Does Math Exist Independent of Our Minds?

[blü 2]

Rather than solely being the product of reason, math is also waiting there for us to discover it.

Or, maths is the product of a particular kind of reasoning, and so far it's been possible to take its various branches, and the relationship of those branches, to greater and greater levels of abstraction ─ bearing in mind that the only place abstractions are found are in brains.

Thus, it comprises structures which exist largely
independently of us.

Seriously? Then I'd be grateful if you could provide an example of a structure 'comprised of mathematics' which exists independently of any observer.

 

[Revoltingest]

Or, maths is the product of a particular kind of reasoning, and so far it's been possible to take its various branches, and the relationship of those branches, to greater and greater levels of abstraction ─ bearing in mind that the only place abstractions are found are in brains.
Seriously? Then I'd be grateful if you could provide an example of a structure 'comprised of mathematics' which exists independently of any observer.

Consider the simple system of counting numbers.
Even if humans never existed, it still exists in non-humans.
Ref....
Number sense in animals - Wikipedia
I'll wager that if we're ever visited by aliens that we will
recognize each other's mathematical systems.
Math differs from other intangible things like art & language
in that there's less variation from culture to culture (except
in notation & degree of sophistication). This points to
universal underlying & independently existing structures.

 

[Nous]

Indeed i have!!

Then state an argument concluding that mathematical realism is false. All you've done here so far is write a bunch of silly vacuous sentences and post pictures.

Arguments for mathematical realism have already been noted and otherwise referred to on this thread. I will specify a few of my own, beginning by quoting myself from another thread -- Scientific Realism Begets Mathematical Realism -- where I stated a couple of indispensability arguments:

Do you agree that from scientific discoveries and theories we can infer the nature of empirical reality, at least insofar as determining if an entity constitutes (some part of) empirical reality, or concluding that the essential terms of scientific theories refer to something objectively existing? This is just the thesis of scientific realism. “Scientific realism is a realism about whatever is described by our best scientific theories”. Scientific Realism (Stanford Encyclopedia of Philosophy)

E=mc2, F=ma, F=k(q1q2)/d2 (Coulomb’s law), ∆S ≥ 0 (second law of thermodynamics), Schrodinger’s equation, the laws of conserved quantities, etc., etc. These are the sorts of entities or facts that physicists discover about empirical reality. Obviously these are mathematical relations, i.e., relations between quantities. Energy is a quantity whose value is the product of two other quantities--the mass of a system multiplied by the speed of light squared. Granted, all the particular mathematical relations or laws just noted may be inexact approximations, their applicability limited to a particular domain or specific conditions. Nevertheless, we can hardly imagine the discovery of more exacting or truer statements about the nature and operation of empirical reality than relations between quantities.

[. . . ]

Perhaps one wishes to claim that physicists discover other kinds of stuff in addition to mathematical relations, such as, say, the discovery of the electron. Few people would quibble with that. I would note that, even so, everything we know about electrons pertains to their mathematical (measurable) nature and their relations with other quantities or mathematical relations. J. J. Thomson’s cathode ray experiments did not involve the discovery of anything of a non-mathematical nature about empirical reality: he deduced the particulate aspect of the rays (which had been speculated), that the particles have a negative charge, and he arrived at estimates of the size of charge and mass by way of calculations and deduction premised on the degree the rays were bent by electrical currents of differing strengths. The discovery of the electron was ultimately the discovery of a quantity or a set of quantities and mathematical relations.

[. . . ]

Thus, taking my cue from some of the characteristic claims of scientific realism--

“The entities described by the scientific theory exist objectively and mind-independently.” https://en.wikipedia.org/wiki/Scientific_realism “The central terms of the best current theories are genuinely referential.” http://www-personal.umd.umich.edu/~delittle/Encyclopedia entries/scientific realism.htm

--I wish to state an argument such as:

P1: All central terms of fundamental scientific laws are genuinely referential.
P2: All central terms of fundamental scientific laws are quantities (/mathematical relations).
C: Therefore, some quantities (/mathematical relations) are genuinely referential.
(AAI-3)

or

P1: All entities (/structures) discovered by physicists using the scientific method are objectively existing.
P2: Some mathematical relations are entities (/structures) discovered by physicists using the scientific method.
C: Therefore, some mathematical relations are objectively existing.
(AII-1)​

The following is just a simple independence argument for mathematical realism:

P1: All objects that are not arbitrarily defined are objects that exist objectively.
P2: All objects whose ratio of circumference to diameter can only be calculated rather than subjectively concocted are objects that are not arbitrarily defined.
C: Therefore, all objects whose ratio of circumference to diameter can only be calculated rather than subjectively concocted are objects that exist objectively.
MaP
SaM
⁂ SaP
(AAA-1)

Obviously the subject term here includes all circles and ellipses, whether Euclidean or otherwise.

