The Hurdles to the Causal Mathematics Hypothesis

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Back in the old PFs, I made this thread to get rid of an idea that was continually side-tracking threads. I thought it was, for the most part, effective, but it appears that this is not the case. So, I have found the thread on the PF Archive C.D., and reposted it here:

The following are the Hurdles to the Causal Mathematics idea (which is the idea that Mathematics creates the phenomena of the Universe), as posted in PF 2.0:

1) Non-physical Hurdle:

Mathematics has no physical presence (nor does logic, for that matter). You can say that electromagnetism (for example) is causal, because it can exert *physical* force on objects. Mathematics, on the other hand, exists only in the metaphysical (or the realm of concepts).

2) The Dictionary Hurdle:

The American Heritage dictionary of the English Language defines mathematics as:

The study of number, form, arrangement, and associated relationships, using rigorously defined literal, numerical, and operational symbols.
The Webster's Dictionary defines it as:

The logical study of quantity, form, arrangement, and magnitude; especially the methods for disclosing, by the use of rigorously defined concepts and symbols, the properties of quantities and relations.
In both of these, it uses the term "study". The word study (according to the aforementioned dictionaries, and a thesaurus) is synonymous to research, observation, or the pursuit of knowledge.

3) The Unconscious Hurdle:

It appears that Alexander would have one believe that the Universe "conforms" to the laws of logic and mathematics. This would imply that the Universe "knows" what those laws are. Unless Alexander wishes to make a case for a "conscious Universe", this is another problem for his hypothesis. (Note: I have added Hurdle #3. It did not appear in the original thread).

In closing, any hypothesis with such giant objections would quickly be discarded by any scientist. But, of course, these are not objections at all, if anyone can prove them invalid.
 
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Alexander's mysticism about everything ultimately being mathematics is nothing new, in fact, it is one of the leading candidate theories attempting to explain Quantum Mechanics. The assertion that mathematics has no physical presence is unproven and clear arguments with physical evidence to the contrary exist.

As for the universe having to be "conscious" of the mathematics that underlie it... that is utter nonsense. Even consciousness itself could be nothing more than another manifestation of mathematics. You are attempting to make an a priori assertion about the idea that axiomatically discounts the idea. You are, of course, welcome to have your own opinions about the idea, but your argument here amounts to nothing more complex than two little kids on the playground shouting at each other:

Is so! Is not! Is not! Is not!

If you really wish to talk about the subject instead of just shouting contradictory assertions at each other, it might be helpful to reframe your arguments along the lines of reductio ad absurdum, that is, that his ideas are no more or less rediculous than a number of alternatives.
 
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Re: Re: The Hurdles to the Causal Mathematics Hypothesis

Originally posted by wuliheron
Alexander's mysticism about everything ultimately being mathematics is nothing new, in fact, it is one of the leading candidate theories attempting to explain Quantum Mechanics. The assertion that mathematics has no physical presence is unproven and clear arguments with physical evidence to the contrary exist.
There are theories that suggest that mathematics has the ability to mold the Universe?

As for the universe having to be "conscious" of the mathematics that underlie it... that is utter nonsense.
No, I didn't say that. I said that, in order for the Universe to conform to mathematics, it would have to be conscious. There's a difference.

Even consciousness itself could be nothing more than another manifestation of mathematics.
Not by the accepted definitions of the term "mathematics". Remember, the language that we are using to discuss these things relies on defined terms. As Alexander himself has pointed out, many times in the past, the terms need to be defined before any rational argument can take place about them.

If you really wish to talk about the subject instead of just shouting contradictory assertions at each other, it might be helpful to reframe your arguments along the lines of reductio ad absurdum, that is, that his ideas are no more or less rediculous than a number of alternatives.
No, his ideas are no more rediculous than many others, but I'm not arguing against others right now, I'm arguing against his.
 

ahrkron

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I think the strongest of Mentat's "hurdles" is the second one. Mathematics is defined as a description. There's no way around that.

What Alexander refers to can at most be stated as "all concepts in math correspond to real entities, the interaction of which causes everything", which is a metaphysical assumption about the degree of validity or the description.
 
