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Mathematics
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2016-04-18 at 10:38 PM UTCMathematics can be used to describe basically everything in our reality. In your opinion is mathematics something that humans created? Or did we discover something that was already there?
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2016-04-18 at 10:46 PM UTCLike with all language humans did not create the things these symbol and operations represent. The knowledge was revealed through contemplation not constructed of thought. Much like a horse has existed before we called it such a set of horses existed before either term was defined.
Mathematics is much like religion. Those who fail to see beauty in it are oft ignorant and those who see the beauty in it are oft arrogant. Math is a very useful and nessecary component of the humans understanding of various phenomenon but it cannot truly express everything the human experience has to offer. -
2016-04-19 at 1:11 AM UTCIn general I lean nominalist and while that doesn't totally commit one to believing mathematics is invented rather than discovered it lends itself to that conclusion and it is my general inclination. I watched a walk by Philip Wadler and he made this argument about how three or four mathematicians seemed to independently discover the decidability problem and that that was an argument for a discovery model of mathematics. Wadler is a really smart guy but I thought that was kind of a disingenuous move, it fails to acknowledge the distinction between axioms and theorems, the decidability problem is the product of systems in which it emerges, yes we may "discover" new properties of a formal system as in this case but that discovery is predicated on the invention of the system to start with. I'll claim that nothing which is discovered can be fully reduced to invented parts (I recently discovered my phone has a "do not disturb" feature, that's not an argument that my phone or that feature are discovered properties of the universe rather than something invented).
One might naturally make some argument from isomorphisms between our mathematics and the world as being evidence that mathematical systems are founded in natural, discovered elements of the world. But this fails too, to model the world post-hoc is not to be discovered. Consider natural languages model the world yet no one would claim that English was "discovered". Likewise the relationship of mathematics to the world is an intentional product of its genesis, it contains similar structures not because it is similar to the world but because it exists to model it. -
2016-04-19 at 5:58 PM UTC
Like with all language humans did not create the things these symbol and operations represent.
This tbh fam. -
2016-04-19 at 9:54 PM UTCWell my statement is true for a majority of things. Given that we are a species of creators we certianly have words for things of human creation. But where it gets dicey is could these concepts or things be created independently of human existence? I'd have to wager a yes. In a universe as vast and chaotic as ours it is quite feasible to imagine a non human civilization creating things such as telephones or canoes or even HTML markup. Sure they may not be our design but so long as the functional result is the same are they not necessarily the same in function which translates them into the same category of thing?
I surely reckon there to be mathematics of human design but these are generally flawed or non pure mathematical objects which are an imaginative speculation. In the realm of physics we can look to the ideas in string theory as an example. If its holes are unable to be mended it is simply an intricate yet irrelevant imaginative construction. Flat earth theory is much the same way. Sure some fellow may have a shred of mathematical or physical evidence that supports the claim but it is easily cast aside as a charade when one studies and understands the entirety of the mathematical or physical evidence supporting the earths rotund structure. -
2016-04-20 at 6:19 AM UTC
Well my statement is true for a majority of things. Given that we are a species of creators we certianly have words for things of human creation. But where it gets dicey is could these concepts or things be created independently of human existence? I'd have to wager a yes. In a universe as vast and chaotic as ours it is quite feasible to imagine a non human civilization creating things such as telephones or canoes or even HTML markup. Sure they may not be our design but so long as the functional result is the same are they not necessarily the same in function which translates them into the same category of thing?
It's not a question of human independence but rather mind independence. Sure other species might come to hold a concept that seems similar to our notions of mathematical objects (although it's interesting to ask what we could count as evidence of mathematical objects existing in the minds of other species) BUT that doesn't really address the question. If no other species has a mathematics, if the universe is devoid of life, do mathematical objects still exist?
And to address OP's question more directly, why does independent formation imply discovery over creation? Multiple people seem to have invented fixed wing flight independently, but that doesn't mean it's a discovered thing, planes were still invented, their design just might have been prompted by shared physical realities. -
2016-04-21 at 1:30 AM UTCDoes the mind have no mathematical properties? Is there any way we could define it as a mathematical object? If I was a smarter man I would say perhaps but all I can say now is I don't know.
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2016-04-21 at 4:37 PM UTCI made this thread after watching a video about math. The theme of the film was that basically everything can be broken down into math. Their idea was that we live in a world of math, that the universe could literally just be a whole lot of math. And there's something about that idea that seems right, it makes a lot of sense. But after reading some of the replies to this thread I think they were wrong about that. Math is like a language, a way to describe something else, like a symbol. We discovered the reality and created the symbol. We invented mathematics after discovering something very similar to math in reality, we use the symbol to describe the reality. Like π. π is a symbol we use to discuss something we discovered that shows up basically everywhere in nature, everywhere we look we see π. π is the way the human attempt to comprehend something that is probably incomprehensible. The symbol π is a metaphor for something that is clearly real and involved in basically everything in our reality.
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2016-04-21 at 5:54 PM UTCThat's pretty accurate. The symbol is just a figment to which we can attach the ideas and properties the symbol displays to us.
