Are numbers as real as rocks?

[Knotted]

Its called sceptcism knotted. No offense, but unless you can provide references of a professor that holds your view, I am inclined ti think that you are talking s*.

I've never liked academic philosophy. Its more about reading and referencing than doing.

But really I haven't been trying to prove anything. I'm giving a description of my thoughts and feelings. If you can actually prove something conclusive on this then you will have made as big an advance as could ever happen in philosophy.

By saying tat we could have an alyernative mathematics to describe how plastecine moulds together, is to say that ,mathematics describes how stars collapse. And you deny this. So you have made a fundamental mistake from the outset.

I can't decipher the above. I don't think there is a unique mathematical formalty that describes either plastecine moulds or collapsing stars. Just like there is not a unique language with which to talk about plastecine moulds or collapsing stars. I don't think either of these topics is more difficult in French.

 

[jayeola]

Numbers are an abstract concept.

Yep and so is mathematics and the sciences in general.

 

[Knotted]

I'mnot sure that you've answered any of my questions beyond reststing that it doesn't matter because you don't think so. This argument is gettinh noweher, its not just my imagination?

As I say I'm not trying to provide all the answers. However I'm really unsure about what you are trying to say. Do numbers have an empirical reality, do they have an ideal reality or are they something else?

 

[muser]

As I say I'm not trying to provide all the answers. However I'm really unsure about what you are trying to say. Do numbers have an empirical reality, do they have an ideal reality or are they something else?

There is a saying "if you argue with a fool, there is a good chance he's doing the same". Knotted, you have made countless concessions to 118's arguements, and despite one or two of his objections being well articulated, he neglects to see the duality of the argument.
There is no definitive right or wrong. 118, why has superstring theory never predicted a single testible quantum event.

Krauss gets closer to the real difference between string theorists and intelligent designers when he says that string theorists “are trying to come up with predictions that actually do something”. More sensible string theorists are well aware that what they are doing isn’t going to be part of science until they figure out a way to use it to make real predictions that can be tested. In general, given a new speculative idea, it will not be obvious how to figure out all of its implications and see whether it can lead to real predictions.

http://www.math.columbia.edu/~woit/wordpress/?p=286

Where I agree with you and knotted is that mathematics is an imperfect way of describing the universe, and its laws were created from empirical events and those laws are subjected to flaws when new phenomena is discovered.

 

[Johnny Canuck3]

Are numbers as real as rocks, but rather more certain?

I].

You can't crack your head open on a number.

Can't smoke a number, either.

 

[nino_savatte]

Can't smoke a number, either.

I don't know about that.

This has been brought to you by Double Entendres r US

 

[Knotted]

There is a saying "if you argue with a fool, there is a good chance he's doing the same". Knotted, you have made countless concessions to 118's arguements, and despite one or two of his objections being well articulated, he neglects to see the duality of the argument.
There is no definitive right or wrong. 118, why has superstring theory never predicted a single testible quantum event.

Yes, we've dragged the question on for too long already. But I hope its clear to all now that it isn't trivial. I would be happier if I made people think more than if I made people agree with me.

 

[muser]

I would be happier if I made people think more than if I made people agree with me.

You always achieve that

 

[weltweit]

I suppose that we need three things before we can have a notion of arithmetic.
Firstly we need to be able to seperate things from each other. I don't think this requires much more than good eyesight.
Secondly we need to be able to group like with like. I understand this is quite a problem in artificial intelligence but most if not all animals seem quite competent as far as I know.
Thirdly we need to be able to have a concept of abstract representation and a notion of equality of these representations. I would think this is a nearly uniquely human.

So you argument is that

1) Rabbits can tell their children are different from a lump of grass.

2) Rabitts can tell each of their 6 children, while similar, are each individuals.

3) Now however the mother rabbit fails to realise that each one of them is just a child and all six are children, and the rabbit fails to count their children, that is if one is missing they fail to notice that one is missing.

Point 3 (if I paraphrased that right) is where the argument falls down because the mother rabbit knows when it has left one behind, it does have some kind of concept that it has 6 rather than 5 and it manages to look after all 6.

