On treeness of Oak1, and other things

[Little Idiot]

Thats why you reach the self-contradictory conclusion there aint no fucking observer - the observer is a subject, not an object. The observer will never be found as an object, but the capacity for you to make the observations and state 'there aint no fucking observer' depends on you observing the observations upon which you reach your conclusion.

Subject and object are words to talk about the private nature of our experience. They aren't things in themselves. I rejected those two smelly words at 14. Haven't used them for anything in 45 years.

so you want me to believe the opinion of a 14 year old kid, who only knew science as it was known in the 60's....Right.

The science is that when these SW's are set up in the brain that there is then recognition. It goes no further than that. There is no special place in the physical brain to deliver this recognition to. It's all that is necessary to explain all of the fundamentals of how we sense, think , and behave.

You know I have great respect for science in general, and this includes neuroscience; exept on this one point - there is no physical cause for coinsciousness.
Here it is; you are saying the physical effect of SW in the brain is the recognition, i.e. this is the awareness of the experience. I ask you; so you can demonstrate that, right?
I know you can not. I know this because there is no physical cause for consciousness as SW or what ever else you guys come up with. I know this one fact despite my total lack of expertise in neuroscience.
Can you? can you demonstrate this claim that you make?
Despite my lack of neuroscience, I am sure that this simply can not be demonstrated, because it is an assumption. You can accept that if you can not demonstrate it, then its not a scientific fact? At best its a hypothesis, I say its a materialistic assumption.

If this recognition persists in some qualia space then it is a conscious percept. It is now causal in further brain activity. This be thinking and planning. It is complicated by all the other semi-persistent things present in that moment. Things such as context and unconscious priming, further sensory input, attention modulation, etc.

it is believed driven by interactions with the basal ganglia that evolved from older mechanisms that allow us to move in sequences of muscular activation.

There is no mind place to deliver this stuff to. IT HAS ALREADY ARRIVED!

It has indeed arrived, but not where you and the neuroscientists are thinking.
It has arrived at the end of the track physical track (as far as is traced at this point in time), but it is still a physical effect, an observable component of experience (ie an object) it is not yet an experience, it may be a 'physical correlate' of the experience but it may not yet be called 'an experience of the orange light'

[Little Idiot]

There aint no fucking observer

Then why do we all have a first person perspective on our own experience?
Then why are neuro scientists trying to find the 'location', or 'source' of the first person perspective?
Subject: Sense of agency is generated in the brain?
If there aint no fucking observer, there aint no fucking first person perspective, because the definition of a first person is the observer, right?

[SpeedOfSound]

Thats why you reach the self-contradictory conclusion there aint no fucking observer - the observer is a subject, not an object. The observer will never be found as an object, but the capacity for you to make the observations and state 'there aint no fucking observer' depends on you observing the observations upon which you reach your conclusion.

Subject and object are words to talk about the private nature of our experience. They aren't things in themselves. I rejected those two smelly words at 14. Haven't used them for anything in 45 years.

so you want me to believe the opinion of a 14 year old kid, who only knew science as it was known in the 60's....Right.

The science is that when these SW's are set up in the brain that there is then recognition. It goes no further than that. There is no special place in the physical brain to deliver this recognition to. It's all that is necessary to explain all of the fundamentals of how we sense, think , and behave.

You know I have great respect for science in general, and this includes neuroscience; exept on this one point - there is no physical cause for coinsciousness.
Here it is; you are saying the physical effect of SW in the brain is the recognition, i.e. this is the awareness of the experience. I ask you; so you can demonstrate that, right?
I know you can not. I know this because there is no physical cause for consciousness as SW or what ever else you guys come up with. I know this one fact despite my total lack of expertise in neuroscience.
Can you? can you demonstrate this claim that you make?
Despite my lack of neuroscience, I am sure that this simply can not be demonstrated, because it is an assumption. You can accept that if you can not demonstrate it, then its not a scientific fact? At best its a hypothesis, I say its a materialistic assumption.

