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If there are two distinct theories that are functionally equivalent — i.e. that make the same predictions, produce the same results, can be verified by the same empirical observations, etc — then why does it matter which we choose? The choice is aesthetic, not analytical. We might choose to use one theory in one case and the other theory in a different case, ...


3

You cannot know in any given experiment that something was not determined, only that it was not determined by the set of rules proposed. So to run your experiment you would need a perfect set of rules. This set of predictive rules would correctly predict all outcomes that can be predicted. But then the set of rules already decided whether there is or is ...


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This has nothing to do with philosophy, or even the philosophy of science. If you look at the book by Einstein and Infeld, The Evolution of Physics, they point out carefully that it’s quite feasible to discuss the tundamental ideas of physics (and of mathematics) in prose as they are few in number. It’s a mistake, that many people make, that mathematics ...


2

The task the OP presents is similar to the Achilles and the Tortoise presented by Zeno in Plato's Parmenides. A task which can be completed is divided into an infinite series of smaller tasks which now cannot be completed. Nick Huggett describes this as a "supertask" and offers the following resolution based on M. Black's "infinity machines" (‘Achilles ...


2

In my opinion, the underlying fallacy of your argument is that you assume that because you have described the motions as divided into an infinite sequence of sub-motions, then somehow they actually ARE divided into an infinite sequence of sub-motions. This is not true; there is only a pair of objects moving continuously. Just because you can mark an ...


1

Philosophically speaking, a paradox (like the version of Zeno's paradox outlined here) is not meant to show that there is something wrong with the world. It is meant to show that there is something wrong with our understanding of the world. Zeno was not disputing that motion was possible, since it self-evidently is. Zeno was pointing out that the mathematics ...


1

If the question at hand is one of modeling, you will likely keep them all as a "toolbox" and use whichever one lends itself best to solving a particular problem. A good example is Newtonian, Lagrangian, and Hamiltonian mechanics. They are all "correct" but they are all also only models of what is "actually happening." They all give the same answers and are ...


1

Taking your example of the two "equivalent" theories (which we will assume are both mathematical models), one will be favored over the other for the following reasons: 1) One model makes testable predictions that the other one does not, 2) One model successfully accounts for observations and data collected in the past, which the other one does not, and/or ...


1

The issues hangs on what we mean by 'empirical'. You say, Given that no empirical evidence will truly disprove either side, it is a matter of probability. Here you are assuming that 'empirical' means 'sensory'. This accords with most dictionary definitions and is not a problem. But consciousness is not an empirical phenomenon and yet we know we are ...


1

I will attempt to make your argument more concise: P1: Free will exists. P2: The theory of infinite universes is true. C1: (From P2) Therefore, there exist an infinite number of unique universes. C2: (From C1) Therefore, in at least one of those universes I must freely commit a specific self-deprecating irrational action (e.g. cutting my leg off). C3: (...


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