The Corner

Re: Jonah and Math

Ramesh: The story I am sure is apocryphal, but it is indeed the case that

the proposition “If P, then Q” is invariably true if P is false. In other

words, from any given false proposition, ALL OTHER propositions follow. So,

of course, do their negations. If 2 + 2 = 5, then I am NOT the Pope. (If 2

+ 2 = 5, then 0 = 1, so the Pope, being one person, is actually zero persons

and does not exist. I however, do exist…) For much, much more on this,

see Russell’s fascinating book INQUIRY INTO MEANING AND TRUTH.

Russell, by the way, defined mathematics to be: “The class of all

propositions of the form ‘If P, then Q’.” He meant this to be understood as

the class of all enquiries into the structure of, and connection between,

such propositions, of all chains of deduction, regardless of whether P is

true in the sense of everyday veridicality, and regardless of what actual

things P might refer to. Whence his other definition of mathematics: “That

subject in which we do not know what we are talking about, nor whether what

we say is true.” Modern philosophers of mathematics are not quite so

reductionist…

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