Part 2, section 2 has served a more explicative purpose than argumentative purpose. It has given reasons, without yet considering in great detail why others might hold other views about these things, why implicit definitions are linguistic conventions. I did this by describing how implicit definition works, when contrasted to explicit definition. I have also given reasons, with Hale and Wright, why implicit definition fixes meaning without the need for further empirical work. Hale and Wright take this to be the case for implicit definition anywhere, but do narrow their focus at times on the definition of logical constants. I have posited theirs as the standard view of implicit definition. In Part 3, a non-standard view is considered (Boghossian, 2006). Gaps in the present arguments, in favour of the standard view, should be filled there.
72 Aside from evaluating a case (Boghossian, 2003) for the inferential a priori knowledge of logical laws in the next section, I shall also be evaluating a case (Boghossian, 2006) for the purported non-arbitrary nature of Implicit Definition in Part 3.
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Over this section and the next I do two things: (1) I reject three proposed epistemologies of linguistic conventions (sections 3) and, (2) I defend another (section 4). I have already proposed that all the arguments comprising in Part 2 will assume the standard account of implicit definition. Since they conventionally determine truth and fix meaning, they are consistent with irrealism about meaning. But irrealism presupposes a non-factualism about meaning facts. This renders the standard account of implicit definition, as linguistic conventions (i.e. working conventionally), consistent with Carnap’s conventionalism about truth and meaning. I have already shown that the Carnapian sense of linguistic conventions is non-factual (Bohnert, 1963).
The traditional connection is the conceptual connection between implicit definition and a priori knowledge (Hale and Wright, 2003). If so, then precisely what claim is being defended when defending the traditional connection?
Wright distinguishes between first-order and second-order claims (Wright, 2004, p. 158). First-order claims are claims such as ‘The law of the excluded middle is valid’ and second-order claims are claims such as ‘Knowledge that the validity of the law of the excluded middle is valid is a posteriori’. Wright holds that claims about the epistemological basis of the laws of logic are second-order claims. So an epistemological account of linguistic conventions would have to offer justification for a claim such as
‘Linguistic conventions are knowable a posteriori’ or ‘Linguistic conventions are knowable a priori’.
The question is how this result might get us what we want: a vindication of the claim that, as I expressed it in my opening paragraph, “[w]e know...that modus ponens, for instance, is a valid rule, and that this knowledge is as rock-solid as any we have”. The notable point is that the claim that has to be vindicated is second-order: it is not the claim that modus ponens is valid but the claim that we know that it is valid that has to be made good. (Wright, 2004, p. 158)
In what follows I marshal support from two distinct papers, one by Wright (Wright, 2004) and one by Hale and Wright (2003). I use some key concepts from these two papers to formulate the criteria against which I have measured the arguments (Boghossian, 2003; Millikan, 2006) which I herein engage. The first paper is Wright’s (2004) ‘Intuition, Entitlement and the Epistemology of Logical Laws’. From here I get the concept of ‘second-order claims’ as being epistemological claims. More to follow soon, but I
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have already indicated above what second-order claims are. And from Wright and Hale’s (2003),
‘Implicit Definition and The A Priori’, I get ‘epistemic arrogance’. Again, more to follow soon. For now, epistemic arrogance is when the truth and meaning of a sentence outruns the justification on offer. The traditional connection is what Hale and Wright (2003) think of as the relationship between a priori knowledge and implicit definition. Their claim about implicit definitions is that they are prime candidates for a priori knowledge. Their claim expressed explicitly looks like this: ‘Knowledge of implicit definitions is a priori (in particular non-inferential a priori).’ But this claim is also, conveniently, a second order claim, by Wright’s (2004) specifications. I combine some key concepts from these two papers in what follows in all the subsections of section 3.
The claim I shall be defending is: ‘Knowledge of linguistic conventions, such as the conventions fixing the meanings of logical constants, is non-inferential a priori’. Since it is implicit definitions which are chiefly the focus here the claim could also read, ‘Knowledge of linguistic conventions, such as the implicit definitions fixing the meanings of logical constants, is non-inferential a priori’. Either way, that the claim is about ‘knowledge’ is what makes it a second-order claim. The claim I defend is, by Wright’s criteria, a second-order claim, and is by Hale and Wright’s criteria, one which eludes epistemic arrogance, unlike some other second-order claims soon to be discussed (sections 3.1, 3.2, 3.3).
The three theories, discussed by me, about how we know linguistic conventions are those respectively proposing intuition (a priori apprehension), inferential a priori knowledge and a posteriori knowledge.
