Mathematics and the Image of Reason by Tiles Mary

Author:Tiles, Mary.
Language: eng
Format: epub
ISBN: 978-1-134-96771-1
Publisher: Taylor & Francis Ltd

But what is it that exists and of what are the axioms true if they are only supposed to be defining a type of structure? As Frege complained:

A is an intelligent being.

A is omnipresent.

A is omnipotent.

Suppose that we know that these propositions, together with all their consequences do not contradict one another. Could we infer from this that there exists an omnipotent, omnipresent, intelligent being? I do not see how. Are there any means of proving consistency other than that of exhibiting an object that has all of the properties? (If one has one then one does not need to prove its existence by going via consistency.)

(Frege 1971 p. 20)

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