Given that we agree with Quine that the analytic/synthetic distinction, at least as traditionally conceived, doesn’t work (I gave my reasons why I think it doesn’t in a previous post, which mainly have to do I think with wrong theory of concepts.), are we left just with sentences which we have to check against the world to see if they are true?
Of course, if we think that a priori coincides with analytical, we should be bound to think so. But, don’t you understand that if you have two things, you have one and one more thing? That if you have three things, you have two things and one more thing, or one thing, and one more and one more thing?
Is THIS something that you need to check the world to see if it is right? HOW do you check the world for these kind of things? We are talking about two aspects of *one and the same* state of affairs. That given that we have two things in the state of affairs, we have one and one more thing in the same state of affairs, and vice versa.
How do we check this against the world? Do we get two things, and by pointing say “one”, then point to the other and say “another one”; and then count them by saying “one, two”? How many times we need to do that to confirm that when we have two things, we have one and one more thing? Does doing something like this strikes you as silly? I think it should :)
Based on this previous thought, maybe we will give this kind of explanation why when there is two there is one and one more thing and vice versa… The practice of counting to two can’t be done if there aren’t one thing (to which we will point and say ‘one’), and then another one (to which we will point and say ‘two’). And when we have one thing, and another one, those can be simply counted as first and second, and hence, we have two things.
But this has nothing to do with counting, pointing and language really. Could this complex statement I gave really be a defense of the simple statement that when there are two things, there is one and one more thing? What is meant by that simple statement has nothing to do with language, nothing to do with our practices, with our words ‘two’, ‘counting’, ‘one’, ‘another’, and so on (except of course the simple fact that we need words to express what we mean). Put attention there on what is meant, that when you have two things (we can think of two things qua two, right?), there is one and one more thing (you can now still staying with the two things, mentally focus on the one of them, or on the other, right?). So, there is that simple awareness which we express by saying that when we have two things we have one and one more thing and vice versa.
This is the same awareness that very young children show when they expect that when you hide one thing behind the screen, and then hide one more such thing, when you open the screen there should be two things. They don’t have words, that is true, but just because they can’t express what they are comprehending, doesn’t mean that they aren’t comprehending it. Maybe they are just tracking one thing, and track another thing? But how do you track one thing and another thing when they are behind the screen? How do you recognize which was which when they open the screen?
Of course, no real-world test like this can point to that actual comprehension, as when one introduces real two things which are observed through time, those might interact with one another becoming one or three things (who knows what could happen behind the screen). The simple comprehension that when you have two things you have one and one more thing abstracts from changes. It isn’t about changing things. I guess if children are aware that those occluded things multiply or reduce in numbers, they won’t tend to abstract from changes, and hence neither of the simple determinations – ‘one and one more thing’, or ‘two things’ won’t be seen as applying. The usual mistake which is made when people think about apriority of ‘if there are two things there is one and one more thing, and vice versa’, is that they think of adding sign in ‘1+1=2’ as standing for some procedure which is supposed to happen in time – of bringing one and one more thing together somehow- joining them somehow. They think that ‘1+1’ expresses something that happens in time, and ‘2’ as some kind of result. But, of course the identity can be written the other way around ‘2=1+1’. Nothing happens! The both sides of the equality are determinations of one and the same thing. Of those one and one more thing, or which is same those two things. That simple comprehension of identity of determinations, has nothing to do with changes. It is simple and abstract (meaning abstracts from changes), about a changeless pair, or changeless one and another thing.
Let’s say that you accept that when you have two things, you have one and another thing, and that it isn’t sensible to check the world to see if it is true. And also, that you accept that this is not analytical truth in the sense that Quine attacked (analyticity of math as far as I know, was also shown inconsistent by Godel’s incompleteness theorem), nor a truth which is solely dependent on linguistic facts (if that was so, infants wouldn’t be able to be aware of this truth) Though, of course, when we express it, the truth of the sentence is dependent to some amount on linguistic facts, because of simple fact that what we mean by that sentence depends on linguistic facts. But what we mean is true or false, independently of the words used to say it. (Same as people existence is independent on the issue if we have names for them or not).
If you accept those two things, then what are those a priori truths? Where they come from? Why is that when we have two things, we have one and one more thing, and vice versa? Are they about the world? Can we come to know something about the world by ‘discovering’ those a priori truths?
I guess I will write more thoughts on this in the next post.
For more on analyticity, apriority and other dangerous things check the posts at DuckRabbit and SOH-Dan.
A brood comb 
But all of this misses the point. The question is ‘where does this undertanding/comprehension come from?’ Pointing out that we have it does nothing to solve teh problem of what its basis is. Neither does the ‘checking’ stuff (since, there may bem as Kant pointed out, synthetic a priori truths…So, here are two alternative explanations for why we just ‘comprehend’ certain things.
(A) Through a long process of evolution and exposure to the regularities of the physical world we have developed certain mental ‘modules’ that deliver the truth that when there is one thing and another there is two. This module has developed in response to the empirical regularity and depends on it; were our experienc edifferent then we would have evolved a differnt module.
(B) Through a distinctively rational facutly of the mind we apprehend, or ‘grasp’ a some necessary fact about reality that in no way depends on any empirical regularity; no matter how the world behaves this fact will be true and grasped by rational beings.
Each of these views can allow that we don’t have to check the world to see if they are true and that we simply comprehend or understand certain facts about reality so nothing you have said differentiates between them.
So let’s see. You distinguish the analytic (which you reject, with Quine) from the a priori (which you accept), and that because we don’t need to “check the world” to see that “1 + 1 = 2” can be known a priori.
How many times we need to do that to confirm that when we have two things, we have one and one more thing? Does doing something like this strikes you as silly? I think it should :)
Of course it does. But so does checking to see that the floor is still there before I get out of bed in the morning, or that that white stuff out there is snow and not white paint, and those aren’t a priori truths. Think about the colloquial use of “a priori,” which basically means “without further investigation”. This strikes me (ironically enough) as a better sense of “armchair philosophy” than the traditional a priori. We learn what “snow” and “white” mean by interacting with snow and other white things, and being corrected in our meanings/judgments by our fellows; and once back inside we need no further investigation to assent to “snow is white”, and since we know that, we call it an “a priori” truth to distinguish it from a scientific discovery. (Frank Zappa warns us against eating “yellow snow,” but we do not take the intelligibility of this warning to threaten the a priority (if that’s what we think it is) of “snow is white”.) This can be a reasonable distinction to make in particular cases, e.g. against empiricist assimilation of philosophy to science; but I don’t see any reason to elevate it any higher.
I would also be very careful in what sort of understanding I attributed to pre-linguistic children able to track distinct objects. That whole idea of non-linguistic understanding (or worse, “thought”) which we subsequently learn to express in language (or which is constitutively “beyond” it) strikes me as very fishy – which of course doesn’t mean I can’t try to express myself and fail. I actually just posted on this subject the other day.
Hey Richard, thanks for the comment!
I actually agree with you, that just pointing that there are a priori truths isn’t enough. But there are two approaches I can see that one can take towards that the issue of what else is needed.
I specifically don’t think that we need to explain a priori truths by translating them into the realm of some theory (be it Kant’s pure forms of intuition and categories of understanding; some formalism based on the theory about the relation between language and world as in Frege or Russell; or on some established practice). I don’t think is that we need to further justify things that we understand (a priori), by showing how in those theoretical realms our a priori claims (be it synthetic or analytic) can be ‘seen’ in the forms which are postulated. When I understand that when there is two things, there is one and one more thing there is nothing further to understand about that! There are no hidden things which are outside of my understanding, which make this thing true. If that was so, I wouldn’t be able to comprehend/grasp the truth, it would probably be just given to me as a truth value, which I would then need to trust or not.
But while I don’t think that we need to further justify a priori claims (that is, to say why are those truths – true), I think that there is problem of how to understand this understanding itself. That is, while I can understand that when we have two things there is one and one more thing, it is another issue to understand the relation between the mind and the world, and so on. And, it is true, that I didn’t say anything about that issue, except just posited those questions at the end of the post.
So, to relate to your proposed examples of the further story told, I think that the first doesn’t work because it is a story of why see some truth as truth, leaving a possibility that what we understand might not in fact be truth (one can imagine scenarios in that kind of story, where we come to understand something which is not true after all.)
I guess my own thinking is more alike your second proposed story, but there is more to be told. As I said I will try to put my own story in some following post.
Hi Dave, thanks for the comment!
You say…
But so does checking to see that the floor is still there before I get out of bed in the morning, or that that white stuff out there is snow and not white paint, and those aren’t a priori truths. Think about the colloquial use of “a priori,” which basically means “without further investigation”. This strikes me (ironically enough) as a better sense of “armchair philosophy” than the traditional a priori. We learn what “snow” and “white” mean by interacting with snow and other white things, and being corrected in our meanings/judgments by our fellows; and once back inside we need no further investigation to assent to “snow is white”, and since we know that, we call it an “a priori” truth to distinguish it from a scientific discovery.
I don’t see why checking that the floor is still there strikes you as silly. Surely you can imagine situation in which it would be rational to check if the floor is still there. Same with checking if the snow outside is white or yellow. Of course, it DOES strikes me as silly to check the presence of the floor, or the color of the snow given that I don’t have reasons to think that something extraordinary has happened in the world. But there is nothing that can happen in the world, as extraordinary it may be, that when there are two things, there won’t be one and one more thing.
I would agree about your skepticism about non-linguistic thought. If I expressed myself that way, I’m sorry. But I still think that there is pre-linguistic understanding (although on level of concrete situations), which is the same understanding which we express in the general form later when we learn the language. Also, as I said, I don’t think that simple story of ‘tracking’ can handle what is seen in experiments with young children (see here for more). When the objects are occluded, there can’t be any sense of tracking. At least it seems to me, what those children expect is a pair of objects, and they won’t really relate one of those objects with the first thing hidden, and the other with the second thing hidden. And I think this grasp of the pair qua pair, is the root of this (a priori) understanding. But I will try to say more on this in a following post.