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My particular aims are to offer, in the first sections of Part 2, a background to the concept of a priori and, in the later sections, to argumentatively engage some current epistemological theories. There I argue in favour of the non-inferential a priori knowledge of linguistic conventions of a particular type. In the meantime, I use the Hume-Mill distinction about a priori knowledge as a device for explaining the more sophisticated explications and arguments to follow. My citing of Mill and Hume serves only as a background positioning of some important concepts to aid my more argumentative engagement with current epistemological theories (sections 3.1, 3.2, 3.3). Where it sounds as if I am suggesting that Hume and Mill were in some sort of actual conversation with each other, this is only done for discursive reasons. I am fully aware that they were not; Hume was working in the last half of the 18th century and Mill in the last half of the 19th century. I am simply posing their positions about a priori knowledge against each other. For future explanatory efficacy I would like to be able to say a position is ‘Humean’
or ‘Millian’ in one way or another, and know that my reader benefits, as I do, from the broad principles abstracted from Hume and Mill’s theories about knowledge.
Hume distinguishes between a posteriori and a priori knowledge,40 and does not, despite being deemed an empiricist, reject the possibility of having a priori knowledge of some truths. The Humean distinction runs as follows: A priori and a posteriori justification are distinct methods of justification and they respectively are either able to justify ‘relations of ideas’ or ‘relations of matters of fact’ (in Hume’s lexicon). When a truth has been ‘justified’ in one or the other manner we say that we have that type of
‘knowledge’ of it; so a posteriori justification yields a posteriori knowledge. Relations of ideas are eventually, from Kant onwards, referred to as ‘analytic’ truths and relations of matters of fact are referred to as ‘synthetic’.41 If Hume’s epistemological distinction is correct it has one relevant, to my immediate project, implication: The a priori justification of a truth means that that truth is trivial. Only trivial truths are justified a priori.42
Part of Hume’s campaign in favour of the conceptual marriage between a priori knowledge and
‘relations of ideas’ is his view on necessity. Hume rejects the possibility of knowing necessary truths from experience (i.e. a posteriori). There is no amount of empirical or observational evidence in support
40 Hume speaks of ‘empirical knowledge’, of course. But, since a posteriori and empirical are less sensitive to issues of location (i.e. theorist location) than the semantic terminology, I have decided to introduce more current terminology at this stage, so that we do not form any unwanted attachment, which will then have to be forgone soon, anyway.
41 Kant, we have seen in Part 1, uses ‘judgment’ instead of ‘truth’.
42 One implication if this is correct, of course, will be that synthetic a priori truths are rejected. And following from this any account of analytic truth which makes it factual (Boghossian, 2006) is wrong.
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of a truth which can yield a necessary truth – one that can be no other way. This for Hume is at the heart of the distinction between induction and deduction. Good induction always only gives high probability;
and always empirical probability. Deduction gives necessity, but because necessity cannot be gained from experience, such necessities must be essentially different to other sorts of truths. Necessity is qualitatively different from even very high degrees of empirical confirmation. Making necessary truths a priori and ‘relations of ideas’ is one way of ensuring that confusions about this don’t arise.
As Hume conclusively showed, no general proposition whose validity is subject to the test of actual experience can ever be logically certain. No matter how often it is verified in practice, there still remains the [logical] possibility that it will be confuted on some future occasion. The fact that a law has been substantiated in the n-1 cases affords no logical guarantee that it will be substantiated in the nth case also, no matter how large we take n to be. And this means that no general proposition referring to a matter of fact can ever be shown to be necessarily and universally true. It can at best be a probable hypothesis. (Miller, 1998, p. 93)
It follows from Hume’s particular account of necessities as being only relations of ideas that he rejects metaphysical necessities, i.e. any part of the world which could not be otherwise. The only necessities there are, are logical.
Mill, on the other hand, even though in agreement with Hume about necessity not being a function of empirical confirmation, reaches a different conclusion. Mill rejects necessity altogether since he rejects a priori knowledge. All knowledge is a posteriori and so, for Mill, even mathematical truths are a posteriori and revisable. Mill opens his essay, ‘Of Demonstration and Necessary Truth’ (Mill, 1969) by posing a conditional, suggesting that if all demonstrative sciences is science by induction then we can have no certainty of the type advocated by making some sciences “Exact Sciences” (Mill, 1969, p. 18). By exact sciences Mill means mathematics and logic. He then goes on to affirm the antecedent of his conditional; that the basis of all sciences is induction and, therefore, there is no exact science – there is no deductive certainty. To endorse Mill’s position about knowledge is to reject that there is any
knowledge which is not gained from the senses and, furthermore, to hold that there are therefore no truths which are not revisable on account of empirical information.
