Some standard examples of propositions which are knowable a priori are ‘All bachelors are unmarried men’, ’14 – 7 = 7’, ‘Every event has a cause’, ‘If P then Q, P therefore Q’ and ‘It is wrong to torture infants just for the fun of it’ (Russell, 2014). One of the reasons why it is thought that all five of these propositions are knowable a priori is because they seem plausibly to be necessary truths. However, even if they are all necessary48 in some way, they are not all sentences expressing the same type of
propositions. For instance, ’14 – 7 = 7’ is a mathematical proposition. ‘Every event has a cause’ is a
48 If we follow Carnap on what propositions express necessary truths, then they are certainly not all necessary truths. But it is important for the immediate explication to not take this for granted.
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metaphysical proposition, ‘If P then Q, P therefore Q’ is a proposition stating a logical principle and ‘It is wrong to torture infants just for the fun of it’ is a moral proposition. If they are all necessary they express different sorts of necessities and might call for distinct epistemic treatments.
The most important modal distinction is that between contingent and necessary truth. A proposition is contingently true only when particular matters of fact in the extra-linguistic world obtain. For example the truth of “It is raining outside” is contingent on it actually raining outside in the relevant sense. On the other hand propositions such as “Rain is the condensed moisture of the atmosphere falling visibly in separate drops” are true whether or not there ever has been rain, or whether or not the speaker using the term ‘rain’ has ever experienced rain. The only requirement for knowing the truth of such a
sentence is that it is true that ‘rain’ is taken to mean (i.e. the sense of ‘rain’) ‘the condensed moisture of the atmosphere falling visibly in separate drops’ within a particular linguistic framework. The truth of the proposition is then based on a logically necessary relationship between ‘rain’ and ‘the condensed moisture of the atmosphere falling visibly in separate drops’. This relationship might exist because speakers say it does. In such cases it is said that the truth has been ‘stipulated’ (Hale and Wright, 2003).
We have seen, in Part 1, that such sentences can be true despite the absence of any corresponding empirical matters of facts. Or the relationship might exist because there are objective and antecedent facts, i.e. facts about the meanings of terms, which determine the relationship between ‘rain’ and ‘the condensed moisture of the atmosphere falling visibly in separate drops’. In such cases the truth of a sentence is determined by these objective meaning facts (Boghossian, 2006).49
For example, it might be asked, how a statement such as ‘There is no largest prime number’ fares if the above suggestion is taken seriously. Does it express an objective logical principle (i.e. a logical fact) or not? Or is it stipulated, thus implying that there might indeed be a largest prime number, had it simply stipulated that there is one? Neither of the aforementioned options expresses the correct conception of stipulated truth. To understand the arbitrary or non-factual nature of stipulation as resulting in an incoherence, such as there being and not being largest prime numbers, is to have misconceived what stipulation is. Carnap (and Hale and Wright) would say that ‘There is no largest prime number’ is true by stipulation, given the further commitments we have to the linguistic conventions about ‘prime’,
‘number’, ‘no largest’ and so on. It is true given our acceptance of the conventions which establish the meanings of these terms and phrases. This makes it conventionally true. What ‘stipulated to be true’
49 ‘Objective and antecedent meaning facts’ has been explained in great detail in the thesis introduction as well as in the introduction to Part 1.
