Mathmatics doesn't conform to the universe.: Philosophy Forums

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Mathmatics doesn't conform to the universe.
Is mathmatics universal?

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Mathmatics doesn't conform to the universe.

quickly
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Posted 04/17/08 - 02:47 PM:	#26
I started reading Deleuze and Guattari's Anti-Oedipus recently (very recently, and as first contact, so this is speculative), but there seems to be a pattern emerging which allows for mathematics to gain a type of practical sovereignty within the world as the construction of a self-reflexive "empirico-transcendental doublet," to use Foucault's term. If I'm reading them correctly (and hereafter, incompletely), since the universe is constituted by series of patterns which are constantly becoming, any type of "ineffable" or non-cognitive reality (a non-patterned reality, something not understandable by the mind) would simply cease to be accessable. But all to say, and this is departure from the typical view I've taken (that mathematics works because it relies upon quasi-transcendent principles) that all "maths" (all calculating procedures) work because they accord with a particular structure, which operates in a mechanical fashion; and that, like a series of events compounding events creating "social organisms," if at base everything works and is identifiable by patterns, and the universe and everything it contains are complex, interacting series of patterns, then any transcendentiality (consciousness) is a patterned process - thus we discover what we are, in a sense. In essence, mathematics works because our brains are mathematical, in a sense; we can't express that which we are not, even if what we are not is the "unthinkable" - it must comprise the subject. Now, if I'm misreading D+G, correct me. Plus, it doesn't explain anything, but I find it interesting. But it seems that we could consider mathematical units aesthetically, as well. They appear coorelative to our ability to have consciousness, or to construct differences, as a fundamental mode of thought (without which everything would become the Same). I believe Cassierer expressed something like this in Symbolic Forms, that to think of abstractions and variables (the highest being "x"), we need to discover their ultimate construction as an evolution of man's self-becoming. They are expressions of ways of thinking abstracted from thought and useful insofar as they accord with how thinking occurs and how awareness of alterity arises. Edited by quickly on 04/17/08 - 03:02 PM
"Monsters cannot be announced. One cannot say: 'here are our monsters', without immediately turning the monsters into pets." -Jacques Derrida

quickly
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Posted 04/17/08 - 02:59 PM:	#27
I am a firm believer that mathmatics isn't a universal description of the universe. I believe mathmatics was invented not discovered. I also believe that historically writing came first and out of it later on was mathmatics constructed. Can anyone here prove to me that I don't know what I am talking about? Perhaps I’m being vague and abusing philosophical terminology. But, if you could clarify several terms here, we could understand you better. As it is, you’re speaking so abstractly it becomes neither speculative nor merely fuzzy logic. What do you mean by: “universal description”; “description”; “universe”; “mathematics”; “invented” and “discovered”; “constructed.” If you won’t clarify these, it’s hard to know where you’re argument’s going. The problem perhaps lies in the word “description.” If you mean a hermeneutics or a representation isn’t known. How do you differentiate between “invented” and “discovered”: are these mutually exclusive? Do they present simultaneities which must necessarily comport themselves to one another, working in tandem to produce the construction? What about construction: constructed things must be assembled from other things, some of which were constructed, some of which are metaphorical “raw materials.” Are you denying that mathematics has use? Are you denying that mathematics has “universal” applicability? Judging by the reference towards Derrida (as I take it), are you claiming that “Number” is a category which suppresses something fundamental about the notion of itself? That mathematics has been constructed for a purpose? That some desire is latent within it? And if no structure escapes play, how exactly do you account for the fact that the concepts mathematics uses (quantity, relation) are in apparent accord with the observable universe?
"Monsters cannot be announced. One cannot say: 'here are our monsters', without immediately turning the monsters into pets." -Jacques Derrida

Baudin
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Posted 04/18/08 - 01:17 AM:	#28
First of all, I'd like to say that when I talk about mathmatics I talk about the following: "Mathmatics draws logical conclusions based on arbitairy axioms." I'm using these terms as stated in http://forums.philosophyforums.com/threads/very-b... When I say 1 + 1 = 2 I create an entire set of axioms which after defining symbols and operators logically produce said equation. The only thing left to talk about is whether or not our sets of axioms and logic is human wrought. I'd say....nope....because axioms are chosen we may say they are “found” or “discovered” in the chaotic jumble of the universe. Because we cannot say if logic is true your guess is as good as mine, and mine tends to believe that there is something like causality, some which keeps us from falling up, something with keeps words written on a page from maintaining their meaning. So I would like to think that logic is here eventhough we could cease to exist. I’m not a believer in scripture because every story told leaves hundreds of stories untold. And nothing is ever “done”. Mathematics on the other hand can conclude a story because everything is based on a fixed set of axioms and a fixed set of logical entities. So, I do believe that mathematics is discovered? Yes, whole heartedly.
“What do I think of Western civilisation? I think it would be a very good idea.” --Mahatma Gandhi

