Rationality Quotes September 2012

Jayson_Virissimo

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Here's the new thread for posting quotes, with the usual rules:

Please post all quotes separately, so that they can be voted up/down separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
Do not quote yourself
Do not quote comments/posts on LW/OB
No more than 5 quotes per person per monthly thread, please.

Ok, I stand corrected on the dates, my mistake.

But still, didn't we already know that if you take a line, two distinct points A and B on it, there are an infinite number of points between A and B, and yet an infinite number of points outside [AB] ? Didn't we know that since the ancient greeks ?

I suspect "infinite" was supposed to mean "having infinite measure" rather than "having infinite number of points / subsets". In the latter sense every being, not only God, would be infinite.

8Tyrrell_McAllister14y

First, Spinoza is not using infinite in its modern mathematical sense. For him, "infinite" means "lacking limits" (see Definition 2, Part I of Ethics). Second, Spinoza distinguished between "absolutely infinite" and "infinite in its kind" (see the Explication following Definition 6, Part I). Something is "infinite in its kind" if it is not limited by anything "of the same nature". For example, if we fix a Euclidean line L, then any line segment s within L is not "infinite in its kind" because there are line segments on either side that limit the extent of s. Even a ray r within L is not "infinite in its kind", because there is another ray in L from which r is excluded. Among the subsets of L, only the entire line is "infinite in its kind". However, the entire line is not "absolutely infinite" because there are regions of the plane from which it is excluded (although the limits are not placed by lines).

2[anonymous]14y

That's a good point. Spinoza himself was a mathematician of no mean talent, so we should assume that he was aware of it as well. So the question is, does his argument avoid the mistake of taking 'infinite' to mean 'all encompassing?' without any argument to that effect? There are certainly questions to be raised about his argument, but I don't think this is one of his mistakes. If you don't want to take my word for it, here's the opening argument of the Ethics. Good luck, it's quite a slog. The idea seems to be that the one substance has to be infinite and singular, because substances can't share attributes (see his definitions), and things which have nothing in common can't interact. Therefore substances can't cause each other to exist, and therefore if any exists, it must exist necessarily. If that's true, then existence is an attribute of a substance, and so no other substance could exist. At any rate, the argument concerns an 'infinity' of attributes, and I think these are reasonably taken as countably infinite. Spinoza also defines infinite as 'not being limited by anything of the same kind', so by that definition he would say that with reference to the 'kind' 'number', the even numbers are finite, though they're infinite with reference to the 'kind' 'even number'.