Refuting the counters to Zeno's paradox

[Xamonas Chegwé]

It is not A BELIEF! It is AN AXIOM! It is defined that way. It can neither be proven nor disproven BUT it agrees with what we know/presume/experience of reality and so it is held to be a valid axiom.

Of course we can dream up a world where everything is completely different to our experience and 2 = 3 and elephants give birth to readymix cement but that is not the point! The point is that the structure of mathematics IS based upon reality as we experience it and does a great job of replicating and predicting that reality as it is applied.

And the possibility of you not having a telephone is covered - in such an instance, the equality is equivalent to {} = {} - ie. the null set equals itself AND IS STILL VALID!

[jamest]

Yeah energy it is called. E=mc^2.

Then later, I'll try to explain why this makes no sense.

Oh dear I'm not looking forward to that. Quantum mechanics destroyed by someone who has no knowledge of physics or maths.

This isn't a matter of destroying quantum mechanics... as if all was explained by said knowledge. This is a matter similar to what I have attempted to do with XC's justification for his utilisation of his initial premise - which itself cannot be proved with mathematics. That is, XC's justification for utilising an axiom with the intention of saying what can be true of reality, is in doubt.
Likewise, I contend that your claims that reality must be comprised of fundamental units of space/time/spacetime & matter, are also irrational and, therefore, in doubt.

I could wax lyrical about the inability of physics (and mathematics) to tell us anything about 'reality'. Indeed, I have done so for about a decade, but you're not expected to know the details of that as you haven't known me for long. However, I have tried bringing this to your attention, but it seems to go right over your head. The fact is, that this is a metaphysical discussion - and you simply haven't grasped that. Perhaps, then, it is you that needs a "crash course" in the relevant topics.

Regardless, I shall ignore this issue and just confront you on your own terms: does it, then, make any rational sense to discuss a reality comprised of fundamental units that are indivisible?

I briefly mentioned this earlier, to another poster. The fact is that any 'indivisible' unit, itself, has to be devoid of space/time/spacetime. That is, if there is nothing smaller than x, then x MUST = 0. That is, let us say - for the sake of clear argument - that if the smallest possible unit of distance was an arbitrary '1 metre', then that would render any distances less than this as 'zero', since nothing can be less than this unit of measure. Further, we can say that the time to traverse an indivisible unit of distance must also be zero [seconds], since, otherwise, we would be implying that this distance was divisible - which it cannot be once we have declared that the unit is indivisible.

The bottom-line is that the fundamental units of matter - in such an advocated reality - would themselves have to be devoid of any material substance, since there would be zero distance/time within them. That is, your 'theory' amounts to equating matter with a ghost... moving through a ghost-like ether.

That is, it makes no rational sense to talk about 'reality' being comprised of fundamental units of finite elements.

Be sure to start with the difference between energy and matter, it's not as obvious as it sounds.

You yourself cannot wholly define, nor contrast, either concept, since there is no [scientific] definition of either that is complete.

[Surendra Darathy]

That is, it makes no rational sense to talk about 'reality' being comprised of fundamental units of finite elements.

If it accords with experimental experience, there's more basis for saying so than declaring that reality is an undifferentiated unity, which is achieved by talking out of your hat.

[jamest]

It is not A BELIEF! It is AN AXIOM! It is defined that way. It can neither be proven nor disproven BUT it agrees with what we know/presume/experience of reality and so it is held to be a valid axiom.

If an axiom cannot be proven, then it is a belief to state it as thus. Furthermore, what we know or presume of 'experience' is not a justification of that axiom in trying to make claims about what can happen in REALITY!!

Of course we can dream up a world where everything is completely different to our experience

In case you have forgotten, it is the EXPERIENCE of motion/distance that is in doubt. That is, we are supposed to be having a discussion about what could be real, REGARDLESS of experience.

The point is that the structure of mathematics IS based upon reality as we experience it and does a great job of replicating and predicting that reality as it is applied.

The point is that Zeno's paradox questions THE 'reality' of motion/distance, beyond the EXPERIENCE of said concepts.

Please don't employ the truth of experience to proclaim the truth of reality.

[Surendra Darathy]

That is, we are supposed to be having a discussion about what could be real, REGARDLESS of experience.