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2016-04-21 at 6:02 PM UTC^ Thanks for saying that, I like that we agree on this. After I posted that I had another thought: Pi as a symbol can never be expressed exactly, it is always approximated. Does this demonstrate a fault in the language we use to express it, or does it mean that Pi as it exists in nature is also never expressed as an exact value but rather somewhat vague?
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2016-04-21 at 6:10 PM UTCI would agree both the former and the latter. Given the nature of space and pi's expression through the golden ratio we probably demonstrate its approximity by measure and conclude that our expression of measure must nessicarily be approximate as well as the principle of pi validated by holding for the approxamite. This demonstrates a fault in both the language we use to express it and our conception of the principle yet at the same time the fault is not large enough to render the principle of the ratio invalid.
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2016-05-09 at 8:09 AM UTC
Mathematics can be used to describe basically everything in our reality.
I don't see how this claim could possibly hold up. Firstly, it's impossible to prove, even if it were true. That is, one could never prove that mathematics was capable of expressing all that is. But the bigger issue is that there are many aspects of even our perceived reality which cannot be expressed mathematically. I'll give an example: the experience of the color red cannot be expressed mathematically. Yes, the color can be expressed in terms of its wavelength, and therefore this is able to be expressed quantitatively, but what red essentially is, its qualitative aspect, cannot be expressed via mathematics. Mathematics is very useful and impressive in the realm of quantity, but is rarely appropriate for the qualitative.
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2016-05-09 at 9:34 PM UTCYeah, as was discussed above, I think mathematics is or is like a language in that while it can be used to describe basically anything it's not the same as the thing itself. I do think math could be used to express or describe basically every aspect of reality, but I agree that's not the same as actually experiencing reality consciously the way (I presume) you and I do. It's like how we can use English to describe a sexual experience for example, but that is not the same as actually having that sexual experience. I also think Mathematics could be used to describe the same experience although it would be beyond my capabilities to comprehend, and again, it would not be the same as conscious experience itself. I agree that colours like red are not just some number representing a wavelength of light but is a word used to describe an actual experience, as are all words really.
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2016-05-09 at 11:02 PM UTCWhile they appear to be the same, I believe you and I are saying different things.
[FONT=arial][SIZE=16px]…[/SIZE][/FONT]I think mathematics is or is like a language in that while it can be used to describe basically anything it's not the same as the thing itself. I do think math could be used to express or describe basically every aspect of reality, but I agree that's not the same as actually experiencing reality consciously the way (I presume) you and I do[FONT=arial][SIZE=16px]…[/SIZE][/FONT]
I am not drawing the distinction between experience and description, but quantity and quality. Mathematics is a language which deals with quantity, and therefore has either no relation or a poor relation to the qualitative. I am tempted to say it deals wholly with quantity and has no ability to express quality in any way, but I do not know enough to say this confidently.
To go to your example of the sexual experience, one could mathematically describe various processes that are involved in arousal and the exchange between the lovers, but nothing essential could be said about the union via mathematics. We can, however, use language that is used to describe qualitative experiences to attempt to convey information that mathematics cannot. Poetry would be especially good in this instance. But I struggle to see how you could even identify sex as such using pure mathematics. That is, to get to this point in your example, you would need to use non-mathematical language to identify it, and all of your terms would employ non-mathematical aspects to hint at the qualitative aspects of sex which differentiate it from other activities. -
2016-05-10 at 12:57 AM UTCAnal
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2016-05-10 at 6:27 AM UTC
I am not drawing the distinction between experience and description, but quantity and quality. Mathematics is a language which deals with quantity, and therefore has either no relation or a poor relation to the qualitative. I am tempted to say it deals wholly with quantity and has no ability to express quality in any way, but I do not know enough to say this confidently.
Based on what exactly? We speak all the time of qualities in mathematics. 3, 5, and 7 all have the quality of being prime. Curves have an number of qualities. Functions have a whole bunch of qualities. And if we want to talk about modeling we can look to discrete sorts of mathematics like category theory which speaks very certainly about qualities of points under transformation. Unless you take "quality" to be somehow inherently immune to modeling (like claiming all quality is radically subjective and talking about it is meaningless) which would be dumb and immediately suspect circularity. -
2016-05-14 at 1:33 AM UTCI struggled with that post because I found myself unable to express your bolded sentence in a satisfactory way. I'm not sure if I've misspoken, but it's certainly possible. I will start again, and then try my best to respond to what you have said.
Mathematics deals with quantity, multitude and magnitude, and the relationships between various quantities. So yes, arithmetic recognizes prime numbers, which are qualitative properties of quantities, but the quality of being prime is one concerned with the relationship between quantities. Circles are curves with many unique qualitative properties, but all that I can think of are expressions of relations between quantities.[FONT=arial][SIZE=16px]…[/SIZE][/FONT]And if we want to talk about modeling we can look to discrete sorts of mathematics like category theory which speaks very certainly about qualities of points under transformation. Unless you take "quality" to be somehow inherently immune to modeling (like claiming all quality is radically subjective and talking about it is meaningless) which would be dumb and immediately suspect circularity.
