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Does math exist?

Started by Plu, June 05, 2013, 02:29:45 PM

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WitchSabrina

Quote from: "josephpalazzo"Got me there... let me rephrase this: If the earth + all the freaking probes  were completely destroyed to smithereens, vaporized to single molecules...

 :twisted:

It's ok.  You're waaay ahead of me on this.  I don't speak 'math'.  I mean I Really don't speak 'math'.  This thread already exceeds my learned-level.  lol
I am currently experiencing life at several WTFs per hour.

missingnocchi

Quote from: "josephpalazzo"
Quote from: "Seabear"Then by the same token I suppose we can say that languages don't really exist either. Or music. Or emotion. Or any abstract concept, for that matter. Including, ironically, philosophy.

Again, it's just a game of semantics, playing with an overly literal application of the word 'exist'.

If the earth was completely destroyed to smithereens, vaporized to single molecules, who would ever know of our alphabet, art, music, or any construct, real or mental that was ever done on this planet?

Does something have to exist for all time in order to exist at all?
What's a "Leppo?"

WitchSabrina

Quote from: "missingnocchi"
Quote from: "josephpalazzo"
Quote from: "Seabear"Then by the same token I suppose we can say that languages don't really exist either. Or music. Or emotion. Or any abstract concept, for that matter. Including, ironically, philosophy.

Again, it's just a game of semantics, playing with an overly literal application of the word 'exist'.

If the earth was completely destroyed to smithereens, vaporized to single molecules, who would ever know of our alphabet, art, music, or any construct, real or mental that was ever done on this planet?

Does something have to exist for all time in order to exist at all?

Good question for Jesus.
I am currently experiencing life at several WTFs per hour.

josephpalazzo

Quote from: "missingnocchi"
Quote from: "josephpalazzo"
Quote from: "Seabear"Then by the same token I suppose we can say that languages don't really exist either. Or music. Or emotion. Or any abstract concept, for that matter. Including, ironically, philosophy.

Again, it's just a game of semantics, playing with an overly literal application of the word 'exist'.

If the earth was completely destroyed to smithereens, vaporized to single molecules, who would ever know of our alphabet, art, music, or any construct, real or mental that was ever done on this planet?

Does something have to exist for all time in order to exist at all?

The issue is not in regard to how long a thing exists but does a thing have an existence on its own. To clarify: "this is a tree". Now the tree exists regardless of whether I say that sentence or not. But the sentence itself wouldn't exist for there are no humans in the universe to say it. I can safely say that whatever was conceived or fabricated by humans, if humans don't exist, those things won't exist either. And that includes our alphabet and our number system.

WitchSabrina

Quote from: "josephpalazzo"The issue is not in regard to how long a thing exists but does a thing have an existence on its own. To clarify: "this is a tree". Now the tree exists regardless of whether I say that sentence or not. But the sentence itself wouldn't exist for there are no humans in the universe to say it. I can safely say that whatever was conceived or fabricated by humans, if humans don't exist, those things won't exist either. And that includes our alphabet and our number system.

Don't things exist in their relation to Other things? Otherwise how would we know?  As in - item B laying on the table exists because I can see it laying there............or you might see it there......... or Colanth might see it there.  If no one sees it and records mentally the existence of said object - how else do we know?
It's the human mind where things are logged, categorized, recognized and recorded or observed & reported or tested.  Kind of qualifies our argument against a supernatural being - like a god --- there's no human recorded data of such an observance; no proof. Things exist in relation to something else - like observation.
Sure things like Item B might exist without me...............   but at some point a human will need to record the evidence of item B. Or there's no items B.
I am currently experiencing life at several WTFs per hour.

josephpalazzo

Quote from: "WitchSabrina"
Quote from: "josephpalazzo"The issue is not in regard to how long a thing exists but does a thing have an existence on its own. To clarify: "this is a tree". Now the tree exists regardless of whether I say that sentence or not. But the sentence itself wouldn't exist for there are no humans in the universe to say it. I can safely say that whatever was conceived or fabricated by humans, if humans don't exist, those things won't exist either. And that includes our alphabet and our number system.

