THE LOGIC NOTES

Presupposition Identity and existence

The theory of definite descriptions stemming from Russell's 1905 paper is not without its critics. Perhaps the best known expression of a contrary view is that put forward by Peter Strawson in an important paper in 1950. Strawson charges Russell with confusion on a number of points. He suggests that Russell has confused:

Mind 1950, pp. 320–344. Reprinted in Strawson.
  • meaning with reference. In particular, Russell thinks that for a name to be meaningful, it has to denote something. He also thinks that for an indicative sentence to be meaningful, it must have a truth value.

  • sentences with the statements which they may be used to make.

  • entailment, or logical implication, with presupposition.

Let us consider each of these in turn.

  1. Russell did have a theory of "logically proper names", whose purpose is simply to refer to things, and which have no place in the language at all beyond that. It follows that for such a name to exist in the language at all, it must be fixed as the name of some particular thing, for there is no other mechanism by which it can function. He also believed strongly in the correctness of orthodox truth-functional logic, according to which every well-formed (meaningful) sentence has a truth value. However, holding that everything meaningful has reference does not convict him of holding that the meaning is the reference. Strawson, on the other hand, sees reference as separate from meaning, so that a particular use of an expression may end in a failure of reference without the meaning being deficient at all.

  2. The distinction between sentences and statements is seen most easily where the sentences involve indexical items such as pronouns ('I', 'he') or tenses ('is now', 'will be tomorrow', etc). These things change their reference from one use of the sentence to another, depending on who says it and when. Said by me on 1 January 2020, the sentence "I am in Canberra" would have made a true statement. Said by someone else, or by me on a different date, it would make a different statement, possibly with a different truth value. The sentence is the same, but the statements made by using it are different. Moreover, the sentence "Slaney was in Canberra on 1 January 2020" could be used to make the same statement, as could "He will be in Canberra tomorrow" said by someone else of me on 31 December 2019. Hence the sentence and the statement are not the same thing.

    Strawson appeals to such examples to suggest that while meaning is a property of the sentence, truth value is a property of the statement (if any) made by an instance of the use of that sentence. We sometimes do speak of the sentence or utterance as being true or false, but this is just a way of speaking: what is really true or false is the statement.

  3. Sometimes a perfectly meaningful sentence may fail to make any statement at all. One of Strawson's examples is the sentence "Here's a fine red one" uttered when there is nothing red in the vicinity. Since it makes no statement, it has no truth value although it does have a meaning. Similarly, the sentence "Bob is older than Alice" makes no statement unless we somehow fix the reference of the names "Bob" and "Alice": which of all the Bobs in the world are we talking about? —or are we using "Bob" to refer to the table and "Alice" to refer to the chair? If the names have no reference in the context of utterance, no statement is made. The fact that the names refer to someone (or something) is presupposed by the utterance. It is not [just] a logical consequence of the sentence; rather it is a condition that has to hold for the use of that sentence to say anything at all.

The suggested alternative view of definite descriptions is that they are, in fact, of the same logical form as the corresponding sentences using names, and that the existence and uniqueness assertions which Russell identifies are among the presuppositions of their use. On Russell's theory, the existence of a President of Australia is part of what is asserted by saying "The President of Australia is in Brisbane", and since there is no such President, the sentence is false. Strawson's contrary view is that someone who says (in 2020) "The President of Australia is in Brisbane today" does not assert that there is a President; rather, the existence of a President is presupposed. Since there is no such President, no statement is made, so there is no truth value. The sentence is perfectly meaningful, but because of the reference failure it says nothing true or false.

It is not my present purpose to pursue the philosophical debate further. For a fuller account of the logic of Strawson's position, or at least of a position deriving from his article, see the 1960 paper by Timothy Smiley Smiley which lays out a version of first order logic suitable for such a view.