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Mathematics, invented or discovered?


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Showing 1-25 of 90 posts in this discussion
Initial post: 14 Mar 2011 16:17:18 GMT
It would appear incredibly coincidental that our mathematics seems to make predictions, such as black holes or gravitational curving of space/time which turn out later to be verified by observation.
It would seem there are two possibilities either our brain builds all our observations using a mathematical algorithm or two so what we observe seems to have a mathematical basis. Or
The universe works on a mathematical basis and we have discovered it's secret. Either way and I would probably subscribe to the first (Kantian) style explanation, mathematics does not seem like a naturally occurring phenomena, which would suggest that either our minds or the universe or both had some form of mathematician for a designer. Perhaps someone can explain how maths could occur naturally.

In reply to an earlier post on 14 Mar 2011 17:57:48 GMT
Spin says:
Newtons: Mathematics is a language employed to reduce complexity to simplicity. In denying complexity it lays itself open to many problems, Maths consists of signs representing a reality that cannot be described in words. But unlike words, maths cannot fully explain the meaning, relevence, concept or truth of the actual being of that which it attempts to describe. Maths is a shortcut to reality, devoid of meaning or relevence.

Posted on 14 Mar 2011 23:22:55 GMT
That doesn't help with the point that maths does seem to deliver empirical reality.

In reply to an earlier post on 14 Mar 2011 23:55:19 GMT
"Mathematics, invented or discovered?" Or a bit of both?

On the Religion discussion forum, often the phrases "natural" or "naturalistic" explanations are mentioned. A couple of questions that spring to mind are: what does a natural explanation mean, and why does a natural explanation rule out a design or designer?

Posted on 15 Mar 2011 13:07:58 GMT
Mathematics is the true logic that we (the human race) have gradually unearthed, by which the workings of the universe may be explained. I am sure that there is much still to be "discovered" or perhaps a more appropriate word might be revealed.

In reply to an earlier post on 15 Mar 2011 19:51:23 GMT
Last edited by the author on 15 Mar 2011 20:13:36 GMT
M. Jolliff says:
NN
There is a third, somewhat silly possibility, that we define the universe by our beliefs and that therefor the universe is merely conforming to our desire for a mathematical explanation.
Or there's the fourth possibility that the apparent mathematical descriptions are illusory being as they only work as descriptions under tightly defined parameters. Anything approaching the complexity of factors involved in real 'events' are far too complex for our ability to process.

Posted on 15 Mar 2011 23:56:09 GMT
Hi MJ
I don't see why the universe should play along with our beliefs or desires, if I desired or believed that a planet existed made out of chocolate, I see no reason for it to appear that way through a telescope unless I was hallucinating, so I would rule out your third option. As for your fourth, Maths seems to work over quite a wide variety of parameters and gets into nearly all forms of observations on the world. And even if events are too complex for our abilities, this again does not mean they don't have a mathematical description.
So we are left (probably) with maths instilled in the way we see the world, or the way the world actually is and with the question how did that happen?

In reply to an earlier post on 16 Mar 2011 00:41:02 GMT
I like this one M.Jolliff... isn't mathematics merely our translation of how we think the universe is...

Is there a mathematical description or equation to show how thought works perhaps...?

I started another thread, where I asked if anyone knew or had seen the equation that Prof. Stephen Hawking had written out many years ago... to describe time.

Posted on 16 Mar 2011 19:03:17 GMT
Spin says:
There are four interpretations of mathematics: First Platonism, which holds that we discover mathematics rather than invent it. Second, Conceptualism, which states that we create an assortment of mathematical structures, symmetries and patterns and then force the world into these constructs. Ultimatelu, mathematics is culturally derived. Third, Formalism, which argues that mathematics is nothing more than the manipulation of symbols according to specified rules. Thus the actual axioms have no intrinsic meaning. the connection between nature and mathematics is irrelevent to the Formalist The only goal of mathematics is to show consistency in axioms. Last, Intuitionism, this view argues that, in order to avoid the assumption of infinite sets sharing a property with finite sets, only quantities that can be constructed from natural numbers (1.2,3...etc) should be regarded as proven "teue". Only the simplest (intuitive) ideas should be used in mathematics. Anything outside experience must be constructed from simple ingredients by a sequence of intuitive steps. Thus, a mathematical formula describes only the set of computations that has been carried out to arrive at that formula. It is not a representation of reality existing independently of the act of computation.