Part of a defence of the traditional connection73 is to offer reasons why the standard three epistemic accounts fail. In terms of second-order claims then, the first part of the defence of the traditional connection is to show that not one of the three epistemologies listed above succeed. They do not succeed in explaining how we know implicit definitions or any other linguistic conventions (by a standard ‘irrealist’ account of linguistic conventions). The second part of defending the traditional connection is to argue that linguistic conventions are knowable non-inferentially a priori.
In short, and as already alluded to, to defend the traditional connection is to persuade that implicit definitions meet certain conditions; these are that they do not refer nor that their meaning is dependent
73 I explain ‘the traditional connection’ in the introduction to the chapter. But it is quickly stated as the epistemic connection between implicit definitions and non-inferential a priori knowledge. So any other epistemology for implicit definitions (Hale and Wright) or linguistic conventions in general (I maintain) is to not uphold the traditional connection.
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on meaning facts. If they meet these two conditions we say that they are not “arrogant”. Those stipulations which assume, for instance, to establish references are called arrogant. The suggestion is that they must be constrained like this: If the sentence is a stipulation of truth then establishing its truth and meaning must not require any further epistemic work, other than the act of stipulation itself. It is for this reason that the qualification of “arrogance” only applies to “stipulations”.
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 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. That will be to have non-inferential a priori knowledge of the truth of the thoughts expressed.
(Hale and Wright, 2003, p. 26)
Mostly (i.e. sections 3.1, 3.2 and 4) my focus will be on the laws of logic and how they define logical constants. Wright refers to the laws of logic as the principles of logic. In his title (Wright, 2004) he uses
‘laws’, but in the content he mostly refers to ‘principles’. I take ‘principles’ and ‘laws’ to be doing exactly the same work within this discussion, so might use either. At times I shall refer to these laws as the axioms of logic – depending on whose view I am discussing and also what it is that I am saying exactly at that point. After all, it is not obvious to everyone that we are able to alight upon the axioms of logic and know that we have done so. It is this uncertainty which gives rise to present debate. The point is to caution that logical constants, the laws of logic (and, perhaps, the axioms of logic) are not used interchangeably below. They are taken to mean different things and I intend to use them accordingly.
For now, ‘constants’ are defined since they are terms. They cannot be true or false by themselves. But they can be part of true or false sentences. So the laws of logic, since they are expressed by sentences, are true or false. But it is how they are made ‘true’ which is at the heart of this discussion. This is the dispute between the conventionalists and, for instance, realists about logic. And how they are made true has a bearing on what meaning the constants might have. Logical ‘axioms’, if they are the laws of logic as we know them, are subject to the same discussions.
Where I address Millikan’s position about language (section 3.3) I do not investigate the laws of logic per se, since her account is a more generalised account of language and how meaning works. However, I
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take the same morals to apply to her account of meaning though. I address Millikan’s account because it seems to me a paradigmatic example of an a posteriorist account of meaning. Whether or not what she says she would regard as similarly applied to logic is not for me to assume, of course. What I do in section 3.3 is to show that it is not possible to account for much of the meaning our sentences (the ones she is interested in) have, by saying their truth and meaning are known a posteriori. I do not, however, level the complaint of epistemic arrogance against Millikan. I argue that her claims about how we know meaning leaves her ‘second-order claim’ unjustified.
Let’s say that the problem faced with landing on the right epistemology for linguistic conventions is to somehow land on the one which best explains our pre-theoretical commitments to knowing those conventions. So, if we have some, for want of a better word, ‘sense’ that logic is factual,74 and that we know the conventions of logic empirically then our attempts to forward an epistemology will perhaps be aimed to match this sense of ours. But whether or not this is the case, generally speaking, the proffering of epistemological theories should proceed in two ways: (1) forwarding a systematic theory explaining our warrant in thinking of our pre-theoretical instincts as constituting knowledge, and therefore showing willingness to advocate a rejection of those instincts if epistemically required (2) if required, isolating or tracking the objective and language-independent matters of fact upon which, in this case, the conventions of logic are based, and therefore showing willing to advocate a skepticism about that ontology if epistemically required.
Most good epistemological theories meet the first requirement. Very few meet the second. However, some epistemologies are not required to meet the second; to provide evidence of objective and language-independent matters of fact. This requirement is redundant when, for instance, the semantic theory in question explains how meaning is fixed in the absence of such matters fact. But all second- order claims (i.e. epistemological claims) paired with semantic theories which do postulate (overtly or covertly) the existence of objective and language-independent matters of fact must, on pain of being unsubstantiated, be supported by evidence of these matters of fact. And to merely advertise the theoretical benefit of there being such things does not do the work.
74 ‘Factual’ here means ‘not trivial’. See my general introduction as well as my introduction to Part 1 (i.e. Goethe and Marlowe conversation) for careful explanation of ‘factual’.
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