Paradox?

What is the basis for reason? And mathematics?

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Re: Paradox?

Post by Philosophy Explorer » Sat Apr 07, 2018 8:33 pm

Arising_uk wrote:
Sat Apr 07, 2018 7:34 pm
It doesn't matter if it's size or distance your points are DIMENSIONLESS and as such will have no relationship to size or distance.

The reason why you think you have a paradox that defies common-sense is that in your OP you are implicitly implying that points are not dimensionless and as such are in some way filling up the space so when you compare an inch line with an inch square common-sense would imply that there should be more points in the latter and if in reality points did work like this then they'd be dimensioned and it would be a paradox that there are the same amount of points in both but you justify your claim that there are by using these dimensionless points and by bloody definition these can have no relation to size or distance so the 'deduction' is pointless.
That's the paradox. People think a larger size implies more points in a solid object (common sense) when such isn't the case. Just because I didn't say the points are dimensionless in my OP doesn't imply each point has a size, in fact it's assumed they don't individually have a size. It's proven by Cantor that both sets of points are the same in number (Aleph null) through one-to-one correspondence (using Cartesian coordinates). And there you have it.

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Re: Paradox?

Post by Arising_uk » Sun Apr 08, 2018 1:03 am

Philosophy Explorer wrote:That's the paradox. ...
There is no paradox.
People think a larger size implies more points in a solid object (common sense) when such isn't the case. ...
Who are these 'people' who think this? But if they did it'd be because they are thinking of actual dimensioned points and in that case there will be more in a solid object than in a line.
Just because I didn't say the points are dimensionless in my OP doesn't imply each point has a size, in fact it's assumed they don't individually have a size. It's proven by Cantor that both sets of points are the same in number (Aleph null) through one-to-one correspondence (using Cartesian coordinates). And there you have it.

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Have what? If you understand how a point is being described as dimensionless in Mathematics then it's obvious that they would have no relation to any actual object whereas if you actually use points to create an object then the 'common-sense view holds.

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Re: Paradox?

Post by Philosophy Explorer » Sun Apr 08, 2018 1:17 am

Arising_uk wrote:
Sun Apr 08, 2018 1:03 am
Philosophy Explorer wrote:That's the paradox. ...
There is no paradox.
People think a larger size implies more points in a solid object (common sense) when such isn't the case. ...
Who are these 'people' who think this? But if they did it'd be because they are thinking of actual dimensioned points and in that case there will be more in a solid object than in a line.
Just because I didn't say the points are dimensionless in my OP doesn't imply each point has a size, in fact it's assumed they don't individually have a size. It's proven by Cantor that both sets of points are the same in number (Aleph null) through one-to-one correspondence (using Cartesian coordinates). And there you have it.

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Have what? If you understand how a point is being described as dimensionless in Mathematics then it's obvious that they would have no relation to any actual object whereas if you actually use points to create an object then the 'common-sense view holds.
Wrong on both counts.Actual solid objects are made up of points, but the size of the object has no relationship to the size of the set of the points within the object. Who are these people who think this? Mathematicians such as Cantor for one. Have you checked Wikipedia?

Just because you can't see dimensionless points doesn't mean they don't exist (hence my reference to making a blind person see). I'm curious - what do you think solid objects are made up of? If not points, then what do you think they're made up of?

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Re: Paradox?

Post by Arising_uk » Sun Apr 08, 2018 1:27 am

Philosophy Explorer wrote:Wrong on both counts.Actual solid objects are made up of points, but the size of the object has no relationship to the size of the set of the points within the object. ...
Bollocks, if they are made of points then these points have a dimension and if so then there will be more of them in a solid object than in a line. If there is no relationship then it is because they are these mathematical constructs called 'dimensionless points' which don't exist in actual solid objects.
Who are these people who think this? Mathematicians such as Cantor for one. Have you checked Wikipedia?
Then they are Platonists and I disagree with them.
Just because you can't see dimensionless points doesn't mean they don't exist (hence my reference to making a blind person see). ...
:lol: It's not that I can't se them that I think they don't exist it's because they are a logical contradiction or at best a mathematical abstraction.
I'm curious - what do you think solid objects are made up of? If not points, then what do you think they're made up of?
I have no idea because I think Kant still not disproved and the noumena holds but who knows maybe Lebiniz was right. The sciences tell me that the answer to your question depends upon the subject at hand but like I say I have no idea and little care about such metaphysics from a philosophical point of view, all I know is that solid means I have to go around something.
Last edited by Arising_uk on Mon Apr 09, 2018 12:08 am, edited 1 time in total.

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Re: Paradox?

Post by Philosophy Explorer » Sun Apr 08, 2018 1:51 am

Arising said:

"I have no idea because I think Kant still not disproved and the noumena holds but who knows maybe Lebiniz was right. The sciences tell me that the answer to your question depends upon the subject at hand but like I say I have no idea and little care about such metaphysics from a philosophical point of view, all I know is that solid means I have to go around something."

Since you don't know, that also means you don't know if dimensionless points exist because you don't have knowledge about abstract math. Therefore I'm debating someone who can't respond to me.

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Re: Paradox?

Post by Arising_uk » Mon Apr 09, 2018 12:08 am

Philosophy Explorer wrote:
Since you don't know, that also means you don't know if dimensionless points exist because you don't have knowledge about abstract math. Therefore I'm debating someone who can't respond to me.