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does not mean is that, free of any specified inferential network of meaning postulates of definitions in which it is embedded, a statement is stipulated to be true. And that, therefore, ‘There is a largest prime number’ can just as readily, be stipulated to be true standing, so to speak, side-by-side with a stipulation of the opposite. For ‘There is a largest prime number’ to be true the definitions of the ingredient terms would have to be different. The whole inferential network of definitions/meaning postulates would have to change. And if they were different in such a way that this makes it a logically coherent sentence, then, yes, the opposite could also have been stipulated to be true. But it would be true relative to a
completely different linguistic framework. What has, unfortunately for the realist about logic or mathematics, not been established by the seemingly indubitable truth of ‘There is no largest prime number’ is that there is, in reality, no largest prime number. What has not been established is that there is an objective fact, beyond a stipulated linguistic fact, that there is no largest prime number. All that has been established is that we evidently are deeply committed to the linguistic framework in which this mathematical axiom finds residence and that relative to that linguistic framework ‘There is no largest prime number’ is true.50
What does justification and knowledge have to do with any of this? We have seen already that Frege and Carnap hold that the method of justification, and therefore knowledge, of truths is a deciding factor for whether we take truths to be analytic or synthetic. So, by such accounts, the distinction between a priori and a posteriori precedes the semantic distinction between analytic and synthetic. In this part I argue that implicit definitions, if of logical terms, should be thought of as trivial since they are justified a priori. Here then is another argument which is premised on the temporal priority of
justification/knowledge over truth.
50 I must clarify, at the outset, that I do not defend any sort of fictionalism in this thesis. Not about logic or mathematics or analytic truths in general. Fictionalism states that “Fictionalism about a region of discourse can provisionally be characterized as the view that claims made within that discourse are not best seen as aiming at literal truth but are better regarded as a sort of ‘fiction’” (Ecklund, 2009). To say that the laws of logic or
mathematics, or that logical truths and mathematical truths, are not literarily true is to misconstrue what analytic truth is. Fiction offers a world steeped in metaphor and analogy. It is a dream world, which is, in a sense, not translatable from one speaker to another – because much of it is figurative. Or, at least, its design is such that it is open to interpretation. But in fiction there are no translation or transformation rules. Everything is open to interpretation and no one knows who is right. On the other hand, analytic truth is truth derived from explicitly stated rules. An analytic truth is constrained by other truths which give us no option but to interpret it a certain way. And this is the case even when all those truths are made up. This is why the rules of chess are not open for interpretation, even if they are stipulated. The postulation that chess is a metaphor for life, or some such literary humbug, might form part of a case for why chess is fiction. But this is hardly speaking to the heart of our present philosophical problem. Analytic truths are not metaphorical or figurative; they are either explicitly stated or they are completely explicable. How could a fictional truth and an analytic truth be more different?
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There is at least one problem arising for the metalinguistic51 relationship between a priori knowledge and necessary truth, if necessity is a varied concept, we have seen that necessities are not always thought of as necessities in the Carnapian sense. Sometimes they are thought of as necessary features of the world, such as ‘all effects have causes’ (Descartes) or ‘necessary’ in “language independent, necessary connections” (Boghossian, 2006, p. 336). Such necessities are, what could be called,
metaphysical necessities. Carnapian necessity, as we have seen, is always linguistic or logical.52 So there could certainly not be necessity which is not also ‘language independent’, if one endorses a Carnapian account of necessity. The question then, for instance, arises whether mathematical propositions are necessary in the same way as sentences which say things about the nature of reality, e.g. ‘Every effect has a cause’. Or are they mathematical sentences expressing necessities in the Carnapian sense; are they necessities derived from (i.e. deductively inferred from) the freely stipulated meanings of the variables and constants of mathematical sentences standing in conventionally determined relationships with each other? And, even more pertinent, does the justification have to be distinct for different types of necessities – if there are even different types?
To answer this question in the negative would require an argument against the inveterate relationships between, on the one hand, analytic and a priori and, on the other hand, synthetic and a posteriori, being championed in this thesis. To do so, one might, for instance, want to present examples of where
contingently true propositions are knowable without experience. Evans (Russell, 2014) argues that ‘If actually p, then p’ is knowable a priori yet is contingently true. This is, we have seen in Part 1, not like Kant’s example of synthetic truths which are knowable a priori, since Kant takes geometric truths to be a priori, yet of this world. It is based on their “strict universality” (Gardner, 1999, p. 53) that they are knowable a priori.53 For Evans the above sentence is a priori, because it expresses an a priori principle;
one that cannot be otherwise. It cannot be otherwise that for something to be actually the case it must also be the case. Yet, Evans insists that its truth is not necessary – it might be otherwise – despite being a priori.