In reply to an earlier post on 16 Mar 2011 19:10:17 GMT
I'm for Platonism as I see this as the simplest explanation (and complies with my post above), and if my life has taught me anything it is to not look for a complicated explanation when the the truth is staring you in the face!

In reply to an earlier post on 17 Mar 2011 15:07:19 GMT
Spin says:
Cornish: You are favour of platonism when it comes to maths? So you believe that mathematics exists, has being, independently of human thought? If there were no living organisms in the universe the statement that "1+1=2" would exist on its own, in some corpereal form? Triangles, circles, squres, infinities and numbers really exist "out there" independently of you and me? Even "pi" exists in some abstract way?

In reply to an earlier post on 17 Mar 2011 19:47:58 GMT
Last edited by the author on 17 Mar 2011 19:49:07 GMT
M. Jolliff says:
NN
So you're happy with the mathematical descriptions of the world and believe that they describe things accurately even though those descriptions are usually couched in terms of unreal, imaginary or complex numbers or require the use of n-dimensional topology? You don't feel the level of abstraction any hindrance or suggestive that things are anything other than those descriptions provide? Fairy Nuff.

In reply to an earlier post on 17 Mar 2011 20:04:45 GMT
In effect "yes" I do Spin. The reality of the mechanics which govern the universe exist whether we do or not. We are learning to understand it though the medium which is known as mathematics. The fact that we work in everyday language using the base ten is irrelevant in my view.

Philosophy should be used to make sense of the world, not attempt to make it more complicated by playing intellectual games for the sake of it.

In reply to an earlier post on 20 Mar 2011 20:30:27 GMT
Spin says:
Cornish: So what created or caused these perfect forms of numbers and shapes? Where do they reside? If numbers exist in reality, point a number out to me (not the collection of items represented by the number, but the independent number itself). If the number "2" exists independently of the two items it is used by us to represent, how do we know theses numbers if not for the existence of the items themselves?

Posted on 21 Mar 2011 23:44:13 GMT
I quite like the conceptualism thesis, this seems to be more likely than Platonism. As our brains 'build' the sensory input, it would see logical that any mathematical processes innate in the brain/mind, ie conceptual schema would cause our minds to see the world/universe in a mathematical way. So the question would seem to be how does the brain end up with a mathematical processing unit? Could it be a natural/evolutionary trait or does it have to be supplied by a logical designer?

In reply to an earlier post on 22 Mar 2011 17:11:10 GMT
Spin says:
Newton: Imagine you are sitting by a table. On the table, to your left is an apple. On your right is an orange. Without any mathematical knowledge you know that there is "a" apple and "a" orange. Also, without any mathematical knowledge you know there are "two" fruits on the table. To express this experience to someone you must differentiate between the existence of a single fruit and many fruits, so you invent numbers, signs to represent the amount of fruit on the table. (if there is one hundred fruits on the table you will not instantly recognise how many there are. I believe 7 is the largest amount recognisable, which ties in with the fact that one can only, on average, remember 7 items through memory). So, in short, the brain is not mathematically hotwired. It simply recognises objective reality and to express this reality to itself and others, it creates signs representative of that reality. Unfortunately, since the system works so well, the brain becomes conditioned into thinking that axioms are real (ie; that there really are "Two" fruits on the table, not "a" fruit and another fruit, and that "One" is an apple, and the other "one" an orange). This conditioning is based on the logic that "1+1=2", even though the "+" (addition) and the "=" (equality) do not exist in the experience itself ( What is it that is being to what? And by "=" do we mean the equality of achievement or that of identity?ie; does 1+1=2 mean that one item alongside another item achieves two items or that one item alongside another item is identical to two items?)

In reply to an earlier post on 23 Mar 2011 16:53:41 GMT
Spin, I consider that you are confusing maths with the symbols that we have devised to describe and understand it.

Look at it this way, gravity will prevent us from floating off the planet and keep the moon orbiting the earth and the earth orbiting the sun whether we understand the mathematics that govern such occurrences or not.

In reality any number "exists" whether it has been written down or not as it is simply a symbol to represent part of the world or universe. The fact that visible light are the only wavelengths of electromagnetic radiation that we can "see" does not mean that the rest of the spectrum does not exist. However, until "discovered", to mankind, to our consciousness, it did not exist.