If this recognition persists in some qualia space then it is a conscious percept. It is now causal in further brain activity. This be thinking and planning. It is complicated by all the other semi-persistent things present in that moment. Things such as context and unconscious priming, further sensory input, attention modulation, etc.

it is believed driven by interactions with the basal ganglia that evolved from older mechanisms that allow us to move in sequences of muscular activation.

There is no mind place to deliver this stuff to. IT HAS ALREADY ARRIVED!

It has indeed arrived, but not where you and the neuroscientists are thinking.
It has arrived at the end of the track physical track (as far as is traced at this point in time), but it is still a physical effect, an observable component of experience (ie an object) it is not yet an experience, it may be a 'physical correlate' of the experience but it may not yet be called 'an experience of the orange light'

It's an hypothesis that can be falsified and has not. It has evidence that stuffs libraries to the brim. It has plausible mechanism and predictive power.

You want proof do you? Ask your fellow metaphyscians for that.

Now what kind of isms your crap ideas are is not so important. What's important is that they have fulfilled the same criteria as mine. What can you show to be true? Or even plausible.

[SpeedOfSound]

You know I have great respect for science in general, and this includes neuroscience; exept on this one point - there is no physical cause for coinsciousness.
Here it is; you are saying the physical effect of SW in the brain is the recognition, i.e. this is the awareness of the experience. I ask you; so you can demonstrate that, right?
I know you can not. I know this because there is no physical cause for consciousness as SW or what ever else you guys come up with. I know this one fact despite my total lack of expertise in neuroscience.
Can you? can you demonstrate this claim that you make?
Despite my lack of neuroscience, I am sure that this simply can not be demonstrated, because it is an assumption. You can accept that if you can not demonstrate it, then its not a scientific fact? At best its a hypothesis, I say its a materialistic assumption.

Pretty strong claim you have there. How do you KNOW this and how can you prove it?

[Xamonas Chegwé]

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.

If, in any given reality, it is possible to conceive of a set of axioms (such as the Peano axioms) which define Natural Numbers as we know them, then Fermat's Last Theorem (and everything other mathematical theorem that is derived from those axioms) will be true in that reality.

I suppose it all comes down to how weird your absolute reality (the one outside of time) actually is. If it is so far removed from what we can observe that the laws of logic do not apply (for example, if

A = B    =/=>    B = A

in absolute reality) then Peano axioms do not hold and nothing can be known about the results based upon them.

Basically, an assumption needs to be made regarding absolute reality. It must be sufficiently like our observable reality for a set of axioms equivalent to Peano to apply. In other words, the concept of Natural Numbers must be expressible within absolute reality. But we can only guess as to its nature based upon our empirical knowledge of this reality, the observable one. So we are back to empiricism, albeit at a far more rarified level than treeness.

[Little Idiot]

Thats why you reach the self-contradictory conclusion there aint no fucking observer - the observer is a subject, not an object. The observer will never be found as an object, but the capacity for you to make the observations and state 'there aint no fucking observer' depends on you observing the observations upon which you reach your conclusion.

Subject and object are words to talk about the private nature of our experience. They aren't things in themselves. I rejected those two smelly words at 14. Haven't used them for anything in 45 years.

so you want me to believe the opinion of a 14 year old kid, who only knew science as it was known in the 60's....Right.

The science is that when these SW's are set up in the brain that there is then recognition. It goes no further than that. There is no special place in the physical brain to deliver this recognition to. It's all that is necessary to explain all of the fundamentals of how we sense, think , and behave.

You know I have great respect for science in general, and this includes neuroscience; exept on this one point - there is no physical cause for coinsciousness.
Here it is; you are saying the physical effect of SW in the brain is the recognition, i.e. this is the awareness of the experience. I ask you; so you can demonstrate that, right?
I know you can not. I know this because there is no physical cause for consciousness as SW or what ever else you guys come up with. I know this one fact despite my total lack of expertise in neuroscience.
Can you? can you demonstrate this claim that you make?
Despite my lack of neuroscience, I am sure that this simply can not be demonstrated, because it is an assumption. You can accept that if you can not demonstrate it, then its not a scientific fact? At best its a hypothesis, I say its a materialistic assumption.

