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Evo
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I am re-opening this thread under the condition that the thread return to specific discussion of the topic.
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Would you say that the painting "Mona Lisa" was always possible from the beginning, and does that imply that Da Vinci "rediscovered" it when he painted it? Or is mathematics demonstrably different from art in terms of which comes from us and which is built into nature? Can you trace the details of how each is done to reach this conclusion using pure logic, or do you just have to assume it as a postulate?chiro said:One thing about mathematics is that, in my opinion, we are simply re-discovering what already existed and what was always possible from the very beginning.
I tend to think that both comes from us but it seems mathematics is much more useful as a scaffolding to attach our claims about physical systems. It seems that there is something more to physical reality (or even our models of physical realty) over and above the mathematics. It seems that the mathematical theories/objects are not the same type of entities that appear to exist in the physical world. We can't get to the physical world without using mathematics because non-mathematical versions of scientific theories just seem to be practically very difficult to do. But, even though the mathematics may be indespinsible and the mathematical equations we use ultimately decide what we believe about the physical world there still seems to be this difference between the two and this just adds fuel to many of the interpretative debates in science, I think.Ken G said:Or is mathematics demonstrably different from art in terms of which comes from us and which is built into nature?
Art is just a useful comparison, and ontological issues are relevent, for they are referred to in the OP itself (just look at choices #4 and #5, which directly connect mathematics to things that actually exist, i.e., claim that mathematics is explicitly ontological). I understand that you must decide what elaboration is off topic, and I might not agree with you, but it's your place to do that not mine. All I'm saying is that this whole thread is about whether mathematics is something inherently semantic and ontological (connecting with meaning in the real world, choices #4 and 5), or something inherently syntactic and epistemological (a kind of procedure for knowing that follows a fixed set of rules and has nothing to do with anything outside those rules, expressed in all the other choices). Since I am not allowed to actually support my stance, I can only state it: neither of those answers could possibly do justice to what mathematics actually is, because what mathematics actually is is a juxtaposition of those two possibilities. Mathematics takes on its meaning in the place where those things come into contact, because neither of them have any value on their own, they are both vacant notions until they are juxtaposed. To actually describe my reasoning might seem verbose, or might need to bring in how art and language also avail themselves of an interplay between syntax and semantics, so I won't belabor the point.micromass said:Please stop the nonsense posts. This thread is about mathematics and its philosophy, it's not about the Mona Lisa nor about determinism nor about the existence of reality, etc.
Ken G said:Art is just a useful comparison, and ontological issues are relevent, for they are referred to in the OP itself (just look at choices #4 and #5, which directly connect mathematics to things that actually exist, i.e., claim that mathematics is explicitly ontological). I understand that you must decide what elaboration is off topic, and I might not agree with you, but it's your place to do that not mine. All I'm saying is that this whole thread is about whether mathematics is something inherently semantic and ontological (connecting with meaning in the real world, choices #4 and 5), or something inherently syntactic and epistemological (a kind of procedure for knowing that follows a fixed set of rules and has nothing to do with anything outside those rules, expressed in all the other choices). Since I am not allowed to actually support my stance, I can only state it: neither of those answers could possibly do justice to what mathematics actually is, because what mathematics actually is is a juxtaposition of those two possibilities. Mathematics takes on its meaning in the place where those things come into contact, because neither of them have any value on their own, they are both vacant notions until they are juxtaposed. To actually describe my reasoning might seem verbose, or might need to bring in how art and language also avail themselves of an interplay between syntax and semantics, so I won't belabor the point.
bohm2 said:I tend to think that both comes from us but it seems mathematics is much more useful as a scaffolding to attach our claims about physical systems. It seems that there is something more to physical reality (or even our models of physical realty) over and above the mathematics. It seems that the mathematical theories/objects are not the same type of entities that appear to exist in the physical world. We can't get to the physical world without using mathematics because non-mathematical versions of scientific theories just seem to be practically very difficult to do. But, even though the mathematics may be indispensable and the mathematical equations we use ultimately decide what we believe about the physical world there still seems to be this difference between the two and this just adds fuel to many of the interpretative debates in science, I think.
sigurdW said:The Philosophy of Mathemathics is essentially the Philosophy of Language!
WHY?
No Formula of Mathemathics cannot in principle be "translated" into ordinary language.
Its awkward to manage without formulae,
but there are no "pure formula" that is not a simplification of language.
An insightful riposte John!John Creighto said:This argument is like: if A is a subset of B and B is a subset of A then A=B. Yet you say math can be translated into language which I can sort of buy but when we think about language we think about non mathematical things. A cow is not a mathematical object but we can represent various aspects of a cow with mathematics. Of course you may contend that language does not really represent the cow either. Yet when we speak of a cow we at least know what we mean independently of some AI recognition system.
Math describes the structure while language describes the meaning. What is meaningful to us depends upon structure, rules and order but not all structures are meaningful to us. Perhaps an algorithm could be devised to identify which types of structures are meaningful to us or perhaps it is just a convenient mix of convention and utility.
John Creighto said:This argument is like: if A is a subset of B and B is a subset of A then A=B. Yet you say math can be translated into language which I can sort of buy but when we think about language we think about non mathematical things. A cow is not a mathematical object but we can represent various aspects of a cow with mathematics. Of course you may contend that language does not really represent the cow either. Yet when we speak of a cow we at least know what we mean independently of some AI recognition system.
