I am now going to offer a more detailed argument in this chapter against the claims of those who will continue to insist that some claims must be accepted as certain on a priori grounds. This chapter is aimed at the likely objections of some analytic philosophers and Kantians, whilst the next is aimed in a similar fashion at theologians. If you are not especially interested in either of these categories of argument you might find it helpful to skip these two chapters and go directly to 1.h.

I have already argued in 1.b against the idea of self-evident truths that are not subject to scepticism, dealing there particularly with the idea that Descartes’ cogito is a self-evident truth. At that point I stated that mathematical and logical self-evident truths could be accounted for in a similar way. In order to clarify why mathematical and logical truths are not examples of justifiable metaphysical truths I will need to adumbrate the account of meaning that will be tackled in more detail in volume 3.

The case for self-evident truths a priori begins with claims that must be universally true, or true in all possible worlds, because of their definitional nature. Thus a bear is an animal, whether or not there are any bears or any animals, whether or not people understand that bears are animals (or whether or not people even exist to have such understanding). The claim is alleged to be absolutely universal because it is hypothetical – if there is a bear (in the sense we usually understand ‘bear’), then that bear must be an animal.

Hume’s empiricist response to this kind of claim is to point out that, although such claims are indeed universal, they are also uninformative and trivial, because they tell us only about the way in which we categorise the universe, rather than the universe itself – they are analytic as well as a priori, and Hume alleges that all a priori claims are analytic. This is the basis for Hume’s ‘fork’ in which only analytic and empirical types of knowledge are allowed[1].

Whilst I find Hume’s fork a very useful starting-point in dealing with a priori claims, it does not quite complete the job Hume wanted it to do, which is that of making experience the only source of justified belief. This is because it is too strong in one respect and too weak in another. It is too strong in claiming that all a priori claims must be analytic, because this would rule out the Kantian a priori, in which a priori claims tell us about the prior conditions for experience (and which I will turn to presently). On the other hand it is too weak in allowing a priori claims even the status of trivial knowledge.

As we saw in 1.a, sceptical argument need not stop at casting doubt on knowledge through the senses. It can also challenge even a priori arguments by requiring further justification, and it can also employ the final two linguistic arguments. However, simply asking for further justification for a priori claims will not convince those who think they are self-evident. It is the linguistic arguments that can do the sceptical work more fully here, because they point out the assumptions made about meaning by those who appeal to a priori certainty.

The main problem with a priori claims to metaphysics, then, is that they assume linguistic categories that are both absolutely consistent and that have unambiguous boundaries. Without such consistency and such boundaries, if you read “a bear is an animal” the terms “bear” and “animal” mean something different to you to what they mean to me. Indeed they may already mean something different even to me now as I write this paragraph to what they meant when I first brought in this example five paragraphs back. They may be different in terms of what counts either as a bear or as an animal, or in terms of what is bear or animal and what is not. We are not only dealing with academic zoological disputes between Linnaeans and Claddists (who have different accounts of species taxonomy) here. For example, is a genetically engineered creature with 95% bear genes a bear? Is a piece of fur on the point of falling out of a bear’s coat “bear”? We may have different answers to these questions, and our answers may vary with context, purpose, and feelings.

One analytic response to this is to continue to insist on the purely hypothetical nature of the claim “A bear is an animal”. Ambiguities in identifying particular bears or animals, or vagueness about their boundaries, it may be argued, make no difference to the claim that if we are agreed that a particular thing is a bear, then it will also be an animal. However, this purely rational insistence would allow a bear to somehow be an animal even if all the things we actually called “bears” were not actually animals. A bear “in the usual sense” now, might in a future context have quite a different sense, yet the usual sense now would still be asserted to be true in all possible worlds and times. More generally, to maintain the metaphysical insistence on the certainty of a priori claims we might have to completely disconnect it from human experience. There can be fewer clearer instances of the abstracted turn in philosophy, where the goal of philosophy in reasoning for the clarification of the beliefs of people is lost, due to attachment to a particular theory with no connection to that goal.

It is also an example of what in other contexts would be called ad hoc reasoning, sticking to a proposition that one insists must be universally true regardless of the practical circumstances. Compare these two scenarios:

1. Jock asserts “No true Scotsman eats his porridge with sugar.” It is pointed out that Hamish is a Scotsman, but he eats his porridge with sugar. “Hamish is not a true Scotsman” asserts Jock.

2. Aldous asserts that “A bear is an animal” is true in all possible worlds where “a bear” is used in the usual sense. It is pointed out that in possible world x “bear” is used to mean anything that is not an animal. “In this possible world ‘bear’ is not used in its usual sense” says Aldous.

What these two scenarios have in common is that ‘true’ in the first and ‘usual’ in the second are entirely abstracted from the context in order to defend a particular claim. The problem with Jock’s idea of a true Scotsman is not just that it hasn’t been fully specified in advance, but that it is impervious to any possible evidence, just like Aldous’s use of ‘usual’. What one takes to be ‘usual’ cannot be specified in advance because it is the result of custom in a particular area rather than definition. Thus a priori claims about things that are necessarily true when we take the words in them in their ‘usual’ sense turn out to be merely asserting the conventions of a particular time and place without any particular reason for doing so. Certainty ascribed to a priori claims is thus just as metaphysical as that ascribed to ‘God exists’.