This is where I start to lose you, but I also suspect this is where our difference of opinion lies, and therefore it is important that I understand you here. I'm unfamiliar with category theory, but based on what my cursory research shows me, I'm not sure it opens possibilities I previously thought impossible. My problem is this: there are many things that are essentially qualitative. I'm no subjectivist; quite the contrary. But the essence of an oak tree is not able to be expressed quantitatively. I don't see how you could use mathematics to describe it. You could use it to describe its shape, project its growth, etc.. But how could you use it to express not its attributes but the oak tree itself? I desire to use many other examples that we have in our shared experience, such as love or the color blue, but I recognize that in this (post-)modern age the existence of these is often doubted, and so I chose the oak tree, a rather concrete example. Please help me understand your point of view. -
2016-05-15 at 1:59 AM UTC
Mathematics deals with quantity, multitude and magnitude, and the relationships between various quantities. So yes, arithmetic recognizes prime numbers, which are qualitative properties of quantities, but the quality of being prime is one concerned with the relationship between quantities. Circles are curves with many unique qualitative properties, but all that I can think of are expressions of relations between quantities.
So yes, number theory will always deal with quantities but mathematics is not number theory. It's not uncommon to talk about non-quantitative qualities however. We might talk about the set of all black ravens, formalize what we mean by black and raven, and investigate the relationship between the quality of "blackness" and "raven-ness". That might seem like a goofy example but it's actually a necessary move in non-trivial arguments like Hempel's ravens.But the essence of an oak tree is not able to be expressed quantitatively. I don't see how you could use mathematics to describe it. You could use it to describe its shape, project its growth, etc.
What would it mean to describe "the essence of an oak tree"? Can you do it in natural language? Do you know what the essence of an oak tree is? It's a whole mereological quagmire as far as I'm concerned.
Put another way, if you can list sets of necessary and sufficient conditions for being an oak then we can trivially quantify the essence of an oak. But if you can't then there's nothing that will serve you better than mathematics. Even things like species membership are ambiguous (google ring species for some fascinating reading).
There's kind of this toy problem you see in phil 100 classes where you ask "when does a puddle become a pond?" and it's like we find things which are obviously ponds and not puddles and conversely we can find thing that are obviously puddles and not ponds but there are some values between the two that are fuzzy, fundamentally so, there's no prescribed volume that a puddle must take on to become a pond. It reveals that language isn't always susceptible to modeling, not because our techniques of modeling are flawed (indeed it would be trivial to model pond vs. puddle status if we had more rigorous definitions of the terms) but because language is ambiguous, we have a lot of constructs for talking about classes of things we don't really have robust classification criteria for. -
2016-05-15 at 5:44 AM UTC
So yes, number theory will always deal with quantities but mathematics is not number theory. It's not uncommon to talk about non-quantitative qualities however. We might talk about the set of all black ravens, formalize what we mean by black and raven, and investigate the relationship between the quality of "blackness" and "raven-ness". That might seem like a goofy example but it's actually a necessary move in non-trivial arguments like Hempel's ravens.
What would it mean to describe "the essence of an oak tree"? Can you do it in natural language? Do you know what the essence of an oak tree is? It's a whole mereological quagmire as far as I'm concerned.
Put another way, if you can list sets of necessary and sufficient conditions for being an oak then we can trivially quantify the essence of an oak. But if you can't then there's nothing that will serve you better than mathematics. Even things like species membership are ambiguous (google ring species for some fascinating reading).
There's kind of this toy problem you see in phil 100 classes where you ask "when does a puddle become a pond?" and it's like we find things which are obviously ponds and not puddles and conversely we can find thing that are obviously puddles and not ponds but there are some values between the two that are fuzzy, fundamentally so, there's no prescribed volume that a puddle must take on to become a pond. It reveals that language isn't always susceptible to modeling, not because our techniques of modeling are flawed (indeed it would be trivial to model pond vs. puddle status if we had more rigorous definitions of the terms) but because language is ambiguous, we have a lot of constructs for talking about classes of things we don't really have robust classification criteria for.
Are you fucking kidding me Lanny? Honestly I thought you were smarter than this. Ive been reading your posts for a while now and they have really gone down hill. But this... this is the absolute epitome of pseudointellectual psychobabble that has no real world applications. Its the drivel of Dawkinsesque atheist liberal antipaths attempting to sound like they got a real education. Well Ill tell you what, your sly tongue wont save you here buddy. Oh no it wont. And you know what the worst part is? In your attempts to sound academic its clear that you have never even studied these concepts a day in your life. Its like you want to compete with the big boys. Its like you think you can even out math us with your philosophy. It sickens me. It literally makes me sick that this is happening and that we allow people like you to procreate. The utter disregard for your attention to the topic at hand displays a flagrant violation of volition. None of what you posted had any shred of organized structure that all I can think is that a schizotypal latent homosexual fem boi would write such utter nonsense. And don't even get me started on youre grammer. If you cant understand the most simple concepts behind organized syntax behind language how do you expect to understand infinitesimally complex mathematical concepts? Ill fucking find you. And you will never say shit like this again. -
2016-05-15 at 6:23 AM UTC
don't even get me started on youre grammer
infinitesimally complex mathematical concepts?
I chuckled
