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All mathematical structure exist.

  1. Nov 3, 2009 #1
    Modal realism!

    1. All mathematical structure exist necessarily.
    2. Our universe/multiverse is a mathematical structure.
    A) Our universe/multiverse exist necessarily.


    1'. All mathematical structure exist necessarily.
    2'. Consciousness is a mathematical structure.
    B) Consciousness exist necessarily.

    Premise 1 and 1' is just tagmark` s mathematical universe hypothesis. Nozick called this the principle of fecundity. It is very similar to David Lewis ` s Modal realism.
    Premise 2 is plausible given all the evidences from physics.
    Premise 2' is thesis of strong AI. Namely, consciousness can be derived by an execution of an algorithm. Any algorithm is itself a mathematical structure. Therefore, 2'.

    What is amazing about premise A, B is that they are known to be contingent. The universe\multiverse need not exist, but they just happen to exist. Similarly, Consciousness need not exist. There need not be any subjective feeling of the self, but it just exist without much reason. Premises A, and B are necessary, because they are arrived at deductively via premises. I say the premises are pretty reasonable.

    This is confusing to many people, but when i say "all possible mathematical structure exist". I don` t just mean the multiverse exist. If the multiverse exist, then our universe would be a substructure. Our multiverse would be just one out of infinitly many mathematical structures! I am say all those *other* structures exist also. Some would be total weird. Some would be similar to our universe/multiverse.

    The set of "all possible mathematical structure exist" is a proper subset of the set of "all logically possible worlds". The fomer is restrictive to realities with a particular mathematical structure, while "all logically possible worlds" are not limited to worlds with a particular mathematical structure. A world could be defined in other ways other than a math structure. Here is an example:

    World W: A world rule by magic as in the harry potter movies.

    The world W would not be a mathematical structure, but W is a "logically possible world". To see why W is not a math structure. Math deals with stable regular patterns. That can` t happen if harry starts changing the world by the power of his spell to doom the sun, and change subatomic structures to cheese.

    Another example:

    World W1: is a world defined by an infinite set of propositions.

    Imagine an infinite list of propositions that specific W1 in every detail imaginable. There is a proposition that specific how each atom moves in W1. Of course, no propositions can ever contradict one another.

    Therefore, we define

    World W1: A maximally consistent set of propositions.
    Last edited: Nov 3, 2009
  2. jcsd
  3. Nov 3, 2009 #2
    On what basis?

    I think sometimes when people spend lots of time doing math, they start thinking that math is more real than the physical world. The ancient greeks did this with geometry, and by extension, Plato had his forms. But our understanding of the universe didn't really start taking off until we started making rigorous empirical observations, and adapting mathematics to these observations. Similarly theories are nothing much better than fantasies, unless they actually correspond to observation, and we don't observe math. Math is just a flexible and convenient shortform description of what really exists.
  4. Nov 3, 2009 #3
    Premise 1 and 1' is just tagmark` s mathematical universe hypothesis. Nozick called this the principle of fecundity. It is very similar to David Lewis ` s Modal realism.
    Premise 2 is plausible given all the evidences from physics.
    Premise 2' is thesis of strong AI. Namely, consciousness can be derived by an execution of an algorithm. Any algorithm is itself a mathematical structure. Therefore, 2'.

    I am not committed to the veiw of modal realism, or ultimate ensamble. I hold it at the back of my mind just like a toy idea. The reason i even take this idea seriously is that this hypothesis give us a nice explanation to some deep philosophical questions.

    Here is a list of goods:

    1. explaining modality in terms of quantifications over possible worlds.

    2. explain why there is something possible, but does not exist, and why something exist. What is the selective rule which dictates what is possible, and what gets to exist.

    3. "What breaths fire into the equation, and make a universe for the equation...to describe?" Hawking.

    4. Why this particular(fundamental) equation, and not something else entirely different?

    I think adopting modal realism( or variation of it) can help us explain 1-4
  5. Nov 3, 2009 #4


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    Actually they could do with a little work.

