On the Topic of Consciousness

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On the Topic of Consciousness

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Post by Divine Insight »

Ooberman wrote: 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"
Ooberman wrote: 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.
Ooberman wrote: 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.

Ooberman wrote: 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.

Ooberman wrote: 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.

Ooberman wrote: 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. ;)
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Post #301

Post by JohnA »

Divine Insight wrote:
JohnA wrote: [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. ;)
JohnA wrote:
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.
DI,
QM has no answer for Gravity. None, zip, zero.
The Standard Model does not attempt to explain gravitation, although a theoretical (hypothetical elementary) particle known as a graviton is proposed.
QM or the Standard model has no known way of describing general relativity
All quantum field theories (conjectures) of gravity generally break down before reaching the Planck scale.
General relativity (GR) is a classical theory and does not take quantum effects into account.

Assuming you refer to continuum vs quantum as continuous vs discrete:
Actually, in the usual definition of general relativity, spacetime is continuous. A recent astrophysical experiment that showed that Lorentz symmetry holds even below the Planck length. Lorentz symmetry holds at very short distances, and it seems difficult to reconcile this experimental fact with a claim of discrete spacetime.
Math isn't even a language of science. It's simply a language that scientists try to use
That is a contradictory statement.

And you have not answered my questions:

What is this scientific version of mathematics?
Since when does scientific version of math/language exist? Please explain this. You seem to still rely on obscurantism.

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Post #302

Post by Divine Insight »

JohnA wrote: And you have not answered my questions:

What is this scientific version of mathematics?
Since when does scientific version of math/language exist? Please explain this. You seem to still rely on obscurantism.
There isn't any.

That's precisely why I'm proposing that there should be.

Why should science rely on a non-scientific mathematics?

All I'm saying is that it's possible to construct such a mathematics. We were almost there in the early going. The early Greeks tried until they got hung up on irrational numbers which was a very early mistake.

Galileo and Newton certainly tried. Newton was almost there with his "fluxions", but he didn't know how to make that rigorous enough. Thankfully Karl Weierstrass stepped up to the plate on that one some time later. Weierstrass's definition of the Calculus limit is perfectly compatible with a discrete mathematics. There would be almost no need to change Calculus at all.

What we might change are some of the conclusions we erroneously draw from Calculus. We actually draw those erroneously conclusions because we aren't paying close attention to the rigorous details put forth by people like Karl Weierstrass.

I watch college courses on calculus quite often, or at least I used to up to a few years ago. It never ceases to amaze me how many calculus professors don't truly understand the formal definition of the calculus limit. I've even heard several of them brush over it rather quickly and then proclaim that even most mathematicians don't truly understand it. :roll:

It's actually quite straight-forward and clear I think.

But these calculus professors do have a point. Once they sweep the formal definition out of the way they get on with the business of actually solving calculus problems, and lo and behold you don't need to understand the definition of the limit at all. All you need to do is know how to show trends and boundaries.

And you NEVER need to show or demonstrate that it's actually possible to complete an infinite number of steps to arrive at an answer.

Calculus neither predicts a continuum, nor depends upon it. Calculus is perfectly compatible with a complete discrete mathematics. Even when it produces irrational "numbers" as the result of a calculation. That doesn't violate a discrete mathematics at all. All that's required is to look at the bigger picture and you'll clearly see that this irrational relationship was actually the product of a self-referenced situation. (something that modern mathematicians aren't even aware of) because they don't understand the true nature of irrational relationships.

But yes you're right, there is no scientific mathematics because the scientists never bothered to create one using scientific reasoning and methods. They just sat by and allowed the mathematical community to have their way with math.

Too bad.

We could be so much further ahead. A scientific based mathematics might have been able to predict a quantized world before the physicist's discovered it experimentally.

Then we'd have a better understanding of why it has to be that way and we'd also have a better understanding of the nature of complementarity.

Everything I'm suggesting is actually in the favor of science.
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Post #303

Post by JohnA »

Divine Insight wrote:
JohnA wrote: And you have not answered my questions:

What is this scientific version of mathematics?
Since when does scientific version of math/language exist? Please explain this. You seem to still rely on obscurantism.
There isn't any.

