Kant’s ‘Synthetic A priori’

Kant believed that claims about the world could be both ‘synthetic‘ in that they could tell us something about the world that isn’t contained in their own terms, and ‘a priori‘ because they can be known independent of experience of the world. 

This is a response to Hume who had denied such a possibility. ‘Hume’s fork‘ (see previous entry) made a strict separation between synthetic propositions, which for him could only be known ‘a posteriori‘ and ‘analytic‘ propositions which could be known a priori, but told us nothing about the world that was not already contained in their terms. 

To understand this we have to look at the way the sentences we use to make propositions and claims about the world work. Sentences consist of subjects (the thing the sentence is about) and predicates (the words that say something about the subject). So, the sentence ‘Some frogs are green’ has ‘Some frogs’ as its subject and ‘are green’ as its predicate. 

Both Kant and Hume thought that ‘analytic‘ statements are those in which the subject contains the predicate and consequently they don’t add any information about the world: an example of this would be the sentence ‘green frogs are green’, or to push it a little further, ‘kangaroos are animals’, because we could claim that the concept of ‘kangaroo’ contains the concept of ‘animal’, so if we already have the concept of ‘kangaroo’ we already have the concept of ‘animal’ and we know this independent of (further) experience’, we know it ‘a priori‘. 

On the other hand the predicates of ‘synthetic‘ statements are not contained in the subject, so they do give us additional information about the world; for example ‘This frog is green’ or ‘this kangaroo has a stamp collection.’

But Kant thought that statements like ‘7 + 5 = 12’ were both ‘synthetic‘ and ‘a priori‘, in fact he thought that ‘Mathematical judgments are all, without exception, synthetic.’ For Kant, there is nothing contained in the concept of ‘7’ and ‘5’  that makes the knowledge that that adding them together will result in ’12’ immediately obvious or unavoidable. What he was getting at is perhaps easier to see if we consider larger numbers like for example, 38976 and 45204; their sum 84180 certainly does leap out at me, but I’m v. poor at maths. I think this gives an inkling of what Kant meant, but an awful lot of reading is really required to work your way into his idea. 

Kant  also thought that science could come up with synthetic a priori statements. He claimed that the statement, ‘In all changes in the physical world the quantity of matter remains unchanged.’ was such an example; he said;

Now, in  thinking the concept of matter I do not think its permanence but only its presence in the space that it fills. Thinking that matter is permanent isn’t like thinking that women are female, or that tigers are animals. In judging that matter is permanent, therefore, I go beyond the concept of matter in order to add to it something that I didn’t think in it. So the proposition isn’t analytic but synthetic; yet it is thought a priori.

He also claimed that the statement, ‘When one body collides with another, action and reaction must always be equal‘ was synthetic and a priori. 

Again it is not obvious (not to most mortals anyway) exactly what he meant, but if we consider his ideas about the ‘categories‘: how we experience the world in the way we do because time, space and cause and effect are built in to the way our minds are set up to experience the world, then we begin to see how we might know ‘a priori’ the stuff above about action and reaction, and such ‘knowledge’ certainly seems to add to our information about the world and is therefore ‘synthetic‘. Hume, of course denied that ideas about cause and effect, action and reaction etc. were anything other than the product of experience and as such, although synthetic, could only be known ‘a posteriori’.

So, I hope that’s clear, now. Another Saturday afternoon bites the dust of metaphysical speculation. And I haven’t marked your essays yet!

Hume’s Fork

I think you were right that the text book makes this much more difficult than it needs to be.

I’ll try to keep it simple. (Not one of my strong areas, I know)

The point of the fork is to keep separate the two kinds of statements we can make about the world. 

The first kind, ‘Relations of Ideas’ are things like  “2 + 2 = 4”, “all bachelors are unmarried”, and truths of geometry, mathematics and logic.

These kind of ideas have certainty, but according to Hume, tell us nothing about the world. It is as if they are sealed off from the ‘physical’ world. The logical ‘purity’ of these ideas, and therefore their certainty, either cannot transfer to the real world, (as in the application of geometry and maths to the construction of bridges that are perfect in ‘theory’ but collapse in the ‘real’ world), or tell us nothing, like a bachelor telling you “Hello, I’m a bachellor, I’m not married!” 

The second kind ‘Matters of Fact’ are statements like, “flowers bloom in the spring”,  “the Earth has precisely one moon”, and “water freezes at 32 degrees Fahrenheit”. These kind of statements are based on our experience and observation of the world. They cannot have the kind of certainty that ‘relations of ideas’ have because:

1. we use our senses to get the information (and we know how dodgy they are!)

2. we can never be certain that the behaviour of these things won’t change. (We might be very, very confident that it won’t change, but we cannot have logical certainty about it.) 

Hume’s purpose was to show that science, cannot bring these two kinds of statements together however much it wants to. It can say very useful things about the physical world based on it’s experiments and observations, and it can describe the various physical phenomena in terms of logic, maths & geometry, but that certainty will never be in those phenomena themselves. 

I think that’s rather brilliant. But, of course, I may be wrong. 

If that’s not enough for you then see Wikipedia which is excellent on this http://en.wikipedia.org/wiki/Hume’s_fork