Are numbers as real as rocks?

[Jonti]

Where difference between any 2 object is perceived then the use of numbers must occur. At least to my mind.

Yes, number is already implicit in the simplest possible mental act -- that of making a distinction.

 

[Aldebaran]

Not necessarily. One can come to the act of making distinction on any other term.

salaam.

 

[118118]

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

I would like to bring up the idea that the earth goes round the sun again. A criteria for this being a good law is it being a literal interpretation of the world, I think you would agree. But it does not begin to explain the whole of the universe without elaboration. So maths is still a good interpretation.

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

I think I disagree that 1+1=1 describes the world literally for reasons that include that I think it would be self contradictory. This makes me think of dialectics, so perhaps I will let this point go.

Maybe I think that mathematics could explain how 1+1=1 follows its logic and represents reality, so all it is is a lower level of explanation. Would you say that that Keplers law can be deduced from Newton's laws means that Newton's laws are less real?

 

[118118]

I'm just showing that direct representation of the world is not a very good one

Again, this makes me think of dialectics - that formal logic is flawed. But I disagree that there are alternatives that could do better.

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?

So you are saying that the truth of mathematics in science is just some kind of illusion? I would say that, though interesting, this is a flawed analogy, science must do more than simply excite the senses. I mean, the idea that flowers are nice that we take away from a painting is not true in the way that the speed of light is true.

Nah, like, I would agree that its possible that its fiction, but, I still feel as if realism is the starting point to work from, and only if the resulting ontology is too outlandish is it to be rejected.

 

[J77]

Can you give me a definition of a triangle without using the notion of the number 3 or standard arithmetical axioms?

Take a 4 sided object, join 2 opposite corners and you have 2 triangles.

Don't think I mentioned 3

 

[Groucho]

If you mean "animals don't have their own concepts and worldview"....Trust me, I know. I'm an undercover animal.

salaam.

I was simply answering the o/p.

I hadn't read the thread. The way I see it there's nothing else to say other than numbers are shit init.

I am willfully ignorant when it comes to pointless abstraction. I am never happy with any model that is entirely Platonic.

 

[Groucho]

Take a 4 sided object, join 2 opposite corners and you have 2 triangles.

Don't think I mentioned 3

That's not a definition but a description.

Numbers are not totally shit. They are useful for counting things.

We do have to work with some abstractions.

 

[J77]

That's not a definition but a description.

It doesn't take much to reword it into a definition tho'

 

[118118]

It doesn't take much to reword it into a definition tho'

Is it not an axiom of arithmetic that you can make a triangle that way.

 

[fudgefactorfive]

Rocks aren't real either.

 

[J77]

Is it not an axiom of arithmetic that you can make a triangle that way.

Someone would have to state these so-called "axioms of arithmetic" to make this a fair game

 

[Jonti]

Arithmetic cannot be axiomatised -- it is more than just a symbol game.

Gödel showed that (Russell & Whitehead's) Principia, or any other system within which arithmetic can be developed, is essentially incomplete. In other words, given any consistent set of arithmetical axioms, there are true mathematical statements that cannot be derived from the set... Even if the axioms of arithmetic are augmented by an indefinite number of other true ones, there will always be further mathematical truths that are not formally derivable from the augmented set.

Read a little more about Gödel's Incompleteness Theorem here.

 

[Knotted]

I would like to bring up the idea that the earth goes round the sun again. A criteria for this being a good law is it being a literal interpretation of the world, I think you would agree. But it does not begin to explain the whole of the universe without elaboration. So maths is still a good interpretation.

The idea that the earth goes round the sun is not a good literal interpretation. I'm torn between saying:
1) Bad example but I take your point but still the difference is that statements like this refer to the specifics of the material world where as mathematical laws do not.
2) Roughly: physical laws are only true in how they describe how the physical world relates to itself. They are not true in their own right. For example, stating that the speed of light is constant is meaningless unless you state that it is constant with respect to other physical constants. I was saying something similar about mathematical truth being about how it relates to itself. So I think there is a strong analogy between mathematics and physical laws.

Obviously this second answer is very sketchy at the minute, and furthermore I'm not too inclined to give myself too much of a headache about it. So regard 1) as the answer to your question and 2) as thinking material.

I think I disagree that 1+1=1 describes the world literally for reasons that include that I think it would be self contradictory. This makes me think of dialectics, so perhaps I will let this point go.

It is reminscent of dialectics. But there is no need for contradiction. What's wrong with saying 1+1=2 is false whereas 1+1=1 is true? Not that that's what I think but its certainly not easy to dissmiss in my mind.