 

[118118]

You can't crack your head open on a number.

Can't smoke a number, either.

Yes, but you can't smoke the speed of light, either, is this real.

Anyway, I don't understand why I'm being called a fool - I *genuinely* can't see the reasoning behind *our* discussion. I try and engage with the arguments against but we have the same two disagreements.

1. I only see the point about plastecine as an argument for the coherence of 1+1=1 - thats just not mathematics in my eyes, that is a "direct representation of reality" (which you claim that any mathematics cannot be) and like you say is predicated on an understanding of our maths. What do you say to this?

2. And, as I've already asked, how does what is only true in the story, as is the definition of fiction, true in science - notice that I am not saying that it is essential to science, just that !+1=2 in science.

If there is any other point that should be included that argues forcibly for your ideas, then say. It should always be possible to write a short list of contested arguments for and against, and people can decide which they think carry weight. The discussion seems more about the sheer momentum of your claim, rather than any propositions, or whatever philosophy is made from. I'm am being honest - to concede would seem to be just to concede to momentum - not proof!

eta:

mathematics is an imperfect way of describing the universe

Yeah, It seems you are using a similar argument to that which is used against the ontological reality of any laws - that they are always being revised. I wasn't very convinced when it came to laws though. In this case, I would imagine that some arthmetic we are so sure about that it's revision is so unliukely that this argument would not work. Do you think that in the future we may discover htat a triangle has not 3 but 4 sides? Would it still be a triangle?

 

[weltweit]

I came intimately together with my partner and shortly afterwards post much screaming, we were three ...

1+1=3

 

[118118]

1+1=3

First of all, that no difference to the plastecine example. Look, you are counting 3 as 1+1+1. So, 1+1+1=1+1, which I also presume that =1, so I would guess unless anyone can show otherise that you cannot make a non-self-contradictory system out of that. Suppose you could say that = is not the same as = or + the same as +, but then you have to ask yourself if this system is actually anything to do with mathematics or is not just a fiction - which it would not be if this system was actually true outside itself - which, I think you are suggesting is the case - it is true outside the system in the event of conception and birth, or sticking bits of plastecine together. I would go as far as to say you are staring to argue against your own belief!

Maybe anyway.

PS: Thats a perfect example of why I am complaining so much on this thread - no attempt to understand my objections - just further elaboration of your belief so that the view has more and more words in its favour or "evidence" behind it.

 

[weltweit]

Sorry 118118 I am not able to follow your argument, can you simplify it for me?

 

[118118]

Sorry 118118 I am not able to follow your argument, can you simplify it for me?

I'm starting to feel a bit stupid. Doh! Erm, what point were you trying to make with your conception and birth post?

 

[weltweit]

It was not a very good point it is just that if you put two humans together allow them to do an intimate act and then 9 months later there is a third human so starts with 1+1=2 but 9 months later 1+1=3

I know it is a weak argument. :-/

I prefer the one about synergy where 2+2=5
The sum of the 4 parts working together as a team makes 5 i.e greater than the sum of the parts as individuals.

2+2=5 is Synergy or also Teamwork.

 

[118118]

I don't think arithmetic is a direct representation of reality and more than that I don't think it would be desirable either

So why do you include it in the list of things that make a good arithemtic I assume also, that you think that it can to a degree, you seem to point to this.
Maths B fits the world better that Maths A, so Maths A does not fit the world at all. The conclusion does not follow. I still cannot work out reasoning behind the claim. I understand that you think maths is a fiction, but I do not even know if you know what this entails. I assume that you do.

You also seem to conclude that this means that Maths B does not fit the world at all either. I would have thought that that has just been ruled out by you saying that Maths B fits the world better than Maths A. Again, I'm not sure that this is your argument.

Sorry

 

[118118]

1+1=2 but 9 months later 1+1=3

Well, in some ways this is true. But how do you conclude that mathematics is a fiction from this?

I am making two points. First of all the system is self contradictory, probably. And also, it seems strange that you are arguing for something being fictional from something similar not being fictional.

