On the Topic of Consciousness

[Divine Insight]

Maybe we should break this out.....

This topic is an offshoot from another thread which was on another topic altogether.

This thread is "On the Topic of Consciousness"

I wouldn't pass judgements. My biggest question is why you have a brain type that is willing to jump into the unknown with some assurance, while I seem to have a brain type that doesn't. If I don't know, I leave it at not knowing.

I don't think it comes down to just the brain alone. I think there are many other factors involved. Clearly even from a secular point of view it is recognize that the brain "evolves" as we grow as individuals based much on how we experience life, etc.

For example the very concept of the "unknown" may mean something entirely different to me than it does to you. I mean, sure we could get out a dictionary and look up the term, but that really wouldn't help much because what you believe you know and what I believe I know are going to clearly be two different things. Especially considering my last sentence of the above paragraph. Our knowledge and beliefs evolve in our own brains based upon our own experiences, which clearly are not going to be the same experiences.

Consciousness: I don't know of any scientist that makes his or her living studying it who declares they know what it is.

This is true, but there may be quite a few scientists who feel like Daniel Dennett. Even though he is just a philosopher.

[youtube][/youtube]

I don't disagree with much of what Dennett says about how the brain functions. I don't disagree at all. But he doesn't touch on the real issues as far as I'm concerned. Near the very end of the above video he state a kind of Deepity of his own, "It's not that the Emperor has no clothes, but rather the clothes have no Emperor". The idea intended to imply that we are attempting to push too much onto consciousness that doesn't need to be there.

But for me none of this is satisfying.

I don't disagree with the fact that the brain is indeed a functional portal for the experiences that we have in this incarnated life. Therefore everything he observes and states about how the brain functions and how it "creates" much of our experience, is not in question for me.

But none of that even begins to address the issue of exactly what it is that is actually having this experience. In other words, if the clothes have no Emperor, then what is it that is having an experience? The brain itself?

This becomes a problem for me, because insofar as we know, the brain itself is made of nothing more than matter and energy. If neither matter, nor energy are capable of having an experience, they why should a brain that is made of nothing more than matter and energy become an "Emperor" in its own right?

This is not an easy question, and I wouldn't hesitate to put this question to Dennett himself. In fact, I would like to hear his thoughts on this. Maybe he does address this sort of issue in one of his many lectures. If you find a lecture where he addressed this heart of the matter please share and I'll be glad to take a gander at it.

I've watched several of his lectures, and thus far I haven't been convinced of his conclusions.

To say it is supernatural vs natural seems a leap.

This is statement here goes back to what I had mentioned above, concerning how you and I may very well think differently due to our different experiences in life.

You speak of the term "supernatural" as though that's a meaningful term.

I have been a scientist my entire life. Isaac Newton, and certain Greek philosophies like Zeno and others were my childhood heroes. Albert Einstein was my next hero as I grew in my scientific knowledge. And today I hold many scientists in high regard and marvel at what they were able to discover and prove.

Just the same, in all of this, I have come to the profound realization that to date we cannot say what the true nature of reality genuinely is. Therefore does it even make any sense to speak of the supernatural, when we can't even say with certain what is natural?

So I'm not prepared to accept the insinuation that I'm "jumping off to assume something supernatural". All I'm doing is recognizing that we can't say where the boundaries of the natural world truly are.

So I don't feel that I'm actually leaping anywhere. I'm just recognizing that we can't know that things need to be restricted to what we believe to be a finite physical existence.

In fact, if you go back to Dennett's very argument perhaps you can see an irony there. He is proclaiming that we can't know nearly what we think we can know, yet he seems to think that he can make very clear conclusions from this evidence that our brains clearly trick us.

That's almost an oxymoron right there. If what Dennett says is true, that our brains can fool us considerably, then perhaps the entirety of physical reality is itself an illusion that we are being tricked into believing. What we believe to be "brains" may not be physical entities at all.

My position is that we know consciousness is affected by natural events, and we know nature exists... seems a very small slide to presume consciousness is a natural phenomenon. But not knowing, sure, I can't say it's not - but I haven't been offered ONE example of the supernatural. So, I simply can't presume it's supernatural. I can't even think of why I'd consider the supernatural when the supernatural has such a horrible track record.

Well, our difference of views here may indeed amount to the extremely different way we view the "supernatural". For you to say that the supernatural has a bad track record implies that you associate the term with just about any guess that anyone might come up with (and especially specific claims that have indeed been shown to be false).

Whilst those do indeed qualify as "supernatural", they may not qualify as the type of "supernatural" that I consider. In fact, the type of "supernatural" that I consider is actually quite natural. It simply amounts to nature that we haven't yet discovered or understood, so it's only in that sense that it seems to be supernatural to us, when in reality it may be perfectly natural.

Given this, there only seems to be the natural. Just because we don't know how consciouness works doesn't means it's because of the gods, or the supernatural or something else, or even "natural vs. I don't know".

Nature exists.
Consciousness exists.

Given these two facts, why presume we can't explain consciousness eventually?

I already gave my answer to this earlier in this post. I'll repeat it here for clarity.

Copy and pasted from earlier in this very same post:

But none of that even begins to address the issue of exactly what it is that is actually having this experience. In other words, if the clothes have no Emperor, then what is it that is having an experience? The brain itself?

This becomes a problem for me, because insofar as we know, the brain itself is made of nothing more than matter and energy. If neither matter, nor energy are capable of having an experience, they why should a brain that is made of nothing more than matter and energy become an "Emperor" in its own right?

This is not an easy question, and I wouldn't hesitate to put this question to Dennett himself. In fact, I would like to hear his thoughts on this. Maybe he does address this sort of issue in one of his many lectures. If you find a lecture where he addressed this heart of the matter please share and I'll be glad to take a gander at it.

End of copy and paste

Yes, consciousness exists. And something is having an experience.

But what is it that is having an experience?

Energy and matter?

Electromagnetic fields?

Something else? Many people have suggested that the thing that is having an experience is some sort of "emergent property of complexity".

I suppose this is a valid philosophical idea, but it seems pretty strange to me that an abstract idea of an emergent property could have an experience.

So I'm still left with a deeper mystery.

To simply say that "consciousness" is a natural result of nature, still leaves me asking, "Who is the Emperor that is having this experience?"

If the clothes have no Emperor, then what is it that is having the experience of conscious awareness? The clothes?

It just seems strange to me that the clothes (i.e. matter and energy) should be able to have an experience.

So this simply leaves the door to the "supernatural" (i.e. nature that we simply don't yet understand) wide open.

I'm not saying that the secular view is necessarily wrong. I'm simply saying that the purely secular view seems every bit as strange to me as the supernatural view.

In other words, that view doesn't "hit the spot" as being an obvious conclusion to accept either.