    What is meant by mathematical structure existing? Does it necessarily exist in a "material" way like the universe or consciousness?

    Why should math have ontic status rather than merely epistemic? And if it exists ontically, is this in some dualistic platonic sense or what exactly?

    So how does the existence of "mathematical structure" actually entail the existence of "physical structure" in practice. Why should we believe in this connection?

    Please define.

    How do we know magic has no mathematical structure as a fact? Perhaps we just haven't discovered the rules. It's possible.

    But then also how can it be logically possible in a sense that would not require "logical" to mean crisply self-consistent in some reasonable fashion? Is it logical that worlds can be illogical?

    Perhaps you could get away with calling magic worlds just possible worlds. Except it would remain illogical that they lacked a most obvious necessary trait of "a world" - the self-consistency that allows it to be defined as "a world" rather than an unprincipled collection of events.

    Please explain.
  6. Nov 3, 2009 #5
    All possible and impossible (impossible from NOW reference) exist, but it's comes purely from nothing. If you see in math books many equations so you already get them and they exist in your minds, but you and your body are not from math, it is from nothing and this nothing makes magic. What you seeing, what you hearding can be transformed into frenquencies, those in bits, your memory less or more also in bits with some bluernes, so you consist of some math, but it's only your consciousnes and everything that you hearding or seeing or touching and so on exist only in your minds/counsciousnes, but not in real. So Math tricked that you exist, but your thinking process is not probably from math, but from magic or some tape, which have math bits, your counciousnes is like Turing mashine, but I believe there is somthing than math to made up your counciousnes and that it would run in time. I don't believe, that math making first some quantum mechanic or that quantum mechanic making counciousnes and first physical body/brain. What you fell is what you feel and it's not from math, but more precisly from magic and this magic from nothing, from what more else can come magic? From simulation? Maybe. But what laws then creates this simulation? Again quantum mechanics? Why? Just it's very easy/good visible that everything or more precisly conciousnes comes from nothing. And since physicists is just part of my mind/counssciousnes then philosophs of course was 99% right saying that everything come from nothing or that mind is primaral raver than matter. So idealists was right 99.999999999999% about primarality of minds and matterialists wrong. So because there still not some smart humans made all internet and so on, but it come from nothing/minds so I just need to play this nothing game how humans smart, how monkeys stupid and how idealists quite right, but still hiding that there is minds (which can be interpretated not nessasary like nothing or what comes from nothing), so I must play this game and to say, mind(s)/consciousnes come from nothing.
  7. Nov 3, 2009 #6
    Modal realism is more closer to principle of fecundity. mathematical universe hypothesis is different to the other two. You need to know that they are different, and the differences matter.

    For our purpose, i opt for modal realism.

    Why would this question matter regarding modal realism?

    The first question ask for why nature choice "this situation", so i don t know.
    I already answer the second with reasons on previous post.

    math deals with stable regular patterns. That can` t happen if harry starts changing the world by the power of his spell to doom the sun, and change subatomic structures to cheese.

    It is like asking if impossible worlds exist. Perhaps a world with true logical contradiction? I don` t think so.

    You suppose possible world *lack* self-consistency, but this cannot happen, because possible worlds are by their nature, self consistency.

    Another example to define a possible world is to called it "A maximally consistent set of propositions".

    So for possible w, there are infinite( finite) many propositions that specific W. This infinite string with not be contradictory, and with can defined W completely in all detail.
  8. Nov 3, 2009 #7
    If something comes from nothing based on the rules of QM, then i can ask why QM is true. That don` t explain anything.

    One can even doubt that there is such a thing as nothing, because nothing is not a thing.
  9. Nov 3, 2009 #8


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    I'm not a regular in the Philosophy forum, my background is actually in science, but I'll have to disagree with this premise.