If this recognition persists in some qualia space then it is a conscious percept. It is now causal in further brain activity. This be thinking and planning. It is complicated by all the other semi-persistent things present in that moment. Things such as context and unconscious priming, further sensory input, attention modulation, etc.

it is believed driven by interactions with the basal ganglia that evolved from older mechanisms that allow us to move in sequences of muscular activation.

There is no mind place to deliver this stuff to. IT HAS ALREADY ARRIVED!

It has indeed arrived, but not where you and the neuroscientists are thinking.
It has arrived at the end of the track physical track (as far as is traced at this point in time), but it is still a physical effect, an observable component of experience (ie an object) it is not yet an experience, it may be a 'physical correlate' of the experience but it may not yet be called 'an experience of the orange light'

It's an hypothesis that can be falsified and has not. It has evidence that stuffs libraries to the brim. It has plausible mechanism and predictive power.

you should, in fairness say 'has not yet'. We all know not to base our science on unproven hypothesis....
What exactly can it or has it predicted, which would not be equally be predicted by other models?
It has plausible mechanism upto the point where it makes what is essentially a leap of faith to jump from an observable object of experience (SW) into being a subjective experience. Only this part do I dispute. And that part I wager predicts nothing, has no plausible mechanism, and I am right again, despite no knowledge of the subject, huh? Funny that, musty be coincidence

You want proof do you? Ask your fellow metaphyscians for that.

Not proof, a demonstration will do. Thats all I asked for, knowing full well you would not have it, as I have been saying for a long time now...such a demonstration van not be achieved because its based on a flawed assumption.

Now what kind of isms your crap ideas are is not so important. What's important is that they have fulfilled the same criteria as mine. What can you show to be true? Or even plausible.

Ouch! I touched a nerve there huh?

Well, you see. Actually, its the other way round.
The fact that I can be so confident about what neroscience can and can not demonstrate is suporting evidence for my model of 'absolute reality'. My model has therefore demonstrable predictive powers, within space-time you see?
Because of my model, I can make accurate predictions about neuroscience not being able to do things which counter the model of reality.
Is that not plausible?

And it is completely plausible that the physical reality could be an imaginative production of a large mind in which all individual minds are in the same relation to it as waves to the ocean.

[Little Idiot]

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.

If, in any given reality, it is possible to conceive of a set of axioms (such as the Peano axioms) which define Natural Numbers as we know them, then Fermat's Last Theorem (and everything other mathematical theorem that is derived from those axioms) will be true in that reality.

I suppose it all comes down to how weird your absolute reality (the one outside of time) actually is. If it is so far removed from what we can observe that the laws of logic do not apply (for example, if

A = B    =/=>    B = A

in absolute reality) then Peano axioms do not hold and nothing can be known about the results based upon them.

Basically, an assumption needs to be made regarding absolute reality. It must be sufficiently like our observable reality for a set of axioms equivalent to Peano to apply. In other words, the concept of Natural Numbers must be expressible within absolute reality. But we can only guess as to its nature based upon our empirical knowledge of this reality, the observable one. So we are back to empiricism, albeit at a far more rarified level than treeness.

Wow.
I owe you an apology for making you think so hard!

I was, to be honest, working on a lot lower level than the response you offer, I was meaning in our reality, there are mathematical proofs (assuming axioms and logic hold) which can produce knowledge that not be demonstrated by emperical method, and there are axioms which do not depend on demonstration by observation to be true. (Such as parallel lines on a plane do not meet before infinity - we cant demonstrate that, but it could be an axiom).
The point is proven, by the accepting of Peano axioms of pure logic.
Therefore there are other ways of us knowing within our reality.


But, although this point has become something of an issue since I 'proclaimed victory' on it, since the first 4 Peano axioms are pure logic, I need not have held the battle so dear, as I too must be allowed to present an axiom of pure logic without need for empirircal evidence.

If I have not exhausted your patience, I can tell you the answer to your question about 'my' absolute reality.(I am not sure if I can ask a meaning full question of what this means for number theory, so I leave that to you - just tell me anything you can from this answer). In order to answer, I am not attempting to offer proof nor justification, so forgive my assertion, but you did ask about 'my' absolute reality so I hope I can be excused. I must however offer the first woo warning, read on at your own risk, if you are easily offended by statements unsupported by empirical evidence STOP!.

For 'absolute reality' there are no numbers because 'absolute reality' is non-dual. It is singular, in the sense of 'one without a second,' there are no things, no space no time, no form, no change. There are no laws of logic because in your example there is no A or B such that we can not even begin with A =B to consider, if

A = B    =/=>    B = A

in absolute reality. There are no words, thoughts or emotions, no goals or motives. No inside or outside of 'absolute reality'.

I did describe it in additional detail, then decided to snip it, for the sake of woo limitation damage

[SpeedOfSound]

You know I have great respect for science in general, and this includes neuroscience; exept on this one point - there is no physical cause for coinsciousness.
Here it is; you are saying the physical effect of SW in the brain is the recognition, i.e. this is the awareness of the experience. I ask you; so you can demonstrate that, right?
I know you can not. I know this because there is no physical cause for consciousness as SW or what ever else you guys come up with. I know this one fact despite my total lack of expertise in neuroscience.
Can you? can you demonstrate this claim that you make?
Despite my lack of neuroscience, I am sure that this simply can not be demonstrated, because it is an assumption. You can accept that if you can not demonstrate it, then its not a scientific fact? At best its a hypothesis, I say its a materialistic assumption.

...
It has indeed arrived, but not where you and the neuroscientists are thinking.
It has arrived at the end of the track physical track (as far as is traced at this point in time), but it is still a physical effect, an observable component of experience (ie an object) it is not yet an experience, it may be a 'physical correlate' of the experience but it may not yet be called 'an experience of the orange light'...

you should, in fairness say 'has not yet'. We all know not to base our science on unproven hypothesis....
What exactly can it or has it predicted, which would not be equally be predicted by other models?
It has plausible mechanism upto the point where it makes what is essentially a leap of faith to jump from an observable object of experience (SW) into being a subjective experience. Only this part do I dispute. And that part I wager predicts nothing, has no plausible mechanism, and I am right again, despite no knowledge of the subject, huh? Funny that, musty be coincidence
...

Not proof, a demonstration will do. Thats all I asked for, knowing full well you would not have it, as I have been saying for a long time now...such a demonstration van not be achieved because its based on a flawed assumption.
...

Ouch! I touched a nerve there huh?

Well, you see. Actually, its the other way round.
The fact that I can be so confident about what neroscience can and can not demonstrate is suporting evidence for my model of 'absolute reality'. My model has therefore demonstrable predictive powers, within space-time you see?
Because of my model, I can make accurate predictions about neuroscience not being able to do things which counter the model of reality.
Is that not plausible?

And it is completely plausible that the physical reality could be an imaginative production of a large mind in which all individual minds are in the same relation to it as waves to the ocean.

Just wanted a snapshot of this in toto.

[Xamonas Chegwé]

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.

If, in any given reality, it is possible to conceive of a set of axioms (such as the Peano axioms) which define Natural Numbers as we know them, then Fermat's Last Theorem (and everything other mathematical theorem that is derived from those axioms) will be true in that reality.

I suppose it all comes down to how weird your absolute reality (the one outside of time) actually is. If it is so far removed from what we can observe that the laws of logic do not apply (for example, if

A = B    =/=>    B = A

in absolute reality) then Peano axioms do not hold and nothing can be known about the results based upon them.

Basically, an assumption needs to be made regarding absolute reality. It must be sufficiently like our observable reality for a set of axioms equivalent to Peano to apply. In other words, the concept of Natural Numbers must be expressible within absolute reality. But we can only guess as to its nature based upon our empirical knowledge of this reality, the observable one. So we are back to empiricism, albeit at a far more rarified level than treeness.

