicitly defined logical constants. Being a proponent of implicit definition, he says, is consistent with holding that there are facts about meaning and that the meanings of the logical constants are established by these facts and, therefore, not by conventions. Rejecting non-factualism and conventionalism makes Boghossian a realist about meaning. We shall call the opposite view (i.e.
the standard view for endorsers of implicit definition) to Boghossian’s view, ‘irrealism’ about meaning, with Hale and Wright (2003). ‘Irrealism’ entails endorsing non-factualism and conventionalism about implicitly defined terms.
How does Boghossian’s realist view of implicit definition relate to his account of “analyticity”
(Boghossian, 2006)? He holds that the sentences of logic, in other words the sentences of logic which have implicitly defined logical constants, are analytically true. So, the arbitrarily stipulated truth, which he thinks such sentences have, is analytic. Analytic truth is therefore an integral part of an account of implicit definition in that it is a consequence of it; implicitly defined terms are parts of sentences which are analytically true. However, Boghossian’s realism about meaning entails that his particular account of
“analyticity” is also consistent with realism about meaning. This, we shall see, has implications for his account of analytic truth and is what makes it fundamentally different to Carnap’s.
The reason why Boghossian is unable to commit to the standard view of implicit definition is because he thinks that the presupposition of objective meaning facts is required for our warrant for the epistemic certainty we seem to have about elementary logical truths. Without such facts, we are not warranted in
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thinking logic is justified. But, since we seem to have knowledge (a priori) about conceptual or analytic truths, there must be facts to be known, says Boghossian.
On the assumption that our warrant for believing in elementary logical truths cannot be explained, the outstanding problem is to explain our a priori knowledge of conceptual truths [these being analytic truths]. For this purpose, the crucial semantical notion is that of Frege-analyticity. I have argued that this notion is bound to be in good standing for a meaning realist. (Boghossian, 2006, p. 358)(Square brackets and emphasis are mine, CR)
I argue that accepting factualism and rejecting conventionalism about the meanings of implicitly defined logical constants, as Boghossian does, is not only not required for the a priori knowledge of the relevant range of sentences, but that it actively undermines the idea that we can have a priori knowledge of the meanings of the terms of such sentences. This argument, of course, rests heavily on the explications and arguments which come before. If the content of knowledge is factual, then the knowledge cannot be a priori. To claim that it can be is to immediately endorse nothing other than the synthetic a priori.
My arguments run as follows: Since the implicit definition of a term is premised on the arbitrary stipulation of the truth of the sentence in which it occurs, holding that there must be facts which determine the truth of that sentence is inconsistent with endorsing implicit definition for its ingredient terms. That is because if the truth is determined by facts it cannot have been arbitrarily stipulated. In this regard I follow Hale and Wright:
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).
Boghossian rejects the idea that ‘speakers saying that a sentence is true’ can make it so. He explicitly commits himself to a notion of truth which requires for it to be determined by the way the world is. This causes some conflict between endorsing implicit definition, of the ‘arbitrarily stipulated to be true’ type, which has says he does, and implicit definition which, he claims, is consistent with realism about
meaning facts. I argue that there is no coherent manner in which both positions can be held.
My suggestion is that overlooking the crucial distinction between minimal truth (Hale, 2006), and the sort of ‘knowledge’ we have of such truths, and inflated or substantial truth (Hale, 2006) and the sort of knowledge we have such truths, is what results in the abovementioned confusion or incoherence.
Boghossian’s arguments against non-factualism and conventionalism do not take into account this
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distinction. This is evidently also the reason why he rejects the positivists’ notion of ‘truth generated by linguistic meaning’ (Boghossian, 2006).
Boghossian explains that the positivists, who were endorsers of implicit definition (he cites Wittgenstein and Carnap), but also conventionalism and non-factualism, held that necessary truth is generated by linguistic meaning. The positivists, he says, were wary of making claims which entailed commitments to
“language-independent” and “objective” truth conditions for necessities (necessary truths). They consequently reverted to what seemed a more conservative and perhaps more plausible or defensible account of necessity; that all necessary truth is linguistic necessity. This they achieved by making truth the product of linguistic conventions. The view that all necessity is linguistic necessity yielded by conventional decision making, for Boghossian, means that truth is “generated” by linguistic meaning.
Guided by the fear that objective, language-independent, necessary connections would be metaphysically odd, they attempted to show that all necessities could be understood to consist in linguistic necessities, in the shadows cast by conventional decisions concerning the meaning of words. Linguistic meaning, by itself, was supposed to generate necessary truth; a fortiori, linguistic meaning, by itself was supposed to generate truth (Boghossian, 2006, p. 336)
What Boghossian means by “objective, language-independent, necessary connections” are the sorts of connection between language (in this case the sentences which express logical principles) and the
“realist” meaning facts he takes to be required for the knowledge of logic (Boghossian, 2006). Such facts are “antecedent” (Hale and Wright, 2003) to language formation (or the formation of logic, in this case) and are the external standards of correctness or truth which our sentences must “track” (Hale, 2006;
Wright, 1987). We shall see that it is only when we presuppose that analytic sentences, in this case the sentences expressing logical principles, correspond to such facts that we can speak about having knowledge of them at all. Boghossian does not think the truth of logical principles is generated by convention. The truth of a sentence (or a ‘class of statements’), in the present discussion the sentences expressing logical principles, to him, is a matter of that sentence corresponding to parts of the world.
In general, I have no idea what would constitute a better answer to the question: What is responsible for generating the truth of a given class of statements? than something bland like ‘the world’ or ‘the facts’;
and, for reasons that I have just been outlining, I cannot see how a good answer might be framed in terms of meaning in particular. (Boghossian, 2006, p. 336)
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Given that the truth of a sentence, for Boghossian, is generated by “the world” or “the facts” and not by linguistic meaning when the truth of that sentence is conventional, he rejects the positivists’ account of analytic truth. A function of Boghossian’s view of truth being determined by facts is that analytic truth is determined by facts about meaning. It is exactly with this understanding of analytic truth where
Boghossian departs from, for instance, the Carnapian account of analytic truth.
Boghossian argues that without holding that there are “objective” facts of some kind to warrant our calling analytic sentences true there is no sensible way for us to speak about ‘knowledge’ of their truth.
Summarily, Boghossian holds these two positions regarding analytic truth: 1. He explicitly rejects a ‘truth by linguistic meaning’ of analytic truth when truth is conventional and, 2. He endorses an “epistemic account” of analytic truth (Boghossian, 2006, p. 332). The “metaphysical notion” is what he attributes to the positivists:
For I believe that an entirely distinct notion of analyticity underlies that explanation, a notion that is epistemic in character. And in contrast with the metaphysical notion, the epistemic notion can be defended. (Boghossian, 2006, p. 332)
What an epistemic account entails is that, for us to have knowledge of the meaning of analytic sentences, there must be some substantial ‘facts’ to have knowledge of. In adopting an epistemic account of analytic truth he therefore argues against non-factualism and conventionalism about analytic sentences. With the particular focus on the analytic status of logical principles and the meaning of logical terms he therefore takes himself to have argued for factualism about logic.
Firstly, I show that Boghossian’s account of the sentences expressing logical principles as analytically true, yet factual, means that his account of analytic truth renders such truths, in the case of logic, non- trivial. Furthermore, he argues that we know both the truth and meaning of such sentences a priori.
Boghossian has, consequently, argued in favour of the a priori knowledge of non-trivial truths. I then argue that such a position is untenable if we take analytic truths to be trivial truths and that only knowledge of trivial truths can be a priori.