On treeness of Oak1, and other things

[SpeedOfSound]

1. Zeno's paradoxes presume that an infinite series cannot sum to a finite amount - this is demonstrably false.

I'm a bit short on time, but wanted to pick-up on this. The issue is not whether Zeno was right or wrong (though I would defend the argument in terms of the distinction between tangible and conceptual infinities). The issue is whether Zeno's argument (or the argument of the guys who allegedly proved him wrong), was a construct not wholly dependent upon observation, so that it went beyond observation. Certainly, one cannot prove that Zeno was wrong by pointing at something within the world. So, to prove Zeno wrong necessitates a logic that goes beyond observation.

Btw, the thing with Euclid - I was just refering to the curvature of spacetime.

Observation is precisely why even Zeno knew he must be wrong. The slower runner is overtaken and the arrow does reach the target. Observation contradicts the suppsed paradox. The later mathematics shows the error in thinking that led to an apparent paradox, which was only a faulty 'way of knowing' (i.e. not knowing).

You mean there are more than one faulty ways of not knowing?

Maybe there infinite ways of not knowing and it's just that we humans are mired in empiricism that leaves us without foundation for thinking up more of them . Could different axioms yield an equally consistent and complex mathematics that contradict our own? If we have no concern for conforming our mathematics to observed reality what are the constraints? Could we have 1+1 = 7 and square circles given the right axioms and definitions?

Put another way, are there any 'fundamental truths' about the particular mathematics humans have developed?

Maybe there are infinite numbers of things that we could believe in and the only reason we don't is because we wrongly assume materialism. There is really no reason why, if I shot an arrow at my child's head it should ever actually hit him in the head.

This jamest guy is on to something. Wonder if he has any kids? Left.

[GrahamH]

Zeno claims that it never should. What we observe is of no relevance, since we cannot be sure that we are observing real events. It might all be in the mind - an illusion.
The only way to prove Zeno wrong, is to employ logic/math that tells us more than any observation ever could!

It should be obvious:

1) Zeno has an argument.
2) That argument cannot be negated via observation because we cannot be sure whether observed motion is just an illusion apparent within the mind.
3) Therefore, Zeno must be disputed via logic that transcends the observed world, or not at all.

But the apparent logic of a mathematical proof cannot be shown to be any less an illusion apparent within the mind.
Between the two supposed illusions one provides an easily apprehended refutation. The other is a little more involved, but what grounds do you have for suggesting the logical disproof is any more 'True'?

Why is your experience of logic more valid than your experience of motion?

[jamest]

1) Zeno has an argument.
2) That argument cannot be negated via observation because we cannot be sure whether observed motion is just an illusion apparent within the mind.
3) Therefore, Zeno must be disputed via logic that transcends the observed world, or not at all.

But the apparent logic of a mathematical proof cannot be shown to be any less an illusion apparent within the mind.
Between the two supposed illusions one provides an easily apprehended refutation. The other is a little more involved, but what grounds do you have for suggesting the logical disproof is any more 'True'?

Why is your experience of logic more valid than your experience of motion?

As I said, we cannot be sure whether 'motion' exists beyond its apparency to the observer. But I'm not sure how you equate that with 'logic', which can only exist within the mind. That is, the reliance upon logic is not determined by whether it exists beyond the mind, as per motion. Your questioning is confused.

The fact is that only logic can be employed to refute Zeno's own logic, as 'observation' proves nothing about the reality of motion. Whether such logic is any good, is open to debate - but we cannot label that logic 'an illusion'.

[SpeedOfSound]

Are you guys have the same conversation in two different threads?

Me and LI agreed to a truce yesterday on this metaphysics issue for this thread. If we fork out again I will be come very old and even more confused.

[GrahamH]

Whether such logic is any good, is open to debate - but we cannot label that logic 'an illusion'.

Why?

Why is your experience of thinking logically more reliable than your experience of moving?
Why is your knowledge of logic more reliable than your knowledge of motion?

[SpeedOfSound]

Whether such logic is any good, is open to debate - but we cannot label that logic 'an illusion'.

Why?

Why is your experience of thinking logically more reliable than your experience of moving?
Why is your knowledge of logic more reliable than your knowledge of motion?

