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What is the meaning of this quote by A.J Ayer

when one buys a pair of shoes, one is buying three things, the right shoe, the left shoe and the pair

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    Apparently, it means that he sees sets of objects (pairs, in this case) as entities over and above their elements. But it is hard to say for sure without context. Where is the quote from?
    – Conifold
    Aug 15, 2021 at 0:52
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    Ayer says something close to this in Language, Truth and Logic, section IX.C (page 204 in the edition I have). He asks it as a question, though. "Are we prepared to say that when a man makes a pair of shoes, he brings three entities into existence, the right shoe, the left shoe and the pair?" It occurs in the context of a discussion of abstract entities and whether quantifying over sets commits one to their existence.
    – Bumble
    Aug 15, 2021 at 5:44
  • @Conifold I dont remeber, I had written it down in a notebook and found it while searching for something else. Aug 15, 2021 at 13:44

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It is a quote from Ayer's book, "Bertrand Russell", in Section ii, Russell's Philosophy of Logic. The full quotes is found in part C, 'The Theory of Types', on page 42:

"Moreover, it seems absurd [emphasis added] to think of a collection as an entity distinct from the items which compose it, so that when one buys a pair of shoes, one is buying three things, the right shoe, the left shoe and the pair".

After reading the quote in context, it is easy to see how the quote in isolation is inadequate. The remainder of the paragraph leads to a conclusion that the conceiving of classes as entities leads to:

"...the self-contradictory result that the number of things that there are is greater than their totality".

Ref: Bertrand Russell by A.J. Ayer.

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  • Thank you! So it means the whole is greater than the sum of its parts Aug 15, 2021 at 13:45
  • Ayer is not describing any claim made by Russell as to the necessary attributes of a whole, but identifies the contradiction that follows from a conception of classes as entities. Ayer goes on to describe how Russell preferred to consider classes. The link does not allow access to the full book. You will have to source one elsewhere. It does however contain a couple of pages following your quote which may be useful to you. Aug 15, 2021 at 14:14

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