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Questionsaboutstuff's avatar

Book on logic and its interconnectedness with physics?

Asked by Questionsaboutstuff (265points) October 7th, 2014

How our logic seems to only work in a universe with our laws of physics and would not work if the laws of physics were different.

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5 Answers

Bill1939's avatar

If in an alternate universe the speed of light was different from ours, their laws of physics would be different, but likely would be analogous.

Questionsaboutstuff's avatar

Suppose we have two stones, the first being lighter than the second. Release the two stones from a height to fall to Earth. Stone 2, being heavier than stone 1, falls more rapidly. If they are joined together, argues Galileo, then the combined object should fall at a speed somewhere between that of the light stone and that of the heavy stone since the light stone by falling more slowly will retard the speed of the heavier. But if we think of the two stones tied together as a single object, then Aristotle says it falls more rapidly than the heavy stone. How do the stones know if they are one object or two?

The logic we use means we couldn’t have a world were heavier objects fall faster and its true for most things in physics that there will be logical inconsistencies

LostInParadise's avatar

I interpret your question to mean whether the basic laws of logic, truth tables and such, depends on the laws of physics. It is a fun question to contemplate, but there is unfortunately no way of knowing the answer. Consider further that all of mathematics can be derived from the laws of logic plus set theory. This seems pretty basic. You would think that in any alternative universe there would be an equivalent to our laws of logic and set theory, which brings up the question of whether mathematics extends to all other universes. For more on this, refer to this very readable paper by the physicist Eugene Wigner on the “unreasonable effectiveness of mathematics”.

flutherother's avatar

I can imagine a universe where the laws of physics are different but I can’t imagine one where logic doesn’t work, although as far as I know it hasn’t been proved that logic will always work in this one.

Bill1939's avatar

@Questionsaboutstuff my understanding of Galileo’s experiments with falling objects is that the fall at the same rate regardless of mass. The link to the lengthy paper that @LostInParadise provides seems to support my understanding. “One such regularity, discovered by Galileo, is that two rocks, dropped at the same time from the same height, reach the ground at the same time.” ”... the length of time which it takes for a heavy object to fall from a given height is independent of the size, material, and shape of the body which drops” (excluding air resistance).

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