I have never been convinced that logic and math do not derive entirely from our material existence in R1. Granted we have reached much further than this but I think the basics are there in such things as two trees are one ... two, different trees.

[GrahamH]

Whether such logic is any good, is open to debate - but we cannot label that logic 'an illusion'.

Why?

Why is your experience of thinking logically more reliable than your experience of moving?
Why is your knowledge of logic more reliable than your knowledge of motion?

I have never been convinced that logic and math do not derive entirely from our material existence in R1. Granted we have reached much further than this but I think the basics are there in such things as two trees are one ... two, different trees.

I agree. It seems we experience thinking in a similar sense to experiencing seeing a tree. I also think we experience certainty or 'truth' in the same way. The feeling that some information is is true could be called a quale, just like the feeling of seeing red (if we were to entertain the folk-psych notion of qualia).

[Little Idiot]

You did not win the point, LI.

You merely claimed that the existence of mathematical proofs somehow validated your point. But mathematical proofs are built upon earlier proofs, etc. (it's proofs all the way down) until, in the final analysis, they are built upon axioms which cannot be proven and are merely taken as being self-evident.

Here's the stinger.

Those axioms are accepted as self-evident because they agree with our observation of empirical data.

Thats a U-turn from your position earlier where you said

A proof in science means only that empirical results agree with predicted results within acceptable margins of experimental error. It is only ever a demonstration that the theory it is 'proving' is a reasonable model, not the truth.

In maths, a proof is far more than this. A mathematical proof, if it is sound, is absolute. It follows directly from clear definitions and previously proven lemmas. Take away the universe and maths will still be true.

So, yes, I would say that things can be known other than by empirical evidence but only very special and completely abstract things.

The point I claim to have won is that we have other ways of knowing, in addition to the empirical, which you clearly agreed with, in the above quote.

Even if the axioms are accepted by people because they agree with our observation of empirical data, does that sufice to prove the axioms truth relies upon such agreement, or does it only show we accept more easily things which agree with observation, regardless of the truth of the thing?

Even if, as you are saying, we accept axioms which agree with emperical observations, that does not mean that (odd + even = odd for all evens and odds) or (irrationality of root 2) can be demonstrated emperically.

Therefore;
Why does my point "emperical evidence can not demonstrate all known knowledge, therefore there is at least one other way of gaining knowledge" not stand?
Since this is the crux of the victory I claimed, why am I not entitled to make the claim?

Later. I have a funeral to go to. But basically, my wording was misleading in the earlier quote. I will elaborate later.

OK. Allow me to explain (and apologise for) the sloppy wording here.

In maths, a proof is far more than this. A mathematical proof, if it is sound, is absolute[2]. It follows directly from clear definitions[1] and previously proven lemmas. Take away the universe and maths will still be true[3].

So, yes, I would say that things can be known other than by empirical evidence but only very special and completely abstract things.[4]

1. The key phrase is "clear definitions". This is synonymous here with "clearly defined axioms", which is the phrase I should have used.
2. No logical system can be built purely upon thin air. There must be a foundation upon which the logic stands. Mathematical proofs are absolute if, and only if, the axiomatic foundation that underlies them is true and the logic that builds upon these axioms is sound. This was not made clear at all - it was sloppy of me and I have no defence for missing it from my statement above except for can't-be-arsedness!
3. With 1 and 2 established, I stand by this statement. Provided the axioms hold, maths is absolutely true.
4. Rigorous logic has proved many theorems in mathematics that can never be demonstrated empirically: that there is an infinite number of primes, the irrationality of π, Fermat's last theorem, etc. All of these flow from precise, axiomatic definitions by clear logical steps. It is such theorems that I refer to in this last sentence - they can only be 'known' through the application of rigorous logic, owing to the infinite number of cases that would require checking empirically. The caveat that is missing though (and again, for which I have no excuse) is that stated in point 2.

Apologies again if I misled you. I should know better than to argue with philosophers without being rigorously accurate in my wording. All I can add in my defense is that I haven't done this for a while.

So you are still saying maths does show knowledge which can not be demonstrated emirically, as long as the axioms hold true and the logic is good. This even applies without the universe, as long as the axioms hold true and the logic is sound.