I'm not going to automatically accept Dennetts "Deepity" that "The clothes have no Emperor" as being the profound answer to this question. That's just as absurd as any other Deepity, IMHO.

So this is where I'm coming from.

I'm not claiming that the supernatural necessarily has to exist. But I am claiming that, insofar as I can see, it's on precisely equal footing with any other conclusions at this point.

Seeing that they are on the same footing, I don't mind using intuition and gut feelings to consider one over the other. So with that in mind, I confess that I lean toward the mystical view. But clearly I could be wrong.

[micatala]

I asked you for a scientific journal. You offered me a math theorem. You said you reject math, so how can you offer this. Besides if Bell's theorem disproves determinism, then it is self refuting since you can not use math in a situation of non-determinism.

I never said that I reject math. That's your misunderstanding.

I simply said, "If modern mathematics is supposed to correctly describe the quantitative nature of the universe, then modern mathematics is wrong."

And I made it clear in several posts that by modern I'm talking about mathematics invented since the 17th century and in particular with respect to the work of Georg Cantor and modern ideas of set theory.

Georg Cantor's work might be somewhat esoteric, but it is well-accepted mathematics and is entirely logically sound. Can you explain what issues you have with Cantor's work? Do you object to his hierarchies of infinity? Do you have issues with uncountably infinite nowhere dense sets?

Besides, if you do not reject that math, then you are stuck with Bell's Theorem. And keep in mind that Bell's Theorem is a theorem not a theory. In other words it has been recognize to be mathematically sound and true.

Yes, Bell's Theorem is valid, just as Cantor's work is valid. However, I am not sure the implications you are drawing from Bell's Theorem are valid.

"If modern mathematics correctly describes the quantitative nature of the universe, then Bell's Theorem proves that science has come to a dead end."

Here are a couple of sources on Bell's Theorem.

http://plato.stanford.edu/entries/bell-theorem/

http://www.felderbooks.com/papers/bell.html

The latter includes the following. Is this what you are referring to when you say Bell's Theorem implies science has come to a dead end?

Almost thirty years later J.S. Bell proved that the results predicted by quantum mechanics could not be explained by any theory which preserved locality. In other words, if you set up an experiment like that described by Einstein, Podolsky, and Rosen, and you get the results predicted by quantum mechanics, then there is no way that locality could be true. Years later the experiments were done, and the predictions of quantum mechanics proved to be accurate. In short, locality is dead.

Perhaps you can provide a source for your view. Your claim here seems to be completely unfounded.

So all I'm saying is that science that continues to rely on modern mathematics is indeed dead in the water (proven by Bell's Theorem) and the Heisenberg Uncertain Relationship. Science cannot move forward until it goes back and corrects the errors that were introduced into mathematical formalism in the the 17th century.

What alleged errors are you referring to????

[Divine Insight]

The latter includes the following. Is this what you are referring to when you say Bell's Theorem implies science has come to a dead end?

Almost thirty years later J.S. Bell proved that the results predicted by quantum mechanics could not be explained by any theory which preserved locality. In other words, if you set up an experiment like that described by Einstein, Podolsky, and Rosen, and you get the results predicted by quantum mechanics, then there is no way that locality could be true. Years later the experiments were done, and the predictions of quantum mechanics proved to be accurate. In short, locality is dead.

Perhaps you can provide a source for your view. Your claim here seems to be completely unfounded.

Yes, that's a good source right there. Locality is dead. That's certainly one aspect of QM that defies scientific explanation. Science is entirely dependent upon locality being true. Take away locality and you mess with cause and effect in major ways.

But that's not all that QM predicts. That's simply what Bell's Theorem has shown to be true from the phenomenon of entanglement. What actually killed science even before that was Heisenberg's Uncertainty Principle. This is what blew Einstein away. Niels Bohr accepted the Uncertainty Principle and rephrased it in terms of "complementarity". Which is a good intuitive way of thinking about it. Although, it's only intuitive if we abandon the ability to divide things up infinitely which is permitted in Modern Day Mathematics. So it's actually the mathematics that's falling apart here in terms of being able to correctly describe physical reality.

Georg Cantor's work might be somewhat esoteric, but it is well-accepted mathematics and is entirely logically sound. Can you explain what issues you have with Cantor's work? Do you object to his hierarchies of infinity? Do you have issues with uncountably infinite nowhere dense sets?

Yes, I have many issues with Cantor's work. And I fully understand why he has created these problems. He's looking at numbers entirely abstractly beyond their actual physical meaning of quantity. There are many problems with Cantor's work. It seriously amazes me that the mathematicians haven't realized the folly of Cantor's methods. I've lost my faith in the mathematical community for not recognizing the flaws in Cantor's work. It's their JOB to expose these flaws. And they aren't doing their job, instead they worship Cantor like as if he's a God.

What alleged errors are you referring to????

Well, for one thing, Cantor's diagonalization "proof" is not a proof at all. On the contrary it's extremely logically flawed. Yet it's published in every math textbook in the world. A totally false proof being held out as if it's absolute undeniable truth. Cantor assumes that these decimal digits can be lined up in a SQUARE, which is impossible. That right there proves that Cantor's "proof" is logically flawed.

But really we can't blame Cantor for this entire mess, at the time that Cantor proposed his ideas there were other mathematicians who were trying to propose the CORRECT ideas, but unfortunately they didn't fully understand how to present their ideas convincingly and ended up losing to Cantor.

I'm not the only one who has recognized this. There are other famous mathematicians. In fact, here's what Henri Poincare had to say about Cantor's set theory.

"Georg Cantor's set theory of transfinite numbers is disease from which mathematics would eventually be cured" - Henri Poincare

I totally agree. It's only a matter of time. But it doesn't appear that it's going to be anytime soon because mathematicians seem to have fallen in love with this disease.

Think about it. Georg Cantor is the only person in all of history to start with nothing (an empty set) and end up with more than everything (i.e. Infinities larger than infinity).

It's also totally unnecessary. We simply don't need this baloney to explain things. It's also wrong. It's wrong in the sense of not properly reflecting the true quantitative nature of the physical universe.

The universe is QUANTUM. It's discrete. We now know that we live in a Quantum Universe.

This goes way back to the ancient Greeks. Leucippus first recognize that the world must be made of "atoms" (individual pieces). Which we now know is true via Quantum Mechanics.

Zeno also figured out that the world had to be discrete because in a continuum motion could not be possible. And clearly we can move. So reality must be discreet. And he was right. We now know that he was right. Quantum Mechanics tells us so.

Cantor's work is entirely based on the idea of a continuum, that you can just keep dividing things up with no reason to ever stop. But that's not how the real universe works. That does not correctly describe the quantitative truth of the universe.

