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Some people think mathematics is not an invention of man, but that mathematics exists independently of human beings, no matter what we think about it.

Some people think god(s) is (are) not an invention of man, but that he or she (or they) exist(s), no matter what we think about god(s).

Some people think mathematics is an invention of man and that it does not exist without human beings.

Some people (especially psychologists) think god(s) is (are) an invention of man and do(es) not exist without human beings.

If god exists, independently of us, then where does he exist? If mathematics exists, independently of us, then where does it exist.

As can be seen, there are many similarities between math and god.

So can we compare the belief that gods exist independently of humans with the belief that mathematics exists independently of humans?

  • See Platonism – Alexander S King Feb 14 '17 at 19:58
  • Take note of how you want to "place" the existence of things -- "Where does he [god] exist?", "where does it [math] exist?" – Dave Feb 14 '17 at 20:46
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    "Am I right?" pseudo-questions are one of those things that are explicitly listed as off-topic on this site. And one can see why: people think a lot of things, so what? What can the "answers" to that possibly be other than more people writing more of what they think. That's good for a forum but not for SE. – Conifold Feb 14 '17 at 22:42
  • I can imagine that gods exist (in a physical place, that is not necessary our Universe, though for the ancient Greeks all gods lived in the same Universe as where we live in) even if we don't think about them, but I can't imagine that the body of mathematics exists, like Plato thinks, somewhere outside the mind of humans. Maybe geometrical objects exist in Nature (though not in the ideal form which Plato imagines, but in an Aristotelian way), or can be constructed, but for example, numbers or relations between them have no place outside the mind. They don't exist in Nature (outside the mind). – descheleschilder Feb 14 '17 at 23:30
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    @AlexanderSKing Under your interpretation it seems like a duplicate of Is mathematical platonism compatible with Platonism?, but it does not read that way to me. It reads more like "here are some similarities between gods and mathematics, what do you think?" – Conifold Feb 15 '17 at 21:01
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All four beliefs you mention are ontological claims, so in that respect they are similar.

  • Gods are real, and exist without human beings
  • Math is real, and exists without human beings
  • Gods are a product of human invention
  • Math is a product of human invention.

All four make statements about "...the nature of being, becoming, existence or reality as well as the basic categories of being and their relations." In that sense they are similar. You could also say the statements are metaphysical, another similarity.

Of course, the class of statements that are ontological are quite wide and diverse. "My wife is beautiful" is also an ontological claim, though not of the same grandeur as the phrases you chose (though I'd also hope that I could argue that that claim was empirical as well, rather than just ontological). If I were to be claiming similarities between "math" and "god(s)," I would want to generate a more complete argument. The direction of that argument may vary, depending on who I was trying to convince. If I was talking to a pastor, I might try to divine an argument that the properties of mathematics encourage kindness to all. If I was talking to a militant atheist, I might dig at the uncertainty in the heart of science using mathematical terminology, and draw relationships to that of the uncertainty of existence of deities.

It's also possible to extend the arguments to show the differences between math and the god(s) instead, though I would leave that to an exercise for the reader.

  • I like your answer though I don't think you can divine an argument (I know it's just an example) that the properties of mathematics encourage kindness (the properties of mathematics encourage quite the opposite in my experience) and neither would mathematical terminology will make the atheist doubt his case. By the way, empiricism is a sub-set of realism. If you say that your wife is beautiful, then that's objectively real for you. – descheleschilder Feb 15 '17 at 0:31
  • @descheleschilder I've had a lot of fun with models built around stationary points on differentiable manifolds which suggest some rather interesting results about how to live your life if you believe you exist on such a manifold. And I'd highly recommend exploring "reverse mathematics," which strives to dig towards the smallest assumptions you can make. Once you get down to the point where mathematics is barely standing up on its own feet, it starts to pick up an interesting beauty. – Cort Ammon Feb 15 '17 at 3:43
  • -Maybe standing on a stationary point on a manifold let you see the beauty of your wife (assuming you're married)! And that surely has grandeur! – descheleschilder Apr 24 '18 at 9:32
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Each system has a core set of concepts/beliefs/definitions:

  • The existence of God
    • God created the universe.
    • There is some kind of after life
    • God affects events.
    • ...

And

  • The existence of numbers
    • The existence of terms, concepts, operators (pi, plus, minus, ...)
    • Definitions of basic operations (0 * 1 = 0, 0 + 1 = 1)
    • ...

As an abstract concept, we can't really prove "numbers" or the most basic operations exist, however if we have "faith" they do, we can build the rest of the system on top of them.

That said, there is a negative proof, specifically we can not use the majority ** of mathematics without numbers existing.

** - there are some basic operators like "Greater than", which don't require numbers. https://www.scientificamerican.com/article/how-animals-have-the-ability-to-count/

Any outcome attributed to religion can be achieved regardless of whether god exists or not.

The majority (see above) of outcomes of mathematics, require numbers to exist.

  • The existence of numbers may be very different from the existence of, lets say, a rock. For mental objects means something like the concept can be thought without contradictions. – borjab Apr 18 '18 at 21:41

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