philosophy of mathematics

What is the basis for reason? And mathematics?

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chaz wyman
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Re: philosophy of mathematics

Post by chaz wyman »

Arising_uk wrote:
chaz wyman wrote:... It is much better than faieries, I agree. More useful for one thing, but it reflects nature in human interested ways, It is apriori, not aposteriori.
Never been to happy about these terms. Are you saying that maths is a Kantian type category? Why is it not built upon experience from the world, you get circles in pools from rain, spiders webs show straight lines, as do claw marks. I accept that symbols are ours but maths appears at source to be the language for describing objects. We counted using heterogeneous sets once, we made right angles with rope and chain, a distance was how far we walked, etc. Not arguing that its not apriori when proving its own theorems, just the idea that it was not experience that gave it its grounds. Just as Logic is entailed by there being objects and states of affairs, why is Maths not the same?
You don't get maths from experience. If you were not taught it as a system you would not simply find it in the world. You seem to be confusing the object with the conception of it.
If you look closely at a spider's thread you will find that it is made of molecules - not a continuous straight line. It also has depth- which a straight line does not. The line is an abstraction for reasons of measurement.
I'm not sure what else I can offer you.
As for Kant - I don't think he has a monopoly on these terms.
Logic is the same as maths. It is a system that unpacks linguistics, and renders it to reason. It is an abstract system. But I see no reason to assume that the universe is written in maths or logic. These are human ways to help understand them. In the human realm they are part of experience, but take the humans away and the universe abides without logic or maths.
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Arising_uk
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Re: philosophy of mathematics

Post by Arising_uk »

chaz wyman wrote:You don't get maths from experience. If you were not taught it as a system you would not simply find it in the world. You seem to be confusing the object with the conception of it.

If you look closely at a spider's thread you will find that it is made of molecules - not a continuous straight line. It also has depth- which a straight line does not. The line is an abstraction for reasons of measurement.
I'm not sure what else I can offer you....
Could be, depends upon which objects and conception we're talking about. My take is your claim is that Maths is not a historical development from the experience of us being a perceiving object in a world of objects. At base Maths is number and there's lot of objects, ten digits for a start. Before the written symbols I guess set counting was popular. At the right distance webs have sorts of close geometrical shapes to provide the ground for the drawn constructs of line, curves, polygons. Rain on still water shows circles endlessly.
As for Kant - I don't think he has a monopoly on these terms.
Logic is the same as maths. It is a system that unpacks linguistics, and renders it to reason. It is an abstract system. But I see no reason to assume that the universe is written in maths or logic. These are human ways to help understand them. In the human realm they are part of experience, but take the humans away and the universe abides without logic or maths.
I don't disagree but the thing for me is, does it unpack linguistics? I accept Logic is based in language and unpacks the declarative proposition and maybe a couple of other things, like symbolism. But we know the failure of trying to give maths a solid ground in logic and the insights it gave(buggered if I truly understand them). So maybe maths is one of those things logic can't talk about but can only be pointed at, as its rooted in a world of objects in the same way logic is, i.e. if there are objects and states of affairs then there is Logic and Maths? And this would be the case even if there were no perceiving objects, just no-one to know about it. :)
So its not that its written in the maths or logic but whatever it is, is a state of affairs and objects, so it has to be be modelled in these systems?
chaz wyman
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Re: philosophy of mathematics

Post by chaz wyman »

Arising_uk wrote:
chaz wyman wrote:You don't get maths from experience. If you were not taught it as a system you would not simply find it in the world. You seem to be confusing the object with the conception of it.

If you look closely at a spider's thread you will find that it is made of molecules - not a continuous straight line. It also has depth- which a straight line does not. The line is an abstraction for reasons of measurement.
I'm not sure what else I can offer you....
Could be, depends upon which objects and conception we're talking about. My take is your claim is that Maths is not a historical development from the experience of us being a perceiving object in a world of objects. At base Maths is number and there's lot of objects, ten digits for a start. Before the written symbols I guess set counting was popular. At the right distance webs have sorts of close geometrical shapes to provide the ground for the drawn constructs of line, curves, polygons. Rain on still water shows circles endlessly.

Rain does what it does to pools of water - but it aint circles. The motion effected is far more complicated that a circle, as each perimeter is actually the crest of a wave, made up of molecules expressing complex energetic forces, and seemingly producing something incommensurable that has baffled science and philosophy; the eternal paradox of the particle and the wave. The existence of ripples on a pond is part of reality, but the maths can only describe it.


As for Kant - I don't think he has a monopoly on these terms.
Logic is the same as maths.

However - I should mention that Russell tried his whole career to prove that and failed.



It is a system that unpacks linguistics, and renders it to reason. It is an abstract system. But I see no reason to assume that the universe is written in maths or logic. These are human ways to help understand them. In the human realm they are part of experience, but take the humans away and the universe abides without logic or maths.
I don't disagree but the thing for me is, does it unpack linguistics? I accept Logic is based in language and unpacks the declarative proposition and maybe a couple of other things, like symbolism. But we know the failure of trying to give maths a solid ground in logic and the insights it gave(buggered if I truly understand them). So maybe maths is one of those things logic can't talk about but can only be pointed at, as its rooted in a world of objects in the same way logic is, i.e. if there are objects and states of affairs then there is Logic and Maths? And this would be the case even if there were no perceiving objects, just no-one to know about it. :)
So its not that its written in the maths or logic but whatever it is, is a state of affairs and objects, so it has to be be modelled in these systems?