This problem actually arose in ancient Greece as well, with the discovery that the square root of 2 is an irrational "number". And this was believed to measure a "distance" that had to be "real". But that was a wrong notion as well. Same is true of a number like Pi. Pi is not a cardinal number. It's just a relative relationship and therefore cannot be thought of in terms of "Set Theory".

We don't need irrational "Cardinal Numbers". On the contrary until we recognize that all irrational numbers that arise are actually the results of a self-referenced relative situation we will forever stand in awe of irrational "quantities". How can they exist? Well, in truth, they don't! They don't exist in our physical universe. And Quantum Mechanics is the proof of this.

In fact, Pi is entirely dependent upon flat or Euclidean geometry. Pi isn't even a constant when considering other types of geometries. It's a relative property of Euclidean geometry.

Apparently it's going to take the mathematical community quite a few more decades or more to actually realize the mistakes they have made by embracing Cantor's work without stopping to truly think about why it is flawed.

If aliens came here from another planet I seriously doubt that they would view mathematics in the same way we do. They would probably be aware of the true quantitative nature of the universe.

In fact, I doubt that we're going to make too much more progress until we realize that folly that the mathematical community has accepted.

Cantor's Set Theory is ridiculous. And his denationalization proof is clearly false. But that's really beside the point, because we don't need to "cardinalize" irrational numbers. That was our real mistake. If we would have recognize them for what they truly are right off the bat we'd be much further ahead.

Now we have truly absurd things like larger and smaller infinities.

That's absurd. Infinity only needs to mean "Endless". That's all it needs to mean. And for something to be "more endless" than something else that is already "endless" is itself absurd.

Ironically mathematicians claim to honor "Proof by Contradiction". If you can show that a logical reasoning leads to an absurdity that is accepted as "Proof by Contradiction".

Well, any mathematics that states that there can be a larger infinity than endlessness, is itself utterly absurd. So Cantor's whole set theory is clearly false because it can be shown to be false by "Proof by Contradiction".

Why mathematicians can't see this is beyond me.

I can prove that Cantor's diagonalization proof is logically impossible too. It's logically flawed. In fact, it's absurdly flawed. I can't believe that no mathematician has yet caught it.

[keithprosser3]

I hadn't noticed that you, DI, are not exactly shy about criticising the mental capacities of mathematicians. But I think it may not be the mathematicians at fault.

The point about mathematics (or pure mathematics) is that it has nothing to do with physical reality, except perhaps by accident. Ignoring Cantor's hierarchy of infinities, the notion of infinity is already non-physical. But even finite numbers aren't physical objects. You can divide a number by 2 as many times as you like and you still have a number, but 'everybody knows' that matter isn't like that, and maybe even time can't be chopped up into ever finer divisions forever.

Cantor's work is mathematics, not physics. As a physical theory Cantor's work is absurd and even rather amusing (ok, only if you have a warped sense of humour), but as pure mathematics, it's fine.

[olavisjo]

[Replying to post 291 by Divine Insight]

I see a lot of criticism but very little for instance. Would you be willing to give us one example, or are you going to save it for the mathematics journals.

You may post your response here...

http://debatingchristianity.com/forum/v ... 638#606638

[Divine Insight]

I hadn't noticed that you, DI, are not exactly shy about criticising the mental capacities of mathematicians. But I think it may not be the mathematicians at fault.

The point about mathematics (or pure mathematics) is that it has nothing to do with physical reality, except perhaps by accident. Ignoring Cantor's hierarchy of infinities, the notion of infinity is already non-physical. But even finite numbers aren't physical objects. You can divide a number by 2 as many times as you like and you still have a number, but 'everybody knows' that matter isn't like that, and maybe even time can't be chopped up into ever finer divisions forever.

Cantor's work is mathematics, not physics. As a physical theory Cantor's work is absurd and even rather amusing (ok, only if you have a warped sense of humour), but as pure mathematics, it's fine.

I agree, it's not really the fault of mathematicians because they actually strove to create a totally "Abstract" concept of mathematics that is divorced from the things that are being quantified. Ironically though, this actually destroys the very notion of quantity and renders it meaningless.

Yes, you are right that mathematics is not physics. And that is precisely my point. It should be physics, and far more importantly it CAN be physics if handled correctly. And that's where the problem is. It wasn't handled correctly.

I'll post more in the thread started by Olavisjo, here:

A New Math: Where Our Understanding is Wrong

[JohnA]

I hadn't noticed that you, DI, are not exactly shy about criticising the mental capacities of mathematicians. But I think it may not be the mathematicians at fault.

The point about mathematics (or pure mathematics) is that it has nothing to do with physical reality, except perhaps by accident. Ignoring Cantor's hierarchy of infinities, the notion of infinity is already non-physical. But even finite numbers aren't physical objects. You can divide a number by 2 as many times as you like and you still have a number, but 'everybody knows' that matter isn't like that, and maybe even time can't be chopped up into ever finer divisions forever.

Cantor's work is mathematics, not physics. As a physical theory Cantor's work is absurd and even rather amusing (ok, only if you have a warped sense of humour), but as pure mathematics, it's fine.

I agree, it's not really the fault of mathematicians because they actually strove to create a totally "Abstract" concept of mathematics that is divorced from the things that are being quantified. Ironically though, this actually destroys the very notion of quantity and renders it meaningless.

Yes, you are right that mathematics is not physics. And that is precisely my point. It should be physics, and far more importantly it CAN be physics if handled correctly. And that's where the problem is. It wasn't handled correctly.

I'll post more in the thread started by Olavisjo, here:

A New Math: Where Our Understanding is Wrong

Math is just a 'tool' used by science, it is one of the languages of science.
"If all of mathematics disappeared, physics would be set back by exactly one week."
Richard P. Feynman (1918 - 1988)

btw Georg Cantor reserved Absolute infinity for his god. And Cantor said that absolute infinity has math properties. Absurd. But he did give a way to deal with infinities which seems to work, even though he never really mentioned potential or actual infinity.

[micatala]

The latter includes the following. Is this what you are referring to when you say Bell's Theorem implies science has come to a dead end?

Almost thirty years later J.S. Bell proved that the results predicted by quantum mechanics could not be explained by any theory which preserved locality. In other words, if you set up an experiment like that described by Einstein, Podolsky, and Rosen, and you get the results predicted by quantum mechanics, then there is no way that locality could be true. Years later the experiments were done, and the predictions of quantum mechanics proved to be accurate. In short, locality is dead.

Perhaps you can provide a source for your view. Your claim here seems to be completely unfounded.

Yes, that's a good source right there. Locality is dead. That's certainly one aspect of QM that defies scientific explanation. Science is entirely dependent upon locality being true.

Really??? I think you are making a hugely generalized and unsubstantiated statement here. You seem to be engaged in a huge false dichotomy.

