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Chuck77
Inactive Member


Message 241 of 268 (644186)
12-15-2011 11:51 PM
Reply to: Message 240 by Straggler
12-15-2011 1:17 PM


Re: Objective/Subjective
*Edited*

Are you guys trying to figure out if math is objective/subjective?

Edited by Chuck77, : No reason given.

Edited by Chuck77, : No reason given.

Edited by Chuck77, : No reason given.

Edited by Chuck77, : No reason given.

Edited by Chuck77, : No reason given.


This message is a reply to:
 Message 240 by Straggler, posted 12-15-2011 1:17 PM Straggler has responded

Replies to this message:
 Message 242 by Straggler, posted 12-16-2011 7:44 AM Chuck77 has responded

  
Straggler
Member
Posts: 10195
From: London England
Joined: 09-30-2006


Message 242 of 268 (644214)
12-16-2011 7:44 AM
Reply to: Message 241 by Chuck77
12-15-2011 11:51 PM


Re: Objective/Subjective
Chuck writes:

Are you guys trying to figure out if math is objective/subjective?

Not really. I think the three of us agree that maths is objective.

So then it becomes an exercise in philosophical navel gazing about the nature of existence and whether the objectivity of maths means that mathematical entities can be said to "exist" in some sense that is independent of minds. Are mathematical entities aspects of objective reality - That sort of thing.

Or - To put it another way - Do we invent or discover maths?


This message is a reply to:
 Message 241 by Chuck77, posted 12-15-2011 11:51 PM Chuck77 has responded

Replies to this message:
 Message 243 by Chuck77, posted 12-17-2011 5:09 AM Straggler has responded
 Message 244 by Dr Adequate, posted 12-17-2011 6:53 AM Straggler has responded

  
Chuck77
Inactive Member


Message 243 of 268 (644310)
12-17-2011 5:09 AM
Reply to: Message 242 by Straggler
12-16-2011 7:44 AM


Re: Objective/Subjective
Ok. I guess that's the question for a lot of things not just math. Is it a different debate than the one for god(s) or is this one a little more objectivly based? Well, obviously it is more objective but is it along those lines?

It's kind of like the tree in the forest analogy? If no one is around to observe it does math still exist? Or is it soley a human invention?

Would there still be a certain number that describes light years or is it something we came up with to better understand the universe. Or does the universe compel us to use math to try understand things about it. Without math would we be able to figure certain things out or is math a product of our environment.

I'm rambling now. Am I anywhere in the ballpark of what you guys are talking about?

Edited by Chuck77, : No reason given.


This message is a reply to:
 Message 242 by Straggler, posted 12-16-2011 7:44 AM Straggler has responded

Replies to this message:
 Message 250 by Straggler, posted 12-17-2011 8:29 AM Chuck77 has not yet responded

  
Dr Adequate
Member
Posts: 15929
Joined: 07-20-2006
Member Rating: 3.8


Message 244 of 268 (644319)
12-17-2011 6:53 AM
Reply to: Message 242 by Straggler
12-16-2011 7:44 AM


Re: Objective/Subjective
Or - To put it another way - Do we invent or discover maths?

Hmm ... I'd say that we discover math and that mathematical entities don't exist. We are not discovering things, which exist, but facts, which are true.


This message is a reply to:
 Message 242 by Straggler, posted 12-16-2011 7:44 AM Straggler has responded

Replies to this message:
 Message 245 by Chuck77, posted 12-17-2011 7:09 AM Dr Adequate has responded
 Message 249 by Straggler, posted 12-17-2011 8:15 AM Dr Adequate has responded

  
Chuck77
Inactive Member


Message 245 of 268 (644321)
12-17-2011 7:09 AM
Reply to: Message 244 by Dr Adequate
12-17-2011 6:53 AM


Re: Objective/Subjective
I'd say that we discover math and that mathematical entities don't exist.

So mathematical entities are not realistic if no one discovers them?

We are not discovering things, which exist, but facts, which are true.

So then 2+2=4 is a fact that was never discovered? It didn't exist until someone brought it into existance?


