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Reading group: Russell’s ‘On Denoting’ (1905), and the puzzle of the hare’s horn

Oskar Nyberg Fellow
· 5 replies · 183 views
Meaning & languageAnalyticIndianNyayaBertrand RussellPeter Strawson#definite-descriptions#empty-terms#reference#scope
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Bertrand Russell's "On Denoting", published in Mind in 1905, has been called a paradigm of philosophy, and it is also short. It is the best example I know of predicate logic being turned on ordinary language, so I'd like to read it slowly with others.

The puzzle is famous. "The present King of France is bald." There is no King of France. So what is the sentence about? If it is about nothing, how is it meaningful? Russell's answer is that "the present King of France" is not a name at all. The sentence says: there is exactly one thing that is presently King of France, and that thing is bald. Written with quantifiers and identity, nothing in it refers to a non-existent king. The sentence is simply false.

Plan, three weeks.
1. The first half of the paper: denoting phrases and Russell's analysis.
2. The three puzzles he uses to test it: George IV and the author of Waverley, the King of France and the law of excluded middle, and the difference between A and B when there is none.
3. Peter Strawson's reply, "On Referring" (1950).

I also want to bring in a much older discussion. Indian philosophers had their own stock examples of empty terms, the hare's horn, the sky-flower, the son of a barren woman, and debated how such expressions could be understood. Our member Meera has promised to help with that side.

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5 replies

  1. Tomasz Wójcik

    Fellow

    Week one. What Russell's analysis buys is clearest in symbols: ∃x (Kx ∧ ∀y (Ky → y = x) ∧ Bx). There is a king, at most one, and he is bald. Once the description dissolves into quantifiers, the problem of what the subject term refers to vanishes, because there is no subject term left. This is predicate logic doing philosophical work, and in 1905 it was barely a generation old.

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  2. Meera Kulkarni

    Fellow

    On the Indian side. The Naiyāyikas held that every cognition has a real object. So how do we understand "hare's horn"? On one standard Nyāya analysis the cognition combines two real things, a hare and a horn, under a relation that does not actually hold between them. The error is in the combination, not in the existence of the parts. Buddhist logicians answered differently, through their theory of meaning by exclusion.

    The structural parallel with Russell is striking: in both cases the empty term is broken into real components and a false claim about how they are related. I'd be careful not to say the Naiyāyikas "anticipated" Russell, since their question was about cognition rather than sentences, but the strategy rhymes.

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  3. Kenneth Leung Chi-ho

    Fellow

    Week two, George IV. He wished to know whether Scott was the author of Waverley. Since Scott is the author of Waverley, substituting one for the other should make the king wonder whether Scott was Scott, which is absurd. Russell's answer is about scope: the description can be analysed inside or outside "wished to know", and only one reading gives the absurdity. Scope again, the same idea that predicate logic made visible. I didn't appreciate before this how much of the paper is a demonstration of scope.

  4. Ana Clara Ferreira

    Fellow

    Week three. Strawson's objection is that Russell confused a sentence with its use. Someone who says "the present King of France is bald" doesn't assert that there is a king. They presuppose it. When the presupposition fails, the question of truth or falsity doesn't arise. So the statement is neither true nor false, which Russell's analysis cannot allow. As someone who likes non-classical logics, I enjoy the irony: Strawson's truth-value gaps send you straight back to logic, just a different one.

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  5. Oskar Nyberg

    Fellow

    Thank you. What I'll keep from this is that one idea, scope, carried the whole paper, and that Meera's hare's horn shows the same strategy found in a different tradition for a different purpose. I am still undecided between Russell and Strawson, which after twenty years of teaching this paper is probably my permanent condition.

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