Yes, both maths and logic are models; maths for number and logic for linguistic reasoning. (though there are cross overs)
spike
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Re: philosophy of mathematics

Post by spike »

This thread asks, "What is the basis for reason? And mathematics?"

The basis, I would say, is curiosity, skepticism and the desire to find a convincing, overarching explanation. To be logical and reasonable about a subject one has to approach it with a sense of detachment, without getting emotional.
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Arising_uk
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Re: philosophy of mathematics

Post by Arising_uk »

spike wrote:... To be logical and reasonable about a subject one has to approach it with a sense of detachment, without getting emotional.
To be reasonable about a subject one has to approach it with a sense of detachment, without getting emotional, may be true.

For it to be logical all parties must agree, or reasonably allow, to the truth of the axioms, for deduction to be of any use to a subject.
spike
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Re: philosophy of mathematics

Post by spike »

For it to be logical all parties must agree, or reasonably allow, to the truth of the axioms, for deduction to be of any use to a subject.
That certainly helps.
chaz wyman
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Re: philosophy of mathematics

Post by chaz wyman »

spike wrote:This thread asks, "What is the basis for reason? And mathematics?"

The basis, I would say, is curiosity, skepticism and the desire to find a convincing, overarching explanation. To be logical and reasonable about a subject one has to approach it with a sense of detachment, without getting emotional.
There is no reason without passion.
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The Jesus Head
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Re: philosophy of mathematics

Post by The Jesus Head »

spike wrote:Ak:
Why should they explain it to you? Or at all?
This is the arrogance of this forum and from monitors like you.
I agree with your opinion here.
lennartack
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Re: philosophy of mathematics

Post by lennartack »

Actually, modern maths is not necessarily about numbers, but about sets. All mathematical objects, including numbers, are sets. Maths is based on set theory, which is described in logic.

Logic is necessary for any kind of reason - whether it is mathematical or linguistic, the only difference that in language we use our intuitive logic and in maths we require a formal system based on our intuition. So it all comes down to our intuitive notion of truth.

It becomes very tricky when we start asking questions like "is our intuition correct?". Since outside our intuition truth and untruth may not even exist. This is easy to understand when you ask the same question with mathematics: a true proposition in maths is true in the mathematical system, but has no meaning outside mathematics. This is why I believe truth exists only inside one's mind, and there is no eternal truth.

Mathematics also made me understand that - like chaz said - it is used to describe reality, rather than that reality is based on mathematics. This is true for language as well, and maybe even our logic.
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Arising_uk
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Re: philosophy of mathematics

Post by Arising_uk »

The Jesus Head wrote:I agree with your opinion here.
You would as you have some utopian fantasy that forums such as these are democracies of some kind.

Do you have a subscription to the magazine? If not then you have no grounds to stand upon as you are a free-loader.
chaz wyman
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Re: philosophy of mathematics

Post by chaz wyman »

Arising_uk wrote:
The Jesus Head wrote:I agree with your opinion here.
You would as you have some utopian fantasy that forums such as these are democracies of some kind.

Do you have a subscription to the magazine? If not then you have no grounds to stand upon as you are a free-loader.

The Forum is free, you have no grounds to make that criticism.
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Arising_uk
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Re: philosophy of mathematics

Post by Arising_uk »

Why not?

Given that a forum costs and part of that cost is presumably paid for from those who subscribe to the magazine.
chaz wyman
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Re: philosophy of mathematics

Post by chaz wyman »

Arising_uk wrote:Why not?

Given that a forum costs and part of that cost is presumably paid for from those who subscribe to the magazine.

Tell that to your Doctor next time you visit him.
Whist you are in the waiting room tell that to the children their that have never paid a penny in tax.
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Arising_uk
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Re: philosophy of mathematics

Post by Arising_uk »

chaz wyman wrote:Tell that to your Doctor next time you visit him.
Whist you are in the waiting room tell that to the children their that have never paid a penny in tax.
I didn't say not to treat them. I pay taxes for the doctor to treat us all, I also pay prescription fees and I assume or hope these children will be paying theirs in future, if not and it is becoming more likely, in the future there will be no NHS in this sense. Should we take note of the complaints of those who do not contribute? Or at least, should they not think twice before complaining about something they do not support? It reminds me of those who can't be bothered to vote or at least spoil their ballot paper who moan about the Govt all the time.
Lynn
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Re: philosophy of mathematics

Post by Lynn »

Arising_uk wrote:Or at least, should they not think twice before complaining about something they do not support? It reminds me of those who can't be bothered to vote or at least spoil their ballot paper who moan about the Govt all the time.
I regard spoiling a ballot paper as different, as it can be used as a mechanism to show disapproval while still participating in the election process. After all, the election candidates are entitled to view the spoiled ballot papers so they can be made aware of the voter intention if they do so. Whether or not they act upon it, to get a good vote next time, is another matter.
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