Monday, December 10, 2012

Descriptions and modality, justification of deduction

To: Stuart B.
From: Geoffrey Klempner
Subject: Descriptions and modality, justification of deduction
Date: 12th December 2008 12:34

Dear Stuart,

Thank you for your email of 2 December, with your essay for the University of London Logic module, in response to the question, 'Can there be a convincing justification for deductive reasoning?', and your email of 9 December, with your Logic essay in response to the question, 'Could the statement, 'The present Prime Minister might not have been the present Prime Minister,' be true? Explain your answer.'

Justification of deduction

In defining a 'deductive' argument, reference should be made to the concept of 'logical form'. A deductive argument, if valid, is valid in virtue of its form. You use the term 'formal' but you don't actually talk about logical 'form' as such.

You quote the Encyclopedia article which refers to 'soundness' and 'completeness' but neglect to say anything about how soundness and completeness proofs are conducted in propositional calculus and first-order predicate logic, using the idea of a semantic model and underlying assumptions about individuals, properties and truth values. This forms the basis for Michael Dummett's British Academy lecture 'The Justification of Deduction' which you must read if you are going to do this topic.

Other classic discussions are A.N. Prior's paper on the imaginary logical connective 'tonk' which inspired much discussion. The rules for 'tonk' are defined as follows:

1. From P it is valid to infer P tonk Q.

2. From P tonk Q, it is valid to infer Q.

Look up 'Tonk', 'Plonk' and 'Plink'.

From the 19th century, Lewis Carroll's 'What the Tortoise said to Achilles' is still discussed. Achilles tries to teach the Tortoise modus ponens. 'If you have P, and 'if P then Q', then you can infer Q.' 'Why?' Before he knows what is happening, Achilles finds himself forced into an infinite regress of 'if...then...' statements.

I am surprised that you were prepared to settle for an 'inductive' justification of deduction, after you had so swiftly dismissed Goodman. Goodman would fully accept that the rules of deductive logic tell us how we 'ought' to reason. But that is consistent with viewing the use of deductive logic as a practice which is deeply embedded in the way we actually think.

Descriptions and modality

'The present Prime Minister might not have been the present Prime Minister.'

You say that 'our title sentence is an example hat demonstrates that both Russell's and Strawson's theory of definite descriptions are at least incomplete, if not actually in error.'

It does nothing of the sort. Russell by means of his theory of descriptions is fully capable of explaining the meaning of the sentence using a scope distinction. In longhand, 'There is an x such that x is the present Prime Minister and for all y, if y is the present Prime Minister then y=x and it is not the case that BOX (x is the present Prime Minister).'

We can leave BOX (the necessity operator) uninterpreted.

Strawson's theory would regard 'The present Prime Minister' as functioning as a name whose semantic value x is contingently dependent on the presupposition that the first part of Russell's analysis is satisfied. If the presupposition fails, then there is a truth value gap. Assuming the presupposition does not fail, the second part of the analysis is unaffected.

I don't see that Donnellan is relevant, although it is true that he utilises the scope distinction to make his point.

Of course Russell can say that the use of a definite description is legitimate even when we don't know who the description refers to. 'The first person to visit the Pathways web site after 1200 GMT' picks out a unique individual even though I have no means of knowing who that person is. (The web server is designed to deal with large numbers of page requests, but there is an order in which it deals with them.)

'The present Prime Minister might not have been the present Prime Minister' is not a counterfactual statement. An example of a counterfactual statement might be, 'Had the economy been doing better at the time of the last general election, then the present Prime Minister would not have been the present Prime Minister'. As it stands, the statement, 'The present PM might not have been the present PM' is true even if it would have required an extraordinary series of events to bring it about that he was not PM.

It is clear that you have made determined efforts to find a philosophical issue to discuss here, even though you have not been very successful in doing so. I would judge that the question is designed to bring out the difference between 'de dicto' and 'de re' modality, causing potential embarrassment to theories which attempt to explain modality in 'de dicto' terms. It is significant that before Kripke, philosophers tended to look askance at the very idea of de re modality, so potentially there is enough here to form the basis of an essay.

All the best,