That's precisely why I'm proposing that there should be.

Why should science rely on a non-scientific mathematics?

All I'm saying is that it's possible to construct such a mathematics. We were almost there in the early going. The early Greeks tried until they got hung up on irrational numbers which was a very early mistake.

Galileo and Newton certainly tried. Newton was almost there with his "fluxions", but he didn't know how to make that rigorous enough. Thankfully Karl Weierstrass stepped up to the plate on that one some time later. Weierstrass's definition of the Calculus limit is perfectly compatible with a discrete mathematics. There would be almost no need to change Calculus at all.

What we might change are some of the conclusions we erroneously draw from Calculus. We actually draw those erroneously conclusions because we aren't paying close attention to the rigorous details put forth by people like Karl Weierstrass.

I watch college courses on calculus quite often, or at least I used to up to a few years ago. It never ceases to amaze me how many calculus professors don't truly understand the formal definition of the calculus limit. I've even heard several of them brush over it rather quickly and then proclaim that even most mathematicians don't truly understand it. :roll:

It's actually quite straight-forward and clear I think.

But these calculus professors do have a point. Once they sweep the formal definition out of the way they get on with the business of actually solving calculus problems, and lo and behold you don't need to understand the definition of the limit at all. All you need to do is know how to show trends and boundaries.

And you NEVER need to show or demonstrate that it's actually possible to complete an infinite number of steps to arrive at an answer.

Calculus neither predicts a continuum, nor depends upon it. Calculus is perfectly compatible with a complete discrete mathematics. Even when it produces irrational "numbers" as the result of a calculation. That doesn't violate a discrete mathematics at all. All that's required is to look at the bigger picture and you'll clearly see that this irrational relationship was actually the product of a self-referenced situation. (something that modern mathematicians aren't even aware of) because they don't understand the true nature of irrational relationships.

But yes you're right, there is no scientific mathematics because the scientists never bothered to create one using scientific reasoning and methods. They just sat by and allowed the mathematical community to have their way with math.

Too bad.

We could be so much further ahead. A scientific based mathematics might have been able to predict a quantized world before the physicist's discovered it experimentally.

Then we'd have a better understanding of why it has to be that way and we'd also have a better understanding of the nature of complementarity.

Everything I'm suggesting is actually in the favor of science.
So, you want X. But you can not tell us what X is. All you can tell us is it should not have Y (it should not have: i) set theory based on an idea of an Empty Set. ii) Absolute Negative Numbers. iii) cardinal numbers / sets. )

How is that logical?

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Post #304

Post by Divine Insight »

JohnA wrote: So, you want X. But you can not tell us what X is. All you can tell us is it should not have Y (it should not have: i) set theory based on an idea of an Empty Set. ii) Absolute Negative Numbers. iii) cardinal numbers / sets. )

How is that logical?
I can easily tell you what X is, and I have already to some degree. You just aren't paying attention evidently.

It's totally strawman on your part to claim that I cannot tell you what X is.

You have already refuted it before you were even willing to consider it or even hear it.

In short John, you don't even have clue what you are arguing against. :roll:
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Post #305

Post by JohnA »

Divine Insight wrote:
JohnA wrote: So, you want X. But you can not tell us what X is. All you can tell us is it should not have Y (it should not have: i) set theory based on an idea of an Empty Set. ii) Absolute Negative Numbers. iii) cardinal numbers / sets. )

How is that logical?
I can easily tell you what X is, and I have already to some degree. You just aren't paying attention evidently.

It's totally strawman on your part to claim that I cannot tell you what X is.

You have already refuted it before you were even willing to consider it or even hear it.

In short John, you don't even have clue what you are arguing against. :roll:
So, tell us what is X.
I asked you a few times now. Or is it one of those that you know the answer when not asked, but you do not know the answer when asked.

