Math vs. Materialism

[OrderoftheSerpent]

This is a hefty topic, and I will try and be as brief as possible. TLDR at the end.

I think one of the most interesting and important metaphysical questions is whether or not mathematics are created by rational beings or discovered by rational beings. This question can be applied across all metaphysics more or less (“are physical laws created or discovered? Are the laws of logic created or discovered?”), and in each case it seems that the laws are, in fact discovered. When science, logic, or mathematics mislead us, this does not devalue you them or invalidate them. Rather, it is precisely because we discover physical, logical, and mathematical laws, that they have been so useful in real-world application, and that we can retrace our steps and return to proper and factual discovery.

Despite all this, physical monism – the position that only physical matter exists, and all things reduce to that physical matter (aka materialism, reductionism, etc.) – is one of the more increasingly popular metaphysical views in Western philosophy. At face value you may ask, “why ‘despite all this’?” Many do not seem to see the contradiction between these two issues. In the briefest words possible: mathematics are something non-physical which objectively exist. Here is the argument of that:

P1: If only physical things exist (physical monism), then non-physical things cannot exist (TRUE)

P2: Non-physical things (i.e. mathematic ontology) exist (CONTENDED)

C: Therefore, physical monism false (TRUE if P2 is true, FALSE if P2 is false)

So, can we show P2 is true? To investigate we will use 4 things that I would like you to imagine and keep in mind. The English word “three,” the numerical symbol “3”, the Roman numeral “III”, and a physical pile of “three apples.” The question at hand is if these are just made up concepts based on the physical, or if they objectively exist. We will explore this through a series of questions, the main topic of this thread. Please note these questions cannot necessarily prove P2 independently, but taken together we come to a rather conclusive answer.

- “Three” is a word specific to certain languages. If we change the language, or even write this in all Wingdings font, has something actually changed about the meaning? If mathematics are made up then yes, but if the word simply describes something objective then the answer is no.

- What if we wrote the symbol “3” as something entirely different? What if we switched the symbol “3” with the symbol “4”, and then made this uniform throughout our culture? Would 4-formerly-3 describe something different now, or has only the symbol changed?

- On this topic, if we change “3” to “4” are there now more apples in our pile of “three apples?”

- “3” and “III” are both symbols that describe the same concepts. Sure, we create these symbols like we create the words “three” and “four,” but do they describe an objectively existent thing?

- Perhaps most important, can you actually show, in a physical manner, the number we call “three?” For “three” is just a word, “3” is just a symbol, and “three apples” is simply one of many examples of the number three, not “three-in-itself.”

- A final question: before rational minds existed, was there a point where a rational mind could not come in and discover mathematics? To elaborate, at basically any point in history, even before life came to exist, there were X number of particles that could, in theory, be counted. If mathematics is made up by humans, there were not a set quantity of particles before minds came to exist. If mathematics objectively exist and are discovered, this is no issue.

I know, “brief, he said.” So let us get to the conclusion. It seems that mathematics is certainly something with objective existence. If it was not, then we could switch the symbol “3” and “4”, and magically “4-formerly-3” apples would increase in quantity. This is obviously not the case. Further, mathematics do not seem to be physical, on the symbols and language we use to describe math are physical. We can show the word, symbol, or quantity of 3, but not what philosophy would call “3-in-itself.” From this we can conclude that P2, and therefore the argument, are sound, and physicalism is invalid.

Of course this does extend past math. For example we can only show examples of the Law of Identity since it is not something that physically exists, consciousness cannot be reduced to the physical, and that’s not even considering that most physical laws can be described mathematically – but this was specifically a response to recent online discussions centering on mathematics. Of course, it also proves that immaterial things can objectively exist.

TLDR: Math is mind-independent, discovered rather than created, and non-physical. Since this seems to be true, physical monism - the position that only physical matter exists, and all things reduce to that physical matter (aka materialism, reductionism, etc.) – cannot be true and must be rejected.
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[Desecrated]

Bertrand Russell have already sorted this out, and explains in it much better terms than I can do on an internet forum. I suggest reading his works.

TLDR: You're wrong

[OrderoftheSerpent]

Bertrand Russell have already sorted this out, and explains in it much better terms than I can do on an internet forum. I suggest reading his works.

TLDR: You're wrong

Russell did not disprove mathematical ontology, even if you happen to agree with his attempts.