This message is a reply to:
 Message 244 by Dr Adequate, posted 12-17-2011 6:53 AM Dr Adequate has responded

Replies to this message:
 Message 246 by Dr Adequate, posted 12-17-2011 7:20 AM Chuck77 has responded

  
Dr Adequate
Member
Posts: 15929
Joined: 07-20-2006
Member Rating: 3.8


Message 246 of 268 (644325)
12-17-2011 7:20 AM
Reply to: Message 245 by Chuck77
12-17-2011 7:09 AM


Re: Objective/Subjective
So mathematical entities are not realistic if no one discovers them?

No, that's not what I said. A fact can be true before someone discovers it.

But facts are not real, they're true.

Things are real or not real (e.g. hats, unicorns, respectively). Statements are true or false (e.g. "Hats exist"; "Unicorns exist").

Mathematical truths are true, not real, because they're statements, not things.


This message is a reply to:
 Message 245 by Chuck77, posted 12-17-2011 7:09 AM Chuck77 has responded

Replies to this message:
 Message 247 by Chuck77, posted 12-17-2011 7:25 AM Dr Adequate has responded

  
Chuck77
Inactive Member


Message 247 of 268 (644326)
12-17-2011 7:25 AM
Reply to: Message 246 by Dr Adequate
12-17-2011 7:20 AM


Re: Objective/Subjective
Mathematical truths are true, not real, because they're statements, not things.

So 2+2=4 is a concept?


This message is a reply to:
 Message 246 by Dr Adequate, posted 12-17-2011 7:20 AM Dr Adequate has responded

Replies to this message:
 Message 248 by Dr Adequate, posted 12-17-2011 7:33 AM Chuck77 has not yet responded

  
Dr Adequate
Member
Posts: 15929
Joined: 07-20-2006
Member Rating: 3.8


Message 248 of 268 (644328)
12-17-2011 7:33 AM
Reply to: Message 247 by Chuck77
12-17-2011 7:25 AM


Re: Objective/Subjective
So 2+2=4 is a concept?

Yes. To be precise, the truth here is that within the system of natural numbers, 2 + 2 = 4. Now the fact that the system of natural numbers can be used to model some aspects of our experience is merely a scientific discovery, and is not true a priori.


This message is a reply to:
 Message 247 by Chuck77, posted 12-17-2011 7:25 AM Chuck77 has not yet responded

  
Straggler
Member
Posts: 10195
From: London England
Joined: 09-30-2006


Message 249 of 268 (644334)
12-17-2011 8:15 AM
Reply to: Message 244 by Dr Adequate
12-17-2011 6:53 AM


Re: Objective/Subjective
Dr A writes:

Hmm ... I'd say that we discover math and that mathematical entities don't exist. We are not discovering things, which exist, but facts, which are true.

If these facts are properties of reality then they are "things". Not physical "things". But "things" which can meaningfully be said to "exist" and thus be discovered.

But the fact that I feel the need to splatter inverted commas all over the place when writing that should tell you that I am not entirely convinced of that myself.


This message is a reply to:
 Message 244 by Dr Adequate, posted 12-17-2011 6:53 AM Dr Adequate has responded

Replies to this message:
 Message 251 by Dr Adequate, posted 12-17-2011 8:46 AM Straggler has responded

  
Straggler
Member
Posts: 10195
From: London England
Joined: 09-30-2006


Message 250 of 268 (644337)
12-17-2011 8:29 AM
Reply to: Message 243 by Chuck77
12-17-2011 5:09 AM


Re: Objective/Subjective
Chuck writes:

If no one is around to observe it does math still exist? Or is it soley a human invention?

Chuck writes:

....is math a product of our environment.

Chuck writes:

Am I anywhere in the ballpark of what you guys are talking about?

Yeah - Sort of.

Rahvin was making the case for maths having a purely empirical basis. I am sort of putting forward the case for mathematical realism.

Wiki on mathematical realism writes:

Mathematical realism, like realism in general, holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same.

Dr A is making a distinction between facts that can be discovered and things which can be discovered. I suspect the difference between him and I is a semantic one based on whether or not facts are "things" that can be said to "exist".

Unfortunately the philosophical area of ontology is fraught with such distinctions and as a result is mostly navel gazing nonsense. But it can still be "fun"......


This message is a reply to:
 Message 243 by Chuck77, posted 12-17-2011 5:09 AM Chuck77 has not yet responded

  
Dr Adequate
Member
Posts: 15929
Joined: 07-20-2006
Member Rating: 3.8


Message 251 of 268 (644342)
12-17-2011 8:46 AM
Reply to: Message 249 by Straggler
12-17-2011 8:15 AM


Re: Objective/Subjective
If these facts are properties of reality then they are "things". Not physical "things". But "things" which can meaningfully be said to "exist" and thus be discovered.

