Philosophy - Are Numbers Real?

[H3LL]

I hesitate to enter into the realms of philosophy but I am aware that there are various philosophical opinions on the subject. Plato-heaven and the Aristotalean ideas I have seen in their most expurgated forms (and totally agree with neither).

For me numbers are not real and cannot exist in and of themselves but are purely a construct to express descriptive concepts.

The number one cannot exist any more than adjectives such as black, cold, or loud; all describing something else.

I cannot have a one, a black, a cold or a loud but can have one, black, cold and loud cat.

Positive integers are no more "real" than negative or other types of numbers, just universally agreed upon adjectives to describe something else, often, but not always, quantity.

Quantity I can accept as real. A cat can be aware of the "threeness" of its kittens , but is unlikely to use numbers.

Numbers are also a concept to describe further concepts. You can't actually have -3 cats.

I also think this is the great power of mathematics (although no expert). The use of descriptive labels to describe concepts (or concepts of concepts etc. etc.) has enabled mathematicians to find the unknown and allow verification by experiment later. The LHC (http://en.wikipedia.org/wiki/Large_Hadron_Collider) being perhaps the most recent attempt at such things.

I mention this as some people express surprise or disbelief in the more bizarre types of numbers (and symbols) used in various mathematical disciplines without realising that everyday integers are just as bizarre, arbitrary and not "real". Positive and negative numbers they use everyday without thought but think other types of numbers are 'weird'.

NB: I mean "real" as in cat - not in the mathematical, numerical sense.

I would be interested in the various ideas on this subjects and your opinions of such. Be aware that I am in no way educated in philosophy but keen to see what you have read and learn. If you do quote someone else, I would be delighted if you would also add your own opinion of what they said.

Thanks in advance.

[FireGarden]

I enjoyed a discussion at this forum some time ago on a similar topic:
http://forums.randi.org/showthread.php?t=114438

I ended up agreeing that maths was a useful fiction.

Different cultures only come up with equivalent mathematical ideas when there is feedback from the real world. Counting is so useful that, once thought of, it will stick around. Other mathematical ideas are forgotten. Unit fractions were once in fashion, not so much today. They're as "real" as any other part of maths.

[yy2bggggs]

NB: I mean "real" as in cat - not in the mathematical, numerical sense.
The problem is semantics. Words like "true", "real", "exist", do not really describe one thing, but a myriad of things. When someone disagrees with you and argues that numbers are real, they mean something else besides real like cat. But real like your bank account balance isn't so far off.

[Soapy Sam]

I agree with the OP and post 3.
We have to be careful what's meant by words here, but I feel "three" is essentially an adjective, not a noun.
There's the accountancy type of arithmetic, where "minus 1" equates to a debt- or a credit owed to someone else, which is not always the same thing.
There's inventory arithmetic, where "3 nuts minus 4 nuts" does not equal "minus 1 nut". It equals no nuts. There is no such thing as minus one nut.

There are all kinds of arithmetic.

Clearly the terms are not always transferable.

Then there's pure or abstract arithmetic, where "one" is a concept, where there is always a number bigger than any other number (This seems to be spilling over into economics),
where , despite the foregoing, 0.9999... is the same as 1, and where infinity is something with a degree of reality realer than orbital teapots.

This is dangerous territory and best avoided by those who value their sanity.

[H3LL]

The problem is semantics. Words like "true", "real", "exist", do not really describe one thing, but a myriad of things. When someone disagrees with you and argues that numbers are real, they mean something else besides real like cat.


This is the very reason that I usually steer well clear of any philosophy discussion. They always seem to roll along the "What is real? What exists? What is truth?" route and I have successfully shot myself in the foot with that one.

:(


.

[H3LL]

This is dangerous territory and best avoided by those who value their sanity.

Mad as a sack of monkeys here so reasonably safe. :D

The bank account analogy and your examples got me pondering for a while but all the examples seemed descriptive to me.

I thought for a while that numbers were evident with quantities (like your three nuts and the three kittens) until I got my head around the inherent "threeness" as a characteristic or property distinguishable without descriptive numbers.

[Elizabeth I]

Well, you most certainly can have a cold. I myself had a particularly miserable one just a month or so ago.

[Roadtoad]

The ultimate question is what is being described, and how are "numbers" being used. When we begin to enumerate things, we're simply trying to quantify what we have, which can further be broken down into subsets based upon what it is we're trying to enumerate.

Hence, I can look at a socket set, and break that down by:

1.) Drivers.
2.) 1/4 inch sockets.
3.) 3/8 inch sockets.
4.) 1/2 inch sockets.
5.) Storage.

It can get pretty interesting once you begin to add in the arbitrary nature of most numeral systems, and the role that language plays in it.

[Skeptic Ginger]

The relationships are real. The numbers are akin to language or vocabulary. They are used to describe the relationships.

[Robin]

The relationships are real. The numbers are akin to language or vocabulary. They are used to describe the relationships.
That is more or less my position, numbers are symbols which we manipulate in a particular way, like language.

And this symbol manipulation has often proved a useful tool in describing the relationships in sense information.

[Gord_in_Toronto]

The mathematician part of me wants to say that only Mathematics is real.

Damn. It won. :scared: