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The Hurdles to the Causal Mathematics Hypothesis

  1. May 24, 2003 #1
    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 Webster's Dictionary defines it as:

    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.
  2. jcsd
  3. May 24, 2003 #2
    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.
  4. May 24, 2003 #3
    Re: Re: The Hurdles to the Causal Mathematics Hypothesis

    There are theories that suggest that mathematics has the ability to mold the Universe?

    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.

    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.

    No, his ideas are no more rediculous than many others, but I'm not arguing against others right now, I'm arguing against his.
  5. May 24, 2003 #4


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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.
  6. May 24, 2003 #5
    Good point, ahrkron.
  7. May 24, 2003 #6


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    Re: Re: The Hurdles to the Causal Mathematics Hypothesis

    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 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.

    Show us one.

    That is not what "reduction ad absurdum" means.
  8. May 24, 2003 #7
    Re: Re: Re: The Hurdles to the Causal Mathematics Hypothesis

    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.

    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.

    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.

    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.
  9. May 24, 2003 #8


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    Re: Re: The Hurdles to the Causal Mathematics Hypothesis

    I summed it up better :wink: - Doubt or shout !
  10. May 25, 2003 #9

    Tom Mattson

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    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.
  11. May 25, 2003 #10
    Re: Re: The Hurdles to the Causal Mathematics Hypothesis

    6) The Emotional Context Hurdle

    Mathematics has nothing to say about emotional context, and without context its meaning and application cannot be assertained.
  12. May 25, 2003 #11
    Re: Re: The Hurdles to the Causal Mathematics Hypothesis

    Excellent additions, Tom. Your input here is highly appreciated.
  13. May 25, 2003 #12
    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 .
  14. May 26, 2003 #13
    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.
  15. May 26, 2003 #14
    Wrong! The Incompleteness Theorem demonstrates that you cannot prove mathematics is the basis of reality. Thus it leads back to the Paradox of Existence.
  16. May 26, 2003 #15
    That's exactly what I was saying.
  17. May 26, 2003 #16

    Tom Mattson

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    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.
  18. May 26, 2003 #17


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  19. May 26, 2003 #18
    Good point.
  20. May 26, 2003 #19


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    Also, the second theorem states that any similarly complicated formal system that can deduce its own consistency must be inconsistent.
  21. May 26, 2003 #20
    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."
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