“Not arbitrarily defined” means that the object is not defined according to the meaning of the adverbial form of arbitrary as denoted by either definitions (1) and/or (5): https://www.dictionary.com/browse/arbitrarily?s=t subject to individual will or judgment without restriction; contingent solely upon one's discretion; undetermined; not assigned a specific value.

“Concocted” means the adjectival form of concoct as denoted by definition (2): https://www.dictionary.com/browse/concocted?s=t devised, made-up, contrived. “Fabricated” as denoted by definitions (3) and/or (4) https://www.dictionary.com/browse/fabricated?s=t can be substituted for concocted.

“Subjectively” means the adverbial form of subjective as denoted by (1) and/or (2): https://www.dictionary.com/browse/subjective?s=t existing in the mind; belonging to the thinking subject rather than to the object of thought (opposed to objective); pertaining to or characteristic of an individual; personal; individual.

“Calculated” means the adjectival form of calculate as denoted by definition (1) https://www.dictionary.com/browse/calculate?s=t to determine or ascertain by mathematical methods; compute.

One can also formulate a sound deduction by substituting “some objects” in P1 (and therefore in C) for “all objects” in the above argument. Doing so would render an AII-1 syllogism

 

[Polymath257]

Consider the simple system of counting numbers.
Even if humans never existed, it still exists in non-humans.
Ref....
Number sense in animals - Wikipedia
I'll wager that if we're ever visited by aliens that we will
recognize each other's mathematical systems.
Math differs from other intangible things like art & language
in that there's less variation from culture to culture (except
in notation & degree of sophistication). This points to
universal underlying & independently existing structures.

Maybe for small integers, but I don't know of any other creature that has envisioned the system of counting numbers as a whole. Primality seems to be a human invention/discovery/production.

I'm far from convinced an alien race would come up with the same mathematical systems. Too much of our system came too late.

 

[wellwisher]

Or, maths is the product of a particular kind of reasoning, and so far it's been possible to take its various branches, and the relationship of those branches, to greater and greater levels of abstraction ─ bearing in mind that the only place abstractions are found are in brains.
Seriously? Then I'd be grateful if you could provide an example of a structure 'comprised of mathematics' which exists independently of any observer.

Math is a like a faithful horse that can be led by the rider. Once that faithful horse called math is given direction he will reliably follow the path. For example, in computer game physics engines, to make the game more fun, we can assume infinite lives and infinite strength of materials. Once we make these assumptions our faithful math horse follows our lead and allows us to support this. The problem is not math but the person who is riding the math horse.

What has compounded the rider problem, are the math procedures connected to approximation methods. It is one thing to be able to set up, solve a bunch of equations, and then reduce it to something simple like E=MC2. Approximation methods are used when it is too complicated to reduce everything to a simple solution. It is a work around that allows even logical inconsistencies to be ignored.

Statistical modeling is a type of math where logic is not even needed such that game engine logic can appear to be hard reality. Most of the problem is within the human mind and connected to illusions that most people cannot see.

The most pronounced illusion was first point out by an artist called Escher in the 1950's. He has a painting called Relativity as shown below.

If you focus on any one man walking, it appears like a valid reference. But if you compare all the men together, side by side, they are not all possible at the same time. As a 2-D image, we can draw 3-D illusions that cannot exist in real 3-D. I call this a spatial illusion. Logic is based on cause and affect which is 2-D. In science, mutually exclusive theories can both be supported with math, even though they all can't be true at the same time. Einstein's Theory of Relativity implies no preferred reference. However that is a 3-D illusion, created in 2-D; flat, which will not work in 3-D.