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Post #306

Post by Divine Insight »

JohnA wrote: So, tell us what is X.
I asked you a few times now. Or is it one of those that you know the answer when not asked, but you do not know the answer when asked.
Who is "us" John? Do you have multiple personalities?

You have clearly failed the origin criteria to even be worthy of my attention.

You have rejected my Proposition P.

You have even tried very hard to reject my entire P -> Q.

And now you are asking me for information about Q?

Get lost.

Why would I bother wasting anymore time on you?

You are clearly only here to make trouble.

You can't have an interest in Q since you have already rejected P.

That was the whole point of the conditional statement which you apparently still do not understand.
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Post #307

Post by JohnA »

Divine Insight wrote:
JohnA wrote: So, tell us what is X.
I asked you a few times now. Or is it one of those that you know the answer when not asked, but you do not know the answer when asked.
Who is "us" John? Do you have multiple personalities?

You have clearly failed the origin criteria to even be worthy of my attention.

You have rejected my Proposition P.

You have even tried very hard to reject my entire P -> Q.

And now you are asking me for information about Q?

Get lost.

Why would I bother wasting anymore time on you?

You are clearly only here to make trouble.

You can't have an interest in Q since you have already rejected P.

That was the whole point of the conditional statement which you apparently still do not understand.
As expected, you can not tell us what is X (scientific version of mathematics).

I reject your conditional statement since it can not conclude anything. The hypothetical proposition (P-Q) is invalid, your hypothesis P has not been demonstrated and your conclusion Q has not been demonstrated.

The US = this forum and users reading the posts. Was that your red herring or attempt and straw manning me again?
I care because you keep on straw manning me, and then beating it to bits.

P is not a proposition, it is a hypothesis.
You need to show cause-and-effect for P -> Q, adressing the problems with using Discrete Math in English Language to show your hypothetical proposition is valid and sound.
Your conclusion Q needs to be demonstrated.
You cannot have a conclusion without having a valid sound argument.

Consider this example:
Given;
P: DI offers a conditional statement
Q: Math is flawed.
Problem; What does P->Q represent?

The sentence, "DI offers a conditional statement" is the hypothesis and the sentence, "Math is flawed" is the conclusion. Thus, the conditional P->Q represents the hypothetical proposition, "If DI offers a conditional statement, then Math is flawed." However, as you can see from the truth table above, DI offering a conditional statement does not guarantee that math is flawed! In other words, there is not always a cause-and-effect relationship between the hypothesis and conclusion of a conditional statement.
Not only that, but if you substitute DI with JohnA, and remember that I am not offering a conditional statement, then regardless if Q is true or false (Math is flawed or not), you still suggest that P->Q is still True. So, you are stating this is still true "If JohnA offers a conditional statement, then Math is flawed." That is just absurd. You are merely begging the question since you already decided that Math is flawed and will persist even if you or I offer a conditional statement.

You are using faulty logic DI. And for that you tell me to get lost?
You should say: "Well thank you JohnA, you helped me today, I should not straw man you."

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Post #308

Post by otseng »

Divine Insight wrote:
JohnA wrote: You do not have any ideas, mumbo jumbo is not ideas since it is self-refuting circular rubbish.
You inability to comprehend my ideas does not translate into mumbo jumbo on my part.
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Post #309

Post by micatala »

Divine Insight wrote:
micatala wrote: 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? :-k

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

And this really highlights my point. Because it basically shows us that as long as modern science depends upon modern mathematics then it will indeed be dead in the water.

&&&&&&&&&

Yes, I absolute must reject modern mathematics (math ideas invented since the late 17th century) because it's wrong. Besides, that math doesn't reveal any answer anyway. On the contrary it runs into extreme paradoxes that cannot be solved.
Saying something is 'dead' or 'dead in the water' is more than a suggestion that it is completely useless and/or wrong. Now, if you wish to back-track on what you meant here, that is fine, but the implication of what you wrote here and elsewhere is that, because of the alleged problems with science and its dependence on "modern mathematics", science is in error.


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



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).
In this, it is you who are creating a straw man. I never said there were two entirely different physical realities. I only alluded to a difference in scale, and that some physical models do not work at the quantum scale.





