Thursday, January 31, 2008

Is the concept a priori passed its sell by date?

The Philosophy Society managed to get Timothy Williamson to give a talk on a priori knowledge last night. The stated aim of the talk was to get people to stop using the a priori/ a posteriori distinction since it had passed its usefulness. The strategy was to show that there are many mixed and borderline cases, and that trying to classify these cases “obscures epistemologically crucial features of the examples”. He concludes that “We should resist the temptation to assimilate new cases either to the stereotype of the a priori or to the stereotype of the a posteriori.”.

Mike Gabbay made a point which struck me as right. I’m not going to get it quite right, but roughly, “a priori” knowledge is knowledge by inference. If we presuppose a body of knowledge K, then we can deduce a larger body K­2 using inference. All the propositions in K2 but not in K will be a priori. There are many techniques and skills that could come under the heading “inference”, and it could be the case that we learn new skills, either collectively, or individually, from experience. What can be deduced a priori will therefore be relative to experience.

For example, if I knew that there were some trees planted in a square that was seven trees long and seven trees wide, I do not yet know how many trees are in the square. If I know about squares and squaring then I can deduce without further observation that there are 49 trees in the square. I will have made this deduction a priori. I could have found out this knowledge by going out and counting each tree. This would have been a posteriori. I may have been told by my line manager that the best way to count the trees is to multiply the length by the breadth on a calculator. Given this information and a calculator, I could discover that there were 49 trees in the square without counting them. Would this be a priori? I guess Professor Williamson’s point is that the concept of a priori has two much philosophical baggage for this to be a useful question. What have we solved by calling this technique for counting trees planted in squares a priori? No part of the process was either necessary, nor innate nor derived purely from reason, nor absolutely certain. Since these are often thought to be properties of the a priori, perhaps we should stop using the term since it just confuses matters.

However I think it highly useful to make a distinction between what we can find out before hand given a body of knowledge K, and what we just have to wait and see. Lets play dice. I’ll throw two dice and I’ll give you £35 if it’s a double six and you give me £1 otherwise. What do we know a priori? We know a priori that there is a 1/36 chance that you will win. We know a priori that the odds are fair. What we don’t know a priori is who will win. We have to actually throw the dice for that. The fact that we know these things a priori is not innate, or intuitive or necessary or any rubbish like that. It has been hard won by the greatest of our species and been passed down through teaching and tested through experience.

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Anonymous David Papineau said...

Comment on Tim Williamson’s Talk Last Night
David Papineau

Part of Tim Williamson's aim last night was to cast doubt on the idea that philosophy and other armchair activities are a priori.

I'm inclined to agree that they aren't a priori--or at least that the interesting bits aren't. But why not just say that they are a posteriori?

I wasn't persuaded by Williamson's arguments that the distinction between a priori and a posteriori can't be made out.

He had various examples (most centrally (A) 'if something is nine inches it is longer than nineteen centimeters') which he wanted to say didn't seem either a priori or a posteriori. But I'd say that this is definitely a posteriori.

Part of my reason for saying this is that I think that any good account of a priori knowledge must mention something like analyticity. The idea is that something will be a priori (known indepedently of experience) only if its truth is guaranteed by its conceptual structure (and logic) and the thinker knows it by being sensitive to this.

If we think of the a priori in this way, then I'd say that all Williamson's examples are clearly a posteriori. Of course, if you know (A) because you've been introduced to INCHES as 2.54 CMS and do the sum, then it would be a priori for you. But Williamson's case was where you know it by imagining nine inches and then imagining nineteen cms, and I say it's then a posteriori. (You have learned from experience that nine inches is like THAT, so to speak, and like THAT is longer than nineteen centimeters.)
Williamson argued that (A) isn't so hugely different from 'crimson things are red' or even 'bachelors are unmarried'. But here I was worried that he wasn't attending sufficiently to a point he'd made earlier, that the a priori/a posteriori distinction attaches primarily to ways of knowing propositions, not to the propositions per se. In arguing that 'crimson things are red' or even 'bachelors are unmarried' are like (A) he had to look at cases where they are known using some kind of imagining, not via sensitivity to conceptual structure. I'd say that in such cases they are known a posteriori, just like his (A)--even though of course in many other cases they are know a priori.

In conversation afterwards, he accepted some of these points, but wasn't happy with my implicit identification of a priori with 'known on the basis of conceptual structure'. One point he made was that many people will say things like 'bachelors are unmarried' are manifestly a priori, and so if they aren't analytic this just shows that the a priori isn't always analytic.

