4

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??

Stephen Meskin
  • 1,829
  • 8
  • 17
  • 5
    My opinion is I don't care. – 5xum Oct 24 '17 at 08:22
  • 4
    "God gave us the integers, all else is the work of man" - Kronecker – Henry Oct 24 '17 at 08:23
  • 2
    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.) – Dave L. Renfro Oct 24 '17 at 08:27
  • @5xum: What is(are) the reason(s) for saying so? –  Oct 24 '17 at 17:09
  • 1
    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. – Daniel Moskovich Oct 24 '17 at 18:31
  • @user170039 I don't see any way of proving the statement one way or another, and I don't see any reason to keep thinking about questions that cannot be answered. Numbers work in real life. When we do things to them, and then accordingly do things in real life, we can make stuff, and in the end, that's what counts. – 5xum Oct 25 '17 at 08:56
  • 1
    @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". –  Oct 25 '17 at 14:09
  • @user170039 I'm referring to the question "Are numbers real, in a metaphysical sense". Also, please keep in mind that the question was apparently quite heavily edited since I posted my original comment. – 5xum Oct 25 '17 at 14:49
  • 1
    @5xum: In that case can you please explain how you concluded that this question is one example among such "questions that cannot be answered"? How do you know beforehand that it can't be answered? –  Oct 25 '17 at 15:04
  • 1
    @user170039 I'm not even going there. Yes, technically, it is not impossible that the question cannot be answered. It's just that the question is in the group of metaphisical questions for which we don't have a good reason to believe they will ever be answerable (unlike mathematical questions, where our track record is much better). But anyway, I don't care for philosophical details and technicalities, just like I don't care if numbers are real (in a metaphysical sense, whatever the heck that means). – 5xum Oct 25 '17 at 15:07
  • I have rewritten the question, more in line with my original intention. Thanks for trying Donald. I think it fits the rules now; is thereby a better question; and the hold should now be dropped. Thanks for all the comments. – Stephen Meskin Oct 25 '17 at 20:58
  • @StephenMeskin the questions you formulated are somewhat related to the original question but the current formulation is not really faithful to the original formulation. Feel free to ask a separate question along the lines of what you proposed. – Mikhail Katz Oct 26 '17 at 07:25
  • @Mikhail Katz I had deleted the material that you restored ("the context") because it was "discussion" which the rules say is not wanted. The questions now are exactly what I wanted to ask originally. I may not have asked them very well at first. It took me a while to figure that out. – Stephen Meskin Oct 26 '17 at 07:44
  • @StephenMeskin, I think the objections focused not on context but rather on opinions. A question formulated as a request for opinions will amost surely be closed even if what you really mean to request is arguments and evidence. So it is better to say what you really mean. Context should obviously be included. – Mikhail Katz Oct 26 '17 at 07:47
  • @DaveL.Renfro, I agree with your sentiment in the sense that "it is easy to get lost in" naive platonist notions about the so-called "real" numbers. Therefore the foundations (or rather lack thereof) of such platonist beliefs can and should be analyzed, so as to correct common philosophical misconceptions. – Mikhail Katz Oct 26 '17 at 08:12
  • Are you, by any chance this user? –  Oct 28 '17 at 05:30
  • @user 170039 No I am not "this user" although our names are weirdly similar. – Stephen Meskin Oct 28 '17 at 06:37
  • Any argument about numbers don't existing is wrong. By way of contradiction suppose there is a valid argument about numbers don't existing. Since the argument is valid, this means one doesn't exist. But the argument is one argument, hence, one exists, which is a contradiction. Therefore, the numbers exist or there are no arguments. – Otakar Molnár López Nov 30 '23 at 15:02

3 Answers3

2

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.

ajotatxe
  • 65,084
1

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".

Mikhail Katz
  • 42,112
  • 3
  • 66
  • 131
  • 2
    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? – Asaf Karagila Oct 24 '17 at 11:26
1

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.

Aaron Chen
  • 21