Please show me how any tally created prior to 3100 BCE represents more than a one-to-one correspondence between an event and a mark on the stick. Can you point to any occurrence of abstract counting prior to that time frame?
What's a number?
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Please show me how any tally created prior to 3100 BCE represents more than a one-to-one correspondence between an event and a mark on the stick. Can you point to any occurrence of abstract counting prior to that time frame?
Since no one wants to talk about the evidence for numbers not being naturally occurring concepts, I'd like to hear why people think that they are somehow independent of human creation.
ParadigmShifter
Random Nonsense Generator
Because we discover new things about them, like we do with the universe.
PeteAtoms
FormulaRandom
How is that different than just discovering new implications of any other invented philosophies or paradigms?
I think this is topic is above my understanding (the last 3-4 pages in particular), but it's really interesting to read
to all of the posters so far.
In so far as philosophy is logical, it's exactly the same, since mathematics is a branch of logic.
warpus
Sommerswerd asked me to change this
We don't discover that though, we infer it.
The same would happen with any other internally consistent abstract system that was as complex.
onedreamer
Dragon
A concept, an element of nature if you want, that helps you in various natural activities. For example realizing you are smoking and drinking too much and stop doing it... something apparently you haven't done before posting
Defining a number is like defining any other concept or natural element: pretty pointless.
onedreamer
Dragon
The fact that in 7 pages there is nothing close to a consensus of definition of number, at my eyes is a clear proof that numbers aren't a human creation but just the name we give to something, like red and yellow.
Mise
isle of lucy
Does "Energy" really exist, or is it just a concept we've invented to help us understand the universe? I can make arguments both for and against, btw.
warpus
Sommerswerd asked me to change this
It's a concept we've invented that encapsulates a whole bunch of things that actually exist, such as electrons and photons.
The conservation of the quantity that we know as energy is a direct result of the symmetry of the laws of physics under time translation. This is called Noether's theorem. This is true for other conservered quantities as well, such as angular momentum (rotation), and linear momentum (spacial translation).
I don't really see how on earth you can say that is an invention. This is of course ignoring the fact that there very much are physical manifestations of energy, such as mass.
warpus
Sommerswerd asked me to change this
I mean that we invented a word, energy, to mean a whole bunch of stuff, such as angular momentum, potential energy, kinetic, etc.
Lack of consensus implies to me that numbers are a human invention and we have yet to agree on what we mean by them.
There is evidence that we did invent them. Lack of consensus among internet forum posters is hardly evidence for anything.I don't see the connection between colors and the use of abstract counting through numbers. Colors are a product of the way our brains interact with the environment though our senses. Color has been a part of the human experience for many hundreds of thousands of years. Numbers and abstract counting only for a few thousand.
Naskra
Emperor
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Numbers are very simple things. So simple that many common categories of thought do not at all apply to them. To ask whether they are created or uncreated is just a bad question; likewise with being or non-being. Numbers are outside those categories just as they are outside the category of color. The expression "7+5=12" reads in english as "seven plus five equals twelve". But this is a very bad and misleading translation. "7" becomes a noun, "=" becomes a verb, when they are neither. "equals" is a verb implying action in time, yet the numbers are atemporal. Numbers are unlike apples, they have really few properties, you should stick to those properties when speaking of them.
But do numbers have an existence outside of the human mind?
Naskra
Emperor
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Sorry to sound all Wittgensteinian, but this an inappropriate question. The property of existence/non-existence does not apply to numbers, and can't sensibly be asked. Roses are red, violets are blue, numbers aren't in the hunt
Apples exist, unicorns don't, numbers don't do either of these things. Numbers have very strictly limited properties: one might be greater or less another, for example. A number might be even or odd. But no number has the property of "existence".
Raca
Chieftain
I just ordered Stephen Hawking's book "God Created the Integers", which discussed the 17 greatest mathematicians through history and their discoverys, which I'm excited about. By the way he had a special this past week on the Discovery Channel about the Universe. He states that the possibility of aliens is very probable, but that they would most likely be nomads or renegades out for exploitation, and that we should avoid contact. He's rarely wrong. Too bad Sid can't do Alpha Centauri 2, then we might get our numbers right.
Then you're referring to the word, not the concept or property of energy itself. That's not particularly meaningful, as it should be quite obvious that the arbitrary signs which we label things which exist are not the same thing as the thing itself. Your comment would mean that we invented dogs because we invented a word, dog, to refer to a member of the species Canis lupus familiaris. That's silly. When I refer to the number 1, I am usually not referring to the arabic numerial, but the number which the grapheme represents. (Also, angular momentum isn't energy. An object with angular momentum has energy, but it's not the same thing as energy.)
I agree that numbers don't exist in the same way that physical things exist. But perhaps existence can be defined in another way, for which numbers do exist. For instance Perfection earlier in the thread used existence to mean existential quantification, and said that the lowest prime number in a certain range may or may not exist. Surely there is a useful definition of existence that implies numbers exist.
For instance, It may be useful to say that not only physical things exist, but also physical properties, like mass. You can't point at something and say that's mass. But still it is useful to say that mass, the measure of an objects tendency to attract other objects with mass, exists. Or similarly the measure of inertia exists. A number of people have connected numbers with they physical properties of quantity and relative size.
Similarly it may be useful to say that abstract things like the id, ego, and superego, the moral compass, exist. Are numbers similar?
ParadigmShifter said:
The unique distributive law doesn't hold for interval numbers nor fuzzy numbers. E. G. Let 4'=[3, 5], 5'=[4, 6], 7'=[6, 8]. Then 4'(5'+7')=[3, 5]*[10, 24]=[30, 120]. While
4'*5'+4'*7'=[12, 30]+[18, 40]=[30, 70]. You can get this from the integers without going up to complex numbers... actually I did so above in the calculation, even though the intervals concern sets of real numbers. I just used the rules,
[a, b]+'[c, d]=[a+c, b+d], [a, b]*[c, d]=[min(ac, ad, bc, bd), max(ac, ad, bc, bd)].
I don't agree with integers as natural constructs. Euclid didn't regard 1 as a number for example. This also applies no doubt to most of the ancient Greek mathematicians, and to plenty of people who learned some mathematics from Euclid.
