Author Topic: What is the justification for the existence of numbers?  (Read 17106 times)

0 Members and 1 Guest are viewing this topic.

Olivianus

• Posts: 208
• Darwins +2/-56
• Gender:
• WWGHA Member
What is the justification for the existence of numbers?
« on: January 14, 2013, 11:56:53 AM »
How do we account for the existence of numbers? Are there multiple physical things to justify the existence of numbers? How do we know there are multiple existing things?
Bertrand Russell, “All inductive argument...is of course, formally fallacious...yet it would not be fundamentally different from the argument upon which all scientific laws are based.” The Scientific Outlook, Limitations of Scientific Method

ParkingPlaces

• Professor
• Posts: 7739
• Darwins +1176/-6
• Gender:
• This space for rent
Re: What is the justification for the existence of numbers?
« Reply #1 on: January 14, 2013, 12:03:44 PM »
Let me count the ways...

We name stuff. Including amounts. We calculate. Including amounts. Amounts have names. Amounts are numbers. Its what we do.

Is it necessary? No. We could continue on as primitive men, indifferent to the number of saber toothed tigers around our cave. For about a week. Then we'd be gone. Eaten up because Og and Dorf weren't sure how many tiggers were left because they couldn't count.

Once two tigers start eating you, you'll know for sure that there are multiple existing things.
What I lack in sophistication I make up for with other shortcomings.

Olivianus

• Posts: 208
• Darwins +2/-56
• Gender:
• WWGHA Member
Re: What is the justification for the existence of numbers?
« Reply #2 on: January 14, 2013, 12:08:36 PM »
Let me count the ways...

We name stuff. Including amounts. We calculate. Including amounts. Amounts have names.

Once two tigers start eating you, you'll know for sure that there are multiple existing things.

But this is all ad hoc. Asserting that there are multiple things is not an explanation of how you know that or how you define the difference between numeric substances.
Bertrand Russell, “All inductive argument...is of course, formally fallacious...yet it would not be fundamentally different from the argument upon which all scientific laws are based.” The Scientific Outlook, Limitations of Scientific Method

Azdgari

• Laureate
• Posts: 14160
• Darwins +475/-40
• Gender:
Re: What is the justification for the existence of numbers?
« Reply #3 on: January 14, 2013, 12:16:41 PM »
How do we account for the existence of numbers?

Practicality.

Are there multiple physical things to justify the existence of numbers? How do we know there are multiple existing things?

There aren't.  Object-division is subjective, something we impose on nature to help us organize and deal with it in our minds.
I always say what I mean. But sometimes I'm a sarcastic prick whose tone can't be properly communicated via text.

ParkingPlaces

• Professor
• Posts: 7739
• Darwins +1176/-6
• Gender:
• This space for rent
Re: What is the justification for the existence of numbers?
« Reply #4 on: January 14, 2013, 12:21:47 PM »
But this is all ad hoc. Asserting that there are multiple things is not an explanation of how you know that or how you define the difference between numeric substances.

I'm going by what they taught me in grade school. It has worked so far. I'm a practical kind of guy. If you are looking for a discussion on the philosophy of mathematics, first order logic, Xenocrates's theory of knowledge, mathematical intuitionism, Zeno's paradoxes or stuff like that, you're out of my league.

And do keep in mind that you're asking via a medium that requires, at a minimum, 0's and 1's or it doesn't work. You won't be able to argue that we don't need numbers using a computer because you're reading this now.

This isn't about negative karma, is it?
What I lack in sophistication I make up for with other shortcomings.

sun_king

• Posts: 461
• Darwins +44/-0
• Gender:
• We see things not as they are, but as we are
Re: What is the justification for the existence of numbers?
« Reply #5 on: January 14, 2013, 12:48:11 PM »
How do we account for the existence of numbers? Are there multiple physical things to justify the existence of numbers? How do we know there are multiple existing things?

At this point I would like you ask if you really exist? How do we know Olivianus exists? Do you have a physical form?

wheels5894

• Fellow
• Posts: 4578
• Darwins +294/-1
• Gender:
Re: What is the justification for the existence of numbers?
« Reply #6 on: January 14, 2013, 12:56:52 PM »
How do we account for the existence of numbers? Are there multiple physical things to justify the existence of numbers? How do we know there are multiple existing things?