Wow.
I owe you an apology for making you think so hard!

I don't actually find thinking hard. The hard bit is transferring that thinking into words in an ordered and unambiguous manner.

I was, to be honest, working on a lot lower level than the response you offer, I was meaning in our reality, there are mathematical proofs (assuming axioms and logic hold) which can produce knowledge that not be demonstrated by emperical method, and there are axioms which do not depend on demonstration by observation to be true. (Such as parallel lines on a plane do not meet before infinity - we cant demonstrate that, but it could be an axiom).

It is an axiom - in Euclidian geometry. Usually stated in the equivalent form that, "There exists one, and only one line that can be drawn through any point not on a line which is parallel to that line." It is a bad example though, as taking the counter-assumptions (either that there exists no line, or many lines, parallel to the first) as axioms also leads to internally consistent geometries that have real-world applications. This is the heart of non-Euclidian geometry.

The point is proven, by the accepting of Peano axioms of pure logic.
Therefore there are other ways of us knowing within our reality.

By 'the point', do you mean the parallel postulate that you just referred to? The parallel postulate cannot be proven by the first 4 Peano axioms - or even by using all of them - that is false. The Peano axioms relate to Natural Numbers, not to geometry.

Assuming that we accept mathematical theorems proved using sound logic based upon logical axioms as being different from empirical observation and not merely an extension of it (which I do not entirely concede but am happy to declare a moot point), then that, single, alternative way of knowing exists.

This cannot be extended to imply that there are any other ways of knowing without further justification. And each way of knowing requires its own evidence.

But, although this point has become something of an issue since I 'proclaimed victory' on it, since the first 4 Peano axioms are pure logic, I need not have held the battle so dear, as I too must be allowed to present an axiom of pure logic without need for empirircal evidence.

You may present as many 'axioms of pure logic' as you wish. However, be aware that the beauty and value of the Peano axioms lies in their self-evident simplicity. To argue against them, one must pretty much argue that logical thought itself has no value.

Can you claim the same about your 'axioms of pure logic'?

If I have not exhausted your patience, I can tell you the answer to your question about 'my' absolute reality.(I am not sure if I can ask a meaning full question of what this means for number theory, so I leave that to you - just tell me anything you can from this answer). In order to answer, I am not attempting to offer proof nor justification, so forgive my assertion, but you did ask about 'my' absolute reality so I hope I can be excused. I must however offer the first woo warning, read on at your own risk, if you are easily offended by statements unsupported by empirical evidence STOP!.

I am not offended at all. Why should I be? You are as entitled to your beliefs as anyone. However, I will STOP here and not address what comes after, except to say that it is unsubstantiated, illogical and ultimately meaningless. You describe a singularity where the rules of logic do not apply and call this an 'axiom of pure logic'. It is not. It is woo. It is belief. It is based upon nothing but supposition and vagueness. Sorry if that offhand dismissal offends you.



It has been nice debating with you. I hope you have enjoyed it too and maybe learned a little. I have certainly delved into areas that I have not visited for many years - hence a few contradictions, especially early on. I think I'll go and look for a thread about tits, or cheese, now. I need a little light relief.

[jamest]

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 haven't said that the experience [of motion] is an illusion. I've said that we don't know whether motion can really occur beyond its apparancy within the mind. An illusion would still be a real event happening to the mind, but the reality of that event happening beyond the mind is what is in doubt.
Likewise, the formulation of an argument is still a real event happening within the mind, so it cannot be classed as an illusion. At most, it can only be classed as an erroneous argument. Ideas cannot be illusions - they can only be right or wrong.

Again, the questionable reality of motion beyond its apparency prevents 'observation' from refuting Zeno's argument. What remains, is a capacity to utilise reason alone against Zeno's own reasoning. And that is all we can employ to refute Zeno's argument. And since reason can be used to formulate (and refute) such arguments, the conclusion is that [some] reasoning transcends observation - that some reasoning can be formulated that is not dependent upon, nor verifiable using, observation.

