To: Atilio G.
From: Geoffrey Klempner
Subject: Can we give a non-circular justification of deduction?
Date: 22nd April 2011 14:18

Dear Atilio,

Thank you for your email of 16 April, with your essay for the University of London BA Logic module, entitled, 'Can we give a non-circular justification of deduction?'

As you observe in your essay, there are philosophers who hold that logic needs to be justified, and other philosophers who hold that logic doesn't need to be justified, because 'it is at the core of thought itself'. I'm not sure I fully understand what this means, but presumably this isn't meant to be a kind of backdoor 'justification' of logic. What these philosophers are saying is that it is simply absurd to ask for a justification of logic.

So, if we ask these philosophers (the ones who think it is absurd to ask for a justification of logic) whether a non-circular justification of deduction can be found, the will say no. If it is absurd to ask for a justification then it is equally absurd to offer one, circular or non-circular.

We can leave this view aside, because it is not relevant to the essay question. Those who think that logic doesn't need justification haven't got anything interesting to say, so far as our question is concerned.

I don't really see that contrasting 'empiricist epistemology', 'realist metaphysics' and 'rationalist metaphysics' is helpful either. What we really need to do is concentrate on the issue of ways and means of justifying deduction.

Which brings us to Dummett and Haack (incidentally, it's Susan Haack in *her* article!). You state that Dummett contrasts suasive justification and explanatory justification, but disappointingly you don't offer any more detail about this. That question is really at the heart of this essay. What kind of thing is Dummett talking about when he refers to 'explanatory' justification?

This is the opportunity for you to offer an exposition of Dummett, and to comment on his claim that the explanatory justification of deduction is a legitimate kind of 'justification'.

In order to do that, you would need to modify what you say about justification at the beginning of your essay. 'Justification is an argument that proves some hypothesis.' That's not true. Not all justifications are proofs.

Consider empirical justification. You say to your friend, 'Why did you go out without your jacket? It might rain.' Your friend replies, 'I saw the weather forecast this morning, and it said that it would be sunny all day.' That's not a proof that no rain will fall. It's perfectly reasonable to decide what to wear on the basis of the weather forecast, but, still, we all know that forecasters sometimes get it wrong.

Even though it is accepted that there is no cast iron proof of the validity of induction, couldn't we say that logic is justified because it is tried and tested and has shown itself to be reliable? I would be more confident in the conclusion of a logical argument than in any weather forecast. Deduction works. What more could we want?

In his paper, 'The Justification of Deduction', Dummett raises questions about logic which can't be answered by this pragmatist response. Even though logic 'works', much of the time, that isn't an answer, e.g. to doubts about classical logic and whether classical logic ought to be replaced by intuitionist logic. Both classical logic and intuitionist logic 'work'. In fact, so long as we are confined to reasoning about things we experience, the empirical world, there is no real difference between the two systems of logic. It is only when one comes to mathematics, that the difference becomes apparent.

Dummett's view is that what 'justifies' a system of logic is a theory of meaning. This is not 'suasive' justification which would convince a sceptic who refused to believe in logical deduction as such, but it goes further than merely being 'explanatory', because it is concerned with resolving a debate in the philosophy of mathematics. The implication is that we have to make a reasoned choice, based on the correct theory of meaning. The question of which theory of meaning is the 'correct' theory is one for proof, even though at the present time the debate has still not been resolved.

You also talk about Kant's table of categories. I do think that there is an element here which is relevant to the question of the justification of deduction. Kant is describing basic ways in which we subsume experience under concepts, and what is most notable about this is that human knowledge is essentially inferential. As Kant argues in his 'Refutation of Idealism', there could not be a possible 'reality' which consisted purely of experiences. Our experiences are 'of an external world'. Logic has utility for the very same reason that the world is more than my subjective experience. To show that logic is not redundant but has a necessary role to play in human knowledge is a kind of 'justification'.

All the best,

Geoffrey