By Michael Huemer (auth.)
Approaching Infinity addresses seventeen paradoxes of the countless, such a lot of that have no ordinarily approved recommendations. The ebook addresses those paradoxes utilizing a brand new thought of infinity, which includes that an enormous sequence is uncompletable whilst it calls for whatever to own an unlimited extensive magnitude.
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Additional resources for Approaching Infinity
Sample text
One might say: the physical properties of the switch will determine how many times it can be switched. Depending on how it is constructed, the switch will break at some point, sooner or later. This would of course be true of any real, physical mechanism. But now the theory we’re trying to evaluate claims that it is conceptually impossible to complete an infinite series – we are supposed to see this to be true just in virtue of the meaning of ‘infinite series’. It is hard to believe that the way to vindicate this claim is to point to the fact that switches in the actual world eventually wear out.
This may not sound terribly impressive. But if this works, there is also a way to extract an infinite amount of money from the casino. First, apply the betting strategy as described above, until you win your dollar 20 It is logically possible, consistent with the stipulations of the scenario, that you get stuck with an infinite series of black and green; however, the probability of this happening is zero. 36 Approaching Infinity of profit. Then, instead of walking away, simply start over with the $1 bet on red again.
The logic appears unassailable, and there are only three premises. Of these three premises, I cannot see how one 44 Approaching Infinity can deny #1 or #2. Therefore, if one affirms premise 3 – as the theory we are now considering explicitly does – it is hard to see how one can avoid concluding that motion is impossible. Or, to put the point the other way around: motion is obviously possible. But every motion can be divided into an infinite series of sub-motions, all of which are completed, one after another in sequence, every time something moves.