What then distinguishes Evans’ example from an a priori linguistic or logical truth, such as those proposed by Carnap? For Evans the contingent nature of the proposition becomes explicit when the variables are quantified. So, if the principle is saying something particular (as opposed to just being a general logical principle as stated above), such as saying something about a post box being red, then it
51 See my thesis introduction for an explanation of ‘metalinguistic’ used in this context.
52 See Part 1, for a careful explication of Carnap’s view of necessity.
53 This has been discussed in detail in Part 1, section 1.
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can only be the case that the proposition is necessary when a post box is actually red in every possible world. But that a post box is red is not necessarily the case in every possible world. Hence, says Evans, we have a case of an a priori principle expressing a contingent truth. In Kant’s case, however, Evans’
example of an a priori judgment would have to express a necessary truth about the absolute nature of reality, which we cannot know from experience (Russell, 2014). So, perhaps, for Kant, the general expression and the particular expression would receive distinct treatments. For Carnap they receive distinct treatments depending on whether the quantified sentence is understood to be meaningful in either an intensional or extensional context.
An introduction to the mine field of theories about a priori knowledge is incomplete without mention of Kripke’s contribution to this philosophical terrain. It would be a mistake to not cite, arguably, the most cited account undermining the coupling of ‘analytic’ to ‘a priori’. There are, of course, two ways of doing this: 1. To couple ‘synthetic’ to ‘a priori’ and, 2. To couple ‘analytic’ to ‘a posteriori’. Kripke does the latter by suggesting that there are cases of ‘necessity’ being known ‘a posteriori’. But I have posited that necessities can only be logical, or linguistic, necessities. I have, furthermore, given a detailed account of what it means to be a linguistic necessity according to Carnap, in Part 1. I have explained that Carnap’s account of necessity renders it unsuitable for knowing empirically. So, if Carnap is right then Kripke must be wrong. But, staying rather with our present instructive tool, at the very least, if Kripke is right then Hume is wrong and I am, on the whole, wrong about trivial truth. Let us see why.
Kripke, as we have seen already in the introduction to Part 2, warns against assuming the philosophically rigid relationships between necessary and a priori and contingent and posteriori. (Kripke, 1972, pp. 35 - 38).
The terms necessary and a priori are not obvious synonyms. There may be a philosophical argument connecting them, perhaps even identifying them; but an argument is required, not simply the observation that the two terms are clearly interchangeable. (I will argue below that in fact they are not even
coextensive – that necessary a posteriori truths, and probably contingent a priori truths, both exist.) (Kripke, 1972, p. 38)
He forwards an example of a proposition of which, he says, the truth is necessary and the justification for, and knowledge thereof, a posteriori: “Hesperus is Phosphorus” (two names for the same planet).
The necessary status of the truth is determined, according to Kripke, by the fact that, given the rigid designation of the two names to the same object, there is no possible world in which Hesperus is not
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also Phosphorus. However, says Kripke, given that the truth is only determined after the experiential knowledge of both Hesperus and Phosphorus actually referring to the same object or being
extensionally equivalent, the justification and consequent knowledge of the proposition is a posteriori (Kripke, 1972, pp. 94 - 99).
The compressed response to Kripke is this: Let us assume that the naming of an object is a contingent matter of fact, i.e. there is/was nothing necessitating the naming of Venus as Hesperus nor as
Phosphorus. Kripke agrees. That many names can be given to the same object is evidence of the arbitrary nature of naming – across language groups and even within language groups (Kripke, 1972, p.
