I understand why definite descriptions like 'the king of england' are denoting phrases according to Russell, but why does he suggest that 'a king' is equivalent to 'some king'?

In 'On denoting', Russell states 'By a 'denoting phrase, I meane a phrase such as one of the following: a man, every man, any man...' so clearly he views these as 'denoting phrases'.

For example 'a king' seems equivalent to 'one king', why is this treated as denoting anything but the idea of there being a single entity and that entity being a king.

For example, I could easily say 'one king lives in England', It is a simply a statement about how many kings live in england, I do not need to be using 'one king' to refer to any individual, I can imply that, but the true definition of 'one king' is simply 'a singular entity of type king'.

However, in it's nature 'some king' suggests that there is one king but that we will discuss him in specifics.

In what way are 'a/an X' statements treated as denoting statements, they don't need to necessarily denote anything. I understand why clearly using quantifiers such as 'every, any or some would act as denoting phrases, I am not sure about 'a king' or 'an apple' would be such denoting phrases, however phrases such as 'there exists an apple....' would be denoting phrases.

Why can phrases that seem to denote a concept also denote a real person/object?

  • Is "a singular entity of type king" not referring to some individual? My understanding is that Russell would translate your sentence as "there exists one x such that x is a king and x lives in England", so that bound variable x is your individual.
    – Draconis
    Dec 17, 2022 at 18:40
  • 1
    Right. The existential quantifier presupposes existence, so x exists and x is a king. And since logic is mathematics, all denotations are unreal. It's the language, not the logic, that points to the real world.
    – jlawler
    Dec 17, 2022 at 21:38


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