We can give an example of Laurence BonJour’s logical links between beliefs in the Quinean web.
Take this argument:
((P ∧ Q) ⊃ (R))
Say that we experience something which gets us to reject R above. If that happened, then we must reject the conjunction P ∧ Q because if P and Q are taken together they imply R. Thus either P is true or Q is true; though not both (perhaps neither is true).
In terms of the interactions of beliefs in the web, we may be led to reject or deny Q instead of P in order to achieve an overall equilibrium within the whole system. The point is that although experience inspired us to reject R, it didn't (directly) inspire us to the rejection of the conjunction, P ∧ Q. (Or perhaps it did; though indirectly.) That is, a direct experience got us to reject R, and then that same experience does get us to reject the conjunction, P ∧ Q, in that without it we wouldn't have rejected the conjunction. We can say, then, that experience only indirectly got us to reject the conjunction P∧ Q.
One of BonJour’s main targets is the idea that Quinean ‘systems’ or “the web of belief” somehow escapes from the a priori. Such a web or system is holistic in nature and is only supposed to “touch experience at the edges”. BonJour firstly describes the Duhemian thesis from which Quine derived his holistic position. BonJour writes:
“Quine’s extreme version of this thesis is the holistic claim that nothing less than ‘the whole of science’ can be meaningfully confronted with experience.” (ibid., p. 104/5)
It's because of the holistic nature of the entire system that even “a priori reasons” (or “our cherished logical laws”) may be given up if they don't concur or cohere with the whole system. Thus Bonjour writes:
“From this he infers that any claim in the total ‘web of belief’, including those for which there are allegedly a priori reasons, might be ‘given up’ in order to accommodate ‘recalcitrant experience’, and so, apparently, that such a priori reasons do not exist after all.” (ibid., pp. 104/5)
The interesting thing about this quote is that BonJour himself believes that some a priori reasons (or beliefs) may or can be “given up” due to new experiences. So why not all of them? The point is, however, that they can indeed be given up; though still be a priori in nature (as we shall see in a moment).
The first point that BonJour makes about Quine’s position above is that it “begs the question” against the a priori in that there's a simple assumption that, when it comes to the web of belief, experience (whether ‘recalcitrant’ or not) is everything. BonJour is claiming that the Quinean web of belief must contain a priori links between the individual beliefs contained in the web. However, BonJour is keen to stress that
“the rationalist can freely admit that holistic empirical reasons of this sort may count against a claim for which there is an a priori reason (or the reverse), with the ultimate outcome depending on their relative weight in a particular case”. (ibid., pp. 104/5)
Does this mean that BonJour believes that an “a priori reason” (which has “holistic empirical reasons” which “count against” it) must not thereby be a genuine a priori reason? Or does BonJour believe that a reason can indeed be a priori and still have holistic reasons which count against it?
Despite that acknowledgement of the corrigibility of a priori reasons, BonJour says that the rationalist will still “also insist that the very connections among beliefs that result in the holistic web can only be understood as a priori in character” (ibid., pp. 104-5).
BonJour state two moves here which he believes must be a priori in nature. First, take the ‘conditional’:
P) If a claim satisfies all of the conditions thus specified
Q) Then it's likely to be true.
Clearly the move from P to Q can't be empirical in nature nor based on experience. Thus the inference, according to BonJour, must be a priori. Not only that: BonJour questions the truth of the conditional by asking: “[W]hat reason there is for thinking that this conditional proposition is itself true?” (ibid., p. 105) In other words, our earlier conditional, if P, then Q, is “not directly justified by experience” (ibid., p. 105). Thus can it be included in a system of belief which is based around the importance of the outer beliefs and their direct relations to experience? BonJour thinks that it shouldn't be because an “appeal to its inclusion in such a system of belief would be plainly circular” (ibid., p. 105). BonJour’s general conclusion to this is that
“the idea of an a priori reason is both indispensable for any justification beyond that yielded by direct experience and at least as well understood as the idea of holistic empirical justification, which turns out in fact to depend upon it”. (ibid., p. 105)
BonJour then puts a point which was once expressed by Donald Davidson:
“Only another belief can justify a belief, not experience itself.”
From this we can say that experience, in and of itself, never justifies a belief. It may follow from this that a priori logical connections to previous beliefs and reasons provide us with the complete picture of justification. It's this very link between one belief (close to experience or not) and another that BonJour fixes upon. He writes that
“experience can provide a good reason for thinking that a belief in this category is true only if we have a logically prior good reason”. (ibid., p. 102)
Thus an experiential belief can only be deemed true if it has an a priori link with a “logically priori good reason” (ibid., p. 102) or with other beliefs (as Davidson puts it). That link won't be empirical or experiential in nature.
On Michael Devitt’s “Quinean alternative” we have the following two-fold web. It includes:
i) Beliefs which are ‘close to experience’ (on the ‘periphery’ of the Quinean web).
ii) Beliefs that are in the interior of the web.
According to the Quinean picture, beliefs captured by 2) above are justified “via links with beliefs at the periphery” (2008: Devitt, p. 2). There's a link between interior beliefs and the peripheral beliefs which are “close to experience”. Though, as many aprioristic logicians and philosophers point out, what about these links themselves? That is, “these justifications depend on the links themselves being justified” (ibid., p. 2). These links must be logical. And if they're logical, then they must be a priori in nature. Thus even Quine’s web has an a priori element. Or so the story goes.
BonJour has more to say about the links in Quine’s web of belief (or the links in any such system). He writes (quoted in Devitt, 2008):
“… if there is no a priori insight… no prediction will follow any more than any other… any… sort of connection between the parts of the system will become essentially arbitrary.” (2008: Devitt, p. 3)
BonJour is simply saying that if you don't accept a priori justification (or ‘insight’) for the links in Quine’s web of belief (or any other corresponding system), then the “connection between the parts of the system will become essentially arbitrary”. This must mean that if we don't have a priori justification (or insight), then we effectively have nothing (in such systems). And if we have nothing, then that is bound to lead to the “arbitrary” nature of the “connections between the parts of the system”.
The question remains: Is the a priori way out the only way out?
If we accept BonJour’s prognosis of the rejection of the a priori vis-à-vis Quine’s web of belief (or any other such parallel system), then it's no surprise the BonJour thinks “the rejection of all a priori justification is tantamount to intellectual suicide” (ibid., p. 3).
The question is again: Is the a priori the only game in town?
I mentioned that most people see logic as perhaps the only domain of the a priori (along with mathematics). Devitt says that
“the objection is that logic must be seen as a priori because we need logic to get evidence for against anything”. (ibid., p. 3)
BonJour is saying that, yes, fair enough, evidence is of supreme importance in science and in just about every other disciple. However, without the framework of logic, all this evidence would amount to nothing. Indeed it wouldn't even be evidence “for or against anything” if it were not for this logical framework or the logical links between this beliefs and that belief, or between this bit of evidence and that bit of evidence. Logic ties the whole thing together. That is why people say that “the logic of science” isn't itself scientific or a science. Science, as well as naturalism or empiricism, require logic. Thus science and empiricism (or naturalism) also require the a priori.
BonJour, L. (2008) ‘In Defense of the a Priori’, in Contemporary Debates in Epistemology (eds. M. Steup and E. Sosa, Blackwell Publishing).Devitt, M. (2008) ‘There is no a Priori’, in Contemporary Debates in Epistemology
Quine, W.V.O (1970/78) The Web of Belief