Could I have evidence for that assertion please? And not Zeno.jamest wrote:Euclid's primary claims are not observationally correct.Xamonas Chegwé wrote:I would appreciate evidence of how any of Euclid's postulates and axioms diverge from observation.jamest wrote:I don't believe that this is true. That is, I don't believe that whatever has come out of the mouths of mathematicians, or logicians, has necessarily been a consequence of 'observation'.
1. Zeno's paradoxes presume that an infinite series cannot sum to a finite amount - this is demonstrably false.
2. His paradoxes predate Euclid by over 100 years and were not based upon Euclidean axioms or techniques.
3. Zeno himself knew he was wrong, but just didn't know why. It would take over 2000 years for conclusive reasoning to solve the paradoxes.
See point 1 above. They are reducible to a false assumption.Actually, Zeno's paradoxes are reducible to a critique of the reality of space (and time).Actually, Zeno's paradoxes were derived from (faulty) logic applied to observation, not purely from logic. But continue.I only have to cite Zeno of Elea - who lived about 2500 years-ago - to lend weight to my point. He was famous for his logical parodoxes, derived purely from logic, which made claims contrary to observation!
That is as maybe. I did not dispute the point. I will reiterate, however, that Zeno's logic was faulty.Sure, including - possibly - yourself. The point was that the reality of the world might be questionable - and not, necessarily, either Zeno's or Euclid's logic.People make mistakes and use faulty logic, in other words? I doubt anyone would dispute that.Logical conclusions are not necessarily a subsequent claim of observation. That much is evident in the works of many philosophers, not just Zeno. The same applies to mathematicians.
I will assume that you are again referring to Zeno's paradoxes here when you mention this so called 'proof'. Again, they do not show anything, being based upon faulty logic, except that some falsehoods are notoriously difficult to prove wrong. I made no claims about reality. I never have done.The so-called 'proof' that Euclid's logic was wrong was [apparently] demonstrated by observation. Which actually proves nothing, since that which is observed is not known to be 'reality'.Is it? How please? And are you referring to Euclid's postulates here? Or to the logic which builds upon them to produce mathematical proofs?And, btw, Euclidean logic is not necessarily 'wrong' - it's just at-odds with how 'the world' is perceived.
Again, a case of short-sightedness and ignorance facilitating absolute judgement about absolute logic.
It was facetious, irrelevant and utterly irresistible. Mea culpa.What a Beavis and Butt-head comment that is.People are so short-sighted.
So this is an eyesight issue? Don't prescription lenses help?

You are quite right that we cannot absolutely rely on reality. To do so would require belief. However, I have never made any claim that we should. I have simply claimed that:My point has been made: the observation of something doesn't prove that the logic of something is necessarily wrong. Since we cannot know whether that which is observed is actually 'reality' itself, then we cannot say that 'logic' that aspires to be synonymous with said reality is necessarily wrong as proved by observation.
1. Euclid's axioms are compatible with observation (however flawed a view of actual reality that may be.)
2. The logic which he subsequently used to build upon those axioms was sound.
3. The results derived using those axioms and that logic also agree with observation.
Were a genuinely contradictory counter-example be shown (ie. one where no logical flaw could be shown to exist) all of Euclid's elements and most of mathematics would unravel instantly. This would demonstrate that there was a flaw in the axioms somewhere, which would indeed imply that reality was not as it was observed. This has not happened yet. As a sceptic, I cannot rule it out. I can merely invoke Occam's razor and assert that the probability of such a thing happening is extremely unlikely in my opinion.
Reality may well be an illusion but it is a remarkably persistent and internally consistent one (so far - at least.)
I have no beliefs on this issue. I am quite prepared to accept that reality could be a complete illusion and that I will awaken at any moment to find that I am a purple walrus and that the universe is merely a cage in some cosmic zoo. I would require evidence to that effect, mind you. So far, all of the evidence I have come across points in the other direction.It all boils down to a simple fact: if what we observe was 'reality', then philosophy would be obsolete. Unfortunately - with regards to your own BELIEFS on this issue - nothing confirms that what we 'observe' IS 'reality'.
Philosophy encompasses the entirety of rational thought about the world. Science and mathematics can be considered aspects of philosophy, indeed they once were. Accepting as an axiom that what we can observe actually is reality (not the same as believing - no faith required, merely a working hypothetical model) reduces philosophy to what is usually referred to as science these days. This is not negation of other possibilities, simply pragmatism, and is my preferred view of the universe until proven otherwise.
Rejecting that axiom and replacing it with an unobservable alternative admits the more speculative branches of philosophy back into the mix. These are equally valid (and often fascinating) fields of study but they are, perforce, based upon a model which is purely hypothetical as it has not been (and may never be) observed.
[/quote]Basically, I'm just calling you short-sighted.
Which is true, in a physical sense if not a metaphorical one. And reminds me that I must get my eyes tested soon. I could hope that reality is wrong and that I can actually see perfectly but I am far to blinkered by the observable to accept that I can drive safely without my glasses!

If you read what I have written here carefully, you will see that I am disagreeing with you a lot less than you imagine - solely about Zeno. I make no claims about reality and whether or not it should be accepted.