Is math a Tautology

Is math a Tautology
Ginko-san
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Posted Apr 23, 2013 - 7:24 PM:

Yes, absolutely, math can only ever approximate or describe reality, it can never be life itself, in all its vastness and contradiction. As Lao Tzu says:

To yield is to be preserved whole.

To be bent is to become straight.

To be hollow is to be filled...

Thereforethe sage embraces the one,

and becomes the model of the world.

That being said though, math can approximate life very very closely (calculous for instance), and create very useful symbolic representations of reality, but again, those approximations are only imaginary, with no inherent reality of their own.



Edited by Ginko-san on Apr 24, 2013 - 10:52 AM. Reason: typos
arostu
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Posted Apr 23, 2013 - 9:00 PM:

But what if reality is intrinsically mathematical in nature?
Ginko-san
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Posted Apr 24, 2013 - 10:58 AM:

arostu wrote:
But what if reality is intrinsically mathematical in nature?


You mean what if there's a reality that's more real than the world we perceive, like a Platonic realm of ideas? I suppose it's possible, but the burden of proof is on the Platonist to establish that reality. Imho, Plato made the mistake of thinking that mathematics gives humans direct access to reality, that our own world is somehow flawed because life doesn't live up to the clean, logical and comforting rules of math. Really math just provides us with a symbolic description of life, there is no perfect "circle" or "2" out there that exist independently from our minds.
arostu
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Posted Apr 25, 2013 - 11:34 AM:

For such a discussion, we'd have to first talk about what it means to exist and decide if there are different kinds of existence.

What is a mathematical object? If we can answer that then we can decide if reality is a mathematical object.

No, I don't mean the existence of a reality more real than that which direct, physical experience shows us; I mean an abstract existence in addition to the concrete existence we perceive.

If we know something exits when we perceive it then Platonia exists as it is perceived as well, just not by one of the five sense organs but by the mind instead.

When you say circles and the number 2 does not exist independently of our minds, are you saying that circles, for instance, would not exist if no human ever thought about them?
Ginko-san
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Posted Apr 26, 2013 - 1:25 PM:

arostu wrote:
For such a discussion, we'd have to first talk about what it means to exist and decide if there are different kinds of existence.

What is a mathematical object? If we can answer that then we can decide if reality is a mathematical object.

No, I don't mean the existence of a reality more real than that which direct, physical experience shows us; I mean an abstract existence in addition to the concrete existence we perceive.

If we know something exits when we perceive it then Platonia exists as it is perceived as well, just not by one of the five sense organs but by the mind instead.


Could you say a little more? It sounds like you're proposing an absolute reality accessible by human thought, just that the world we perceive is also real... I'm not sure what exactly you're drawing on for this.


When you say circles and the number 2 does not exist independently of our minds, are you saying that circles, for instance, would not exist if no human ever thought about them?


Honestly I don't think any objects would exist without a perciever. Perceiver and perceived are just two sides of the same coin, absolutely dependent upon one another. The Tibetan yogin Shabkar says:

Look for yourself beyond at outer objects,

these[objects], first, from whence do they arise?

Where do they abide? Where do they go? and so on..
Thoroughly investigate [this]. Like clouds in the sky,
[they] arise from the sky, abide within the sky,
and again pass into the sky's expanse.

Phenomena seen and heard arise from mind,
abide within the mind, and again,
pass into the mind's expanse. Realize the faulty nature of those things!


Mathematical objects then are just a certain kind of mentally perceived object. "Two" and "circle" for instance are simply ideas that arise in our minds, in dependence upon our ability perceive and distinguish them as separate, abstract objects. Imho, if there is an "absolute reality," then it is the very absence of this distinction, the clear sky free from the clouds of subject and object.
deathcallsusbyarename
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Posted Apr 27, 2013 - 2:38 PM:

I for one believe that within Mathematics there is displayed our creative energies that unveil propostions that cannot be seen within the purely logical realms of pure logic. Mathematics is not a mere tautolgy but reveals part of that which makes us human.
Saranya
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Posted Apr 27, 2013 - 3:01 PM:

Measured mathematics(i.e.: estimating dimensions of an object l x w x h) is not a tautology because we can always be more precise in our measurements, but pre-existing mathematics(the exact nature of the object in reality we are trying to describe) is a tautology.
deathcallsusbyarename
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Posted Apr 27, 2013 - 3:18 PM:

Saranya wrote:
Measured mathematics(i.e.: estimating dimensions of an object l x w x h) is not a tautology because we can always be more precise in our measurements, but pre-existing mathematics(the exact nature of the object in reality we are trying to describe) is a tautology.



I would heartily disagree. Mathematical thinking is a creative and human (i.e. social) enterprise.
Gen11
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Posted Apr 28, 2013 - 11:57 AM:


This means math statements do not say anything about the world, they are statements about other statements. 1+1=2 is neither true nor false statement; it is a meta-statement. Note 1+1 and 2 are well formed formula (wff) in FOPL. 1+1=2 simply states that a wff 1+1 can be sustituted by another wff 2 in any FOPL wff.

This is what I conclude. What do you think.




I would say that;

Burger + Bap = Hamburger

Mathematics, in my humble opinion, is just another medium of the expression of language. In a more general sense, variables are 'adjectives', the describe a 'quantity of something'. 'Operators'; +, -, multiple, divide, as well as higher forms of operation such as taking dot products or derivatives are essentially 'verbs'.They represent action upon something.

Thus together an expression represents;

[A variable] undergos [action] with respect to [Another variable] …

When we write an 'equals sign' ( = ) to make an equation, what we are really saying is;

[A variable] undergos [action] with respect to [Another variable] … let us now call this [A third variable]


Therefore if we are to ask the question; 'is mathematics 'true' in every possible interpretation?' or 'is mathematics true without self reference' then quite clearly no. It depends entirely on the semantics of the language being used to describe such concepts.

Ergo, the meaning of the [variables] or [actions], have to be a priori defined. One might ask the question of how do you define the property of 'twoness' or 'addition'. To take addition, obviously you cannot add 'ham' to 'egg' and get the property of 'twoness' unless one was talking about the concepts of 'quantity', rather than the concepts of 'property'. Hence we always must have a notion about the semantics of the language being used to explore manipulations of concepts and ideas.
Drago Deadblaze
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#30 - Quote - Permalink
Posted Apr 29, 2013 - 9:50 AM:

the.yangist wrote:
Yeah, Wittgenstein said that, but did he prove it?


He rarely lowered himself to the necessity of ‘proving’ most of his poetic–sounding announcements。I consider him more a philosophising poet than a philosopher。
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