Might come back to this tommorow.

 

[weltweit]

Oh Ah, well I am not arguing that Maths is fiction.

I am arguing that maths makes its own sense, has its own logic and as long as it is retained within its own laws it makes plenty of sense.

But there are things many things as it happens for which maths offers no help, no solutions, the natural world for example cannot be explained by maths. Maths for me is a humanly constructed set of theories and laws which if you keep within, support themselves well.

But they are no more than that imho.

 

[118118]

Oh Ah, well I am not arguing that Maths is fiction.

I am arguing that maths makes its own sense, has its own logic and as long as it is retained within its own laws it makes plenty of sense.

But there are things many things as it happens for which maths offers no help, no solutions, the natural world for example cannot be explained by maths. Maths for me is a humanly constructed set of theories and laws which if you keep within, support themselves well.

But they are no more than that imho.

Back again! It would seem t that hat would be arguing that maths is a fiction, however. Fiction = truth in the story alone.

And, maths has made quite a significant contribution to our understanding of the world, in science.

Ok - why would mathemtics be able to describe any event in the world without further elboration, if it was objectively true and false? I would imagine that no-one claims that 1+1=2 alone can explain every event that has or will happen.

It could be asid that it is objectively true that the earth goes round the sun. However, this alone does not explain every event in the history of the universe.

 

[weltweit]

Ok - why would mathemtics be able to describe any event in the world without further elboration, if it was objectively true and false? I would imagine that no-one claims that 1+1=2 alone can explain every event that has or will happen.

No that is quite right, maths only needs to explain things that are within its own domain, physics biology chemistry also limit themselves to their own domains.

Within the sphere of mathematics maths makes sense and can be proven mathematically to do so.

It could be asid that it is objectively true that the earth goes round the sun. However, this alone does not explain every event in the history of the universe.

Indeed.

Mathematics is a thing, a system created by humans and taught to humans as they grow.

It is likely that basic addition and subtraction are almost innate to human animals and other animals but they may not use mathematical notation in their explanations for this.

Advanced maths however is taught to humans and not to non human animals.

Rabbits do not need differential equations.

Neither actually do I if the truth be known

 

[118118]

Within the sphere of mathematics maths makes sense and can be proven mathematically to do so

as long as it is retained within its own laws

So is mathematics real?

 

[weltweit]

So is mathematics real?

What is real?

Is real reality?

 

[118118]

What is real?

Is real reality?

Talk about avoiding the question. Yes, reality is real.

Is it objectively true that 1+1=2?

 

[weltweit]

Talk about avoiding the question. Yes, reality is real.

No it is not avoiding the question.
The original question was :

Are numbers as real as rocks?

Rocks we can see and touch and throw and we know they are physical objects thus are arguably real, reality, they have a presence.

Brings also the question what is reality, see other thread in which it is suggested we make our own reality.

Is it objectively true that 1+1=2?

Numbers however are not physical things, they are thoughts logical constructions to explain things like addition or subtraction, we can write them down but not everything we write down is real, some of it is fiction.

Do numbers exist outside the heads of humans?

Is something real because it exists in the heads of humans?

If humans make their own reality and numbers are part of that then yes in that understanding numbers are real.

 

[118118]

Oh my. Are you arguing that mathematics *is* fiction now. And, I think that I have shown that the plastecine example has no bearing as to whether numbers are real - do you agree?

So, we are back on the "you can't smoke a number" argument. A few things - neither can you smoke the speed of light - is this objectively true? And, I would say at the moment, that the "depends, how many rocks" example has bearing here.

But its reassuring that you think numbers are real.

 

[Knotted]

You always achieve that

Oh shucks

 

[Knotted]

So you argument is that

1) Rabbits can tell their children are different from a lump of grass.

2) Rabitts can tell each of their 6 children, while similar, are each individuals.

3) Now however the mother rabbit fails to realise that each one of them is just a child and all six are children, and the rabbit fails to count their children, that is if one is missing they fail to notice that one is missing.