The reason this magic trick works is based on the way the brain works. In simple terms the left and right brain process data differently. The left is more differential and 2-D, while the right is more integral and spatial and is 3-D. Science is more left brained. It differentiates reality. This is why we have more data collected than integrating theory. Although science specializes ib 2-D, we all still use the right brain which is less conscious; integrates. The net affect is an overlap affect than makes 2-D appear to be 3-D. It take practice to see the hidden wires of the right side.

 

[Revoltingest]

Maybe for small integers, but I don't know of any other creature that has envisioned the system of counting numbers as a whole. Primality seems to be a human invention/discovery/production.

Humans are just more advanced (in math) than other critters.
Chimps can prolly add 2 + 2.
But we can add 2 billion + 2 billion.

I'm far from convinced an alien race would come up with the same mathematical systems. Too much of our system came too late.

I'd expect much (rather than total) sameness.

 

[Thief]

Humans are just more advanced (in math) than other critters.
Chimps can prolly add 2 + 2.
But we can add 2 billion + 2 billion.

I'd expect much (rather than total) sameness.

saw a demo.....
numbers one through ten displayed on a tv screen in random location
the numbers disappear
the chimp then points to the locations......in ascending order
gets a treat

the demo is then done for the at home sapien

typically we humans get as far as the number five.....and then lose it

we would starve

 

[David T]

Then state an argument concluding that mathematical realism is false. All you've done here so far is write a bunch of silly vacuous sentences and post pictures.

Arguments for mathematical realism have already been noted and otherwise referred to on this thread. I will specify a few of my own, beginning by quoting myself from another thread -- Scientific Realism Begets Mathematical Realism -- where I stated a couple of indispensability arguments:

Do you agree that from scientific discoveries and theories we can infer the nature of empirical reality, at least insofar as determining if an entity constitutes (some part of) empirical reality, or concluding that the essential terms of scientific theories refer to something objectively existing? This is just the thesis of scientific realism. “Scientific realism is a realism about whatever is described by our best scientific theories”. Scientific Realism (Stanford Encyclopedia of Philosophy)

E=mc2, F=ma, F=k(q1q2)/d2 (Coulomb’s law), ∆S ≥ 0 (second law of thermodynamics), Schrodinger’s equation, the laws of conserved quantities, etc., etc. These are the sorts of entities or facts that physicists discover about empirical reality. Obviously these are mathematical relations, i.e., relations between quantities. Energy is a quantity whose value is the product of two other quantities--the mass of a system multiplied by the speed of light squared. Granted, all the particular mathematical relations or laws just noted may be inexact approximations, their applicability limited to a particular domain or specific conditions. Nevertheless, we can hardly imagine the discovery of more exacting or truer statements about the nature and operation of empirical reality than relations between quantities.

[. . . ]

Perhaps one wishes to claim that physicists discover other kinds of stuff in addition to mathematical relations, such as, say, the discovery of the electron. Few people would quibble with that. I would note that, even so, everything we know about electrons pertains to their mathematical (measurable) nature and their relations with other quantities or mathematical relations. J. J. Thomson’s cathode ray experiments did not involve the discovery of anything of a non-mathematical nature about empirical reality: he deduced the particulate aspect of the rays (which had been speculated), that the particles have a negative charge, and he arrived at estimates of the size of charge and mass by way of calculations and deduction premised on the degree the rays were bent by electrical currents of differing strengths. The discovery of the electron was ultimately the discovery of a quantity or a set of quantities and mathematical relations.

[. . . ]

Thus, taking my cue from some of the characteristic claims of scientific realism--

“The entities described by the scientific theory exist objectively and mind-independently.” Scientific realism - Wikipedia “The central terms of the best current theories are genuinely referential.” http://www-personal.umd.umich.edu/~delittle/Encyclopedia entries/scientific realism.htm

--I wish to state an argument such as:

P1: All central terms of fundamental scientific laws are genuinely referential.
P2: All central terms of fundamental scientific laws are quantities (/mathematical relations).
C: Therefore, some quantities (/mathematical relations) are genuinely referential.
(AAI-3)

or

P1: All entities (/structures) discovered by physicists using the scientific method are objectively existing.
P2: Some mathematical relations are entities (/structures) discovered by physicists using the scientific method.
C: Therefore, some mathematical relations are objectively existing.
(AII-1)​

The following is just a simple independence argument for mathematical realism:

P1: All objects that are not arbitrarily defined are objects that exist objectively.
P2: All objects whose ratio of circumference to diameter can only be calculated rather than subjectively concocted are objects that are not arbitrarily defined.
C: Therefore, all objects whose ratio of circumference to diameter can only be calculated rather than subjectively concocted are objects that exist objectively.
MaP
SaM
⁂ SaP
(AAA-1)

Obviously the subject term here includes all circles and ellipses, whether Euclidean or otherwise.

