New answers tagged

-1

The whole world is taught that there is no math without axioms. I am appalled. Why don't people try it? I suggest trying to define these terms first: number, procedure, element, collection, set, ordered set, one, two, zero, numeral, and one-to-one correspondence. You need the starting point of realizing that our perceptions include perceptions that are ...


0

Whether an event is a miracle or a non-miracle, does it depend on the point of view? No, of course not! -- tho when stated like that, your question kinda implies that we were looking from, yes, different points, but at the same event. Which is not what your example described. In your example, we are looking at two different events: getting a certain result ...


0

First, we're not sure that the universe is made of particles (groups or sets can only be made by particular objects). Particles and bodies are biased perceptions (the bias comes from our senses, see George Berkeley). An empirical truth, therefore, is that bodies exist (empirical: according to experience, not according to science or philosophy). In such case, ...


0

How do mathematical formalists account for the unreasonable effectiveness of mathematics? Formalism is internal to the mathematical system. It does not "leak out" of mathematics and "infect" the real world. Mathematics was designed to match up with reality in many respects. Much of early mathematics flowed directly from geometry, which ...


0

Your "computationally omnipotent God" is really just an oracle in disguise (as it should be). Call it oracle and be done.


0

Short Answer First, note that science is not a monolithic entity. Second, technically speaking, the role of statistical certainty in using models to determine what constitutes reality is the heart of a primary metaphysical debate in the philosophy of science: realism vs. instrumentalism. The most prominent example of this in practical science is in quantum ...


0

I'd like to hear more about what you mean by "computational step." If by "computational" you mean what we normally mean when we speak of computation, then my hunch is that there is no such entity, since we finite humans have a pretty good grasp on what computation is, and there are some sets with Turing degrees >1. If you mean ...


2

The expression " the number of sheep in this problem" is a definite description , " the so and so". And definite descriptions seem to be referring expressions, while they may not be, either due to the fact that (1) there is more than one object that satisfies the property, or (2) there is no such object. More deeply, definite descriptions ...


0

I was drawn here from a recent similar math.se question, for which I drafted this answer before it was closed: This is a tricky question because it's unclear whether the answer is epistemic, metaphysical or a mixture. Let's try those two options separately, each simplified but hopefully not beyond the point of usefulness: Epistemology, i.e. how mathematical ...


1

As with every part of mathematics applied in natural sciences one can embrace the point of view of instrumentalism. When investigating some natural phenomena (which I call the target system and denote it by T) scientist constructs a mathematical model M together with some sort of interpretation of that model I:M->T such that the pair (M,I) adequately ...


0

"If one experiences something that is not mathematically commensurate, is it not a real experience?" No, number theory can not express or explain everything. From Wikipedia: Examples of undecidable statements The combined work of Gödel and Paul Cohen has given two concrete examples of undecidable statements (in the first sense of the term): The ...


Top 50 recent answers are included