Point 3 (if I paraphrased that right) is where the argument falls down because the mother rabbit knows when it has left one behind, it does have some kind of concept that it has 6 rather than 5 and it manages to look after all 6.

Is this last actually true? Does a rabbit notice when one of its many children go missing? Even if it does, this does not mean that the rabbit has counted its children. It might be that each has a unique scent and the rabbit knows can tell when this scent is missing. Humans deal with the world partly by employing abstractions but this does not mean that there are not more primative ways of dealing with the world.

 

[Knotted]

1. I only see the point about plastecine as an argument for the coherence of 1+1=1 - thats just not mathematics in my eyes, that is a "direct representation of reality" (which you claim that any mathematics cannot be) and like you say is predicated on an understanding of our maths. What do you say to this?

I take it that this is directed to me rather than Johnny Cannuck 2.

I'm not disagreeing with you on this. If by mathematics you mean the thing that is generally understood to be mathematics then it can only be one thing. This is utterly circular though. You need criteria for what you regard as mathematics and what you do not regard as mathematics. I'm just showing that direct representation of the world is not a very good one.

Incidently there is not universal agreement amongst mathematicians. There are standard and nonstandard analysis, depending on whether you prefer to talk about limits or infinitetessimals. There are also issue to do with the axiom of choice and the continuum hypothesis.

2. And, as I've already asked, how does what is only true in the story, as is the definition of fiction, true in science - notice that I am not saying that it is essential to science, just that !+1=2 in science.

Why is it that in a still life painting you can see a bowl of fruit, but there is no bowl of fruit just paint and canvass?

Your question is difficult, but may main point is to show that this sort of question is difficult. I can't answer it. Can you?

If there is any other point that should be included that argues forcibly for your ideas, then say. It should always be possible to write a short list of contested arguments for and against, and people can decide which they think carry weight. The discussion seems more about the sheer momentum of your claim, rather than any propositions, or whatever philosophy is made from. I'm am being honest - to concede would seem to be just to concede to momentum - not proof!

I think that the arguments that you rail against are easily backed up. All I am saying is that mathematical formality is not real. It is a formality, its daft to think its real. I am leaving open the possibility of a non formal mathematical reality. This latter, as far as I am concerned, is the really difficult question.

eta: Yeah, It seems you are using a similar argument to that which is used against the ontological reality of any laws - that they are always being revised. I wasn't very convinced when it came to laws though. In this case, I would imagine that some arthmetic we are so sure about that it's revision is so unliukely that this argument would not work. Do you think that in the future we may discover htat a triangle has not 3 but 4 sides? Would it still be a triangle?

A concave object with 3 vertices (corners) but 4 sides? I'll see what I can come up with.

 

[Knotted]

So why do you include it in the list of things that make a good arithemtic I assume also, that you think that it can to a degree, you seem to point to this.

Where did I say anything about these arithmetics being 'good'? They fit a criterion that insists upon the idea that arithmetic is a direct, literal interpretation of the world. The fact that they are not 'good' is evidence that this is not a good criterion.

Maths B fits the world better that Maths A, so Maths A does not fit the world at all. The conclusion does not follow. I still cannot work out reasoning behind the claim. I understand that you think maths is a fiction, but I do not even know if you know what this entails. I assume that you do.

You also seem to conclude that this means that Maths B does not fit the world at all either. I would have thought that that has just been ruled out by you saying that Maths B fits the world better than Maths A. Again, I'm not sure that this is your argument.

Sorry

Go back to the post 100. The first thing I am trying to do is show that criterion A and criterion B are not equivalent nor even particularly complementary. I don't think that the usfulness of mathematics is evidence that it is based on a literal description of the world or visa versa.

The second thing that I am trying to argue is that criterion B and C are more important than criterion A at least outside of primary school education.

 

[Knotted]

A concave object with 3 vertices (corners) but 4 sides? I'll see what I can come up with.

Actually I don't think I can. Can you give me a definition of a triangle without using the notion of the number 3 or standard arithmetical axioms? We're back to Kronecker again.