Come on, look down at the keyboard. What has been typing on the keys (whoops, multiple keys!). Yes, that's right, it was your hands. Now notice you have 2 hands and each hand has multiple fingers, 4 plus on thumb each. This may be ad hoc but we can't ignore what we see.
No testimony is sufficient to establish a miracle, unless the testimony be of such that its falshood would be more miraculous than the facts it endeavours to establish. (David Hume)

naemhni

• Global Moderator
• Posts: 4377
• Darwins +208/-6
• Gender:
• Je bois ton lait frappé
Re: What is the justification for the existence of numbers?
« Reply #7 on: January 14, 2013, 01:01:59 PM »
Quote
First use of numbers

Bones and other artifacts have been discovered with marks cut into them that many believe are tally marks. These tally marks may have been used for counting elapsed time, such as numbers of days, lunar cycles or keeping records of quantities, such as of animals.

A tallying system has no concept of place value (as in modern decimal notation), which limits its representation of large numbers. Nonetheless tallying systems are considered the first kind of abstract numeral system.

The first known system with place value was the Mesopotamian base 60 system (ca. 3400 BC) and the earliest known base 10 system dates to 3100 BC in Egypt.

Source:

http://en.wikipedia.org/wiki/Number#First_use_of_numbers

Or, to put it more simply, numbers were invented to keep track of stuff.  (And they're still used for that purpose today, although they're obviously used for a lot of other things as well.)
[On how kangaroos could have gotten back to Australia after the flood]:  Don't kangaroos skip along the surface of the water? --Kenn

screwtape

• The Great Red Dragon
• Laureate
• Posts: 15326
• Darwins +1176/-40
• Gender:
• We stand on the shoulders of giants
Re: What is the justification for the existence of numbers?
« Reply #8 on: January 14, 2013, 01:16:52 PM »
How do we account for the existence of numbers? Are there multiple physical things to justify the existence of numbers? How do we know there are multiple existing things?

Let me guess... is it god?

What's true is already so. Owning up to it does not make it worse.

Garja

• Posts: 759
• Darwins +38/-0
• Gender:
• WWGHA Member
Re: What is the justification for the existence of numbers?
« Reply #9 on: January 14, 2013, 01:20:55 PM »
Humans label stuff. "Blue" doesn't exist anymore than "one", or even "man" or "woman". They are semi-arbitrary labels used to describe the world.
"If we look back into history for the character of the present sects in Christianity, we shall find few that have not in their turns been persecutors, and complainers of persecution."

-Benjamin Franklin

Fiji

• Posts: 1857
• Darwins +158/-2
• Gender:
Re: What is the justification for the existence of numbers?
« Reply #10 on: January 14, 2013, 01:47:53 PM »
Why do numbers exist? We needed to describe amounts; we needed a common language to talk 'amounts' in.
"I want this many coins for that many sheep."
Now, coins and sheep are easy. It's kind of hard to trade in half living sheep. Dead half sheep, now there's a different matter entirely. But still, two parties agree on a standard amount to trade in and from there on it's a matter of counting.
A container, this big , filled with grain, or butter, or wine, is counted as 1, etc.

This is also why zero was an unknown in the west until well into the middle ages. Why would you want a number that represents nothingness ... "there are no cows in this pasture, how many coins will you give me for that?"

Ever seen the Roman numeral for zero? The Greeks and Hebrew used letters and assigned them numerical values ... which is where the number of the beast, for instance, comes from. The Babylonians too had no concept of nothingness. They wrote their number pretty much like we do, except, in stead of 0 they left a space. So 206 was written 2 6. Easy enough, right? Except that 26 and 260 were written the same. You had to tell the difference through context.

Zero had to be invented, just like the wheel.[1]
You might as well ask how we account for roundness. Why is it that round things roll while other shapes, at best, hobble along?

Are amounts a purely human thing? No. As an impromptu experiment in my kitchen showed. Dogs know when the number of treats they get is too small. But dogs don't have a language for amounts. So numbers are purely human, right? Well, no, bees can communicate distances. A distance is an amount.

 1 Zero was invented in India and arrived in the west via Muslims
2 Interwebs 7:42
And in the seventh year, thou shalt cast out the Nam from thine assembly for he haveth a potty mouth.

Garja

• Posts: 759
• Darwins +38/-0
• Gender:
• WWGHA Member
Re: What is the justification for the existence of numbers?
« Reply #11 on: January 14, 2013, 01:58:51 PM »
^ true, my dog won't get out of your chair unless you let his belly twice. TWICE.  They also seem to count if one dog gets more than the other, but that one is harder to prove.
"If we look back into history for the character of the present sects in Christianity, we shall find few that have not in their turns been persecutors, and complainers of persecution."