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Originally posted by ahrkron
I think the strongest of Mentat's "hurdles" is the second one. Mathematics is defined as a description. There's no way around that.

What Alexander refers to can at most be stated as "all concepts in math correspond to real entities, the interaction of which causes everything", which is a metaphysical assumption about the degree of validity or the description.
Good point, ahrkron.
 

ahrkron

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Re: Re: The Hurdles to the Causal Mathematics Hypothesis

in fact, it is one of the leading candidate theories attempting to explain Quantum Mechanics.
What are you talking about? The only possibility I can think of is Max Tegmark's idea of the "Ultimate ensemble", but even that does not rely on attributing causal powers to math, but on the idea that all self consistent structures are realized in nature.

The assertion that mathematics has no physical presence is unproven
The matter does not even require a "proof". It is a much simpler matter, since it comes from the definition of math. If you want to refer to a different concept, you need to use a different word.

and clear arguments with physical evidence to the contrary exist.
Show us one.

it might be helpful to reframe your arguments along the lines of reductio ad absurdum, that is, that his ideas are no more or less rediculous than a number of alternatives.
That is not what "reduction ad absurdum" means.
 
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Re: Re: Re: The Hurdles to the Causal Mathematics Hypothesis

Originally posted by Mentat
There are theories that suggest that mathematics has the ability to mold the Universe?


Sure, one of the better theories attempting to explain Quantum Mechanics is that information itself is a material substance. Other leading theories propose everything is geometry or logic, albeit, rather strange geometries and logic.

No, I didn't say that. I said that, in order for the Universe to conform to mathematics, it would have to be conscious. There's a difference.
Whether any different or not, such a statement is an a priori assumption which can easily be turned on its head to assert that, "In order for the universe to be conscious it must conform to mathematics." In addition, it can also be argued that you can not have consciousness without mathematics and vice versa, that both involve symbolic logic or reasoning at the very least. In fact, if Alex really wanted to he could simply argue that consciousness is an illusion of mathematics.

Not by the accepted definitions of the term "mathematics". Remember, the language that we are using to discuss these things relies on defined terms. As Alexander himself has pointed out, many times in the past, the terms need to be defined before any rational argument can take place about them.
Natural language is finite and of limited usefulness, especially when discussing such extreme metaphysical concepts. Just because the english language does not have words for concepts that other languages do possess does not mean those concepts don't really exist. As much as I admire and espouse using dictionary definitions, I also acknowledge their limitations. To do otherwise is patently absurd.

No, his ideas are no more rediculous than many others, but I'm not arguing against others right now, I'm arguing against his.
My point is that you are not arguing against his idea, all you are doing is espousing an alternative by default and using shaky arguments that can easily be totally trashed. By merely using the english dictionary definitions you are asserting the dualistic worldview that is the origin of the english language. Mathematics, however, is not limited to dualism and contains many concepts that defy english language definitions.

In other words, by asserting as you are that The Map (mathematics) is not the Territory, you are axiomatically excluding the possibility that the map is actually a piece of paper made from a tree someone cut down from within the territory. Thus, the map is and is not the territory, the map both is shaped by and, in turn, shapes the territory.

Again, dictionaries are wonderful tools except when you forget they are only tools and start to worship them as the word of God or somesuch.
 

drag

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Re: Re: The Hurdles to the Causal Mathematics Hypothesis

Originally posted by wuliheron
Is so! Is not! Is not! Is not!
I summed it up better :wink: - Doubt or shout !
 

Tom Mattson

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Since I have a lot of experience in these threads, let me add to your list.

Originally posted by Mentat
1) Non-physical Hurdle:

2) The Dictionary Hurdle:

3) The Unconscious Hurdle:
4) The Post Hoc, Ergo Propter Hoc Hurdle

Post hoc, ergo propter hoc ("After this, therefore because of this") is a logical fallacy that assumes a causal connection between two things that are simply coincidental, or that reverses the direction of causality.