Even if it is easier for us to accept axioms because they agree with our empirical or experienced observations, the axioms can be of un-observed systems - who ever observed a pair of infinite lines, say, to confirm if they actually do or do not meet at infinity? Or, the first 4 Axioms of Peano which you linked to are described in the wiki link as 'in modern treatments these are often considered axioms of pure logic.' Therefore the truth of the axioms does not depend on being observed, we could say some axioms depend on being reasonable or logical.

Therefore, there is still knowledge proved by maths which can not be demonstrated by emirical method.

Also, mathematics offers absolute proof, if its axioms hold true and its logic is good. Empricism does not offer proof. This point alone establishes maths can provide knowledge that empiricism alone can not.

Therefore my claim of 'victory' on this point (that at least one other method of gaining valid knowledge) still stands.

[SpeedOfSound]

Whether such logic is any good, is open to debate - but we cannot label that logic 'an illusion'.

Why?

Why is your experience of thinking logically more reliable than your experience of moving?
Why is your knowledge of logic more reliable than your knowledge of motion?

I have never been convinced that logic and math do not derive entirely from our material existence in R1. Granted we have reached much further than this but I think the basics are there in such things as two trees are one ... two, different trees.

I agree. It seems we experience thinking in a similar sense to experiencing seeing a tree. I also think we experience certainty or 'truth' in the same way. The feeling that some information is is true could be called a quale, just like the feeling of seeing red (if we were to entertain the folk-psych notion of qualia).

That is spot on. This feeling of truth or understanding is actually just a feeling. It probably develops early and hard because it is informed by the limbic and reward systems.

[SpeedOfSound]

Therefore my claim of 'victory' on this point (that at least one other method of gaining valid knowledge) still stands.

Well. Your truce violation doesn't put you in a position of victory but rather in a position of being further fired upon.

[Little Idiot]

The point I claim to have won is that we have other ways of knowing, in addition to the empirical...

In light of what XC has written about geometry and 'reality', I think it safe to say that a means of producing assumptions is not a way of "knowing". The willingness to check assumptions and drop them in the face of a single counterexample is a way of knowing, but I don't know what you would call it. Rejection of perversity, or something like that?

What should we call a willingness to delete an axiom based on a contradiction of it?

The fact that we can invent instruments to expand the spatial scales of data collection (microscopes and telescopes, generically) and increasingly-accurate clocks (dependent on rate processes taking place in a spatial context) does not mean that space-time is anything more than a model for organising the data.

As XC points out, it organises data so well that one feels rather a sense of surprise in discovering the universe is a mite on the back of a turtle shell, and more turtles all the way down...

There are no constraints as to metaphysical descriptions of what the nature of "real reality is". Metaphysics is ungrounded.

I will hold judgement on my point about ways of knowing until XC responds to my previous post, but I think I have provided enough evidence between these two posts that my point still holds....

How about this as a grounding axiom for metaphysical study of 'absolute reality' or 'absolute truth'

It is self evident i.e. an axiom that;
If there is an absolute reality it must not be possible for it to change - Axiom 1.
It is self evident because if 'absolute reality' changed it would not be absolute.

This, like the first 4 of the Peano axioms (which XC linked to) is an axiom of pure logic, it can not be empirically demonstrated, because we would need 'absolute reality' and infinite time to verify it.

Note, that at this first stage, the 'absolute reality' refered to is hypothetical, and must be so to avoid begging the question of its being absolute reality.

Here we have an important reason why 'all we've got is the empirical' has to fall, to validate the first axiom of the metaphysics of truth.
However, it seems like a 3 week battle for naught, if Peano can have 4 axioms of pure logic, so can I. QED.

The 'metaphysics of truth' is now grounded, and we have constraints as to what 'absolute reality' can or can not be.
For example, it can not be my laptop, SoS's trousers nor any physical object, all of which change.

A final point; I for one have only argued for the defence of metaphysics for one reason, the validity of the search for 'absolute reality' should anyone wish to argue that this is the realm of science, or suggest a less woo-like name that that I have used 'the metaphysics of truth', feel free. It is the validity of the human search for absolute reality that I defend, not 'metaphysics.'

[Little Idiot]

Therefore my claim of 'victory' on this point (that at least one other method of gaining valid knowledge) still stands.