[SpeedOfSound]

that some reasoning can be formulated that is not dependent upon, nor verifiable using, observation.

No one here has disputed that if you and your sidekick put together axioms that are as solidly grounded as those we find in math and reasoning to the same standard that you wouldn't have an argument. It is logic after all that we attack you with.

But if you create your own abstract language description, create rigorous rules and operations for it, the results will still not escape the bounds of what you have created.

"woo-boo ?>> boo-hoo" is not particular persuasive.

R2 is a much larger system of logic and reasoning based upon the requirement of evidence by observation. I have not the background in epistemology to formally ground it or argue it. But to my knowledge nothing anyone has ever come up with has ever successfully escaped it's bounds. It encompasses us all. It seems to have as a subset the realms of math and reasoning as laid out by man and to my knowledge none of those systems have ever escaped their bounds and leapt into R2.

Zeno's Paradox strikes me as a word game with math that attempts to leap it's bounds and miserably fucking fails to do so every time a train arrives on schedule.

But lets' see what you can come up with. You and your LittleIdiot have made such a big deal of axiomatic systems that I believe you are going to wow us with such a system to prove X-God and Big Mind respectively.

I'm certain that you are also aware that what you come up with has to do a little more than be a pure axiomatic system to convince us. That would be your second step.

[SpeedOfSound]

Not an expert on Tarski either but my read of it has him proving logically that no system can be created without reference to a superset of that system. Nor can any system prove anything outside of itself.

SO. What we have here is the claim that if we make shit up it is a new way of knowing. Somehow I'm not surprised that we would have a couple of posters around here buying into that.

[SpeedOfSound]

Let this thread go to Tarski and the new way of knowing .

LI. Let's take the BM vs neuroscience discussion over here:
http://rationalia.com/forum/viewtopic.p ... 41#p398041
It's getting fucking confusing.

[GrahamH]

For 'absolute reality' there are no numbers because 'absolute reality' is non-dual. It is singular, in the sense of 'one without a second,' there are no things, no space no time, no form, no change. There are no laws of logic because in your example there is no A or B such that we can not even begin with A =B to consider, if

A = B    =/=>    B = A

in absolute reality. There are no words, thoughts or emotions, no goals or motives. No inside or outside of 'absolute reality'.

I did describe it in additional detail, then decided to snip it, for the sake of woo limitation damage

That is the ultimate self-refuting argument. You are trying to employ logic and math to reason about reality, where logic and math don;t exist. You are arguing that our experience is not any part of reality, since logic and math work here.

What you are arguing, in summary, is that there is no absolute reality (reality = nothing).

[Little Idiot]

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.

If, in any given reality, it is possible to conceive of a set of axioms (such as the Peano axioms) which define Natural Numbers as we know them, then Fermat's Last Theorem (and everything other mathematical theorem that is derived from those axioms) will be true in that reality.

I suppose it all comes down to how weird your absolute reality (the one outside of time) actually is. If it is so far removed from what we can observe that the laws of logic do not apply (for example, if

A = B    =/=>    B = A

in absolute reality) then Peano axioms do not hold and nothing can be known about the results based upon them.

Basically, an assumption needs to be made regarding absolute reality. It must be sufficiently like our observable reality for a set of axioms equivalent to Peano to apply. In other words, the concept of Natural Numbers must be expressible within absolute reality. But we can only guess as to its nature based upon our empirical knowledge of this reality, the observable one. So we are back to empiricism, albeit at a far more rarified level than treeness.

Wow.
I owe you an apology for making you think so hard!

I don't actually find thinking hard. The hard bit is transferring that thinking into words in an ordered and unambiguous manner.

I was, to be honest, working on a lot lower level than the response you offer, I was meaning in our reality, there are mathematical proofs (assuming axioms and logic hold) which can produce knowledge that not be demonstrated by empirical method, and there are axioms which do not depend on demonstration by observation to be true. (Such as parallel lines on a plane do not meet before infinity - we cant demonstrate that, but it could be an axiom).