…it is customary to say that the points, lines, circles and squares which are the subject of geometry, exist in our conceptions merely, and are parts of our minds; which minds, by working on their own materials, construct an a priori science, the evidence of which is purely mental, and has nothing whatever to do with
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outward experience. By howsoever high authority this doctrine may have been sanctioned, it appears to me psychologically incorrect. (Mill, 1969, p. 19)
Very crudely my defence of a priori knowledge is based on Hume’s epistemological distinction; that all facts are known empirically and that all knowledge which has not been derived empirically is knowledge of conceptual truths only. Conceptual truths are taken to be non-factual in the sense explained in the main introduction and again in the introduction to Part 1. There are, however, more recent and much more sophisticated accounts of Hume’s distinction between a priori and a posteriori knowledge and what is known in either way. I draw from these more recent accounts43 in various sections in Part 2, but it seems to me that the overarching principle remains the same: If the two paths which empiricist philosophers can follow are either that of Mill (i.e. an outright rejection of a priori knowledge) or Hume (i.e. a very singular category of truths can and must be known a priori), then what follows is an
endorsement of Hume.
I shan’t consign any part of this thesis to the very interesting view that mathematics is a posteriori. I do, however, consider in some detail the apriority of logic insofar as it is supposed to be analytic
(Boghossian, 2006; Wright, 2004; Hale and Wright, 2003). I also look in section 3.3 at Millikan’s (1984;
2006) defence of linguistic conventions as a posteriori. If Mill were right this would have many
implications for a project such as this one, since this project excludes the possibility of logical truth being knowable a posteriori. If Mill were to be followed on all accounts of knowledge it would mean that even linguistic conventions are a posteriori. Millikan (1984; 2006) propounds such a view of language.44 I argue against Millikan’s view in section 3.3; that a posteriorist views of linguistic conventions fail to forward a plausible semantic theory for how many of our linguistic conventions are, in reality, understood.
43 Hale and Wright (2003)
44 I could have chosen to use any of a range of naturalistic (a posteriorist) philosophers for the purposes of this section. It could have been, for instance, Quine himself, Dretske, Papineau or Dennett. I was keen to keep my choice contemporary and, therefore, in line with the more current or contemporary choice of theorists investigated in Parts 2 and 3. Dennett would have been an excellent choice in terms of making even easier allegations of the synthetic a priori against him. I don’t know much about Dretske. And I did not investigate Papineau in this regard, because I found Millikan before I could. I believe I have chosen, in Millikan, a strong opponent. This is important for obvious reasons. I think of her as strong because her naturalised semantic theory is, in my view, very well worked out and conveniently detailed. But also, her commitment to being a posteriori in her methods is admirably pursued. Even though, in the end, it is not achieved. This, needless to say, will be my accusation. But my thoughts are that if Millikan can stand accused, then no other proponent of a naturalised semantics, whom I know of – but I have not read widely or deeply in this area – will escape the accusation of the synthetic a priori easily.
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Whether to be Millian or Humean about a disputed set of sentences (e.g. mathematical, logical or definitional) and the ‘propositions’ they express is sometimes a function of whether one takes them to be necessities or not. So, one of the ways in which a theorist might argue in favour of either a priori or a posteriori justification of the disputed set is to argue in favour of a particular modal status of such propositions. A Millian empiricist might argue that logical entailments are not necessary and, therefore, must be justified a posteriori. And a Humean empiricists might argue that logical entailments are necessary and therefore cannot be knowable a posteriori. Such accounts prioritise the semantic status and make the epistemic status a function thereof. However, sometimes arguments about these matters run the other way round; such as, if a sentence is justified and knowable a priori then its truth must be analytic and necessary (logically necessary). I assume the priority of the epistemic status – following Frege (Part 1, section 2) and Carnap (Part 1, section 3.2) in this regard. But the arguments, irrespective of which direction they run in, usually have, in one way or another, to do with the modal status of the propositions in question; it either presupposes it or entails it.
