Number

[GrowingSmaller]

The indispensibility arguments in the philosophy of mathematics.

The indispensability argument in the philosophy of mathematics, in its most general form, consists of two premises. The major premise states that we should believe that mathematical objects exist if we need them in our best scientific theory. The minor premise claims that we do in fact require mathematical objects in our scientific theory. The argument concludes that we should believe in the abstract objects of mathematics.

 

[quatona]

metherion,

I understand what you're saying. I just disagree. It's not really something I think is worth arguing about, so I'll just explain how I see it.

Every object that is to be counted is assigned a "unit." Since some units are obvious, I think you're trying to make it "self-evident", and then excluding as uncountable those objects that don't have obvious units.

If I count pennies, I have implicity assumed a unit of "penny." But I don't have to. I could count 1/2 pennies (that used to be legal tender). It would not be proper to claim that because one has adopted the 1/2 penny unit that pennies are uncountable.

Not that I necessarily disagree - but I´d like to give a caveat here: It seems to me that with this line of reasoning you are abandoning the idea that there are distinct objects.
I do not disagree simply because the conviction that there aren´t any distinct objects is essential part of my philosophy. I am just warning you that - depending on your worldview and philosophy - you might run into huge problems with the implications of this line of reasoning.

 

[quatona]

The indispensibility arguments in the philosophy of mathematics.

Extremely interesting quote, GS. Thanks.

 

[LOCO]

metherion,

I understand what you're saying. I just disagree. It's not really something I think is worth arguing about, so I'll just explain how I see it.

Every object that is to be counted is assigned a "unit." Since some units are obvious, I think you're trying to make it "self-evident", and then excluding as uncountable those objects that don't have obvious units.

If I count pennies, I have implicity assumed a unit of "penny." But I don't have to. I could count 1/2 pennies (that used to be legal tender). It would not be proper to claim that because one has adopted the 1/2 penny unit that pennies are uncountable.

Counting does not become necessary until objects are considered in such generalised form that their individualities are entirely lost sight of.

When my large immediate family of 9 sits down to dinner, we notice someone is missing even though no headcount is done. Prior to the invention of counting, families noticed when someone was not present or a chicken/cow was missing from the family farm.

Blessings

 

[Resha Caner]

Counting does not become necessary until objects are considered in such generalised form that their individualities are entirely lost sight of.

When my large immediate family of 9 sits down to dinner, we notice someone is missing even though no headcount is done. Prior to the invention of counting, families noticed when someone was not present or a chicken/cow was missing from the family farm.

A very interesting observation.

 

[Resha Caner]

... I guess people don't think this is quite as cool as I do ...

So, what about infinity? It's not a number, but it's a concept that stems from number.

If something infinite existed - not as a concept but as a real thing - is there any way we could detect it? Or, would it be indistinguishable from something that is really big (or numerous)?

 

[Naraoia]

Hmm. I can see how "uncountable" is a possibility, and maybe that's good enough. But I can't actually think of something that is uncountable.

Real numbers

I tried to do the same with the ordinals. Is it possible that there is something that can't be ordered?

Anything that exists in many identical copies? A bunch of photons of the same wavelength, polarised in the same plane, for instance.

And, I think you'll find that most dictionaries list "one", "two", "three", etc. as nouns. That is very curious.

That's language-specific. In Hungarian, numbers are classified as a separate part of speech. Or were, back when teachers tried to stuff grammar in my head.

 

[diychristian]

I've been thinking about the concepts of numbers alot lately. I was listening to a William Lane Craig debate. He mentioned infinity in relation to the Big Bang and how there couldn't have been an infinite number of events that proceeded creation because it would have taken an infinite amount of time for us to get here. Therefore we would have never existed!

This got me to thinking of other arguments I have heard. Where scholars seem intrigued but skeptical of things like string theory where there is a heavy usage of abstract functions to explain speculations/theories to fix the problems of string theory. (paul davies is one).

In my mind only non-negative integers would be realistic. Maybe fractions that when converted don't equal some infinite decimal could also be considered. Negative numbers are a philosophical number. While a bank account may show a negative balance, I can't make a withdrawal of all my negative money.

Good Topic!

 

[diychristian]

As far as the "countability" of things I'm sure Chaos Theory is lurking around in the details.