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.