-Benjamin Franklin

Fiji

• Posts: 1857
• Darwins +158/-2
• Gender:
Re: What is the justification for the existence of numbers?
« Reply #12 on: January 14, 2013, 03:21:37 PM »
^ Well, in all fairness, only one of the two dogs notices the missing treat. But then again, we have always refered to her as the dumb one.
2 Interwebs 7:42
And in the seventh year, thou shalt cast out the Nam from thine assembly for he haveth a potty mouth.

ParkingPlaces

• Professor
• Posts: 7739
• Darwins +1176/-6
• Gender:
• This space for rent
Re: What is the justification for the existence of numbers?
« Reply #13 on: January 14, 2013, 03:38:19 PM »
In a thread like this, it would be nice if the OP was a bit more specific about the question and why they have interest in it. Is the question in relation to a practical matter or a philosophical one, for instance. Or is he OP just trying o f**k with our heads.

What I lack in sophistication I make up for with other shortcomings.

screwtape

• The Great Red Dragon
• Laureate
• Posts: 15326
• Darwins +1176/-40
• Gender:
• We stand on the shoulders of giants
Re: What is the justification for the existence of numbers?
« Reply #14 on: January 14, 2013, 04:22:49 PM »
If god is responsible for numbers - and why would olivi bother to ask the question if the thought for a moment there could possibly be any other answer - then I wonder why god wouldn't have taken credit for them sooner?

You know how yhwh would brag about how awesome he was back in the OT - smiting the egyptians with those plagues, inventing good and evil, etc?  Well, why wouldn't he brag about numbers and fine tuning universal constants and such?

Seems to me, that bragging about stuff like that the hebrews never heard of would be better evidence of yhwh's existence than just "numbers exist, why is that?"  We'd be all like, "whoa!  yhwh said in the bible that he created partial differential equations 2000 years before Newton invented them!"

But that's not what yhwh did.  Perhaps because yhwh was only as awesome as the hebrews' imagination.  Since the hebrews didn't understand math as an abstraction nor calculus, and were not aware of universal constants, they were limited in what they could imagine yhwh knowing and doing.  But if yhwh were real, he would have known about that stuff and could have told a prophet or two to, you know, sort of undisputably show he exists.

Funny.  It is almost as if god is imaginary.

What's true is already so. Owning up to it does not make it worse.

wheels5894

• Fellow
• Posts: 4578
• Darwins +294/-1
• Gender:
Re: What is the justification for the existence of numbers?
« Reply #15 on: January 14, 2013, 04:33:01 PM »
True, but he did lead them into the oddest calculation of all - well the Christians really -

1 + 1 + 1 = 1

God, Jesus and Holy Spirit = 1 god that is!
No testimony is sufficient to establish a miracle, unless the testimony be of such that its falshood would be more miraculous than the facts it endeavours to establish. (David Hume)

• Posts: 1848
• Darwins +858/-1
• Gender:
• Your Friendly Neighborhood Cephalopod Overlord
Re: What is the justification for the existence of numbers?
« Reply #16 on: January 14, 2013, 05:00:50 PM »
How do we account for the existence of numbers? Are there multiple physical things to justify the existence of numbers? How do we know there are multiple existing things?

Sorry dude, but accounting kinda requires numbers.

Humanlike sapient beings, such as the one (or is it three?)[1] Christians worship--and especially a super-duper one/three like Christians worship--are incredibly complex entities, very high up in the Jenga tower of causality and explanatory "accounting."  Trying to "account" for Number by means of anything like the royal decree of a cosmic King is like trying to explain how the foundation of a house rests upon the roofing tiles.

"Number" is a much more fundamental concept (whether you're talking about 'Hey, there are six cows over there' or the way mathematics can actually model the behavior and form of Nature) than the notion of an omni-everything supernatural Sky King who needs status among humans (worship, obedience, praise) and wants to regulate things like the fiber content of people's clothes and the consumption (or not) of shrimp wrapped in bacon.  And that's long before you get to intricacies like, "while Jesus was dead, were there only two Persons of the Trinity?" or how, precisely, a properly-blessed Host can "be" Jesus in essence, while remaining an inanimate cracker in substance (i.e., as detected by every conceivable means of telling what anything "is").

Before we precede any farther, how do you "account for numbers?"
 1 Speaking of having difficulties dealing with number...
"The question of whether atheists are, you know, right, typically gets sidestepped in favor of what is apparently the much more compelling question of whether atheists are jerks."