Science in the large, at scales larger than the quantum scale, might be perfectly sound without even considering the issues regarding locality brought up by Bell's Theorem. If locality is dead on the quantum scale, that does not negate what science claims at larger scales.



I think your entire argument falls apart on the basis of this one fallacy.

Take away locality and you mess with cause and effect in major ways.

Again, perhaps this is true on quantum scales. It does not follow that Bell's THeorem negates all cause and effect arguments in science.

But that's not all that QM predicts. That's simply what Bell's Theorem has shown to be true from the phenomenon of entanglement. What actually killed science even before that was Heisenberg's Uncertainty Principle. This is what blew Einstein away. Niels Bohr accepted the Uncertainty Principle and rephrased it in terms of "complementarity". Which is a good intuitive way of thinking about it. Although, it's only intuitive if we abandon the ability to divide things up infinitely which is permitted in Modern Day Mathematics. So it's actually the mathematics that's falling apart here in terms of being able to correctly describe physical reality.

You are confusing the logical validity of mathematics with its applicability in modeling the physical world. Infinite divisibility is quite logically sound as a mathematical concept, and the modern mathematics of real analysis and its extension in Cantor's set theory and Lebesgue's work regarding measureable sets is as well. Whether physical reality is or is not infinitely divisible is irrelevant to mathematics.


So, no, mathematics is not falling apart. What might be in question is the applicability of certain mathematical concepts to the real world, but that issue is not a new one. It certainly predates what you are counting here as "modern mathematics."

Georg Cantor's work might be somewhat esoteric, but it is well-accepted mathematics and is entirely logically sound. Can you explain what issues you have with Cantor's work? Do you object to his hierarchies of infinity? Do you have issues with uncountably infinite nowhere dense sets?

Yes, I have many issues with Cantor's work. And I fully understand why he has created these problems. He's looking at numbers entirely abstractly beyond their actual physical meaning of quantity.

He is generalizing from what might be called the experiential basis for the concept of number, yes. Again, this is hardly new. Legend has it that the Pythagoreans did away with the first person to realize that irrational numbers existed. Are we going to throw out irrational numbers because they somehow do not exist in the real world?

How about complex numbers? Do we throw those out because they are 'unreal?' Does that unreality negate all the concrete applications of complex numbers in electricity and physics?

There are many problems with Cantor's work. It seriously amazes me that the mathematicians haven't realized the folly of Cantor's methods. I've lost my faith in the mathematical community for not recognizing the flaws in Cantor's work. It's their JOB to expose these flaws. And they aren't doing their job, instead they worship Cantor like as if he's a God.

Well, feel free to share what you think are the flaws with Cantor's work.

What alleged errors are you referring to????

Well, for one thing, Cantor's diagonalization "proof" is not a proof at all.

Actually, it is completely logically sound. It is perhaps counterintuitive to the layperson, and it does depend implicitly on the so-called Axiom of Choice, but, just like your discussion of 'conditional statements' in the other thread, if you accept the infinite version of the Axiom of Choice, the proof is completely fine.

On the contrary it's extremely logically flawed. Yet it's published in every math textbook in the world.

It is typically only published in books designed for senior level math majors or graduate students, or you can find versions in a few 'popular' books on the infinite.

A totally false proof being held out as if it's absolute undeniable truth. Cantor assumes that these decimal digits can be lined up in a SQUARE, which is impossible. That right there proves that Cantor's "proof" is logically flawed.

Cantor's proof does make use of what might be termed an infinite matrix. Perhaps this is what you mean by 'squareness.' You are simply incorrect to assert that such a mathematical structure is impossible.



Let me ask you this.

Would you agree that

1 + 1/2 + 1/4 + 1/8 + 1/16 + . . . . = 2?


If not why not? If you do agree, why are you not concerned about the infinitude of the series?

But really we can't blame Cantor for this entire mess, at the time that Cantor proposed his ideas there were other mathematicians who were trying to propose the CORRECT ideas, but unfortunately they didn't fully understand how to present their ideas convincingly and ended up losing to Cantor.

I assume you are referring to Kronecker. Feel free to share what you think are the 'correct' ideas.

I'm not the only one who has recognized this. There are other famous mathematicians. In fact, here's what Henri Poincare had to say about Cantor's set theory.

"Georg Cantor's set theory of transfinite numbers is disease from which mathematics would eventually be cured" - Henri Poincare

Did Cantor's work engender opposition and ridicule? Yes. Can you find an example where Poincare or anyone else proved Cantor's ideas logically invalid????

Consider that one can find similar statements ridiculing complex numbers, and even negative numbers made at the time those numbers were coming into use through innovative mathematicians.

I totally agree. It's only a matter of time. But it doesn't appear that it's going to be anytime soon because mathematicians seem to have fallen in love with this disease.

This is like creationists insisting that any minute now, the scientific community is going to come to its senses and throw out the Theory of Evolution.

Think about it. Georg Cantor is the only person in all of history to start with nothing (an empty set) and end up with more than everything (i.e. Infinities larger than infinity).

Not true. You might look up the work of Peano and others who created a logically sound basis for nothing more complicated than the natural numbers and the integers.

It's also totally unnecessary. We simply don't need this baloney to explain things.

Well, I'll grant you that Cantor's work, at least to my knowledge, is not used as the foundation for any great mathematical explanation of physical phenomenon, but again, that does not mean it is baloney. For a long time, there was no physical application for the infinitude of the prime numbers, even though Euclid has a proof of it in his Elements from around 300 B.C.

Today, the infinitude of primes is foundational to maintaining all kinds of internet security.


So, perhaps you should avoid the blanket condemnation of the applicability of "modern mathematics." It could easily be (the idea of quantum computers comes to mind) that this mathematics will some day be foundational to a great advance in technology, as yet undreamed of. There are quite a few precedents for this, including the one I just mentioned.

It's also wrong. It's wrong in the sense of not . . .

This continues you fallacy of thinking everything in mathematics has to correspond to physical reality.


That is a huge philosophical assumption that is typically not made by either mathematicians nor physicists. If this is your belief, it is no wonder you are misunderstanding what counts as valid mathematics.

The universe is QUANTUM. It's discrete. We now know that we live in a Quantum Universe.

I think you are probably right. However, this is irrelevant to your claims about mathematics in general and Cantor in particular. Consider that Cantor's system INCLUDES the notion of discrete sets, both finite and infinite.


Again, consider that the universe, as far as we know, is FINITE.

Following your logic, we should throw out Isaac Newton's Calculus because it involves infinities. Keep in mind calculus (which Newton referred to as fluxions) was mocked in its day. One Bishop Berkeley referred to it as the use of "the ghosts of departed quantities."

Zeno also figured out that the world had to be discrete because in a continuum motion could not be possible. And clearly we can move. So reality must be discreet. And he was right. We now know that he was right. Quantum Mechanics tells us so.