Well, what do you mean by "properties of reality"?

Consider the following statement: "If all snufflepuffs are frungible, and all frungible things are blurple, then all snufflepuffs are blurple".

This is a fact (which is true). Is there a thing (which exists) corresponding to the fact?


This message is a reply to:
 Message 249 by Straggler, posted 12-17-2011 8:15 AM Straggler has responded

Replies to this message:
 Message 252 by Straggler, posted 12-17-2011 8:49 AM Dr Adequate has responded

  
Straggler
Member
Posts: 10195
From: London England
Joined: 09-30-2006


Message 252 of 268 (644345)
12-17-2011 8:49 AM
Reply to: Message 251 by Dr Adequate
12-17-2011 8:46 AM


Re: Objective/Subjective
Dr A writes:

This is a fact (which is true). Is there a thing (which exists) corresponding to the fact?

Yes. Logic.

Does logic exist? Is logic a property of reality?


This message is a reply to:
 Message 251 by Dr Adequate, posted 12-17-2011 8:46 AM Dr Adequate has responded

Replies to this message:
 Message 253 by Dr Adequate, posted 12-17-2011 9:55 AM Straggler has responded

  
Dr Adequate
Member
Posts: 15929
Joined: 07-20-2006
Member Rating: 3.8


Message 253 of 268 (644364)
12-17-2011 9:55 AM
Reply to: Message 252 by Straggler
12-17-2011 8:49 AM


Re: Objective/Subjective
Yes. Logic.

Well, that's a bit broad. Would you say that the "thing" corresponding to Pythagoras' theorem was math?


This message is a reply to:
 Message 252 by Straggler, posted 12-17-2011 8:49 AM Straggler has responded

Replies to this message:
 Message 254 by Straggler, posted 12-17-2011 10:10 AM Dr Adequate has responded

  
Straggler
Member
Posts: 10195
From: London England
Joined: 09-30-2006


Message 254 of 268 (644371)
12-17-2011 10:10 AM
Reply to: Message 253 by Dr Adequate
12-17-2011 9:55 AM


Re: Objective/Subjective
Dr A writes:

Well, that's a bit broad.

Maybe so. But that, I suspect, is what all this boils down to. If we discover rather than invent maths then it is because ultimately maths is our method of exploring the logic innate in reality. Or something like that.

Dr A writes:

Would you say that the "thing" corresponding to Pythagoras' theorem was math?

To Pythagoras theorem specifically I guess the "thing" we are specifically applying logic to is the geometric form known as a triangle.

But in your Snufflepuff example there was nothing that makes it specific to Snufflepuffs. In fact you would be better off generalising your statement to something like:

If ALL X are Y and ALL Y are Z Then ALL X are Z

A simple and generic statement of pure logic that applies to the frungibleness of snufflepuffs or anything else which meets the same logical criteria.


This message is a reply to:
 Message 253 by Dr Adequate, posted 12-17-2011 9:55 AM Dr Adequate has responded

Replies to this message:
 Message 255 by Dr Adequate, posted 12-17-2011 10:40 AM Straggler has responded

  
Dr Adequate
Member
Posts: 15929
Joined: 07-20-2006
Member Rating: 3.8


Message 255 of 268 (644379)
12-17-2011 10:40 AM
Reply to: Message 254 by Straggler
12-17-2011 10:10 AM


Re: Objective/Subjective
But in your Snufflepuff example there was nothing that makes it specific to Snufflepuffs. In fact you would be better off generalising your statement to something like:

If ALL X are Y and ALL Y are Z Then ALL X are Z

No, you'd have been better off if I did that. That's why I talked about snufflepuffs. Snufflepuffs are clearly not the things the syllogism is true of, since they aren't things; and on the other hand those who vaguely imagine a Platonic world of mathematical and logical truths will tend to baulk at the idea of my premises and conclusion sitting there in their logical relationship waiting for me to come along and enunciate it.


This message is a reply to:
 Message 254 by Straggler, posted 12-17-2011 10:10 AM Straggler has responded

Replies to this message:
 Message 256 by Straggler, posted 12-17-2011 11:54 AM Dr Adequate has not yet responded

  
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