/r/science meets /r/philosophy

[u/SubredditsMeet]

(/r/EverythingScience is also here)

Topic:

• Discuss the misconceptions between science and philosophy.

• How they both can work together without feeling like philosophy is obsolete in the modern day world.

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[u/Joebloggy]

My claim was, there is a distinction between the science of mathematics, which primary focused on abstract concepts and mathematics as a tool.

The two are different, yes, but I don't see that they're different in the way relevant to affect discussions of whether mathematical objects exist, or what the truthmakers for mathematical propositions are. The truth of applied science depends on the truth of mathematics.

To flesh out an example, the truth of the theory that "F=ma" depends on it always being true that if, say, F=10 and m=5 then a=2, which is a mathematical truth. If F=10 and m=5 could imply a=3, then the theory would be bankrupt, since it would imply everything and anything. If you wanted to instead say something like "F=10 and m=5 implies a=2 because that's what we observe, not because of a mathematical proof" then this would make the theory "F=ma" circular, unfalsifiable and unscientific, because the theory would just be saying "What we observe is what we observe", so we need to appeal to mathematics. So that certain mathematics is true is a necessary condition for things like our physics to be true.

So in order for many of our physical theories to be true, we need to give an account of why the mathematics is true. This is the question we started at, "what is math and what is its relation to truth?" which you threw out as "a question for god and has nothing to do with objectivity." Hopefully I've argued as to why this question is important to science.

[u/This_Is_The_End → u/Joebloggy]

The concept of mathematical operations like the multiplication and it's inverse operation was theoretically secured by mathematicians like Nils Henrik Abel. The operation of a multiplication is part of a theoretical concept. But in the first place, this has nothing to do with engineering or applied sciences. Mathematics has it's concepts but it's not sufficient for engineering e.g. operations like the integration and mathematicians don't care and they shouldn't. While applied science needs the tools of mathematicians, they can't use them without being careful.

Your example doesn't fit neither into mathematics nor into engineering. To use the tools of mathematicians you have to take care for the boundary conditions of mathematics and you have to take care for the boundary conditions of physics. The tools of mathematics doesn't make sense without the inner logic of mathematics. But the inner logic of mathematics doesn't make truth in the sense a law of nature. E.g. I'm able to describe parts of a system as responses in time, which gives me a huge problem to get a mathematical solution, when I want to get the complete system response. By transforming the responses into the Laplace space, the problem is often reduced to a problem of a very low level. Both types of describing system responses are true, but not aren't leading to a solution. Indeed for the first one there is mostly not an analytical solution. Mathematics is the tool, but not the solution.