--Greta Christina

• Posts: 1848
• Darwins +858/-1
• Gender:
• Your Friendly Neighborhood Cephalopod Overlord
Re: What is the justification for the existence of numbers?
« Reply #17 on: January 14, 2013, 05:05:45 PM »
@ Screwtape:

Yeah, if only the ancient Hebrews had been the ancient Greeks.  Then the Bible-bashers would be able to claim things like the concept of the atom, the Pythagorean "unified theory" between geometry, music, astronomy and mathematics ("the music of the spheres"), the development of philosophy, logic, a whole slew of great art...  As it is, they're stuck coming up with explanations for why pi isn't 3.
"The question of whether atheists are, you know, right, typically gets sidestepped in favor of what is apparently the much more compelling question of whether atheists are jerks."

--Greta Christina

jaimehlers

• Global Moderator
• Posts: 8867
• Darwins +1118/-27
• Gender:
• WWGHA Member
Re: What is the justification for the existence of numbers?
« Reply #18 on: January 14, 2013, 06:56:04 PM »
Ah, I see Olivianus is still trying to prove that reality doesn't exist, or whatever it is.

Remember how he tried to prove that we couldn't tell it had been raining when the streets were wet and the sky overcast?  Or how he tried to prove that atoms had to be indivisible in order for us to believe in them?

This is even more silly.  Numbers are a human invention.  They don't have an independent existence.
Nullus In Verba, aka "Take nobody's word for it!"  If you can't show it, then you don't know it.

William

• Fellow
• Posts: 3563
• Darwins +92/-2
• Gender:
Re: What is the justification for the existence of numbers?
« Reply #19 on: January 14, 2013, 07:36:39 PM »
CAVEMAN:  "Darling, remind me again, how many kids have we had?"

CAVEWOMAN:  "Nine my dear."

CAVEMAN:  "Why can I only see six?"

CAVEWOMAN:  "It's the hyenas - they keep taking the little ones when you're away on long hunting trips."

CAVEMAN:  "Oh!  Feels like cold weather again tonight, come over here then and lets justify the existence of numbers ...."
Git mit uns

ParkingPlaces

• Professor
• Posts: 7739
• Darwins +1176/-6
• Gender:
• This space for rent
Re: What is the justification for the existence of numbers?
« Reply #20 on: January 14, 2013, 07:49:26 PM »
Ironically, he will count up how many stupid answers he got from atheists.

Then he'll say something about numbers not existing right after using some.

I vote we talk about something else.
What I lack in sophistication I make up for with other shortcomings.

HAL

• Professor
• Posts: 5203
• Darwins +109/-17
• Gender:
Re: What is the justification for the existence of numbers?
« Reply #21 on: January 14, 2013, 08:09:42 PM »
Don't waste your time folks. If you don't believe me I want to make you aware of a past conversation between Olivianus and yours truly -

Me (asking about how he knows the streets are wet after a light shower) -

Quote
So you, Olivianus, have no means to obtain knowledge of wet streets? Is this correct?

Olivianus -

Quote
I have no means to obtain knowledge of wet streets. Yes that is correct. Which is completely irrelevant because your view of the world does assert it can obtain knowledge of wet streets.
Seriously, you guys are the meanest people I have ever met.  I hope you are happy and feel really good about yourself.

kin hell

• Professor
• Posts: 5386
• Darwins +152/-9
• Gender:
• - .... . .-. . /.. ... / -. --- / --. --- -.. ...
Re: What is the justification for the existence of numbers?
« Reply #22 on: January 14, 2013, 10:08:21 PM »
proof of the existence of numbers numbnuts

there are two kinds of people in this world

those who get the joke
and those who are the joke

....and yes, I'm looking at you Oily

« Last Edit: January 14, 2013, 10:12:00 PM by kin hell »
"...but on a lighter note, demons were driven from a pig today in Gloucester."  Bill Bailey

all edits are for spelling or grammar unless specified otherwise

Olivianus

• Posts: 208
• Darwins +2/-56
• Gender:
• WWGHA Member
Re: What is the justification for the existence of numbers?
« Reply #23 on: January 15, 2013, 12:53:58 AM »
How do we account for the existence of numbers? Are there multiple physical things to justify the existence of numbers? How do we know there are multiple existing things?

At this point I would like you ask if you really exist? How do we know Olivianus exists? Do you have a physical form?

Having received in the historical order-the genus of being, the self attestation of the coherency of scripture-the logical order of propositions-the genus of epistemology, my ego wakes up to the reality of its regeneration. The knowledge of my existence and the assurance of my salvation is thus implied from the teaching of scripture and the conviction that the scripture is true.