I wasn't convinced by this. The main philosophical friends of the a priori (Jackson, Chalmers, . . .) think that various interesting philosophical theses are a priori because they are analytic. If I come along and show them that these theses aren't analytic, I doubt that they are going to say--'well, all right, maybe so, but still the important point is that they are a priori for all that'. And I think the reason they won't do this is that it's not clear what a priori knowledge could be if it's not derivative from analyticity.

Williamson also had some other worries about the equation of a prioricity with analytic-based knowledge. In particular, he felt that it's obvious that mathematics and logic are a priori, but not at all clear that they are analytic. At that point I'm not sure I want to resist. There's lots to say about the epistemology of maths and logic, but I too am doubtful whether mathematical and logical knowledge are best explained as due to sensitivity to conceptual structure. Yet I'm not in a hurry to count them as a posteriori on that account.

So perhaps I should relativise my response to Williamson. Put maths and logic to one side. Keep the a priori vs a posteriori distinction for other propositions. Then non-mathematical and non-logical claims are known a priori if the knowledge derives from sensitivity to conceptual structure plus maths and logic--and a posteriori otherwise.

And then I say again, as I wanted to say at the start, that the interesting things we philosophers do in armchairs are not only not a priori, but (maths and logic aside) definitely a posteriori.

David Papineau

6:59 PM  
Anonymous James said...

I agree with everything David says.

7:09 PM  
Anonymous Jonny Blamey said...

In a standard Gettier counterexample, Jones is justified in believing that Smith gets the job and that Smith has ten coins in his pocket. But it is Jones who gets the job and Jones has ten coins in his pocket. It seems that from our armchairs we *know* that Jones didn't know that the person who was to get the job had ten coins in his pocket. How do we know this?
Not a posteriori. Not from experience. The counterexample is hypothetical. Jones does not exist. Even were he to exist, we could learn from observation all the facts of the case without learning whether or not he knew. There would be no extra observation that we could make that would reveal that Jones did not know.
It is not analytic. There is no analysis of knowledge, and the most plausible analysis seems to entail that Jones does know.
I put it that we know a priori. It is known in advance that such cases are not cases of knowledge. It maybe that our concept of knowledge is innate, a part of a "theory of mind" module or it maybe that we have learned it through experience, or a bit of both. But once we have the concept of knowledge, it seems to follow a priori that certain cases are cases of knowledge and other cases are not. Maybe this counts as a case of analyticity. But given the intractability of the analysis of knowledge it is not clear what this means.

3:24 PM  
Blogger Stephen Law said...

Comment by Stephen Law

I did not attend the talk, unfortunately. But I'll chip in anyway.

I am not sure I agree with David Papineau that all a priori knowledge must be conceptual/analytic.

If you are a reliabilist about knowledge, for example (and I think David is), then an innate belief, brought about by a reliable, truth conducive mechanism (perhaps natural selection can do this, under the right circumstances), will qualify as knowledge. But it will be a priori.

We may not have any such innate knowledge, but I don't see why we could not have. Hence my doubts about the claim that all a priori knowledge must be conceptual.

8:27 AM  
Anonymous david papineau said...

I take the points made by Jonny and Stephen.

Of course it is possible that natural selection could instil in us synthetic beliefs whose truth is non-accidental enough for them to qualify as knowledge. And that certainly looks like a priori knowledge that isn't analytic.

I must confess that in my earlier posting I was implicitly assuming that I could simply count such beliefs as a posteriori, on the grounds that they depend on ancestral experience, so to speak, even if not individual experience. But I now see that this way of putting things would be a bit eccentric. OK--I'm happy to allow that there is non-analytic a priori knowledge of this kind.

Jonny half-suggests that our intutions about Gettier cases may be of this kind. I myself think this may be right. But most philosophers will need persuading that the Gettier intuitions don't simply fall out of our concept of knowledge. Jonny points out that there is no accepted nec.-and-suff. condit. account of knowledge. But that's not decisive, surely. The concept of knowledge could have enough structure to guarantee the Gettier intuitions without being analysable in terms of nec and suff condits.

On the more general issue Williamson raised, I'm now inclined to agree that the a priori/a posteriori distinction is pretty mushy in itself. This is because it really only carries content in the context of some specific theory of how a priori knowledge is possible (eg God-given insight, analytic knowledge, Kantian trs arguments, biologically innate knowledge). Each of these gives us a clear notion of an a priori/a posteriori distinction, and I don't see that Williamson gives us reason to doubt that. But I agree that a distinction that is supposed to be independent of these theories of a priori knowledge is no use.

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