Maybe I think that mathematics could explain how 1+1=1 follows its logic and represents reality, so all it is is a lower level of explanation. Would you say that that Keplers law can be deduced from Newton's laws means that Newton's laws are less real?

Not sure if I follow you here. 1+1=1 is useless and doesn't imply anything of interest. 1+1=2 cannot be deduced from 1+1=1.

 

[Knotted]

Take a 4 sided object, join 2 opposite corners and you have 2 triangles.

Don't think I mentioned 3

Very nice! But you have defined two triangles rather than one triangle.

 

[Knotted]

Again, this makes me think of dialectics - that formal logic is flawed. But I disagree that there are alternatives that could do better.

You're still labouring under the illusion that I want mathematics to directly represent the world. How many times do I have to say that I think direct representation is not the same as a useful tool. In fact the two are not even complementary in my view.

So you are saying that the truth of mathematics in science is just some kind of illusion? I would say that, though interesting, this is a flawed analogy, science must do more than simply excite the senses. I mean, the idea that flowers are nice that we take away from a painting is not true in the way that the speed of light is true.

Its not a perfect analogy but its not bad. I think a good scientific theory and a good work of art should share a similar trait - efficiency of expression.

Besides I didn't say that the truth of mathematics in science is an illusion. I think that mathematics has truth in science. However mathematical objects have only a nominal existance.

Nah, like, I would agree that its possible that its fiction, but, I still feel as if realism is the starting point to work from, and only if the resulting ontology is too outlandish is it to be rejected.

Can't fault that.

 

[Knotted]

Arithmetic cannot be axiomatised -- it is more than just a symbol game.

Absolutely. But even without considering Godels theorems, different sets of axioms can be equivalent. Its very silly to talk about the axioms of arithmetic (or geometry).

I think this is why I find the talk about the formality of numbers having a concrete existence silly. There's no particular reason we should agree on what they fundamentally are before we can agree on what they are in practice.

 

[weltweit]

Rocks are physical things on which you can stub your toes, they are undisputably real objects.

Numbers are ideas that exist in our heads and can be written on pieces of paper, and used for arithmatic, again usually on paper. On paper numbers have a logic to those that have learnt and therefore believe in mathematics.

However if numbers are as real as rocks, then surely so is god.

God is something that exists in the minds of humans, God has been written about on parchment and paper and for those who believe in God, God is real to them, for them God is as real as a rock.

So for numbers to be real as rocks, God must also be real as rocks.

 

[weltweit]

Yes, number is already implicit in the simplest possible mental act -- that of making a distinction.

Not the case, a Lion is faced with a young Springbok and a tree, the Lion knows it cannot eat the tree, it chases the Springbok for its dinner.

Did it ever need to know a number to make this choice?

 

[Aldebaran]

Rocks are physical things on which you can stub your toes, they are undisputably real objects.

I would say that they are real but within the frame of our vision of reality.

Numbers are ideas that exist in our heads and can be written on pieces of paper, and used for arithmatic, again usually on paper. On paper numbers have a logic to those that have learnt and therefore believe in mathematics.

They can be just as much real when not written on paper = in the abstract, for those who believe in - or at least know of - their existence and hence attribute them a functionality in reality, wether they are written down or not or used or not.

However if numbers are as real as rocks, then surely so is god.

Not necessarily. Numbers are created and can be used, God is uncreated and can't be used. Numbers can be made to disappear, God can't, etc...
Yet if one accepts that numbers can exist in the abstract - which they do - then so does God exist in the abstract. (proof of this I gave months ago in the course of a very different discussion, but that was not on this website)

God is something that exists in the minds of humans, God has been written about on parchment and paper and for those who believe in God, God is real to them, for them God is as real as a rock.

God is much more real to me then a rock could ever be. A rock is merely a created object and can disappear.

So for numbers to be real as rocks, God must also be real as rocks.

See above.

salaam.

 

[118118]

What about my continual reference to the speed of light. Is the speed of light real?

(I really think that its not "nonsence")

 

[118118]

I'm just showing that direct representation of the world is not a very good one

Again, this makes me think of dialectics - that formal logic is flawed. But I disagree that there are alternatives that could do better

You're still labouring under the illusion that I want mathematics to directly represent the world. How many times do I have to say that I think direct representation is not the same as a useful tool. In fact the two are not even complementary in my view

Then why are you trying to show it? Please explain your chain of reasoning in post 100, as I am beginning to suspect that you are working on a feeling.

statements like this refer to the specifics of the material world where as mathematical laws do not

I think you are begging the question here as I was trying to make the opposite point.
The rest of will have to wait until I work out wtf you are arguing.

