Monday, September 16, 2013

Leibniz's Law and opaque contexts

To: Radhika R.
From: Geoffrey Klempner
Subject: Leibniz's Law and opaque contexts
Date: 11th November 2010 12:17

Dear Radhika,

Thank you for your email of 2 November, with your essay for the University of London BA Logic module, in response to the question, ''Someone might believe that George Eliot wrote Middlemarch without believing that Mary Anne Evans did, even though George Eliot is Mary Anne Evans.' Discuss.'

In your essay you have answered the question by offering an exposition of Frege's theory of sense and reference in his essay 'On Sense and Reference' ('Uber Sinn und Bedeutung'). This is good so far as it goes. A reader would gain some understanding of the problem raised for the principle of substitutivity by the phenomenon of propositional attitudes, and also of Frege's view of the problem and his solution to it.

You get credit also for referring to Leibniz's principle of the indiscernability of identicals and also to the principle of substitutivity (identity substitution). You could also have said something about how the two principles are connected, in particular, how it is that the second principle sometimes fails even though the first principle is taken to definitive of what we mean by 'identity'.

Even if the question were focused more narrowly on Frege's explanation, however, an examiner would expect you to do more: e.g. to offer criticisms of Frege's theory and possible responses to those criticisms. Do you agree with Frege? Can you see any potential difficulties with his account?

For example, is it true that every proper name is associated with a particular sense, as Frege seems to imply? Consider the examples of '10+2' and '4x3'. These expressions are good examples for Frege's theory, because they display the 'route to reference' on their face. Computing the function 'plus' for 10, 2 gives the same result as computing the function 'times' for 4, 3. The route to reference is different even though the reference of each expression, 12, is the same.

In natural language, definite descriptions work in a similar way: The director of Pathways to Philosophy is GK. The owner of the white Reliant Scimitar GTE parked on Chesterfield Road is GK. Computing the 'function' in each case takes you to the same object, GK.

But proper names are not like this. It seems implausible to suppose that a proper name is equivalent to some particular description, nor does it seem plausible to hold that every speaker has the same understanding of a given proper name, such as 'Mary Anne Evans'. How do you distinguish the Fregean 'sense' of a name from various beliefs about its bearer? Where do you draw the line? Even if we go along with Frege and accept that in addition to the actual referent there is an explicit route to reference or mode of presentation of the object referred to in the case of the mathematical expressions or in the case of definite descriptions, it is harder to accept that a similar explanation applies to common or garden proper names.

But does it really matter if each speaker associates a different Fregean 'sense' with a given proper name? So long as there is agreement over the reference, there would be no misunderstanding. Perhaps we don't need to distinguish between the sense of a proper name and beliefs about the bearer or 'informational content'. What do you think?

I once heard a paper where the philosopher P.F. Strawson described proper names as analogous to a card index system. When you hear a 'new' name you write out a card in your mind, which might remain blank. Then, as you acquire more beliefs, you add entries to the cards. One card might be 'George Eliot' and another card might be 'Mary Anne Evans'. Then you discover the vital piece of information that the two names refer to one and the same person. So now you can add this further information to the two cards, in the form of a cross-reference: 'Mary Anne Evans (see George Eliot)'. This seems initially plausible. Can you think of any objections?

Probably the best defence of Frege can be found in Michael Dummett's brilliant, but lengthy books: 'Frege: Philosophy of Language' and 'The Interpretation of Frege's Philosophy'. Since Quine, contemporary philosophical logicians have generally been sceptical of Frege's notion of sense. Probably the most well known critique, together with the beginnings of an alternative approach to an account of the truth conditions for indirect discourse is Donald Davidson's paper 'On Saying That'.

As the question does not explicitly refer to Frege, you would be expected to at least show that you are aware of alternative accounts, as well as criticizing or evaluating Frege's theory.

This is work you have got to do for yourself. Any good text on Philosophical Logic will offer guidance on this, as well as books and articles that you could refer to. A good starting point is the chapter on Logic in A.C. Grayling Philosophy: A Guide to the Subject.

As it stands, your essay earns credit for clarity but would lose marks for failing to do much more than offer an exposition of Frege.

All the best,