We should, however, be cautioned that a position which advocates that some necessities can be known a posteriori is as departed from the Humean position as a position which holds that it is possible to know propositions about ‘relations of matters of fact’ a priori (i.e. the synthetic a priori). Miller lays out the options for propositions expressing logical and mathematical truths like this:
…there appear to be three choices available: (1) secure factual significance for the statements of logic and mathematics by denying that they are necessarily true; (2) argue that they are analytic; or (3) reject them as literally senseless, as failing to have literal significance. (Miller, 1998, p. 93)
Mill, according to Miller, famously argued for option (1). Theorists such as Wittgenstein and Carnap argued for (2). I am not concerned, in this thesis, with theorists who have opted for the third possibility.
Miller (1998, p. 94) explains that “Mill’s view that the statements of logic and mathematics are a posteriori is widely rejected”. Whether Miller is rightabout Mill’s view being widely rejected or not I leave as a topic of investigation for another project. But there seem to be philosophical positions which do not fall neatly into either options (1) or (2); we soon look briefly at Kripke. In the meantime, Miller is right about this: If Hume is right, then there are only the three abovementioned mentioned options for mathematical and logical propositions. In other words, those who take Hume to be right in terms of his epistemic-semantic distinctions, must also maintain that, for instance, logical entailments are either contingent and a posteriori, or logically necessary, without factual content, and a priori. And it would,
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therefore, be deeply inconsistent to be explicitly committed to Hume’s ‘dogma’ (à la Quine) but endorse any other sort of combination of modal status and mode of knowing.
Kripke, of course, famously argued for the uncoupling of necessity from a priori knowledge. Kripke (1972, p. 34) warns against the often confused usage of ‘can’ and ‘must’ in discussions about the relationships between semantic and epistemic concepts. He says that philosophers do not take to heart the significant distinction between, for instance, holding that a truth must be justified a priori and can be justified a priori. These two terms are respectively responsible for two completely different claims. I concur. Kripke argues that they import a distinct modality to each of, for instance, the following claims
‘X can be known a priori’ and ‘X must be known Y’.
I will say that some philosophers somehow change the modality in this characterization from can to must.
They think that if something belongs to the realm of a priori knowledge, that it couldn’t possibly be known empirically. This is just a mistake. Something may belong in the realm of such statements that can be known a priori but still may be known by particular people on the basis of experience. (Kripke, 1972, p.
35)
Kripke explains that to say that all conceptual truths must be justified and known a priori is to say that there is no other way of justifying and knowing conceptual truths. Such a view has particular
implications for what we think conceptual truths are, of course. However, he says, to say that all conceptual truths can be justified and known a priori is, of course, to say that they might also be known another way. And this, again, is to say something towards the explication of ‘conceptual truth’. In section 1, to follow, I discuss Kripke in a little more detail. When I do so it should, however, still be borne in mind with what purpose I have included a mention of Kripke
Despite Kripke’s cautioning, and advocating of ‘can’ rather than ‘must’, I shall argue throughout this project that ‘relations of matters of fact must be justified a posteriori’ and that ‘relations of ideas’ must be justified a priori’. The purpose of my thesis is to argue for the necessary relationship between ‘a priori’ and ‘conceptual (or analytic)’. However, this necessity is itself a conceptual necessity – as all necessities are. As already stated, the conclusions I draw from the arguments in this thesis are not factual claims. They are metalinguistic tools for the organisation of our knowledge about certain things. I believe there might be other ways of organising our thoughts about a priori and a posteriori knowledge as well as different types of truth. I argue, however, that the Humean distinctions, as further refined by Carnap and some others, is a good (and, to my mind, the best) way to do so, and I give my reasons. So,
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when I say ‘must’ and it seems to signify some sort of unpalatable modal necessity as it does to Kripke, the unpalatability is based on a mistaken view of the spirit in which I have engaged in this project. The modal implication of my arguments, a necessity no doubt, is a trivial necessity. It is a necessity relative to the language system, which has been here defended in a, hopefully, concise but informal manner. But to use ‘can’ would be to lose what is at the heart of all three parts: a claim about a conceptually
necessary relationship between ‘a priori’ and ‘analytic’. This I cannot forego. Nor must I.
We now take leave of Hume’s ‘relations of matters of fact’ and ‘relations of ideas’ and we revert back to our already established terminology of ‘synthetic’ and ‘analytic’ and, even more descriptive, ‘non-trivial’
and ‘trivial’.
