By Michael Huemer (auth.)
Approaching Infinity addresses seventeen paradoxes of the countless, such a lot of that have no as a rule permitted strategies. The e-book addresses those paradoxes utilizing a brand new concept of infinity, which includes that an unlimited sequence is uncompletable while it calls for anything to own an enormous in depth magnitude.
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Additional info for Approaching Infinity
41 42 Approaching Infinity Kant was not really endorsing this argument (nor, however, was the argument supposed to be a mere fallacy); his purposes in giving this argument, however, do not concern us here. The italicized phrase in any case has a certain intuitive plausibility as an account of (one species of) the impossible infinite. I take it that what Kant means is that an infinite series cannot be completed by going through each stage of the series, one after the other (on the other hand, if one could somehow perform every stage simultaneously, perhaps matters would be different).
The infinite rod is initially oriented perpendicular to the finite rod (parallel to the plane). Assume that the rods and plane are unbendable, unbreakable, and impenetrable. What happens to the infinite rod in this example? Even though the force of gravity is pulling it downward, and even though it is supported on only one end, the rod cannot tilt downward, because any nonzero amount of downward rotation would require the rod to intersect and break through the plane somewhere. 8 In modern physics terminology, the rod undergoes an infinite net torque, yet it maintains a constant angular velocity of zero.
It appears that the result must be an infinite number of slices of the stick. How thick will each slice be? For any nonzero size you name, there was a point in the series when the pieces were cut smaller than that size. Therefore, the slices have no nonzero size; that is, they have a size of zero. How much matter could each of these slices contain? It seems that the answer must, again, be zero. 11 Thomson’s lamp Suppose there is a lamp with an on/off switch. The lamp starts out on. After half a minute, it is switched off.