Don't things exist in their relation to Other things? Otherwise how would we know?  As in - item B laying on the table exists because I can see it laying there............or you might see it there......... or Colanth might see it there.  If no one sees it and records mentally the existence of said object - how else do we know?
It's the human mind where things are logged, categorized, recognized and recorded or observed & reported or tested.  Kind of qualifies our argument against a supernatural being - like a god --- there's no human recorded data of such an observance; no proof. Things exist in relation to something else - like observation.
Sure things like Item B might exist without me...............   but at some point a human will need to record the evidence of item B. Or there's no items B.

Here you are talking about knowledge, and not existence. In terms of philosophy ( ha, hum) we've moved from metaphysics to epistemology.  :-D

 So how do I know that tree or that table exists?

So for that, we need to look at  truth, belief, justfication, and different schools espousing certain things like the empirical method, or logiccal rational thinking, or revelation/insight, etc.


You've just open another can of worms.  :Hangman:

WitchSabrina

Quote from: "josephpalazzo"Here you are talking about knowledge, and not existence. In terms of philosophy ( ha, hum) we've moved from metaphysics to epistemology.  :-D

 So how do I know that tree or that table exists?

So for that, we need to look at  truth, belief, justfication, and different schools espousing certain things like the empirical method, or logiccal rational thinking, or revelation/insight, etc.


You've just open another can of worms.  :Hangman:

Sorry.  Go back to math.  I can't speak math.  I was just kinda chiming in.  Ignore my ramblings.
 :rolleyes:
I am currently experiencing life at several WTFs per hour.

josephpalazzo

I was expecting sarcasm! What happened?  :P

missingnocchi

Quote from: "josephpalazzo"The issue is not in regard to how long a thing exists but does a thing have an existence on its own. To clarify: "this is a tree". Now the tree exists regardless of whether I say that sentence or not. But the sentence itself wouldn't exist for there are no humans in the universe to say it. I can safely say that whatever was conceived or fabricated by humans, if humans don't exist, those things won't exist either. And that includes our alphabet and our number system.

If the earth exploded, no one would know about the tree.

But moving on to the actual issue, I think we're getting to the root of it (no pun intended.) People who say that math is real are generally not saying that numbers exist as an observable substance, but that the numbers are descriptions of the observable rules we see nature following. And in that sense, yes, math does exist. Because even if the earth exploded, the same descriptions would be valid for as long as the universe continued to work in the same way. I think the original video draws a false line between "what a study is" and "what it studies." Sure, the laws of physics as we describe them exist, but does Physics exist? Can you touch a momentum? What about chemistry? Are little PV = nRT's floating around in the void? That's the kind of question being asked about math here, and it's really somewhat silly. If gathering one thing and another thing together made three things, that's how our formal, written math system would work. We didn't make it up, we observed it. Just like any other science.
What's a "Leppo?"

josephpalazzo

Quote from: "missingnocchi"
Quote from: "josephpalazzo"The issue is not in regard to how long a thing exists but does a thing have an existence on its own. To clarify: "this is a tree". Now the tree exists regardless of whether I say that sentence or not. But the sentence itself wouldn't exist for there are no humans in the universe to say it. I can safely say that whatever was conceived or fabricated by humans, if humans don't exist, those things won't exist either. And that includes our alphabet and our number system.

If the earth exploded, no one would know about the tree.

But moving on to the actual issue, I think we're getting to the root of it (no pun intended.) People who say that math is real are generally not saying that numbers exist as an observable substance, but that the numbers are descriptions of the observable rules we see nature following. And in that sense, yes, math does exist.
It exists as a mental construct, just like our alphabet.
QuoteBecause even if the earth exploded, the same descriptions would be valid for as long as the universe continued to work in the same way.
The universe would exist. Its human description would not, since the humans upholding those mental construct don't exist anymore. Where would those human thoughts exist???


QuoteI think the original video draws a false line between "what a study is" and "what it studies." Sure, the laws of physics as we describe them exist, but does Physics exist?

Physics is a human description of the universe, a model that we have refined over the years with constant observations, experiments and hypothesis. Therefore it is a mental construct produced by our minds.

QuoteCan you touch a momentum? What about chemistry? Are little PV = nRT's floating around in the void? That's the kind of question being asked about math here, and it's really somewhat silly. If gathering one thing and another thing together made three things, that's how our formal, written math system would work. We didn't make it up, we observed it. Just like any other science.

I believe you are conflating two things: the mental constructs - ideas, theories, thoughts, beliefs, theories, physics, math etc - exist as long as they are hold by human brains. And the things these mental construct describe - particles, stars, the universe, etc. which exist independently of our thoughts.