You can talk about whatever you want to, James. Eventually you'll be by yourself, which is where a solipsist feels most at home:

Of course we can dream up a world where everything is completely different to our experience and 2 = 3 and elephants give birth to readymix cement but that is not the point!

The point is, it is relatively easy to make all sorts of shit up about what reality might REALLY be like, but hard to publish it except in places like this.

[jamest]

That is, it makes no rational sense to talk about 'reality' being comprised of fundamental units of finite elements.

If it accords with experimental experience, there's more basis for saying so than declaring that reality is an undifferentiated unity, which is achieved by talking out of your hat.

Again, please don't employ the truth of experience to proclaim the truth of reality.

[jamest]

That is, we are supposed to be having a discussion about what could be real, REGARDLESS of experience.

You can talk about whatever you want to, James. Eventually you'll be by yourself, which is where a solipsist feels most at home

If I am a solipsist, then it is so in a sense that embraces 'you', also.

Of course we can dream up a world where everything is completely different to our experience and 2 = 3 and elephants give birth to readymix cement but that is not the point!

The point is, it is relatively easy to make all sorts of shit up about what reality might REALLY be like, but hard to publish it except in places like this.

The point is, that his proof attempted to state what 'reality' is REALLY like, as a retort to what reality cannot be.

[Surendra Darathy]

That is, it makes no rational sense to talk about 'reality' being comprised of fundamental units of finite elements.

If it accords with experimental experience, there's more basis for saying so than declaring that reality is an undifferentiated unity, which is achieved by talking out of your hat.

Again, please don't employ the truth of experience to proclaim the truth of reality.

The safest course, James, to avoid talking out of your hat, is not to proclaim the truth of reality at all. That was the whole point of "Relativism is Self Refuting", "Metaphysics as an Error" and all the follow ups to it.

Nobody here is assaying to discuss the truth of reality but you, and you are making a fool of yourself doing it whilst ordering everyone else to avoid a confusion none of us has, and broadcasting your own prejudices about it with ex recto assertions about the Oneness of All. The only coherent statements that anyone is making about the world at present are expressed in terms of empirical models. The metaphysical approach just involves making up shit and talking out of your hat with it.

The point is, that his proof attempted to state what 'reality' is REALLY like, as a retort to what reality cannot be.

Sorry, James. You are the only person in this discussion who is confused enough about the use of mathematics to imagine it purports an ontological significance to its models of physical data. But go on attacking straw men all you like. I'm just here for the show.

[Xamonas Chegwé]

The point is, that his proof attempted to state what 'reality' is REALLY like, as a retort to what reality cannot be.

Please show where I claimed to be doing that. I would love to see it.

The proof merely showed that the mathematics 'of this reality' was quite capable of modelling the witnessed events 'of this reality' and that the apparent failure for it to do so was, in fact, caused by an assumption by Zeno that was out of step with reality - namely his claim that an infinite series cannot have a finite sum.

THAT is what the thread is about - your claim that Zeno's paradoxes show flaws in our perception of reality because the counters to them are somehow invalid - well they aren't - NOT SO LONG AS YOU STAY GROUNDED IN THIS REALITY. They are perfectly consistent.

I make no claims about any other 'greater' reality. We could all be the dream of a cosmic barnacle for all I care - the fact is, the maths is sound unless you step outside of THIS REALITY and add a load of made-up stuff to the mix.

[GrahamH]

It is not A BELIEF! It is AN AXIOM! It is defined that way. It can neither be proven nor disproven BUT it agrees with what we know/presume/experience of reality and so it is held to be a valid axiom.

If an axiom cannot be proven, then it is a belief to state it as thus. Furthermore, what we know or presume of 'experience' is not a justification of that axiom in trying to make claims about what can happen in REALITY!!

And where do you think that gets you? A=A is only based on observed reality. Throw that out and you have no basis for any axioms, no language or maths or logic to talk about 'reality' at all.

This why people say 'Metaphysics is an error'

[colubridae]

[quote="jamest"]
If an axiom cannot be proven, then it is a belief to state it as thus. Furthermore, what we know or presume of 'experience' is not a justification of that axiom in trying to make claims about what can happen in REALITY!!
[quote]


2 + 2 = 4 is an axiom as well.

It accords with reality; it ‘maps’ onto reality but that does not prove it true.

If you choose to question

inf. = inf.

