mardi 3 avril 2012

On the Regress to Infinity Backwards Being Still Impossible

The creationist arguments and its variants rely on supposing that an infinite regression is impossible. I wonder, why precisely is such an infinite series held to be impossible.

It is actually the argument of St Thomas Aquinas. As in The Five Ways. Furthermore, it is not per se Young Earth Creationist.

If one places two mirrors facing each other, there is one mirror the image of the other, which contains its own image, which contains the image of the other, which contains its own image, et cetera ad infinitum.

Has the infinitude of mirror images been truly verified? But even so, it is not an infinitude backwards in causes, but forwards in effects.

It is not infinite regression, since it regresses to the two mirrors and what is put between them as first cause, together with light, of that particular effect.

If one divides 10 by 3, the answer is 3.3333333333333, etc. ad infinitum.

The value of pi, is held to be 3.14159, etc., etc.

If become aware that I think, I think that I think, and I think that I think that I think, etc. ad infinitum.

Are each of these not infinite regressions?

If one divides 10 by 3 one gets 3 and 1/3. If one uses duodecimals, that has a finite expression: the third length of ten feet is three feet and four inches. However, a seventh would be as impossible to express in duodecimals as in decimal fractions.

Since decimal fractions are not thirds, they are incommensurable with the third, and expressing the third in decimals becomes potentially infinite - i e whenever the mathematician gives up, he knows he could theoretically go on. And that however far he went on, he would not have exactly expressed that other ratio, as he exactly expresses it by saying 3 and 1/3.

That infinitude is precisely because it is impossible to express thirds in terms of decimals - unlike halves, fourths, fifths, twentyfifths, twentieths and so on.

Similarily the relation between periphery and diameter of a true circle is irrational, because these two have no common measure. It is therefore as impossible to express in either decimals or any other fractions as are into decimals those fractions of nominators including factors other than two or five.

If the universe itself contains these infinite regressions, why should there not be an infinite regression of causes?

Neither in double mirrors, nor in decimals do we find a regress into the infinite backwards in causation.

In the case of expressing thirds, sevenths, et c. in decimal fractions or of expressing irrational geometric relations in any kind of fraction (but you can say of any decimal acquired that it is below or above the value that cannot be expressed, as you can say of any non-decimal fraction in the case of irrational relations.

Such infinitude is purely accidental, and in the effect of expressing improperly, not in causation.

In the case of double mirrors, you have just maybe an infinitude forwards in effect (not really, I think), but certainly not backward in causation.

Hans-Georg Lundahl
UL of Nanterre,
Tuesday Holy Week
(Latin and Uniate Cal.)
Year of Our Lord MMXII.

2 commentaires:

Hans Georg Lundahl a dit…

Quotes are from starting point of this thread:

Why is infinite regression held to be impossible?

On Catholic Forums, I cannot answer this, since banned. The threads I did participate in are typically collected on:

A thread from (more may be added) =

HGL a dit…

New shortlink to previous link (since o-x short links were taken down):

By the way, try to express a tenth in ... duodecimals ... or in a system of positions where each position is three times more than the one to its right.

Either way you will have a fake "regress to infinity" because you have a real case of expressing a perfectly rational fraction in an incompatible unit of expression.