I was reading this, and came across the paragraph

Working realism is the methodological view that mathematics should be practiced as if platonism was true (Bernays 1935, Shapiro 1997, pp. 21–27 and 38–44). This requires some explanation. In debates about the foundations of mathematics platonism has often been used to defend certain mathematical methods, such as the following:

As a computer programmer, this is the point of view I must adopt on a daily basis.

Question: How can I even parse the contents of that article and get a feel for its content without that same working realism outlook applied to that article itself?

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    Welcome to philosophy.SE :) I'm wondering about the reason you say you "must" adopt the working realist position as a programmer. Platonism is, roughly, the view that mathematical entities exist in some realm. Why should a programmer have any stance on these ontological/philosophical issues to do her work? May 30 '14 at 7:28
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    Thanks for the welcome! To answer your question: I program as if I were working with math objects, and the laws associated (at least with working realism) with them. For example, I have to believe (at least during my work day!) that something is either true or false - otherwise I's never be able to write a so-called "IF" block. Thanks!
    – user
    May 30 '14 at 7:39
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    You certainly don't have to believe that every proposition is either true or false. Even the classical "principle of excluded middle" doesn't imply this. And if you use SSE2 to improve the performance of your code, you can have conditional statements that execute the different branches simultaneously during a single operation. The conditional is simultaneously evaluated for all 4 registers, and nobody forces you to regard this as 4 separate operations. Just because some things are either true or false doesn't imply that every proposition is either true or false. May 30 '14 at 8:33
  • @bryanj, A conditional in a computer program is not "true/false" in a philosophical way. Surely you understand that all it means is that a particular location in a particular memory location has a certain value or not. This is a question about electrical engineering, not philosophy. And if you know a little about hardware, you know that the value in a memory location may be indeterminate, depending on when you look. You have to look at a particular point in the clock cycle in order to know that the value is definite. Again, this is electrical engineering, not philosophy.
    – user4894
    May 30 '14 at 15:37

In philosophy of mathematics we usually speak of platonism, while in philosophy of other branches of science we prefer the term realism, which seems more "palatable" and less ontological committed.

Basically, what the common sense of the scientific community share is some sort of belief about the existence of an external reality which is the reference for scientific language and theories.

Trivially, newtonian mechanics assume the existence of the planet, of an attractive force called gravitation, and so on. The same for relativity or biology.

Of course we have some issues here: see quantum mechanics, but the scientific community devotes a lot of time and money searching some empirical support to the existence of (e.g.) Higgs' boson. This presuppose some sort of belief in the reality of Higgs' boson.

Assuming this very rough introductory discourse, my point of view is that it is natural for a mathematician to share a common sense belief in some sort of realism regarding the mathematical language.

In other words, I think that the natural point of view of the mathematicians regarding the language of mathematical theories is that mathematical concepts must have some sort of reference.

And this is the source of troubles : where are numbers ? where are sets ?

The platonist answer troubles us because it is hard to maintain the common sense realist view regarding abstract entities.

But, and this is the point of view shared by some distinguished philosophers which have studied the philosophy of mathematics, like Frege and Russell, and currently debated under the headings of Naturalism and Indispensability argument, can we make sense of all mathematical science only considering it some sort of "formal game" deprived of any reference ?

  • You wrote: 'But, and this again is my personal point of view, can we "make sense" of all mathematical science only considering it some sort of "formal game" deprived of any reference ?' If this is your personal point of view, then don't post it as an answer to my question.
    – user
    May 30 '14 at 9:02
  • I was hoping, as someone very poorly versed in philosophy, for a well-establsished "party line".
    – user
    May 30 '14 at 9:06

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