It is an axiom - in Euclidian geometry. Usually stated in the equivalent form that, "There exists one, and only one line that can be drawn through any point not on a line which is parallel to that line." It is a bad example though, as taking the counter-assumptions (either that there exists no line, or many lines, parallel to the first) as axioms also leads to internally consistent geometries that have real-world applications. This is the heart of non-Euclidian geometry.

I used it as an example because it cant be empirically demonstrated, but can be used as a sound axiom (in Euclidian geometry). This shows an axiom not demonstrated by empirical observation, and is used specifically to show the axiom is not based on empirical observation, only that.

The point is proven, by the accepting of Peano axioms of pure logic.
Therefore there are other ways of us knowing within our reality.

By 'the point', do you mean the parallel postulate that you just referred to? The parallel postulate cannot be proven by the first 4 Peano axioms - or even by using all of them - that is false. The Peano axioms relate to Natural Numbers, not to geometry.

Sorry, bad lay out on my part. I mean the point that empiricism can not provide all knowable knowledge, therefore at least one other way of knowing must be possible.
I am not trying to prove or disprove Euclid's axioms

Assuming that we accept mathematical theorems proved using sound logic based upon logical axioms as being different from empirical observation and not merely an extension of it (which I do not entirely concede but am happy to declare a moot point), then that, single, alternative way of knowing exists.

This cannot be extended to imply that there are any other ways of knowing without further justification. And each way of knowing requires its own evidence.

Agreed. Any other method needs to be proved, this does not validate my dreams as statements of reality
But it does prove empiricism is not enough alone to know all that we do know.
It proves correct logic based on true axioms can provide knowledge without requirement of 'supporting empirical observations.'

But, although this point has become something of an issue since I 'proclaimed victory' on it, since the first 4 Peano axioms are pure logic, I need not have held the battle so dear, as I too must be allowed to present an axiom of pure logic without need for empirircal evidence.

You may present as many 'axioms of pure logic' as you wish. However, be aware that the beauty and value of the Peano axioms lies in their self-evident simplicity. To argue against them, one must pretty much argue that logical thought itself has no value.

Can you claim the same about your 'axioms of pure logic'?

I only presented one, and I think its fairly self evident. But feel free to attack it with a counter, disprove it if you wish.

If I have not exhausted your patience, I can tell you the answer to your question about 'my' absolute reality.(I am not sure if I can ask a meaning full question of what this means for number theory, so I leave that to you - just tell me anything you can from this answer). In order to answer, I am not attempting to offer proof nor justification, so forgive my assertion, but you did ask about 'my' absolute reality so I hope I can be excused. I must however offer the first woo warning, read on at your own risk, if you are easily offended by statements unsupported by empirical evidence STOP!.

I am not offended at all. Why should I be? You are as entitled to your beliefs as anyone. However, I will STOP here and not address what comes after, except to say that it is unsubstantiated, illogical and ultimately meaningless. You describe a singularity where the rules of logic do not apply and call this an 'axiom of pure logic'. It is not. It is woo. It is belief. It is based upon nothing but supposition and vagueness. Sorry if that offhand dismissal offends you.

I am not in the least offended. I did clarify exactly that it was offered as an unsupported assertion, and so your response is perfectly OK by me.
One point though; my axiom applies here in the experienced world, regards what we can say about absolute reality if there is such. It is not an axiom from within reality, it is an axiom within space time about what we can say without being in error. This is, in my humble opinion, an important point.
The axiom is not that rules of logic dont apply in reality.

It has been nice debating with you. I hope you have enjoyed it too and maybe learned a little. I have certainly delved into areas that I have not visited for many years - hence a few contradictions, especially early on. I think I'll go and look for a thread about tits, or cheese, now. I need a little light relief.

I too have enjoyed debating with you. I know we have different positions, which is the point of a debate, but we have clashed our ideas not our ego's, which is again, the point of a debate.
I have learned a great deal form our exchange, and I respect your knowledge and civilized manor of communication.
And, tits is a good enquiry, which does require empirical investigation.