5) The No Perfect Equation Hurdle

If someone claims that math creates things in the universe, then a perfectly reasonable request would be, "Please present the equation that does it." Indeed, I have made this request many times, but still have not gotten it. Every equation we have is an imperfect model, and so cannot be a candidate for the creator of anything.
 
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Re: Re: The Hurdles to the Causal Mathematics Hypothesis

Originally posted by Tom
Since I have a lot of experience in these threads, let me add to your list.

4) The Post Hoc, Ergo Propter Hoc Hurdle

Post hoc, ergo propter hoc ("After this, therefore because of this") is a logical fallacy that assumes a causal connection between two things that are simply coincidental, or that reverses the direction of causality.

5) The No Perfect Equation Hurdle

If someone claims that math creates things in the universe, then a perfectly reasonable request would be, "Please present the equation that does it." Indeed, I have made this request many times, but still have not gotten it. Every equation we have is an imperfect model, and so cannot be a candidate for the creator of anything.
6) The Emotional Context Hurdle

Mathematics has nothing to say about emotional context, and without context its meaning and application cannot be assertained.
 
3,754
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Re: Re: The Hurdles to the Causal Mathematics Hypothesis

Originally posted by Tom
Since I have a lot of experience in these threads, let me add to your list.



4) The Post Hoc, Ergo Propter Hoc Hurdle

Post hoc, ergo propter hoc ("After this, therefore because of this") is a logical fallacy that assumes a causal connection between two things that are simply coincidental, or that reverses the direction of causality.


5) The No Perfect Equation Hurdle

If someone claims that math creates things in the universe, then a perfectly reasonable request would be, "Please present the equation that does it." Indeed, I have made this request many times, but still have not gotten it. Every equation we have is an imperfect model, and so cannot be a candidate for the creator of anything.
Excellent additions, Tom. Your input here is highly appreciated.
 
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I've just noticed that I forgot entirely about Godel's Incompleteness Theorem, which clearly shows the flaw (or "incompleteness") of mathematics. If mathematics cannot describe itself, and yet it is the producer of all reality, then mathematics is not real .
 
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Alexander, I don't want this to seem like a bunch of members are just ganging up on you, you are expected to attempt a counter-argument to any/all of the arguments here presented.
 
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Originally posted by Mentat
I've just noticed that I forgot entirely about Godel's Incompleteness Theorem, which clearly shows the flaw (or "incompleteness") of mathematics. If mathematics cannot describe itself, and yet it is the producer of all reality, then mathematics is not real .
Wrong! The Incompleteness Theorem demonstrates that you cannot prove mathematics is the basis of reality. Thus it leads back to the Paradox of Existence.
 
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Originally posted by wuliheron
Wrong! The Incompleteness Theorem demonstrates that you cannot prove mathematics is the basis of reality. Thus it leads back to the Paradox of Existence.
That's exactly what I was saying.
 

Tom Mattson

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Originally posted by wuliheron
Wrong! The Incompleteness Theorem demonstrates that you cannot prove mathematics is the basis of reality.
The incompleteness theorem says that any formal system at least as complicated as arithmetic is either incomplete or inconsistent. It says no more, and no less. To try to extrapolate this to some comment on "the basis of reality" is to make the same mistake that Alexander is making: confusing concrete objects and abstract objects.
 

drag

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Originally posted by Tom
The incompleteness theorem says that any formal system
at least as complicated as arithmetic is either incomplete
or inconsistent. It says no more, and no less. To try to extrapolate this to some comment on "the basis of reality"
is to make the same mistake that Alexander is making:
confusing concrete objects and abstract objects.
Indeed.
 
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Originally posted by Tom
The incompleteness theorem says that any formal system at least as complicated as arithmetic is either incomplete or inconsistent. It says no more, and no less. To try to extrapolate this to some comment on "the basis of reality" is to make the same mistake that Alexander is making: confusing concrete objects and abstract objects.
Good point.
 

Hurkyl

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Also, the second theorem states that any similarly complicated formal system that can deduce its own consistency must be inconsistent.
 