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.

If you are saying that everything in the macro world reduces to the quantum, and are saying the errors in our understanding of the quantum level automatically negates every other scientific model, then I'll stand by my previous statement regarding your 'dead in the water' remarks.




micatala wrote:
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.

Well, I am happy to stand corrected on what your view are. I agree with what you say here.

I still reject your other comments regarding science in general.






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.

To say that ideas of the infinite did not stem from more rudimentary ideas regarding finite quantities or sets is historically and factually wrong. Cantor's theories grow out of concepts related to discrete phenomenon, and our understanding of the infinite is based on our understanding of the finite. What you are claiming here is in fact erroneous.


I'll accept that you were not previously stating all of this modern mathematics is useless, but still wonder how you can state that and then also think it means math is wrong and science is 'dead in the water.'


Keep in mind Cantor's ideas anyway are not ones that have had a huge impact in applied mathematics. Most mathematicians consider his work a side issue or curiosity. However, they accept it is logically valid.









micatala wrote: 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.

Mathematicians are well aware of the difference between cardinal numbers and real numbers, or irrational numbers, or ordinal numbers.

You still have shown no reason to consider irrational numbers some kind of logical contradiction or that they do not exist in a mathematical way. Sure, if you want to say there is a difference between actual infinities and potential infinities, fine. This does not negate the logical soundness of actual infinities.




micatala wrote:
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.
The empty set might present interesting questions for philosophers. It presents no logical contradiction in mathematics. If you claim so, please prove it.








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.
You are just playing with words here. Your entire argument is nothing but semantics and suffers severely from equivocation.

The number of elements in the empty set is zero. There is no problem giving it a quantitative meaning.


Your problem in part is that you think that you are confusing mathematically defined objects and concepts with physical reality. Some mathematical concepts can and do have a correspondence in physical reality. However, all that is necessary for mathematics is to have a set of defined objects and axioms on those objects that are consistent.

The irony here is that the empty set easily can be given a real-world correspondence. The set of female U.S. Presidents is the empty set, for example.









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

Not sure what your point is. Yes, zero as a number is different from the empty set.

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. :roll:

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. :roll:
Sorry, eye-rolling has no mathematical meaning or relevance in proof. You still have not in anyway shown the empty set is some kind of logical contradiction. If you wish to mock the idea, that is your choice. However, mockery bears no weight in mathematics.





micatala wrote: 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.



Well, step up to the plate.

You claimed it is wrong. Prove it.





micatala wrote:
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.
I await your proof.



















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. ;)
I await your proof.



















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.
Need? Need for what? If you personally don't feel you "need" these types of numbers, fine. But that lack of need is not the same as proving they are somehow logically inconsistent.











micatala wrote:
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.
Well, you have yet to point out any logical flaws. You have engaged in a lot of ranting and railing about us not "needing" these concepts, and other diversions and mockery, but no logical contradictions as yet. Please back up your assertions.









micatala wrote:
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.

Yes, I am pointing out the security and encryption theory depends on there being infinitely many primes. If there were not, these systems would eventually become obsolete.

I don't want to belabor the point, but if you object to the notion of 'cardinal infinities,' for personal reasons, that is fine. If you want to try and make the case that the notion of actual infinities is not very useful, fine. But those points will not prove that they are logically contradictory.







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.
Well, if you want to argue semantics some more regarding what should or should not be part of mathematics, again feel free. I am not interested in that discussion. Certainly Boolean algebra is today considered a part of mathematics. It can actually be reduced to a quantitative system if you wish. Still, all of this is irrelevant to your claims of logical inconsistency.










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.
How words are understood is dictated by usage. Some mathematicians would consider logic a branch of mathematics, and their are good historical reasons for that usage. Others would say mathematics is a branch of logic, and they have a case to make too.

But word usage is not "wrong." You might find it objectionable, and you might wish it were different, but that does not make it wrong. You are confusing philosophical and semantic issues with logical validity.







micatala wrote: 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".

