By James. Harkness
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Echoing Aristotle, the constructivist matl1e matician Leopold Kronecker rejected the reality of such abstractions, con demning them as artificial and m1real compared to the 'natural: potential infinity enshrined in the progression 1, 2, 3, . . '! But what is it that makes the mm1bers 'natural: that prompts matl1e maticians to call them so and conceive of them as given, always somehow 'there: before and independent of tl1e hmnan mind and its works? And why invoke God as tl1eir creator? ' Tl1is leads to a ques tioning of Aristotle's nous, the source of the supposedly natural ability to repeat endlessly.
For what rl1e alphabet eliminates is the body's inner and outer gestures which extend over speech segments beyond individual words. Both those visually ob servable movements rl1at accompany and pw1ctuate speech (which it was never its ftmction to inscribe) and, more to rl1e point, those inside speech, the gestures which constitute the voice itself-the tone, the rhyrlm1, rl1e variation of emphasis, rl1e loudness, rl1e changes of pitch, rl1e mode of attack, discontinuities, repetitions, gaps and elisions, and rl1e never absent play and musicality of utterance that makes human song possible.
Can tl1ey be transposed into words? What, for example, is the speech equiva lent of a wink? Or, for that matter, a shrug? a slap on the back? folding one's arms? hands clasped in prayer? And do their mode of operation and outcomes resemble those of speech? If so, why as speaking beings do we bother with them? The cultural range, robustness, and persistent use of emblems, tl1eir way of refusing and displacing speech, calls for an explanation. McNeill offers one in terms of 'word magic? "Spoken words are special and carry witl1 tl1em tl1e responsibility for being articulated.
A Treatise On the Theory of Functions by James. Harkness