The Bible speaks of men having a body yes. I have a physical form depending on your defintion of the word physical. Physical is something positive but my knowledge of it is only negative. Thus something physical is not something intellectual or spiritual.
Bertrand Russell, “All inductive argument...is of course, formally fallacious...yet it would not be fundamentally different from the argument upon which all scientific laws are based.” The Scientific Outlook, Limitations of Scientific Method

Olivianus

• Posts: 208
• Darwins +2/-56
• Gender:
• WWGHA Member
Re: What is the justification for the existence of numbers?
« Reply #24 on: January 15, 2013, 01:03:11 AM »
How do we account for the existence of numbers? Are there multiple physical things to justify the existence of numbers? How do we know there are multiple existing things?

Let me guess... is it god?

That answer simpliciter would be unsatisfying. It depends on what kind of God one believes in. I believe the only God that can provide the complexity for the distinctions necessary for numbers is the Christian God of the Bible who has a mind and makes man according to that image. Thus the ultimate principle is not a monad. I think Pythagoras had no coherent explanation of how multiplicity extended from the Monad, which makes me wonder: do atheists who believe in the reality of numbers believe in a Parmenidian One?
Bertrand Russell, “All inductive argument...is of course, formally fallacious...yet it would not be fundamentally different from the argument upon which all scientific laws are based.” The Scientific Outlook, Limitations of Scientific Method

Olivianus

• Posts: 208
• Darwins +2/-56
• Gender:
• WWGHA Member
Re: What is the justification for the existence of numbers?
« Reply #25 on: January 15, 2013, 01:04:49 AM »
Humans label stuff. "Blue" doesn't exist anymore than "one", or even "man" or "woman". They are semi-arbitrary labels used to describe the world.

So then the laws of science are not realities, they are conventions? Colloquialisms?
Bertrand Russell, “All inductive argument...is of course, formally fallacious...yet it would not be fundamentally different from the argument upon which all scientific laws are based.” The Scientific Outlook, Limitations of Scientific Method

Olivianus

• Posts: 208
• Darwins +2/-56
• Gender:
• WWGHA Member
Re: What is the justification for the existence of numbers?
« Reply #26 on: January 15, 2013, 01:23:05 AM »
...

But that's not what yhwh did.  Perhaps because yhwh was only as awesome as the hebrews' imagination.  Since the hebrews didn't understand math as an abstraction nor calculus, and were not aware of universal constants, they were limited in what they could imagine yhwh knowing and doing.  But if yhwh were real, he would have known about that stuff and could have told a prophet or two to, you know, sort of undisputably show he exists...

Hold on cowboy. So are you saying that you understand calculus? I think I buried that myth here: http://eternalpropositions.wordpress.com/2012/04/04/book-review-morris-klines-mathematics-the-loss-of-certainty-picking-up-where-dr-clark-left-off/

Are you saying that there are universal constants. I thought the above posters had agreed that there were no universal constants but,

Quote
"Object-division is subjective, something we impose on nature to help us organize and deal with it in our minds."
Azdgari

Bertrand Russell, “All inductive argument...is of course, formally fallacious...yet it would not be fundamentally different from the argument upon which all scientific laws are based.” The Scientific Outlook, Limitations of Scientific Method

Olivianus

• Posts: 208
• Darwins +2/-56
• Gender:
• WWGHA Member
Re: What is the justification for the existence of numbers?
« Reply #27 on: January 15, 2013, 01:25:56 AM »
True, but he did lead them into the oddest calculation of all - well the Christians really -

1 + 1 + 1 = 1

God, Jesus and Holy Spirit = 1 god that is!

That is a Roman Catholic myth that I have been exposing for a long time:

and recently:

Bertrand Russell, “All inductive argument...is of course, formally fallacious...yet it would not be fundamentally different from the argument upon which all scientific laws are based.” The Scientific Outlook, Limitations of Scientific Method

Olivianus

• Posts: 208
• Darwins +2/-56
• Gender:
• WWGHA Member
Re: What is the justification for the existence of numbers?
« Reply #28 on: January 15, 2013, 01:28:26 AM »
Ah, I see Olivianus is still trying to prove that reality doesn't exist, or whatever it is.

Remember how he tried to prove that we couldn't tell it had been raining when the streets were wet and the sky overcast?  Or how he tried to prove that atoms had to be indivisible in order for us to believe in them?

This is even more silly.  Numbers are a human invention.  They don't have an independent existence.

Then the laws of science do not have independent existence for mathematics is the essence of science. Kline says, “As we shall see, the most well developed physical theories are entirely mathematical.” [Mathematics: The Loss of Certainty (New York: Oxford University Press, 1980), pg. 7]
Bertrand Russell, “All inductive argument...is of course, formally fallacious...yet it would not be fundamentally different from the argument upon which all scientific laws are based.” The Scientific Outlook, Limitations of Scientific Method