And what would be the problem if that were the case? Again, semantics does not dictate logical validity.








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
So? What's the problem?








micatala wrote:
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).
Again, your objections are highly subjective and semantic. If you want to say too many mathematicians are engaged in work that has no useful purpose, make that case. But even if you are correct on that point, that has no bearing on the logical validity of the math they are engaged in.


















micatala wrote:
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.
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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.
You are entirely and completely incorrect. Not only are there no logical problems with the empty set, it would in fact be possible to prove the uncountability of the real numbers and the existence of hierarchies of infinity without alluding the empty set at all.





micatala wrote: 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.
I'll allow we are not 100% sure, but most physicists today would posit that the universe is finite. It's expanding, but it is finite.









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.

Fair enough, but none of this provides an argument that 'actual infinities' are logical contradictions. However, I'll accept that you at least accept these what might be termed potential infinities.



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, in your view, does the square root of 2 exist, or does it not exists?


























micatala wrote:
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.


What do you mean by "things?" Are you still focused on physical things, or only numerical quantities or concepts?


Have you ever taken Calculus? Have you ever had to prove that a limit exists?
I am very, very well-acquainted with calculus, but this is a side issue. I brought it up because you seemed to be denying anything infinite. If you don't, fine. But accepting calculus does not negate the logical validity of other notions of infinity.












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.


Here again the "need." What relevance does your notion of "need" have? If you want to argue that irrational numbers do not exist in nature, fine, but again, that does not make them nonexistent in the mathematical sense, or logically inconsistent.




micatala wrote: 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.

Again, semantics is not relevant to logical validity.









micatala wrote: 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.

Well, first off I would say that, at this point, you have accepted as legitimate mathematics almost everything that I would also accept. Given this, I find it odd that you denigrate mathematics when much of what mathematicians do is very useful in describing physical reality. The parts of mathematics you do object to are actually not areas most mathematicians get into (although I wonder what you would think of group theory and abstract algebra).

But you are totally off base in thinking that those parts you object to are "wrong" or absurd. There logical underpinnings are very sound, and in asserting otherwise, especially when your arguments are based on semantics and, might I say, bluster, you are simply erroneous.





micatala wrote:
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. ;)

Well, at this point you made the claim that Cantor was wrong, so I am going to ask you to step up to the plate and prove your assertions.







micatala wrote:
Now we have truly absurd things like larger and smaller infinities. :roll:

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? :-k
Again, you have provided not a single valid reason to consider the empty set some kind of logical contradiction.


Furthermore, cardinality can be defined using bijective functions. The set of fingers on my left hand can be put into one-to-one correspondence with the fingers on my right hand, so they exhibit the same cardinality. The set of integers can be put into one-to-one correspondence with the set of even integers, or the set of prime numbers, or even the set of rational numbers, so those sets all have the same cardinality. The set of real numbers cannot be put into one-to-one correspondence with the set of integers, and so it is of a different cardinality. Defining cardinality via bijective functions is consistent with cardinality for finite sets, and presents no logical contradictions.


So, again, since you are making the rather large claim that all of this is not logical, the onus is on you to show that.








micatala wrote:
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.
You have yet to illustrate a single one, never mind many. However, I am glad to hear you accept that proof by contradiction is a valid technique.




micatala wrote:
DI wrote: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.


I might consider this, but since you made the original claim, the onus is on you to prove Cantor was wrong.


Certainly you can find standard discussions in a variety of places on the internet.

Even Wikipedia has a page.

http://en.wikipedia.org/wiki/Cantor's_diagonal_argument


If you are interested, here is a diagram indicating the general idea of proving the rational numbers are countable.
" . . . the line separating good and evil passes, not through states, nor between classes, nor between political parties either, but right through every human heart . . . ." Alexander Solzhenitsyn

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micatala
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Post #310

Post by micatala »

Here is a Youtube video, under 10 minutes, of Cantor's diagonalization argument.

" . . . the line separating good and evil passes, not through states, nor between classes, nor between political parties either, but right through every human heart . . . ." Alexander Solzhenitsyn

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