In that case, you need to throw out calculus, which was a product of the 17th century. This would mean you cannot fly space-ships to the moon, or design earth-orbiting satellites, or any of a hundred other things we actually do each day. Your insistence that mathematics has to coincide with the real-world is eventually going to end up snuffing a large part of present day civilization completely out of existence at this rate.

Cantor's work is entirely based on the idea of a continuum, that you can just keep dividing things up with no reason to ever stop. But that's not how the real universe works. That does not correctly describe the quantitative truth of the universe.

Newton's work also depends on the notion of a continuum. He himself did not fully understand the logical underpinnings of the continuum, that would come later with the work of Cauchy, Riemann, and yes, Cantor.

Do you really want to tell us that calculus is "wrong" and we should discard it as a disease, or at least a precursor to the disease you objected to above?

This problem actually arose in ancient Greece as well, with the discovery that the square root of 2 is an irrational "number". And this was believed to measure a "distance" that had to be "real". But that was a wrong notion as well. Same is true of a number like Pi. Pi is not a cardinal number. It's just a relative relationship and therefore cannot be thought of in terms of "Set Theory".

We don't need irrational "Cardinal Numbers". On the contrary until we recognize that all irrational numbers that arise are actually the results of a self-referenced relative situation we will forever stand in awe of irrational "quantities". How can they exist? Well, in truth, they don't! They don't exist in our physical universe. And Quantum Mechanics is the proof of this.

Well, I see that you really do seem intent on abolishing not only Cantor, but also Newton and even the notion of irrational numbers.




Again, it all boils down to your thinking that mathematics that does not have an exact parallel in the physical world is some how erroneous.

This is an incorrect notion, and certainly not one that mathematicians, nor in general other scientists, share.


Most scientists take mathematical models to be useful as approximations or simplifications of reality or a portion of reality. They do not think of mathematics' relation to the real world in the way you are taking it.

In fact, Pi is entirely dependent upon flat or Euclidean geometry. Pi isn't even a constant when considering other types of geometries. It's a relative property of Euclidean geometry.

True. In hyperbolic or elliptical geometry, you would not have Pi as we know it. Mathematicians well understand this.

If aliens came here from another planet I seriously doubt that they would view mathematics in the same way we do. They would probably be aware of the true quantitative nature of the universe.

If aliens make it to our planet, I am quite sure they will have some understanding of notions that are equivalent to Newton's calculus at the very least. They wouldn't be able to make it here otherwise.

Cantor's Set Theory is ridiculous. And his denationalization proof is clearly false.

Well, it might be best left to another thread, but I would be happy to step you through the (I think you mean diagonalization?) proof if you wish.

Now we have truly absurd things like larger and smaller infinities.

That's absurd. Infinity only needs to mean "Endless". That's all it needs to mean. And for something to be "more endless" than something else that is already "endless" is itself absurd.

It may be mind-bending, but the idea of larger and smaller infinities is on a completely sound logical basis.

Ironically mathematicians claim to honor "Proof by Contradiction". If you can show that a logical reasoning leads to an absurdity that is accepted as "Proof by Contradiction".

Do you realize that Euclid makes extensive use of proof by contradiction?

Well, any mathematics that states that there can be a larger infinity than endlessness, is itself utterly absurd. So Cantor's whole set theory is clearly false because it can be shown to be false by "Proof by Contradiction".

Really?? I would be open to seeing your proof by contradiction that Cantor's Set Theory is false.

Why mathematicians can't see this is beyond me.

I can prove that Cantor's diagonalization proof is logically impossible too. It's logically flawed. In fact, it's absurdly flawed. I can't believe that no mathematician has yet caught it.

Please share your proof.

[Divine Insight]

Really??? I think you are making a hugely generalized and unsubstantiated statement here. You seem to be engaged in a huge false dichotomy.

Science in the large, at scales larger than the quantum scale, might be perfectly sound without even considering the issues regarding locality brought up by Bell's Theorem. If locality is dead on the quantum scale, that does not negate what science claims at larger scales.

I think your entire argument falls apart on the basis of this one fallacy.

Where did I ever suggest that science is wrong at larger scales?

I think you are the one who is pushing a lot of your own incorrect assumptions onto what I'm actually saying.

However, along these same lines it is incorrect to believe that there are two entirely different physical realities (i.e. the quantum world and the macro world).

Almost any modern physicist will tell you that this is now the case. There is only one physics, and quantum physics appears to be it. The macro world can be explained in terms of the laws of quantum physics. The opposite is not true.

Moreover, all of the phenomenon of the macro world, including a consistent macro causality and even an apparent one-way entropy can be explained in terms of Quantum Mechanics. Although something that has not yet been explained is why entropy started off so low to begin with. But there are credible theories as to why this might have been the case.

Take away locality and you mess with cause and effect in major ways.

Again, perhaps this is true on quantum scales. It does not follow that Bell's THeorem negates all cause and effect arguments in science.

I never said that it did. Where did I ever make that claim? All I'm saying is that the scientific method of relying upon clear-cut cause and effect cannot be carried into the quantum realm. That's all I'm saying.

Nowhere have I ever claimed that local cause and effect cannot apply to macro events.

So you're arguing against a misunderstanding of my position.

But that's not all that QM predicts. That's simply what Bell's Theorem has shown to be true from the phenomenon of entanglement. What actually killed science even before that was Heisenberg's Uncertainty Principle. This is what blew Einstein away. Niels Bohr accepted the Uncertainty Principle and rephrased it in terms of "complementarity". Which is a good intuitive way of thinking about it. Although, it's only intuitive if we abandon the ability to divide things up infinitely which is permitted in Modern Day Mathematics. So it's actually the mathematics that's falling apart here in terms of being able to correctly describe physical reality.

You are confusing the logical validity of mathematics with its applicability in modeling the physical world. Infinite divisibility is quite logically sound as a mathematical concept, and the modern mathematics of real analysis and its extension in Cantor's set theory and Lebesgue's work regarding measureable sets is as well. Whether physical reality is or is not infinitely divisible is irrelevant to mathematics.

That's correct, in terms of our current mathematical formalism.

I won't argue with that. In fact, I won't even argue that those types of mathematical investigations are necessarily useless. They may indeed be useful. But thinking that these ideas actually stem from the original quantitative properties of the universe (the foundation of the birth of mathematical inquiry) is simply wrong. We would simply be better off understanding why and how these type of logical inquiries differ.

That's all I'm saying.

So, no, mathematics is not falling apart. What might be in question is the applicability of certain mathematical concepts to the real world, but that issue is not a new one. It certainly predates what you are counting here as "modern mathematics."