“Not arbitrarily defined” means that the object is not defined according to the meaning of the adverbial form of arbitrary as denoted by either definitions (1) and/or (5): the definition of arbitrarily subject to individual will or judgment without restriction; contingent solely upon one's discretion; undetermined; not assigned a specific value.

“Concocted” means the adjectival form of concoct as denoted by definition (2): the definition of concocted devised, made-up, contrived. “Fabricated” as denoted by definitions (3) and/or (4) the definition of fabricated can be substituted for concocted.

“Subjectively” means the adverbial form of subjective as denoted by (1) and/or (2): the definition of subjective existing in the mind; belonging to the thinking subject rather than to the object of thought (opposed to objective); pertaining to or characteristic of an individual; personal; individual.

“Calculated” means the adjectival form of calculate as denoted by definition (1) the definition of calculate to determine or ascertain by mathematical methods; compute.

One can also formulate a sound deduction by substituting “some objects” in P1 (and therefore in C) for “all objects” in the above argument. Doing so would render an AII-1 syllogism

state that mathmatical realism is false? Hahahaha.

its not a "real"cow its a golden cow. Is it real? Yes as i have already stated. Is there objectivity in math? Absolutely not.

Does english exist independent of the human mind? You insist yes!!! I say no. I keep talking neurology and you keep pretending your view is objectively independent from neurology which is false and somehow math is magically objective. That view is not scientific in any form and is reductive childish nonsense of particular neurological types. Smart and dumb at the same time.

 

[Skwim]

But you haven't addressed the real issue. The "quantities" of which you speak only exist as differentiations in the human mind's perception of existence.

Haven't a clue as to how this figures into the existence of quantity, but quantity is an expression of number. Or, as the Google dictionary puts it: the amount or number of a material or immaterial thing not usually estimated by spatial measurement." And, an amount (quantity), say the eight trees in my back yard, exists whether or not a mind exists to perceive it or not.

.

 

[blü 2]

Number sense in animals - Wikipedia

No argument. In this sense a crow can be an observer.

I'll wager that if we're ever visited by aliens that we will recognize each other's mathematical systems.

In old SF stories, maths is spoken of as the universal language, and indications such as dots representing primes are mentioned in order to explore a basis for communication. But that's not how it worked on earth. If there's one or more advanced alien races out there, one of the most interesting things we could learn from them would be what they use where we use maths, and how it compares to our own.

Math differs from other intangible things like art & language in that there's less variation from culture to culture (except in notation & degree of sophistication). This points to universal underlying & independently existing structures.

No, it points to the needs of living beings with a certain degree of intelligence to keep an arithmetical reckoning of the quantities in their world - the number of offspring, acorns, and so on.

And I notice you didn't provide n example of a structure 'comprised of mathematics' which exists independently of any observer. I don't know of any, and I can't think of how such a thing could exist, given the abstractions involved are only found in brains.

 

[blü 2]

Math is a like a faithful horse that can be led by the rider. Once that faithful horse called math is given direction he will reliably follow the path. For example, in computer game physics engines, to make the game more fun, we can assume infinite lives and infinite strength of materials. Once we make these assumptions our faithful math horse follows our lead and allows us to support this. The problem is not math but the person who is riding the math horse.

So you agree that maths is abstraction, and abstractions are only found in working brains? That maths does not exist independently of the observer?

 

[PureX]

Haven't a clue as to how this figures into the existence of quantity, but quantity is an expression of number. Or, as the Google dictionary puts it: the amount or number of a material or immaterial thing not usually estimated by spatial measurement." And, an amount (quantity), say the eight trees in my back yard, exists whether or not a mind exists to perceive it or not.

No, it really doesn't. The trees would still exist. But the perceived and labeled quantity of them would not. That only exists in the mind that's doing the quantifying.