Simple Occam
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Posted 06/10/08 - 10:44 AM:	#29
It is a fact about the physical universe that 2 apples and two more apples adds up to 4 apples. It is empirically true, not rationally necessary. Just like, no matter what circle you measure, if you divide the length of the circunference by the length of the diameter, it will equal pi. These are empirical, measurable, predictable facts about the world we live in. Math is essentially just counting. The 3-dimensional structure of space is also something we observe in everyday life. Everyone here seems to assume that it's an invention and not a description of the universe. But look around you, everything in the universe can be numbered and counted. We observe regularities about how things 'add up' in nature, and notice that the world universally conforms with mathemetical and logical truths. Plato is the one who got us seduced into thinking that, because of its universality, mathematical knowledge had somehow to be better or more certain than empirical knowledge, which sometimes can be mistaken. Rationalism claims that math is self-evidently true or, worse, just invented because it was somehow useful. In either case math is considered true or useful not because of how it corresponds to the world but because of how we think. But why do we all think the same? What causes our universal agreement about 2+2=4 or C=(2pi)R? Do we just make it up?? More likely, it's something univerally true about the universe that we discover through our ordinary experience of the world.

Cusserl
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Posted 06/12/08 - 05:33 PM:	#30
What licenses our cavalier generalisations about mathematics? Is it really unitary? I would say it is. I would venture the view that Frege was fundamentally right to aver in the logical foundations of mathematics (whether or not all of maths is reducible to maths is another question.) But wait. What do I mean by logic? Not, to be sure, the apodictic, necessary, universal, unimpeachable, true-in-all-worlds logic to be found in Leibniz or even David Lewis. It seems to me that this bears only a very poor realtion to maths. The logic I have in mind is the logic which the various branches of maths not only share with each other but every other discipline: logic as the night-watchman of thought. This avowedly prosaic order of logic, resting on Aristotle's three laws and ruling, by decree, which inferences are and are not valid - this is the bedrock on which maths rests. And it follows that if a thought is thinkable then it is mathematically valid. What, then, is its relation to "reality"? I would say that it figures forth logically possible structures which may or may not be empirically actual. Mathematics proceeds according to its own laws, but every often, and almost inexplicably, there is a sort of Law of Pre-established Harmony between it and the world.

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Posted 06/12/08 - 05:34 PM:	#31
What licenses our cavalier generalisations about mathematics? Is it really unitary? I would say it is. I would venture the view that Frege was fundamentally right to aver in the logical foundations of mathematics (whether or not all of maths is reducible to maths is another question.) But wait. What do I mean by logic? Not, to be sure, the apodictic, necessary, universal, unimpeachable, true-in-all-worlds logic to be found in Leibniz or even David Lewis. It seems to me that this bears only a very poor realtion to maths. The logic I have in mind is the logic which the various branches of maths not only share with each other but every other discipline: logic as the night-watchman of thought. This avowedly prosaic order of logic, resting on Aristotle's three laws and ruling, by decree, which inferences are and are not valid - this is the bedrock on which maths rests. And it follows that if a thought is thinkable then it is mathematically valid. What, then, is its relation to "reality"? I would say that it figures forth logically possible structures which may or may not be empirically actual. Mathematics proceeds according to its own laws, but every often, and almost inexplicably, there is a sort of Law of Pre-established Harmony between it and the world.

Cusserl
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Posted 06/12/08 - 05:36 PM:	#32
What licenses our cavalier generalisations about mathematics? Is it really unitary? I would say it is. I would venture the view that Frege was fundamentally right to aver in the logical foundations of mathematics (whether or not all of maths is reducible to maths is another question.) But wait. What do I mean by logic? Not, to be sure, the apodictic, necessary, universal, unimpeachable, true-in-all-worlds logic to be found in Leibniz or even David Lewis. It seems to me that this bears only a very poor realtion to maths. The logic I have in mind is the logic which the various branches of maths not only share with each other but every other discipline: logic as the night-watchman of thought. This avowedly prosaic order of logic, resting on Aristotle's three laws and ruling, by decree, which inferences are and are not valid - this is the bedrock on which maths rests. And it follows that if a thought is thinkable then it is mathematically valid. What, then, is its relation to "reality"? I would say that it figures forth LOGICALLY POSSIBLE STRUCTURES which may or may not be empirically actual. Mathematics proceeds according to its own laws, but every often, and almost inexplicably, there is a sort of Law of Pre-Established Harmony between it and the world.

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