Posted on 23 Mar 2011 16:58:16 GMT
Spin
Experiments on babies have shown that mathematics to a limited extent is 'hotwired' into the brain, and also of certain animals. They can usually recognise upto 4 things.Known as 'subitizing'. The mind then can conceptually understand certain functions such as addition and subtraction through basic metaphor, which seems to be innate to a degree. If A is a larger group than B and you add C to both groups then A plus C is larger than B plus C, conceptualisation of the world translates into basic maths.
So I suppose the real question is do we adapt our maths to the way we conceptualise the world or do we perceive the world in a mathematical way?

In reply to an earlier post on 23 Mar 2011 17:36:31 GMT
Spin says:
Cornish: That is exactly the point I am contending. Gravity exists as a phenomena in itself. It is not composed of numbers or axioms (which are signs used to represent that reality) There is no inherent mathematical ability in the brain, since even species without mathematical knowledge can distinguish between one and many items before them. In short, a phenomena exists, which we inherently isolate as seperate from the rest of the environment, and we allocate a sign to it, due to the development of language instincts, If we could not isolate one phenomena from another, regardless of whether we allocate a sign to it or not, we could not engage with the environment in any way. It is this isolating of phenomena thar leads to the allocation of subjectively formulated signs. Mathematics, as a body of knowledge, is simply the ordering of seperate isolated phenoma into a paradigm based on artificial, subjective signs. If an isolated phenomenon does not fit into this paradigm, it is not the paradigm that is considered at fault but that we have failed to isolate a further phenomenon within that which is isolated. Having isolated the hidden phenomenon we then allocate a sign to that; a sign based on the consistency of prior signs and axioms, ad infinitum. The more phenomena, the more signs and axioms, leading to a development of maths as an actual language. And, just as the word "Tree" does not exist in reality, (only the object that the word represents exists) so a number does not exist,( only the phenomena or state-of-affairs it represents exist)

In reply to an earlier post on 26 Mar 2011 22:23:43 GMT
Last edited by the author on 26 Mar 2011 22:27:48 GMT
Valis, the book by Philip K Dick has the answer you seek, Newt.

The Big Questions - Physics by Micheal Brooks also interestingly comes to the same conclusion as PKD. It is also well worth reading.

In reply to an earlier post on 27 Mar 2011 13:43:00 BDT
Spin, in your imagined experiment, 1 apple + 1 orange EITHER equals (still) 1 apple + 1 orange OR 2 pieces of fruit. Both statements are equally valid when you add descriptive terms to the numbers.

In reply to an earlier post on 27 Mar 2011 13:48:25 BDT
Hi Cornish Deadhead,

"In reality any number "exists" whether it has been written down or not as it is simply a symbol to represent part of the world or universe. The fact that visible light are the only wavelengths of electromagnetic radiation that we can "see" does not mean that the rest of the spectrum does not exist. However, until "discovered", to mankind, to our consciousness, it did not exist."

Something "discovered" would have to exist already, for us to discover it, surely? Gravity was always there, but then Newton observed it...?

In reply to an earlier post on 27 Mar 2011 15:51:39 BDT
M. Jolliff says:
DW
Gravity wasn't discovered. It is an explanation to account for observed phenomena. As yet no-one has managed to discover quite how it works. Hence the search for the Higgs boson, which if it exists as theory suggests and is as described by said theory then we may have an understanding of how gravity does what it does.

In reply to an earlier post on 27 Mar 2011 19:57:12 BDT
I agree Darren. The point I was trying to make (badly from the looks of it) was that we are only aware of what we have "discovered". I anticipate there are many more phenomena awaiting discovery out in the universe, but until we become aware of them, to us they do not exist as we have no knowledge of them.

In reply to an earlier post on 27 Mar 2011 20:24:11 BDT
I agree Spin with certain reservations, as I agree with viewpoint that Darren has illustrated above. The symbols we use are simply the method of explaining the world about us. The fact that everything (with the exception of black holes) appears to operate in a logical and organised way allows us to "discover" the "rules" or "laws" which govern the physical world. The symbols we apply to this logic do not matter, but whatever we use, it does not effect the absolute "truth" they represent.

In simplistic terms, the apple and the orange are "2 objects" whatever symbol we decide to denote them, but there will always be "2 objects" present. Therefore in the abstract the symbol "2" exists, or whatever you choose to denote the items.
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Total posts:  90
Initial post:  14 Mar 2011
Latest post:  12 Aug 2011

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