77). In fact, our present example is a case in point. After the naming events it is then discovered, a posteriori, as Kripke says, that ‘Hesperus’ and ‘Phosphorus’ name the same object. They now both
“rigidly” designate a certain planet visible from Earth. We therefore have, at the very least, a factual truth about two viewings of, what seems to be, two planets over 24 hours; the truth being that those two viewings are, in fact, of the same planet. However, now that we know (a posteriori) that ‘Hesperus is Phosphorus’ we might ask whether this claim is necessarily true or contingently true. Kripke answers, yes it is necessarily true, and I answer, no. Kripke’s reason is that there is no possible world in which Hesperus cannot be Phosphorus after the ‘a posteriori’ discovery of the rigid designation of the two terms to the same object. Hume would say that the a posteriori discovery of this relationship of identity is irrevocably a contingent matter. For Kripke, the identity relationship, so conceived, becomes a necessity.
Here is my reason for denying the necessary status of ‘Hesperus is Phosphorus’:
If the co-extensiveness of these two names has been established conclusively, then we simply have a case of a true fact, which happens never to be revised because we happen to be right about the co- extensiveness. But to call this a ‘necessity’ is an equivocation of ‘necessity’. It is simply a true fact; a true fact which is also never revised does not become a necessary truth. There is, of course, no reason why Kripke should not give his own explication of ‘necessity’ (such as the one just refuted by me). But to do so is to confuse at least two ways in which ‘necessity’ is used within the established discourse; that it is intensional and that it is trivial. Kripke would deny both these features when pertaining to his
explication of ‘Hesperus is Phosphorus’. So, in having argued, in the way that Kripke does, that there are indeed necessary a posteriori truths does not seem, to me, to settle the matter at all. All that has been established is that there is an empirically determined co-extension. If it is empirically determined, even if never revised, it cannot be a trivial truth. This is the point that Hume makes about his absolute yoking
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of analytic to a priori and synthetic to a posteriori. A truth cannot be analytic, and certainly not trivial, if it has received its justification a posteriori. In any event, what Kripke has done, at most, is given a different explication for ‘necessity’; necessity as an absolute empirical truth. To Carnap, ‘absolute empirical truth’ is an oxymoron. To the contrary, had Kripke managed to show that a necessity, such as would be conceded by Hume and Carnap to be a necessity, is something which can be known a
posteriori, then he would have achieved his aims; to unsettle the idea that necessity “must” be known a priori. To say that an absolutely true empirical statement (e.g. one expressing an unrevisable identity relation) is a necessity is, however, to my mind, to change the goal posts. Nothing other than a new explication of necessity is on offer, from Kripke.
The seminal contribution that Kripke’s semantics makes to my already established Hume-Mill ‘device’ is to add to it this moral: To argue against the synthetic a priori is not only to pay attention to the
illegitimacy of knowing synthetic truths a priori, but it is also to proffer that the concept ‘a priori’ is a part of an explication for ‘trivial truth’, and therefore ‘necessity’ (and finally, ‘analytic’). This is Kripke’s mistake and also why it is important, to this thesis, to make mention of Kripke. From here on, therefore, to refer to ‘Kripke’s mistake’ is to refer to the mistaken view that necessity can be known in any other way than a priori (without first changing what ‘necessity’ means). On pain of inconsistency then, agreeing with Kripke asks for dissent with Hume.
I have been making claims to endorsing a particular sort of empiricism; Humean empiricism which I take to be a precursor to the empiricism of the logical positivists, such as endorsed by Carnap. My evaluation of Kripke’s position, despite Kripke advocating the a posteriori (i.e. empirical!) justification of a truth, I have maintained is contrary to the empiricism here endorsed. Does this make Kripke a rationalist? I am not able to make such a judgement without a decent study of Kripke’s work. But to answer this question is not required for the advancement of my case. I am also not particularly interested in what makes arguments rationalist arguments, since there seem to be at least a few interesting cases where rationalist justification is not the overt objective, yet certainly the inadvertent outcome.54 I am,
therefore, less interested in the labels of ‘empiricism’ and ‘rationalism’ and more interested in offering principled arguments against what seem to be ill-conceived (by Humean empiricist standards)
epistemological and semantic theories.
54 In Part 3 there is Boghossian (2006), in Part 2 Boghossian (2003) and in Part 2 Millikan (2006).