Part 2 is an investigation of how linguistic conventions are justified and known. Or rather, I look at what it is that we can legitimately take ourselves to know, when our knowledge is a priori. The aim is to argue for two related conclusions: 1. That if a statement or claim is justified without reference to empirical matters of fact then it should be regarded as a non-referring definition, or ‘linguistic convention’. 2. That such linguistic conventions are to be regarded as trivial truths, in the Carnapian sense of ‘trivial’. Even though much of the work for these two related conclusions will be executed in this part, its yields will extend to the arguments I make in Part 3. In Part 3 I argue that the a priori justification, and therefore knowledge, of logical laws must mean that the sentences expressing logical laws are analytic. But that
‘analytic’ must be ‘analytic’ as advocated in Part 1.
A linguistic convention is a principle or norm that has been adopted by a person or linguistic community about how to use, and therefore what the meaning is of, a specific term. To study ‘linguistic
conventions’, in this discourse, is not to study the genealogy of words (or/and sentences) like “Cross from port to starboard” – which perhaps appear as stark examples of ‘conventions’ in language, in this particular case, sailing language. It is not a study of the cultural and social use of terms and how they have become entrenched in our or other’s linguistic behaviour. To investigate linguistic conventions, as done within the ambit of this discourse, is to investigate the metatheoretical positions about how meaning and truth are related to each other and what knowledge has to do with all of this (Dummett, 2006; Wright and Hale, 2003). ‘Convention’, in the latter sense, is used in a more technical sense; to indicate something that works like a definition. The debate is then about what definitions are exactly, and whether or not there is a factual basis for the meanings of our words. An example of a linguistic convention, when it is an implicit definition, is “Let’s call the perpetrator of these ghastly crimes, ‘Jack
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the Ripper’” or ‘The perpetrator of these ghastly crimes is Jack the Ripper’ (Hale and Wright, 2003, p.
6).45
A more exact explication of linguistic conventions is in section 2 and then I engage argumentatively in sections 3 and 4. For now, bear with a more superficial introduction; linguistic conventions, by the standard conventionalist account of them, define terms irrespective of what the world or facts are like.
In other words, whether or not there is one murderer who committed all those crimes, whether or not they are a man or woman, the crimes were committed by some wild animal or strange natural disaster, it is still possible to, meaningfully, use the phrase, ‘Jack the Ripper’. The above convention is, let us say, a suggestion as to how we shall use ‘Jack the Ripper’. If we take seriously this suggestion, or adopt this convention, then it means that there are wrong ways of using the phrase. Such as; we cannot say, in the context of discussing the serial murders of women committed over a particular period of Victorian London, “Jack the Ripper, the foremost inspector from Scotland Yard, will soon discover who committed those heinous crimes”. This would be to use the phrase inconsistently. The nub of what is at stake in our ensuing arguments, however, is that some theorists hold that linguistic conventions work despite settling on a referent or assuming any sort of prior knowledge of what meaning such a phrase should have (Hale and Wright, 2003).
The linguistic conventions we shall consider over this part are, in sections 3.1 and 3.2, the laws of logic.
There I talk about laws such as Modus Ponens. It is considered to be a linguistic convention because it determines the truth and fixes the meaning of one or other of its ingredient terms, i.e. the definiendum at the time, without an appeal to any justificationary work (e.g. empirical verification or logical
deduction), aside from the act of stipulation. In section 3.3 I consider more general linguistic
conventions, such as sentences which implicitly define some term, e.g. ‘implicatures’ in a sentence such as “Consider, then, tokens that are used in nonconventional ways, for example, fresh figures of speech or fresh Gricean implicatures” (Millikan, 2006). Either way, a generalised principle for linguistic
conventions could be stated like this, taking ‘f’ to be the definiendum in question: “Let “f” have whatever meaning it would need to have in order that “#f” be true” (Hale and Wright, 2003, p. 6). But the definiendum can be used whether or not the world ‘cooperates’ to make the sentence in which it occurs true. So ‘worldly’ truth is not what is at stake in the truth of linguistic conventions – this is not the
45 Hale and Wright use this as an example of an implicit definition. But they regard implicit definitions as paradigmatic examples of linguistic conventions (Hale and Wright, 2003).