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I live and work with numbers almost all the time and have done so for most of my 77 years. I can almost feel them. But it is only almost. I have to believe, contra Plato, that they and moreover all of mathematics is unreal in a metaphysical sense. They are not something "out there that we will stumble over." What we see when we say we see numbers in the wild is our translation of what is into a mathematical idea.

My feeling is that Mathematics is an outstanding instrument for constructing models of aspects of the real world. We started with counting and have gone on to particle physics, astrophysics, biostatistics, and even models of mathematics itself.

1) Are there any problems with assuming that numbers and all of Math is not metaphysically real?
2) Are there any problems with assuming that numbers and all of Math are just models of the real world??

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    $\begingroup$ My opinion is I don't care. $\endgroup$ – 5xum Oct 24 '17 at 8:22
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    $\begingroup$ "God gave us the integers, all else is the work of man" - Kronecker $\endgroup$ – Henry Oct 24 '17 at 8:23
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    $\begingroup$ If I stumble over an object while walking on a sidewalk, how do I know the object (or even my walking process) is real? Maybe I'm in something like The Matrix, or perhaps I'm in a matrix that exists within The Matrix, or I'm in a matrix that exists within a matrix that exists within The Matrix, etc. If I'm 17 levels down such a rabbit hole of embedded matrices, is this "17" the same as the "17" I arrive at by counting the number of steps I make while walking in such a situation? (Moral: It's easy to get lost in stuff like this.) $\endgroup$ – Dave L. Renfro Oct 24 '17 at 8:27
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    $\begingroup$ I've rewritten the ending to turn it into a question that is not "primarily opinion based". I hope I succeeded in faithfully reflecting the original intention of the OP. $\endgroup$ – Daniel Moskovich Oct 24 '17 at 18:31
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    $\begingroup$ @5xum: "I don't see any reason to keep thinking about questions that cannot be answered" - What "questions" are you referring to here? Do you mean OP's question in the title along with the ones in the body of the post? If this is so, I am not sure how can you say that they are "questions that cannot be answered". $\endgroup$ – user170039 Oct 25 '17 at 14:09
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I feel that numbers don't have a physical existence. They are semantemes, software. In fact, the only things that have physical existence can be detected in some way: mainly, matter and radiation. But no "numberscope" has been invented so far.

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    $\begingroup$ Haven't you noticed the numberscope in your bank that counts your bills with lightning speed? $\endgroup$ – Mikhail Katz Oct 26 '17 at 11:12
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Yea, math is simply a language to modeling the living world we live. I supposed that If we go to another universe, the mathematical method/approach would soon help us build scientific concepts and models over there. Just like transformations in mathematics, literally, if I assume principle "a" works in universe "A" and principle "a" can derive principle "b". And principle "a" was behaving in universe "B" in a different way, we may find an approach for "b" in universe "B" ... If someone thinks it is reasonable, translate it. Otherwise, throw it away.

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The so-called "real" numbers were first called real by Descartes. Descartes called them real not as a claim of authentic reality of any sort but rather to distinguish them from imaginary numbers that were already beginning to be used in the 17th century.

A more appropriate term for these numbers would be Stevin numbers rather than real numbers. Indeed, Simon Stevin already in the 16th century was the first one to develop in detail the scheme of representing each number by an unending decimal; see this publication for details.

The term rational is justifiable as the numbers in question are ratios of whole numbers. Also, natural numbers arise naturally in processes such as counting, etc. It is more far-fetched to claim that an undefinable real number occurs in any reasonable sense of the qualifier real leading to much confusion as to their ontological status.

Such a real number doesnt't have a referent in any meaningful sense, furnishing evidence in favor of the view that it is not "metaphysically real".

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    $\begingroup$ Why don't we call the natural numbers the Archimedean numbers, then? Or the rational numbers the Pythagorean numbers, or something else in that historical fashion? $\endgroup$ – Asaf Karagila Oct 24 '17 at 11:26

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