Yes, it does predate what I'm talking about. But I think you need to understand that these ideas weren't "formalized" until the formal introduction of the empty set by Georg Cantor. Prior to this these ideas were entirely viewed as intuitive and potentially even "self-evident'. But not formally defined. And therein lies the difference.

He (Cantor) is generalizing from what might be called the experiential basis for the concept of number, yes. Again, this is hardly new. Legend has it that the Pythagoreans did away with the first person to realize that irrational numbers existed. Are we going to throw out irrational numbers because they somehow do not exist in the real world?

Yes. We must throw out the concept of irrational "number" especially in a cardinal sense. Does this mean that we can't still recognize these relative quantitative relationships? No it doesn't mean that at all. On the contrary it's actually quite enlightening the moment we realize that they aren't cardinal numbers. We suddenly realized that all irrational relative quantities are indeed just that, as well as being caused by self-referenced situations. Something that current mathematicians aren't even aware of because they are trying to treat irrational relative relationships as thought they can be treated as cardinal ideas of number.

And that is one of the many things that comes out of making this correction.

How about complex numbers? Do we throw those out because they are 'unreal?' Does that unreality negate all the concrete applications of complex numbers in electricity and physics?

Absolutely not. In fact complex numbers are indeed cardinal quantities, at least when their aren't irrational. There is no problem with complex numbers. All we need to do is recognize that the i is a vector sign not unlike the negative sign.

There are many problems with Cantor's work. It seriously amazes me that the mathematicians haven't realized the folly of Cantor's methods. I've lost my faith in the mathematical community for not recognizing the flaws in Cantor's work. It's their JOB to expose these flaws. And they aren't doing their job, instead they worship Cantor like as if he's a God.

Well, feel free to share what you think are the flaws with Cantor's work.

The very concept of an "empty set" is a logical contradiction to the very meaning of a set. A set is a collection of things. An empty set would be a collection of things that does not contain a thing. That's an oxymoron. Moreover, it introduces a phantom property for a set (i.e. for the empty set) that has no quantitative meaning whatsoever.

Zero is not an empty set. It's the absence of a set. A totally different concept.

And this is paramount because Cantor needs his empty set that is not the collection of any thing because he's going to start treating it as though it is a THING.

And that is the root of all his problems, and precisely why he ends up with infinities that are greater than infinite. Collections of things that contain more than an endless quantity of elements.

These are absurdities.

What alleged errors are you referring to????

Well, for one thing, Cantor's diagonalization "proof" is not a proof at all.

Actually, it is completely logically sound. It is perhaps counterintuitive to the layperson, and it does depend implicitly on the so-called Axiom of Choice, but, just like your discussion of 'conditional statements' in the other thread, if you accept the infinite version of the Axiom of Choice, the proof is completely fine.

No it's flawed because in order to work it must be square, I can prove why it can't be square.

On the contrary it's extremely logically flawed. Yet it's published in every math textbook in the world.

It is typically only published in books designed for senior level math majors or graduate students, or you can find versions in a few 'popular' books on the infinite.

Sure, it's considered "Higher Level Math", but its still based on a logical flaw. Cantor's proof requires that his list be square. But that's impossible and I can prove it.

A totally false proof being held out as if it's absolute undeniable truth. Cantor assumes that these decimal digits can be lined up in a SQUARE, which is impossible. That right there proves that Cantor's "proof" is logically flawed.

Cantor's proof does make use of what might be termed an infinite matrix. Perhaps this is what you mean by 'squareness.' You are simply incorrect to assert that such a mathematical structure is impossible.

I can prove that Cantor's diagonalization argument is logically flawed. It has to be square in order to work, and I can easily prove why it can't be square.

Let me ask you this.

Would you agree that

1 + 1/2 + 1/4 + 1/8 + 1/16 + . . . . = 2?

If not why not? If you do agree, why are you not concerned about the infinitude of the series?

I have no problem with this because to begin with this mathematical statement assumes that this process could be carried out to infinity. It's merely stating that the quantity on the left is equivalent to the quantity on the right. It is NOT saying that you could actually complete this addition.

But really we can't blame Cantor for this entire mess, at the time that Cantor proposed his ideas there were other mathematicians who were trying to propose the CORRECT ideas, but unfortunately they didn't fully understand how to present their ideas convincingly and ended up losing to Cantor.

I assume you are referring to Kronecker. Feel free to share what you think are the 'correct' ideas.

No, I was actually referring to Giuseppe Peano. Kronecker also rejected Cantor's ideas of completed infinities, but to my knowledge he never really offered a better way to define numbers.

Kronecker did say, "God created the Integers the rest is the word of man".

In some ways I agree with. Although there's no need to bring any God into it. He could have better said, "The universe reveals integer quantities the rest is the work of man". And he would have been right.

We created the irrational "cardinal numbers" by failing to recognize them for the self-referenced relative quantities that they actually are.

I'm not the only one who has recognized this. There are other famous mathematicians. In fact, here's what Henri Poincare had to say about Cantor's set theory.

"Georg Cantor's set theory of transfinite numbers is disease from which mathematics would eventually be cured" - Henri Poincare

Did Cantor's work engender opposition and ridicule? Yes. Can you find an example where Poincare or anyone else proved Cantor's ideas logically invalid????

No unfortunately I can't find any examples where other mathematicians have stepped up to the plate. But I can prove that Cantor's ideas are logically invalid, and that's good enough for me.

Consider that one can find similar statements ridiculing complex numbers, and even negative numbers made at the time those numbers were coming into use through innovative mathematicians.

We don't need either. Both complex numbers and negative numbers can be easily shown to be just cardinal quantities that have a specific spacial orientation.

No we don't need negative "numbers" and we don't need "complex" or "imaginary" numbers. All we need is negative vectors and imaginary vectors.

In fact, I can easily show why both negativity and the imaginary property of numbers are NOT absolute cardinal properties of sets but rather they are relative properties between different sets.

In fact, the mathematical community has actually dealt with this by using the Absolute Function. But we never needed to define negative numbers and complex numbers in the first place. They have always been relative VECTORS not absolute cardinal quantities.

So yes, those were mistakes that were made eons ago. But they are rather trivial mistakes because we have actually recognized that they are vectors unofficially anyway. The silly thing is that we continue to treat them as though they are absolute numbers in their own right. That's simply not necessary for mathematics to work.

I totally agree. It's only a matter of time. But it doesn't appear that it's going to be anytime soon because mathematicians seem to have fallen in love with this disease.

This is like creationists insisting that any minute now, the scientific community is going to come to its senses and throw out the Theory of Evolution.

Not even close. The Theory of Evolution is rock solid. Cantor's empty set theory is extremely logically flawed. Why mathematicians ever embraced it in the first place is beyond me.

Think about it. Georg Cantor is the only person in all of history to start with nothing (an empty set) and end up with more than everything (i.e. Infinities larger than infinity).