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Originally posted by Tom
The incompleteness theorem says that any formal system at least as complicated as arithmetic is either incomplete or inconsistent. It says no more, and no less. To try to extrapolate this to some comment on "the basis of reality" is to make the same mistake that Alexander is making: confusing concrete objects and abstract objects.
In other words, any system we use that is at least as complex as arithematic must be taken on faith to a certain extent.

Sorry if I'm sounding redundant, but this leads inexorably back to the paradox of existence. Beneigth the level of arithmatic lies metaphysics, which also must be taken on faith. Including the metaphysical idea that existence is "concrete" and mathematics is "abstract."
 

Tom Mattson

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Originally posted by wuliheron
Beneigth the level of arithmatic lies metaphysics, which also must be taken on faith.
In what sense is arithmetic "beneath" metaphysics?

Including the metaphysical idea that existence is "concrete" and mathematics is "abstract."
So then it is metaphysics, not incompleteness, that takes this to the paradox of existence?
 

drag

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Originally posted by wuliheron
In other words, any system we use that is at least as complex as arithematic must be taken on faith to a certain extent.

Sorry if I'm sounding redundant, but this leads inexorably back to the paradox of existence. Beneigth the level of arithmatic lies metaphysics, which also must be taken on faith. Including the metaphysical idea that existence is "concrete" and mathematics is "abstract."
Yeah, but while this may be relevant to reality
when Alexander says math is it, it's not
relevant to the subject in general, I think
(beyond being another example of a reasoning
system that can not explain its own origin).

Live long and prosper.
 
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Originally posted by Tom
In what sense is arithmetic "beneath" metaphysics?

So then it is metaphysics, not incompleteness, that takes this to the paradox of existence?
Arithematic is built upon metaphysics, precisely the kind you advocate. Of course, these metaphysics are based in turn on observation and whatnot, but they remain metaphysical concepts nonetheless. The belief that reality can be described using rational constructs is an inherently metaphysical idea.

Incompleteness leads back to these metaphysical foundations, which, in turn lead back to the paradox of existence. It is this continuous and apparently unavoidable thread of evidence that makes the paradox of existence a likely candidate for the source of all metaphysical ideas.

Originally posted by drag
Yeah, but while this may be relevant to reality
when Alexander says math is it, it's not
relevant to the subject in general, I think
(beyond being another example of a reasoning
system that can not explain its own origin).

Live long and prosper.
No, it is critical in the sense that when one is talking about vague and poorly defined concepts you can still often reduce them down to a single connundrum. As far as I am concerned, Alex is just talking about the paradox of existence. He can argue otherwise of course, but so far all of his arguments involve not only vague terms, but an attempt to seriously redefine the english language to favor his metaphysics. In fact, not only to redefine the language to favor metaphysics, but his particular brand of mysticism.

This is patently absurd. Words are used for communication, outside of that context what you do with them is your personal affair.
 

Alexander

Looks like almost nobody here understands Goedel theorem. Thus the wrong conclusions this thread is choke full of. Can you guys lift your fingers and learn more about it?

In brief: it says that out of rich enough bunch of axioms you can build a conclusion which is impossible to prove by these axioms only, but which nevertheless is CORRECT conclusion.

It simply means that math is open (more rich than the axioms it started with) yet always CORRECT.

And that math is correct we see each and every day - it makes correct predictions of behavior of things in universe. We use math to predict behavior of unexisting yet devices and mechanisms with owerwhelming success.
 
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Originally posted by Alexander
Looks like almost nobody here understands Goedel theorem. Thus the wrong conclusions this thread is choke full of. Can you guys lift your fingers and learn more about it?

In brief: it says that out of rich enough bunch of axioms you can build a conclusion which is impossible to prove by these axioms only, but which nevertheless is CORRECT conclusion.

It simply means that math is open (more rich than the axioms it started with) yet always CORRECT.

And that math is correct we see each and every day - it makes correct predictions of behavior of things in universe. We use math to predict behavior of unexisting yet devices and mechanisms with owerwhelming success.
Mathematics do not make predictions... people make predictions. Sometimes we use math incorrectly and make false predictions because math as we know it is not a perfect system for making predictions.
 

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