Math describes the structure while language describes the meaning. What is meaningful to us depends upon structure, rules and order but not all structures are meaningful to us. Perhaps an algorithm could be devised to identify which types of structures are meaningful to us or perhaps it is just a convenient mix of convention and utility.
Hi Chiro! You are delightfully confusingchiro said:You might want to think about information in terms of its role in information theory as opposed to the intuitive ideas of most people called language which is a relative and contextual thing.
Information theory defines information to have no context or interpretation at all: you have an alphabet, a collection of sentences (both finite) and a probability distribution characterizing the event space for the nature of the grammar and subsequent mappings of probability to constructed sentences.
Context basically relates pieces of information together and most language (including mathematics but it does it in a very different way to the spoken languages) is contextual and relative.
Each word that you read and the existing context creates relationships automatically in comparison to say a string of random letters which probably just confuses people.
Mathematics is actually relative and doesn't just describe structure. There are dualities everywhere in mathematics and this gives it part of its relativity. For all and there exist are dualities. The AND/OR statements in set theory are dualities. The inequalities have dualities. There are dualities within the language itself everywhere.
The dualities themselves are important because they give context to the actual descriptions just like the combination of words in a sentence give context to the other words, the entire sentence, and anything even remotely related to the ideas and terms of the sentence.
sigurdW said:Hi Chiro! You are delightfully confusing
"Duality" "Context" "information theory"
The context of the sign is Mind and its relation to Reality
(Whatever they might be.)
sigurdW said:Excuse me my "friends". I am not all rational. I am a poem. And a formula. Fused into one.
Again:Theres pure thought. And its echo: "Rational thought"
Theres more than one proof, here's the beginning of a proof.sigurdW said:I got a problem for you, lovers of truth,,,
Maths rests on PROOF! Doesnt it?
Then please prove that sentence three below does not follow,
and mind you,you are not allowed to exclude self reference!
1 Sentence 1 is not true
2 Sentence 1 = " Sentence 1 is not true "
3 Sentence 1 is true
.
lugita15 said:if you believe that mathematics arises from the properties of nature, then you would be an adherent of physism. But then how would you respond to the objection that there is so much mathematics that we do that is not directly grounded in our knowledge of the physical world?
DragonPetter said:What about mathematical equations that possesses both solutions that are grounded in the physical world and solutions that would seem impossible physically? There are solutions to equations that give positive and negative energies for example, and we simply ignore/throwaway the negative roots since our laws of nature say you can't have negative energy/mass.
apeiron said:Good point. The simple answer would be that the equations describe a higher symmetry which nature then breaks. So there is more to the story than the equations can tell. Further information, further constraints, have to be supplied somehow.
DragonPetter said:In another thread I thought of the negative roots problem as a type of computational efficiency. You have to waste some computation on abstract solutions to be able to get the physically grounded solutions.
DragonPetter said:All of the times our brains computed the negative roots as solutions, that information was imprinted into the universe through our thought processes as configurations of memory or symbols written into paper, and has some how interacted with the universe following the laws of the universe.
apeiron said:I see the analogy. But in the context of the OP - whether maths is generally Platonic or utilitarian - the Platonic claim would seem to be that it is not the computation that is the issue. The answers would "exist" regardless of whether some human calculated them.
apeiron said:The difficulty comes only at the point of chosing one computation to be real, and discarding the other one as unphysical. And this seems a non-mathematical decision. The maths itself does not offer the grounds for making the choice.
To the first question: Our brains are part of the universe, and so the interaction is with parts of the universe. The neurons exchange signals, consume energy, generate heat, organize synapses to form ideas, etc. This is all physically governed by the laws of the universe. If the laws of the universe don't allow our brains to do something, then there is no possibility for it to exist in our thoughts. Likewise, if our brains can process the information that generates abstract mathematical logic, then its only because it is built into the interaction of the universe's laws.apeiron said:But how is there any interaction apart from that we create ourselves? This is where the utilitarian part of the story comes in. To the universe, any symbols scribbled out on paper are just noise - meaningless entropy. It is only to our minds that the symbols are information - one root being the definitely true, the other being the definitely false. And our minds decide this through further measurement - we observe the world and make the distinction.
DragonPetter said:If you write a computer program to find the roots of a solution to give you an answer that matches physical reality, the throw away roots are still processed. At some point we make a decision to stop finding roots or throw away roots, which costs energy and creates heat by the computer, and so I think it might be more than just an analogy.
DragonPetter said:I am taking the step to say that the universe's rules makes the choice automatically, but the universe's rules also allowed for the existence of the negative root solution as well, even if it has no other physical grounding to the world than its own existence.
DragonPetter said:But if what you suggested is the case, that the universe breaks symmetry from math, then the universe is not purely mathematical or does not include all math. If that is the case, I would guess that we should not even be aware of these abstract ideas.
DragonPetter said:To the first question: Our brains are part of the universe, and so the interaction is with parts of the universe. The neurons exchange signals, consume energy, generate heat, organize synapses to form ideas, etc. This is all physically governed by the laws of the universe. If the laws of the universe don't allow our brains to do something, then there is no possibility for it to exist in our thoughts. Likewise, if our brains can process the information that generates abstract mathematical logic, then its only because it is built into the interaction of the universe's laws.
DragonPetter said:Also, I don't see the organization of those symbols as noise if there is no brain around to interpret them. That organization of symbols still exists, regardless of anyone to interpret it. I don't know for sure though :P