Wednesday, January 19, 2011

Another nod to "Quine"

[A footnote to this.]

A bit later in the same anthology (Hahn & Schilpp, eds., The Philosophy of W. V. Quine (1986), p.  400), our hero disburdens himself  more at large:

I recognize indenumerable infinites  only because they are forced on me by the simplest known systematizations of more welcome matters.  Magnitudes in excess of such demands, e.g. … inaccessible numbers, I look upon only as a mathematical recreation  and without ontological rights.  Sets that are compatible with ‘V = L’ in the sense of Gödel’s monograph, afford a convenient cut-off.

Eminently sensible.  Yet further:  it is one of the contentions (not yet much buttressed) of the essays in the “Theologia Mathematica” thread, that such entities are “forced on” us  via multiple independent routes, quite in the manner of material objects (the seen, the seized, yea scented  coffee-cup), and not merely (in Quine’s phrase) by “rounding out”.   The latter could be seen as mere convenience. -- More, obviously, anon.

Anyhow, until such undertakings be fulfilled, let us frankly concede, that simply “sounding mathy” is no free pass to the status of Reality.   It is case by case, just as with coffee-cups and unicorns.

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