 

[Skwim]

No, it really doesn't. The trees would still exist. But the perceived and labeled quantity of them would not. That only exists in the mind that's doing the quantifying.

Right! there is nothing to perceive them or label them. However, the quantity, "the amount or number of a material or immaterial thing not usually estimated by spatial measurement." of eight would still exist.

Consider:
Setting aside the questionable status of Pluto, in our solar system there are eight major celestial bodies moving in elliptical orbits around a star. Taking the planets as representing a quantity of eight, this quantity has a mathematical relationship with the quantity of stars in the solar system, which is one. So the relationship is 8:1. And, this relationship holds true whether there's a human mind, or any kind of mind, in the universe or not. So the 8 and1 have values aside from any perception of them.

.

 

[Revoltingest]

No argument. In this sense a crow can be an observer.
In old SF stories, maths is spoken of as the universal language, and indications such as dots representing primes are mentioned in order to explore a basis for communication. But that's not how it worked on earth. If there's one or more advanced alien races out there, one of the most interesting things we could learn from them would be what they use where we use maths, and how it compares to our own.
No, it points to the needs of living beings with a certain degree of intelligence to keep an arithmetical reckoning of the quantities in their world - the number of offspring, acorns, and so on.

And I notice you didn't provide n example of a structure 'comprised of mathematics' which exists independently of any observer. I don't know of any, and I can't think of how such a thing could exist, given the abstractions involved are only found in brains.

I don't see our need for math as eliminating its existence independent of us.
By analogy, we need matter, but matter exists independently too.
The upshot:
Many of the structures of math exist without humans being around to discover them.


Btw, one could argue that some cryptographic versions
of math are invented rather than discovered though.

 

[blü 2]

I don't see our need for math as eliminating its existence independent of us.
By analogy, we need matter, but matter exists independently too.
The upshot:
Many of the structures of math exist without humans being around to discover them.

Rather, if structures exist which conform to the maths, the maths describes (that aspect of) the structures, but the only place the maths exists is in the brain of the onlooker. That's because every part of the maths is an abstraction, and abstractions are found only in working brains, not in the wild. The map is not the territory, the maths is not the physics we use it to describe.

Btw, one could argue that some cryptographic versions of math are invented rather than discovered though.

You got me thinking about codebook codes (2314 = "mouse", kind of thing), which aren't mathematically derived; but although the problem can be defended against, statistical methods may work for such codes.

 

[Revoltingest]

You got me thinking about codebook codes (2314 = "mouse", kind of thing), which aren't mathematically derived; but although the problem can be defended against, statistical methods may work for such codes.

I was thinking of modulo arithmetic rather than mere codebooks.

 

[blü 2]

I was thinking of modulo arithmetic rather than mere codebooks.

The mereness of the codebooks is because they're not mathematical; that was what made me think of them when you mentioned codes.

 

[Revoltingest]

The mereness of the codebooks is because they're not mathematical; that was what made me think of them when you mentioned codes.

But unlike ordinary arithmetic, modulo arithmetic
seems more invented than discovered.
This is why I limited my claim to some
mathematical structures.

 

[james blunt]

Does Math Exist Independent of Our Minds?

The answer to this is a complex answer that maybe imperceptible to some readers , thus I'll try to keep the answer as simple as possible .

The complexity of numbers that represents quantifiable values exist in our minds as ingenuity representation of process . The processes exist independent of our minds thus requiring no existence of math to be that process . However , the state of existence requires an uncertainty . In a holographic universe math would exist independent of ourselves to create the Matrix of ourselves .

 

[blü 2]

But unlike ordinary arithmetic, modulo arithmetic
seems more invented than discovered.

Hmm. On the one hand, clocks have been modular since the 15th century, and devices for counting fixed repetitive quantities work on a modular basis. On the other hand, it took one of the pre-eminent mathematicians of the ages, Gauss, to turn it into a body of highly abstract maths.

At that level the line between invented maths and discovered maths has more or less vanished, as the better mathematician goes looking for ways to express ideas that come to her when contemplating the maths that already exist. Have you read Simon Singh's highly readable "Fermat's Last Theorem"? It follows Andrew Wiles through the whole creative adventure of marshaling known maths and devising new bridges between various parts to crack the Fermat riddle. Again, invention or discovery, or no clear line between the two?