Not true. You might look up the work of Peano and others who created a logically sound basis for nothing more complicated than the natural numbers and the integers.

Peano's original work did not require infinities larger than infinity.

It's also totally unnecessary. We simply don't need this baloney to explain things.

Well, I'll grant you that Cantor's work, at least to my knowledge, is not used as the foundation for any great mathematical explanation of physical phenomenon, but again, that does not mean it is baloney. For a long time, there was no physical application for the infinitude of the prime numbers, even though Euclid has a proof of it in his Elements from around 300 B.C.

Today, the infinitude of primes is foundational to maintaining all kinds of internet security.

But now you are talking about security and information encryption. This is actually quite different from the original idea of quantities.

In fact, this is precisely why I'm saying that mathematics needs to address these issues. It will actually be in their favor to recognize when they are addressing concepts of quantity, and when they are addressing other totally unrelated ideas.

In fact, think about it. Boolean algebra is considered to be part of mathematics. But doe s Boolean algebra have anything at all to do with cardinal quantities? No, it doesn't. It has to do with how logic gates behave. It shouldn't even be placed under the umbrella of "Mathematics". It's a totally different thing. I'm not saying that Boolean algebra has no place. Of course it has a place. It's the foundation of all modern computing. But it's not the same as the concept of quantity.

This brings up the question, "What is mathematics anyway?"

Is it the study of quantity and the relationships between quantities? Or has it just become a large academic umbrella under which to place anything that is deemed to be based on some sort of logical structure?

In fact, if the latter is true, then what is the difference between Mathematics and Logic? There is no difference at all. The Mathematical Community simply stole logic and placed it under their umbrella.

This is why I'm saying that mathematics should have stuck with the study of quantities and when other logical ideas came up they should have recognized them to be something OTHER than the study of quantities.

But now they try to just shove everything under the same umbrella.

So, perhaps you should avoid the blanket condemnation of the applicability of "modern mathematics." It could easily be (the idea of quantum computers comes to mind) that this mathematics will some day be foundational to a great advance in technology, as yet undreamed of. There are quite a few precedents for this, including the one I just mentioned.

Sure it will. Information technology will be seen as a branch of "Mathematics".

Buy why? Why not let information become it's own discipline? It may use (and indeed does use) many ideas that have nothing at all to do with ideas of quantity, and other mathematical functions.

Tossing all of this stuff under the heading of "Mathematics" only serves to dilute and confuse the actual concepts that each of these different logical formalisms represent.

But, unfortunately that's the route the Mathematical Community has chosen to take.

It's also wrong. It's wrong in the sense of not . . .

This continues you fallacy of thinking everything in mathematics has to correspond to physical reality.

I'm saying that mathematics COULD have been a legitimate SCIENCE. But instead it has taken the path into more abstract philosophical thinking that is often based on purely whimsical logic (not unlike philosophy itself).

In fact, modern mathematics has indeed become far more philosophical than scientific.

I'm saying that scientists should be concerned about this. I'm sure that mathematicians themselves couldn't give a hoot. They probably enjoy the idea that they OWN everything that has anything at all to do with LOGICAL thinking.

I'm saying that they have abandoned the physical world and they have made the turn toward pure philosophical thought.

Therefore they have abandon SCIENCE, and have become a PHILOSOPHY.

That is a huge philosophical assumption that is typically not made by either mathematicians nor physicists. If this is your belief, it is no wonder you are misunderstanding what counts as valid mathematics.

I understand what counts as "valid mathematics" in today's modern mathematical formalism. So it's not that I misunderstand it. I simply disagree with the path the mathematical community chose to take.

I don't think they did themselves any great favors.

The universe is QUANTUM. It's discrete. We now know that we live in a Quantum Universe.

I think you are probably right. However, this is irrelevant to your claims about mathematics in general and Cantor in particular. Consider that Cantor's system INCLUDES the notion of discrete sets, both finite and infinite.
[/quote

Cantor's system is totally illogical. It's based on the logically flawed notion of an "empty set". A collection of things that is not a collection of a thing. That is a logical oxymoron right there.

He creates a "phantom set" right there, and then he uses this phantom creation to build his entire set theory which leads to infinities larger than infinity (i.e. Endless collections that are more endless than other endless collections)

Cantor's work is absurd, and a logical disaster.

Again, consider that the universe, as far as we know, is FINITE.

What? To the best of my knowledge we have no clue whether the universe is finite or not.

Following your logic, we should throw out Isaac Newton's Calculus because it involves infinities. Keep in mind calculus (which Newton referred to as fluxions) was mocked in its day. One Bishop Berkeley referred to it as the use of "the ghosts of departed quantities."

I'm fully aware of the history of Newton's "vanishing quantities" and Bishop Berkeley's objections to this.

I might add a this point that Cauchy, and then later Karl Weierstrass formalized this definition of the derivative in a very precise and rigorous way. In fact, I totally embrace Weierstrass's definition of the calculus limit. It's PERFECT. He couldn't have done a better job. I totally applaud his work. And his definition is in total agreement with my position on precisely what mathematics should be.

So hallelujah! Some mathematicians were indeed on the ball.

In fact, if you fully understand the formal definition of the Calculus Limit you'll also understand that it is not demanding that any limits actually "Exist" as any physical entities. In fact, some limits in Calculus have no actual reality, but they still "exist" by this definition. Which is fine if you truly understand the definition. The fact that a limit "exists" mathematically does not imply that it needs to actually be reachable by an actual process.

In fact, if you're every taken a course in Calculus you know that to show that a limit exists all you need to do is prove boundary conditions and trends. Moreover you can even show that limits exist for functions there the limit itself is undefined, or ill-defined.

In other words, the existence of a Calculus limit does not meant that the actual quantity that the limit is referring to must exist. On the contrary, it may not exist at all.

So there is no problem with the Calculus Limits thanks to Karl Weierstrass.

Zeno also figured out that the world had to be discrete because in a continuum motion could not be possible. And clearly we can move. So reality must be discreet. And he was right. We now know that he was right. Quantum Mechanics tells us so.

In that case, you need to throw out calculus, which was a product of the 17th century. This would mean you cannot fly space-ships to the moon, or design earth-orbiting satellites, or any of a hundred other things we actually do each day. Your insistence that mathematics has to coincide with the real-world is eventually going to end up snuffing a large part of present day civilization completely out of existence at this rate.

Absolutely not.

Modern day mathematicians simply don't understand what Zeno was saying, or they don't understand their own Calculus Limit.

All Zeno was saying is that an infinite number of processes could never be completed. The Calculus Limit DOES NOT demand otherwise.

The Calculus Limit does not disprove Zeno. In fact, Weierstrass' formal definition of the Calculus Limit actually vindicates Zeno.