Well. Your truce violation doesn't put you in a position of victory but rather in a position of being further fired upon.

Oh, I thought we had a truce on Tarksi.
And I am just responding to CX's points with, what I think, are reasonable counters;
The axioms he linked to include 4 'pure logic' axioms.
It seems to me that he has not retracted, only qualified, his agreement with my point on 'other ways of gaining knowledge.'

[Little Idiot]

Whether such logic is any good, is open to debate - but we cannot label that logic 'an illusion'.

Why?

Why is your experience of thinking logically more reliable than your experience of moving?
Why is your knowledge of logic more reliable than your knowledge of motion?

I have never been convinced that logic and math do not derive entirely from our material existence in R1. Granted we have reached much further than this but I think the basics are there in such things as two trees are one ... two, different trees.

I agree. It seems we experience thinking in a similar sense to experiencing seeing a tree. I also think we experience certainty or 'truth' in the same way. The feeling that some information is is true could be called a quale, just like the feeling of seeing red (if we were to entertain the folk-psych notion of qualia).

That is spot on. This feeling of truth or understanding is actually just a feeling. It probably develops early and hard because it is informed by the limbic and reward systems.

But 'our feeling of truth' is only an R1 event, logic does not bow to my feeling about it's validity

[Little Idiot]

LI

Your ideas go dual as soon as you say that the BM imagines the PW. Unless the BM IS the PW rather than imagines it. Which is sort of kind of what I believe.

'cept it ain't a mind it's a universe thingy.

The science of the brain does not suffer this dualism. But the science of the brain can show you why humans suffer the dualistic illusion.

But again you are just 'telling me' ie asserting this. You are not supporting this in any way I can consider; either I doff my cap and drop everything I think based on one sentence, or I have to scoff.

WHY is it a duality between a 'Big Mind' and a mental cosmos created by that mind?
A duality requires teo things of a dissimilar nature. I see only mind and its products in my model.

[Little Idiot]

This is going to take a little work. You believe the stuff out there is the mental stuff of the Big Mind. I believe it's just stuff. Lets call it Stuff and not worry about what it is. We have substance monism.

Our brain and sense are Stuff too. They interact with the Stuff to do the stuff that Stuff does. We sense the Stuff and the brain sets up in these interactive patterns with it. The brain is Stuff. The patterns are made of the same Stuff. The brain Stuff makes our body Stuff do things.

I stop at just Stuff. YOU keep adding this mind that observes the Stuff. That is a Transform from one kind to another. From process of observation to the observer. You have jumped a level somewhere inside the brain to your idea of mind.

Objection! There is no transformation involved in mind knowing thought, no duality there.

[/quote]
For you the Stuff is made of BM imaginings. BMI. BMI interacts with BMI in the PW.
[/quote]

Objection! The 'BMI' is not in the physical world; it IS the physical world. There is no physical world other than the imaginings as you are calling the ideas. The 'things' we experience are the imaginings. The interaction of the 'imaginings' IS the PW, the laws of physics which we perceive are descriptions of this interaction of imaginings.

That interaction is ensing. You then have a Transform to get the interaction of the BMI back again to your individual minds imaginings.

Not at all. Thats a strawman.
The experiences are creations of the individual mind (in the individual mind) as response to the imaginings of the Big Mind. Both the imagining and the individual mind never leave the Big Mind. There is no transformation.

If what you believe were true none of this sensing/brain shit would have any use whatever. It's BMI and our brains are bubbles in the BM so the we could DIRECTLY experience it. But we don't so you have to hand it off to the mind again.

I have answered this very objection perviously; the senses and brain/CNS are to make the world which is internal to mind be experienced as external to the body.
Both body and environment are internal to both individual and Big mind, but the environment is external to the body; without the senses and CNS this externalization is not possible.
Consider a dream; we 'see' and 'hear' in the dream, evenm though it is an imagination. We cant experience the mental world of our dream as-if external to our dream-body without the action of our dream-senses.

You still have mind containing imaginings and that is dualism. The mind is one thing and the BMI is another.

I have, in my opinion, shown why it is not dualism, and why the senses are essential for the experience of the world which is internal to mind as external to the body.