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:lol: Go on then bigbrain tell me how Kant's reasoning was wrong?

Explain how abstract maths establishes that dimensionless points exist?

Explain how such a thing as a dimensionless point can interact in a dimensioned world and if it does it how it remains dimensionless?

Oh! And by the by I think you need to brush up upon what Mathematicians now think the state of play is with respect to the relationship between truth, mathematics and reality.

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Re: Paradox?

Post by Philosophy Explorer » Mon Apr 09, 2018 1:24 am

Arising_uk wrote:
Mon Apr 09, 2018 12:08 am
Philosophy Explorer wrote:
Since you don't know, that also means you don't know if dimensionless points exist because you don't have knowledge about abstract math. Therefore I'm debating someone who can't respond to me.

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:lol: Go on then bigbrain tell me how Kant's reasoning was wrong?

Explain how abstract maths establishes that dimensionless points exist?

Explain how such a thing as a dimensionless point can interact in a dimensioned world and if it does it how it remains dimensionless?

Oh! And by the by I think you need to brush up upon what Mathematicians now think the state of play is with respect to the relationship between truth, mathematics and reality.
You're as blind as a bat. You already stated that math is beyond you. Just because you can't see the points doesn't mean they don't exist. It's like saying you can't see atoms which isn't true because they can be seen with an electron microscope. Since you know nothing about math (your words), then there's no point in trying to discuss it with you, is there? Read up on Cantor who also did philosophy to start learning. I'm not going to take your word, a nonmathematician, that points don't exist.

Let me add that while Kant is a philosopher, he's not a mathematician so he's irrelevant to our discussion.

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Re: Paradox?

Post by Arising_uk » Mon Apr 09, 2018 9:51 am

Philosophy Explorer wrote:You're as blind as a bat. ...
And you're a classic example of an interweeble posting upon a forum the subject of which you have no clue about.
You already stated that math is beyond you. ...
But Philosophy of Maths isn't when it asserts ontology as it's essentially epistemology and really metaphysics.
Just because you can't see the points doesn't mean they don't exist. ...
Then explain to me how you know they do?
It's like saying you can't see atoms which isn't true because they can be seen with an electron microscope. ...
:lol: You really think there are little rounds 'balls' down there? But there is no logical issue with 'atoms' actually existing as they are dimensioned particles however you are asserting a dimensionless point exists and I want to know how?
Since you know nothing about math (your words), then there's no point in trying to discuss it with you, is there? ...
Discuss what as you so far can give no explanation as to how Maths empirically establishes that dimensionless points actually exist.
Read up on Cantor who also did philosophy to start learning. I'm not going to take your word, a nonmathematician, that points don't exist. ...
Then you need to read some of your more philosophical mathematicians as they don't think Maths is the route to empirical truth anymore.
Let me add that while Kant is a philosopher, he's not a mathematician so he's irrelevant to our discussion.
:lol: He was a student and teacher of Mathematics all his life. You've obviously not read him then as his critique is about Reason and what it can and cannot say or are you saying that Maths is irrational?

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Re: Paradox?

Post by Philosophy Explorer » Mon Apr 09, 2018 11:24 am

Arising said:

"He was a student and teacher of Mathematics all his life. You've obviously not read him then as his critique is about Reason and what it can and cannot say or are you saying that Maths is irrational?" Tossing out the bollocks again. All Wikipedia says is he's a philosopher. :lol:

Oh math is many things, has many branches which includes both the discrete and irrational. Do you have a degree in math?

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Re: Paradox?

Post by Philosophy Explorer » Mon Apr 09, 2018 11:32 am

Arising said:

"Then you need to read some of your more philosophical mathematicians as they don't think Maths is the route to empirical truth anymore."

And who are these "more philosophical mathematicians?" Certainly not Kant as he's not listed that way by Wikipedia. :lol: Do you have any quotes?

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Re: Paradox?

Post by Philosophy Explorer » Mon Apr 09, 2018 11:34 am

Arising said:

"Discuss what as you so far can give no explanation as to how Maths empirically establishes that dimensionless points actually exist." Read Georg Cantor.

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Re: Paradox?

Post by Arising_uk » Mon Apr 09, 2018 11:36 am

Philosophy Explorer wrote: Do you have a degree in math?

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Do you?

Amongst the bits of paper I have one is a degree in Philosophy and another is a Masters in Foundations of Advanced I.T.

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Re: Paradox?

Post by Philosophy Explorer » Mon Apr 09, 2018 11:37 am

Arising said:

"You really think there are little rounds 'balls' down there? But there is no logical issue with 'atoms' actually existing as they are dimensioned particles however you are asserting a dimensionless point exists and I want to know how?" Georg Cantor and other mathematicians already provided the explanation. You might also read up on midpoints of lines.

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Re: Paradox?

Post by Philosophy Explorer » Mon Apr 09, 2018 11:38 am

Arising_uk wrote:
Mon Apr 09, 2018 11:36 am
Philosophy Explorer wrote: Do you have a degree in math?

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Do you?

Amongst the bits of paper I have one is a degree in Philosophy and another is a Masters in Foundations of Advanced I.T.
Yes I do.

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Re: Paradox?

Post by Philosophy Explorer » Mon Apr 09, 2018 11:42 am

Arising said:

"Then explain to me how you know they do?"

Simple I read their works online and from books. Just because you flap your lips doesn't make you an authority.
:lol:

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