It's actually wrong for Calculus instructors to teach that Calculus solves Zeno's paradoxes. All they are doing when they do that is displaying their own ignorance of the formal definition of the Calculus Limit as formalized by Weierstrass.

Cantor's work is entirely based on the idea of a continuum, that you can just keep dividing things up with no reason to ever stop. But that's not how the real universe works. That does not correctly describe the quantitative truth of the universe.

Newton's work also depends on the notion of a continuum. He himself did not fully understand the logical underpinnings of the continuum, that would come later with the work of Cauchy, Riemann, and yes, Cantor.

Do you really want to tell us that calculus is "wrong" and we should discard it as a disease, or at least a precursor to the disease you objected to above?

Calculus is not wrong.

But if you think that Calculus is confirming that you can divide things up infinitely then you are wrong.

Have you ever taken Calculus? Have you ever had to prove that a limit exists?

If so what did you have to show?

1. That an infinite number of task could be completed?

2. That there are boundaries and trends that demand a certain conclusion allowed by the Weierstrass definition of the Calculus Limit?

I'm pretty sure it was #2.

This problem actually arose in ancient Greece as well, with the discovery that the square root of 2 is an irrational "number". And this was believed to measure a "distance" that had to be "real". But that was a wrong notion as well. Same is true of a number like Pi. Pi is not a cardinal number. It's just a relative relationship and therefore cannot be thought of in terms of "Set Theory".

We don't need irrational "Cardinal Numbers". On the contrary until we recognize that all irrational numbers that arise are actually the results of a self-referenced relative situation we will forever stand in awe of irrational "quantities". How can they exist? Well, in truth, they don't! They don't exist in our physical universe. And Quantum Mechanics is the proof of this.

Well, I see that you really do seem intent on abolishing not only Cantor, but also Newton and even the notion of irrational numbers.

I have no problem with Newton, or Calculus, especially thanks to Weierstrass.

And yes, we don't need to think of irrational relative relationships as cardinal quantities. There's no need to do that. That's a big mistake to even move in that direction, which unfortunately is precisely where the mathematical community has moved.

Again, it all boils down to your thinking that mathematics that does not have an exact parallel in the physical world is some how erroneous.

This is an incorrect notion, and certainly not one that mathematicians, nor in general other scientists, share.

Mathematics CAN BE MADE SCIENTIFIC. Current is it not scientific.

Why any scientist wouldn't be interested in that fact is beyond me.

Most scientists take mathematical models to be useful as approximations or simplifications of reality or a portion of reality. They do not think of mathematics' relation to the real world in the way you are taking it.

Of course they don't. Why should they? Mathematicians have been fruitcake philosophies since the times of the Early Greeks. Scientists have no reason to take mathematics seriously.

But they could have a reason if they actually had a scientific version of mathematics, which I'm saying is possible.

In fact, Pi is entirely dependent upon flat or Euclidean geometry. Pi isn't even a constant when considering other types of geometries. It's a relative property of Euclidean geometry.

True. In hyperbolic or elliptical geometry, you would not have Pi as we know it. Mathematicians well understand this.

Yes, they do, and they should realize that this is indeed a clue about something far deeper.

If aliens came here from another planet I seriously doubt that they would view mathematics in the same way we do. They would probably be aware of the true quantitative nature of the universe.

If aliens make it to our planet, I am quite sure they will have some understanding of notions that are equivalent to Newton's calculus at the very least. They wouldn't be able to make it here otherwise.

There is nothing wrong with Calculus. I never claimed there was.

Cantor's Set Theory is ridiculous. And his denationalization proof is clearly false.

Well, it might be best left to another thread, but I would be happy to step you through the (I think you mean diagonalization?) proof if you wish.

That could be interesting. If you do, please start a new thread just for that discussion alone.

Now we have truly absurd things like larger and smaller infinities.

That's absurd. Infinity only needs to mean "Endless". That's all it needs to mean. And for something to be "more endless" than something else that is already "endless" is itself absurd.

It may be mind-bending, but the idea of larger and smaller infinities is on a completely sound logical basis.

A sound logical basis based on what? An empty set?

Ironically mathematicians claim to honor "Proof by Contradiction". If you can show that a logical reasoning leads to an absurdity that is accepted as "Proof by Contradiction".

Do you realize that Euclid makes extensive use of proof by contradiction?

Yes, and I agree that proof by contradiction is great. This is why I can't believe that mathematicians are accepting Cantor's empty set theory when it's based on some many logical contradictions.

Well, any mathematics that states that there can be a larger infinity than endlessness, is itself utterly absurd. So Cantor's whole set theory is clearly false because it can be shown to be false by "Proof by Contradiction".

Really?? I would be open to seeing your proof by contradiction that Cantor's Set Theory is false.

Well, step me through his diagonalization proof in another thread, and we'll see where that leads.

Why mathematicians can't see this is beyond me.

I can prove that Cantor's diagonalization proof is logically impossible too. It's logically flawed. In fact, it's absurdly flawed. I can't believe that no mathematician has yet caught it.

Please share your proof.

Start a new thread on that and step me through the original proof. Then I'll show you why it's flawed.

[JohnA]

[Replying to post 297 by Divine Insight]

You wrote:

The macro world can be explained in terms of the laws of quantum physics.

Really? Since when does QM have an answer for gravity?

Scientists have no reason to take mathematics seriously. But they could have a reason if they actually had a scientific version of mathematics, which I'm saying is possible.

Really? Can you back this up?
What is this scientific version of mathematics?
Math is only one "language" of science. Since when does scientific version of math/language exist?

[Divine Insight]

[Replying to post 297 by Divine Insight]

You wrote:

The macro world can be explained in terms of the laws of quantum physics.

Really? Since when does QM have an answer for gravity?

Every macro event associated with gravity can be explained using Quantum Mechanics. The only place where there exists a problem is when gravity tries to explain quantum events.

In fact, doesn't the Standard Model of Particle physics propose that gravity can be explained via the exchange of gravitons?

It's Einstein's General Theory of Relativity that breaks down at the quantum level. Not the other way around. In fact, this supports my views.

General Theory of Relativity presumes a continuum, but it breaks down at the quantum level.

Quantum Theory demands a discrete quantized reality, and it doesn't break down at the macro level.

Chalk one up for a discrete mathematics.

Scientists have no reason to take mathematics seriously. But they could have a reason if they actually had a scientific version of mathematics, which I'm saying is possible.

Really? Can you back this up?
What is this scientific version of mathematics?
Math is only one "language" of science. Since when does scientific version of math/language exist?

Math isn't even a language of science. It's simply a language that scientists try to use the best they can. But the language of mathematics is itself not a science.

There currently is no scientific version of mathematics. And that's my whole point.

I'm simply saying that there should be. And there could be. All we need to do is create one and demand that it remains scientific.