Because you can’t ‘map’ it onto reality, then you must question:-

2 – 3 = -1.

This does not ‘map’ onto reality either. Yet most of the world you live by exists by virtue of such maths.
The justification is that it ‘works’.
The ‘mapping’ is that it works.

Just as 1 + 1 = 2 is justified because it works.

All you have actually done is accepted lots of ‘hidden’ axioms, because their ‘validity’ is immediate and obvious.

You have then arbitrarily rejected inf. = inf. because it is not so obvious to you.

Inf. = inf. does ‘map’ onto reality but in a much more intricate, roundabout way; a not so obvious way.
E.g. the tortoise and the hare.
Since it works for that scenario it is justifiable to use it for Zeno’s arrow.


If you arbitrarily reject that mapping because it is too tortuous that’s your choice, but it is an arbitrary one.
Using your arbitrary choice you can ‘reject’ XG’s proof, but by the same token you must reject lots of other useful ‘proofs’.


What’s worse using your requirements actually ‘proves’ that the arrow will never reach the target.
Would you feel comfortable standing in front of the target…

[jamest]

It is not A BELIEF! It is AN AXIOM! It is defined that way. It can neither be proven nor disproven BUT it agrees with what we know/presume/experience of reality and so it is held to be a valid axiom.

If an axiom cannot be proven, then it is a belief to state it as thus. Furthermore, what we know or presume of 'experience' is not a justification of that axiom in trying to make claims about what can happen in REALITY!!

And where do you think that gets you? A=A is only based on observed reality.

So too is the notion that 'motion' can occur! Though the point of Zeno's reasoning was to show that motion isn't a phenomena that could occur in reality. Therefore, one cannot counter such reasoning with axioms determined from observation. Especially so when reasoning has been forthcoming that A = A is only true for finite entities - even ones that eternally expand.

Throw that out and you have no basis for any axioms, no language or maths or logic to talk about 'reality' at all.
This why people say 'Metaphysics is an error'

My response to this rubbish has been made in the relevant thread.

[colubridae]

My response to this rubbish has been made in the relevant thread.

Wow an axiomatic statement not based in reality...

Double standards. Never seen that on these forums before.

[jamest]

2 + 2 = 4 is an axiom as well.

It accords with reality; it ‘maps’ onto reality but that does not prove it true.

If you choose to question

inf. = inf.

Because you can’t ‘map’ it onto reality, then you must question:-

2 – 3 = -1.

Hello.
I don't choose to question inf. = inf. because it won't "map onto reality". I've questioned it because it's irrational to discuss the equivalence of something which itself may not be possible. The details can be found in previous posts.

The justification is that it ‘works’.
The ‘mapping’ is that it works.

Sure, science "works" too. But it's no good employing empirical knowledge in a discussion about potential reality.

What’s worse using your requirements actually ‘proves’ that the arrow will never reach the target.
Would you feel comfortable standing in front of the target…

You're missing the whole point of the discussion. If Zeno was correct, then beyond the mind, there are no targets... no arrows. I am not ready to surrender my experienced body yet, so I will abstain from placing it in front of experienced targets.

[GrahamH]

It is not A BELIEF! It is AN AXIOM! It is defined that way. It can neither be proven nor disproven BUT it agrees with what we know/presume/experience of reality and so it is held to be a valid axiom.

If an axiom cannot be proven, then it is a belief to state it as thus. Furthermore, what we know or presume of 'experience' is not a justification of that axiom in trying to make claims about what can happen in REALITY!!

And where do you think that gets you? A=A is only based on observed reality.

So too is the notion that 'motion' can occur! Though the point of Zeno's reasoning was to show that motion isn't a phenomena that could occur in reality. Therefore, one cannot counter such reasoning with axioms determined from observation. Especially so when reasoning has been forthcoming that A = A is only true for finite entities - even ones that eternally expand.

Throw that out and you have no basis for any axioms, no language or maths or logic to talk about 'reality' at all.
This why people say 'Metaphysics is an error'

My response to this rubbish has been made in the relevant thread.

You have failed to make a case that A != A for infinities/infinitesimals with identical definitions. Indeed you have no basis to argue anything of the sort, since your argument dismisses the very foundations of reason.

If you reject all axioms apprehended to be true by experience, and all learned language, what do you have left with which to assess Reality?