 

[Knotted]

What about my continual reference to the speed of light. Is the speed of light real?

(I really think that its not "nonsence")

What about it? Its real as it refers to the properties of light within the framework of physical reality.

 

[118118]

Sorry, I didn't read that post. I *have* spent several days trying to work out why you conclude that mathematicla laws are not objectively true, though, and I am still lost. I can't argue against a view that is not expressed in a way that I can understand it.

 

[littlebabyjesus]

If you look at this from a purely existential viewpoint, the problem disappears.

There is the perceiver (me) and perception - everything else. So the content of the perception, from the rocks I see and feel down to any ideas I may have, is all equally 'real' in that it exists within my perception.

This is not a useful way to approach life because we all assume that the agreement of our various perceptions about the qualities of the objects we all perceive lead us to assume that these objects exist independently of us. We assume this, just as we assume that somehow we act with free will, because this is the best way to get through life. As with free will, however, we cannot prove it, and once we accept that, there is no problem.

 

[118118]

What about it? Its real as it refers to the properties of light within the framework of physical reality.

Yes, but that speed of light analogy shows that you do not have to be able to kick something for it to be real. Imo. Do you disagree

 

[Jonti]

Not the case, a Lion is faced with a young Springbok and a tree, the Lion knows it cannot eat the tree, it chases the Springbok for its dinner.

Did it ever need to know a number to make this choice?

Well, not its multiplication tables, obviously enough, no.

But "two" is implicit in the distiction between background and object already.

 

[118118]

how is what is only true in the story, as is the definition of fiction, true 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 (?

I didn't say that the truth of mathematics in science is an illusion. I think that mathematics has truth in science. However mathematical objects have only a nominal existance

I mean, the splashes of yellow are a bowl of fruit in the story of the other colours (just like 1+1=2 is true the story of mathematics). Now, in the still life painting a fiction (that those splashes of colour are a bowl of fruit) is true. Reasoning by analogy you can say that it is possible that the fiction of 1+1=2 is true in sceince. This is correct, no?
Importnatly, the painting and sceince are as real as each other, or you are just pointing out that something that is fictional can be true in a fiction - not very useful. So that I conclude that you are talking about the brute physical picture, not an abstraction, or you be bizzarely conceding that although mathematics is not real, the idea of a picture, is.
Now comes my inspiration:
Now, the way I see it is that that these splashes of colour are a bowl of fruit in the patinting, must be an illusion. That is quite intuitive, especially considering that you do say that there is no bowl of fruit. So I conclude that maths is true in science as an illusion, or the analogy is flawed.
Thats my reasoning. Please explain if its nothing like what you meant.


I mean: How can x be y? The same way that A is B. The splashes of colour are true in the painting by illusion (or how else - I assume that this is where we disagree). If you have answered the question, then x must be y by an illusion (if you agree that a splasges of colour are true in a painting by illusion), otherwise you have not answered the question and gained no credibility to the view that it is possible, as the analogy is flawed at the very root.

 

[weltweit]

They can be just as much real when not written on paper = in the abstract, for those who believe in - or at least know of - their existence and hence attribute them a functionality in reality, wether they are written down or not or used or not.

To my way of thinking if something is abstract it is less real than something that is physical and has a physical presence like a rock.

Not necessarily. Numbers are created and can be used, God is uncreated and can't be used. Numbers can be made to disappear, God can't, etc...

Don't forget that you are speaking to someone who believes in rocks because I have handled them and also in arithmetic because I have seen the laws and understand 1+1=2 but I do not believe in God either in a physical or an abstract sense. God is not real to me, it does not exist.

Yet if one accepts that numbers can exist in the abstract - which they do - then so does God exist in the abstract. (proof of this I gave months ago in the course of a very different discussion, but that was not on this website)

This is my argument, numbers can exist in the abstract for people who believe in mathematics and therefore as an abstract thing, or an idea in the mind, they exist, numbers and God are similar, those that believe they exist, bellieve they exist.

But that does not make them as real as a rock.

God is much more real to me then a rock could ever be. A rock is merely a created object and can disappear.

I would like to see you make a pile of rocks dissapear, how do you intend to set about it?

 

[weltweit]

Well, not its multiplication tables, obviously enough, no.

But "two" is implicit in the distiction between background and object already.

I am not sure I follow your "distiction between background and object".

But consider the Rabbit with 6 babies that it manages not to loose.

Have to come back to the question:

what is real, what is reality?

 

[Jonti]

That's the wider question of ontology.

But we can recognise things as real, or discuss why we think of this or that as real or not, or in what ways, even while being unable exactly to define what we mean by "real".