An even more abstracted case than that of a categorical statement like “a bear is an animal” is that of the laws of logic. It may be claimed, for example, that “a=a” is an absolutely certain proposition. However, one does not get beyond the inconsistency and ambiguity of linguistic categories by using algebraic constants. To be correct, “a=a” must be true for any term inserted in the place of a. Even in the time it takes me to think that “a=a”, any term that I may insert in the place of a may change its meaning by the time I get to considering its equivalence to itself. For example, if the meaning of ‘bear’ is constantly changing, and I insert ‘bear’, then the bear I consider at the beginning of the statement is no longer precisely equivalent to itself by the time I get as far as considering its equivalence. More obviously, if I insert “Proteus”, a creature who completely changes form every millisecond, Proteus has obviously changed during the time elapsed in reading the proposition. It does not matter if the change in meaning is miniscule, because the equivalence has to be absolutely perfect for the law of logic to be absolutely true in the way asserted.

Similar points apply to the assertion that mathematical claims are certain. 1+1=2 is only true a priori by virtue of the fact that whenever we find two objects that we regard as singular and put them together, there will be two of them, regardless of what the objects are. However, by the time we complete this reflection, the meanings of the object terms that we regard as singular may have changed. One what? Two what? What makes any object discrete other than a set of conventions that are subject to change? Even two people can become one, if the wording of some traditional marriage services is to be believed, and one person can become two, by a different convention, if they have multiple personality disorder. If this is the case for people, how much more flexible might be the conventions attached to the singularity of stones, blades of grass, or electrons!

What I have been doing here is trying to show some of the ways in which the theory of meaning assumed by a priori metaphysics is self-contradictory. The theory of meaning assumed, under which the traditional assertions appear to make sense, is a truth-conditional theory in which the meaning of a proposition consists in the conditions according to which it would be true. This theory is inadequate for all sorts of reasons, which will be discussed more fully in volume 3. Chief amongst these is its complete abstraction from what we actually take to be meaningful in experience, which in brain terms involves the dominance of the left hemisphere to the exclusion of the right. The reason it is proving self-contradictory here, however, is because it is a static theory that assumes meanings to be fixed and eternal, rather than a changing property of living human beings. But it is our right hemispheres that engage with experience, including that of changes in time. As soon as we introduce temporal changes of meaning into a system that relies on this exclusive left-hemisphere fixedness, the whole system collapses. This is a further indication that scepticism is on the side of the humans against the angels, not the other way round.

There is an alternative way of understanding meaning, which you will need to read in detail in volume 3, and which forms an important link in the coherence of the alternative approach of Middle Way Philosophy. Briefly for now, this approach to meaning recognises that meaning is not just a cognitive matter, separated falsely from emotive meaning, or ‘meaningfulness’, and from physical experience. Instead, the theory of George Lakoff[2], which relates meaning to physical experience, can be used to unite cognitive and emotive aspects of meaning into a single type of explanation. If meaning arises from our physical experience, it is certainly variable and dependent on our complex individual states. However, one other effect of this account of meaning is to remove the eternal certainty from a priori propositions.

This approach does not deny all usefulness to mathematics, logic, and taxonomy, but merely limits the more arrogant claims for universality that might be made for them. If the meaning of terms used in mathematics, logic or taxonomy is dependent on our physical conditions, then we have to share enough of those conditions for those ways of working to be useful to us when communicating. Mathematics remains useful for those who share a sufficient understanding of it, for practical purposes where the ambiguities that might obtrude are not practically speaking a problem. Similarly, logical reasoning (such as the reasoning in this book) remains valid, but only to those who share enough of the same cultural basis to find it so. Even those may understand and apply it in very different ways.

One other sense of the a priori must be considered here – the Kantian. In these terms, a priori claims must be considered certain because they identify the conditions required for our experience and/or judgement to occur. For example, “Objects exist in space” might be considered metaphysically true, just because existing in space is a necessary condition for any object we can conceive.

One long-standing problem with this kind of assertion, identified by Körner[3], is that we cannot prove the uniqueness of our particular transcendental deduction: in other words, spatiality may be necessary for all objects for us, but we cannot prove that there may not be other creatures who perceive objects without spatiality. We cannot say anything about such alternative categorial worlds, because (if they exist) they lie beyond even the categories upon which our imagination is founded. Yet there may nevertheless be such categorial worlds for other beings.

The linguistic sceptical arguments we have already discussed also apply to this kind of a priori claim of certainty as much as to the more traditional kind. The meanings of the terms ‘objects’ and ‘space’ may differ between me and others, or even for myself at different times. If I am going to create an a priori metaphysical certainty that is true in all circumstances, I need not just consistency of experience but also consistency in the language used to describe that experience. Again, that does not prevent Kantian discussions of the conditions for experience being extremely valuable, but it means that they should be judged as theoretical claims to be judged by their consistency with experience like any other theory. The requirement of provisionality applies to theories of the Kantian a priori very much as it does to empirical theories, with the conditions theorised about just being those required for all experience so far rather than being about the objects of that experience. To theorise about the conditions of experience is, after all, just an extension of theorisation about the conditions for anything else: for example the conditions for life or the conditions for combustion. Just as sceptical argument successfully undermines all claims about “Laws of Nature” that are said to apply across the universe despite the limitations of the evidence used to support them, similarly Kantian theories about the a priori amount to generalisations about all experience so far, but it would be an over-extension of the justification of such theory to claim that they were true of all possible evidence whatsoever.

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[1] Hume (1975) p.163-5

[2] Lakoff 1987

[3] Körner (1967)