Author Topic: Mathematics and Physical Monism  (Read 263 times)

Xepera maSet

Mathematics and Physical Monism
« on: June 21, 2017, 06:10:33 pm »


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. 
"You look up into the night sky - whether as a child or an adult - and if you open yourself honestly, then it is a gateway to mystery, to the unknown."
- Dr. Stephen E. Flowers

Onyx

Re: Mathematics and Physical Monism
« Reply #1 on: June 21, 2017, 07:28:41 pm »
In my view, all knowledge is discovered rather than invented. Dr. Ohm did not invent electricity, but was able to describe his measurements of real phenomena in terms of a simple and reliable formula. I do not believe the clockwork of the natural universe requires a mind to control it, but do believe that a mind is required to give it contrast and definition.

One thing that confused me about Platonic Forms is how to sort them all out in some logical way. But that really isn't necessary, all of the infinite combinations of transcendental things are there for the taking. Through the "magic" of consciousness, we have the capacity to understand the abstract concepts that apply to our own individual Xeper.
« Last Edit: June 21, 2017, 07:30:26 pm by Onyx »

merytseth

  • Guest
Re: Mathematics and Physical Monism
« Reply #2 on: June 22, 2017, 10:12:05 am »
A well reasoned piece.  In physical monism, mathematics arises as a consequence of physics.  This would seem to imply that mathematics is an abstraction of the features and behavior of the physical universe - however, the foundations of mathematics have nothing to do with the observable universe, and mathematical truth is not determined by any physical relation, but rather by reason.  Further, mathematics is not sufficient to describe the interactions of the physical universe, as noted in the limitations of Newtonian mechanics, General and Special Relativity, etc.  

I take it you're enjoying the book on Godel?

Kapalika

Re: Mathematics and Physical Monism
« Reply #3 on: June 22, 2017, 03:52:48 pm »
I'm not sure why you just don't refer to it as materialism. Also I kinda feel that a lot of the arguement was just changing around meanings as opposed to intent.

Also to get this contradiction the person has to believe that mathematics are their own abstract thing, which many materialists don't. Instead many view it as just like language, something invented to describe things.

I hold the view that math is a language but that what is abstract is the logical rules it follows, not math itself. It's one of the arguments I use against materialism since they are without form, locality, or mass and yet they seem to be omni-present (same as the laws of nature). There does seem to be some interaction between natural laws and physical nature, in terms of values, but I'm not sure that proves that they are physical, just that they have a close relation with the physical and so more interdependent rather than transcendent.
My Music // My Blog

Formerly known as Shamira

Kapalika

Re: Mathematics and Physical Monism
« Reply #4 on: June 22, 2017, 05:23:45 pm »
Something I should clarify, it seems to me the logical rules that govern math and natural laws itself is transcendent, but that the natural laws are more interdependent with the physical universe, and math a language governed by logic. There are many layers to my system... I should make an updated chart sometime...
My Music // My Blog

Formerly known as Shamira

merytseth

  • Guest
Re: Mathematics and Physical Monism
« Reply #5 on: June 22, 2017, 05:27:16 pm »
I'm not sure why you just don't refer to it as materialism. Also I kinda feel that a lot of the arguement was just changing around meanings as opposed to intent.

Also to get this contradiction the person has to believe that mathematics are their own abstract thing, which many materialists don't. Instead many view it as just like language, something invented to describe things.

I hold the view that math is a language but that what is abstract is the logical rules it follows, not math itself. It's one of the arguments I use against materialism since they are without form, locality, or mass and yet they seem to be omni-present (same as the laws of nature). There does seem to be some interaction between natural laws and physical nature, in terms of values, but I'm not sure that proves that they are physical, just that they have a close relation with the physical and so more interdependent rather than transcendent.
Fair point about materialism, but I have to offer a clarifying point on math.  Mathematics is the application of reason. There isn't really a distinction between mathematics and its logical structure. One doesn't need numbers, or even the familiar binary operations like addition/subtraction, multiplication/division to do mathematics.  The use of a number (three, in this case) as an example of a mathematical object is just in the interest of using something familiar.  Many non-numerical things (like the symmetries on a regular n-gon, for instance) are also mathematical objects.

Edit:  On reflection, I suppose something like the 'addition with carrying the 1' arithmetic algorithms or following the rules of derivatives or integrals could be seen as math that isn't the same thing as the logical structure underneath - so I see your point. :)
« Last Edit: June 22, 2017, 05:36:01 pm by merytseth »

Xepera maSet

Re: Mathematics and Physical Monism
« Reply #6 on: June 22, 2017, 07:35:39 pm »
A well reasoned piece.  In physical monism, mathematics arises as a consequence of physics.  This would seem to imply that mathematics is an abstraction of the features and behavior of the physical universe - however, the foundations of mathematics have nothing to do with the observable universe, and mathematical truth is not determined by any physical relation, but rather by reason.  Further, mathematics is not sufficient to describe the interactions of the physical universe, as noted in the limitations of Newtonian mechanics, General and Special Relativity, etc.  

I take it you're enjoying the book on Godel?
I had to put it down for a bit, switch back over to Moral Philosophy for a while haha. I got to the point where we showed the axiom of parallel lines to be a false axiom, which despite the obviousness in hindsight really blew my mind. A similar thing happened with your Imperishable Star article, where you pointed out that all numbers can be described by primes. 
"You look up into the night sky - whether as a child or an adult - and if you open yourself honestly, then it is a gateway to mystery, to the unknown."
- Dr. Stephen E. Flowers