GurrenLagann

Erg, nominalism. Well, I'd have to say no. This is like a discussion I had the other day with a proponent of a version of the transcendental argument for the existence of God, wherein they repeatedly claimed that the "laws" of informal logic exist and are "invariant, universal", etc, and that was (somehow) evidence for the existence of God. But that misses is that when you say "A=A" (law of identity, LoD), that statement isn't itself the law of identity but just that, a statement referring to what we mean by the LoD. Also forgetting that they are ways of drawing proper inferences and that they can't be denied without being coherent. Basically, it's a language thing really.

And I think that mathematics is similar to those, though it lacks a truly logical basis (damn you Gödel!).
Which means that to me the offer of certainty, the offer of complete security, the offer of an impermeable faith that can\'t give way, is the offer of something not worth having.
[...]
Take the risk of thinking for yourself. Much more happiness, truth, beauty & wisdom, will come to you that way.
-Christopher Hitchens

josephpalazzo

Quote from: "GurrenLagann"Erg, nominalism. Well, I'd have to say no. This is like a discussion I had the other day with a proponent of a version of the transcendental argument for the existence of God, wherein they repeatedly claimed that the "laws" of informal logic exist and are "invariant, universal", etc, and that was (somehow) evidence for the existence of God. But that misses is that when you say "A=A" (law of identity, LoD), that statement isn't itself the law of identity but just that, a statement referring to what we mean by the LoD. Also forgetting that they are ways of drawing proper inferences and that they can't be denied without being coherent. Basically, it's a language thing really
.

Yep, math is nothing but LoD + the substitution principle.  

QuoteAnd I think that mathematics is similar to those, though it lacks a truly logical basis (damn you Gödel!).

Hmm. I'm not sure what you're trying to say here. Gödel's theorem just shows that any system must start with a set of axioms - truths taken to be given. If one wants to prove/disprove one of those assumptions, you need to go out of the system, but you will end up with other assumptions, if you enlarge the system to include the new assumptions, you're back to square one. Hence, no system is ever completed.

Sal1981

Quote from: "josephpalazzo"
Quote from: "GurrenLagann"And I think that mathematics is similar to those, though it lacks a truly logical basis (damn you Gödel!).

Hmm. I'm not sure what you're trying to say here. Gödel's theorem just shows that any system must start with a set of axioms - truths taken to be given. If one wants to prove/disprove one of those assumptions, you need to go out of the system, but you will end up with other assumptions, if you enlarge the system to include the new assumptions, you're back to square one. Hence, no system is ever completed.
Doesn't Gödel's Incompleteness theorem also imply that there can be an infinite amount of mathematical structures or something?

GurrenLagann

Quote from: "josephpalazzo"
QuoteAnd I think that mathematics is similar to those, though it lacks a truly logical basis (damn you Gödel!).

Hmm. I'm not sure what you're trying to say here. Gödel's theorem just shows that any system must start with a set of axioms - truths taken to be given. If one wants to prove/disprove one of those assumptions, you need to go out of the system, but you will end up with other assumptions, if you enlarge the system to include the new assumptions, you're back to square one. Hence, no system is ever completed.

Hm, I thought that's basically what I said? I wasn't very clear at the end there I see. Damn my lazy fingers. ;)
Which means that to me the offer of certainty, the offer of complete security, the offer of an impermeable faith that can\'t give way, is the offer of something not worth having.
[...]
Take the risk of thinking for yourself. Much more happiness, truth, beauty & wisdom, will come to you that way.
-Christopher Hitchens

josephpalazzo

Quote from: "Sal1981"
Quote from: "josephpalazzo"
Quote from: "GurrenLagann"And I think that mathematics is similar to those, though it lacks a truly logical basis (damn you Gödel!).

Hmm. I'm not sure what you're trying to say here. Gödel's theorem just shows that any system must start with a set of axioms - truths taken to be given. If one wants to prove/disprove one of those assumptions, you need to go out of the system, but you will end up with other assumptions, if you enlarge the system to include the new assumptions, you're back to square one. Hence, no system is ever completed.
Doesn't Gödel's Incompleteness theorem also imply that there can be an infinite amount of mathematical structures or something?

I don't know about infinite number, but theoretically yes. There are no complete systems, so as long as humans are creative, new ones can always be found.