    My view is that mathematics is a language, used to describe quantitatively what we observe. So to say that mathematical structures exist is like saying that the words in our spoken language exist. They don't, at least not in a real physical sense.
  10. Nov 3, 2009 #9
    So what is then in phylosophy mind? I thing that mind comes from nothing like british idealism states that possible everything do not exist, why you denying it? "He argued, for instance, in The Unreality of Time that it was not possible to produce a coherent account of a sequence of events in time, and that therefore time is an illusion. His book The Nature of Experience (1927) contained his arguments that space, time, and matter cannot possibly be real." http://en.wikipedia.org/wiki/Idealism#British_idealism

    Okay now why quantum mechanic true IN OUR minds. So QM is true only in this simulation of your minds (but it still can be not true, at least because you don't sow QM experiments personaly, so they can be falsified like any narcotics effect can be placeb or due some over reasons).

    But maybe I don't get your point And maybe you don't get my in preious post. Because I didn't say that somthing comes from nothing based on QM. I say that somthing comes from nothing and I believes into it with 99.999999999999% certainty. And over possiblity is that simulation of your conciousnes is not brain effect, but is from some over quantum mechanical tricks - I was meaning this and realy not such strange thing like somthing comes from nothing and this nothing is from quantum mechanic. So If you say there quantum mechanic can't create brain without physical body then I can easily to say to you that then simulation is based on some real laws, but this lows are not from nothing but they are real, but also they are not quantum mechanical laws.

    So you dissagre with this quate:
    "His book The Nature of Experience (1927) contained his arguments that space, time, and matter cannot possibly be real." http://en.wikipedia.org/wiki/Idealism#British_idealism

    Yes nothing can produce whatever thing you want, nothing is just absolutly empty space, and if it have inside some matterial wall then it is not nothing. Then this walls may form box and it's becomes not nothing. But nothing is purely empty space. And in this empty space apears counciousnes/minds - you or more precisly I because you from my reference point do not exist. Why in empty space can't apear invisible imaginary equation? Yes it can or at least is such possiblity that it can, so if it can then everything can apear imaginary like counciousnes.

    I thing just nothingnes in any possible way trying to hide it's existence if possible that to say. Because if you realise that nothing exist. Then QM is fake, your body existance laws is fake, all humans are just iliusion to you to believe that everything have some laws. So then what world should apear to your eyes? So then you realising that nothing exist and you see black and hear silence then you becoming don't see your legs and your and then only memories is for you, so would you like such a live? And now memmories based also on nothing so you itself will dissapear so you just need to play this game that you somthing doing for reason and I would say that this reason is just to exist, because everything still don't have any logic and all humans still are not real, but part of your counciousnes. QM is maximaly maded to fool you to believe that everything exist and can be real, it maximaly maded to almost like looks like very possible laws of nature, no shapes no questions, you also don't thinking too real because you are simulation from nothing so you or I still not real, but raver I want one thing - exist forever because real or not but still somthing felling and seeing.

    Now where is flaw in QM? QM saying that wavefunction colapsing from big wave to small area/point, this area is up to 1000 or bilions times smaller than initialy wave. So then all energy is teleportated to small point. But you can say, there flying small gnome in small spaceship and each time he stroking different point according some plan, but then there must be very collective plan of all electrons which shooting measuring device through slits etc. But isn't this story not the same like Earth holds on turtle or elephant and this turtle on over turtle or elephant this on another ant to infinity. So this exactly the same electron have counciousnes or energy is teleportated choose one from those or argue that counciousnes come from nothing and there no matterial, real things, just imaginary ones.
  11. Nov 3, 2009 #10


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    This is the obvious common sense approach - the map is not the territory. So no surprise that philosophical approaches like modal realism give philosophy a bad name.

    As is being asked in the conspiracy theory thread, do these guys really believe their own arguments? Or is it just a way to spin out a career?

    The natural approach (also described carefully in the branch of philosophy known as semiotics) is that the world would exist. It self-organises in some averaging, regularising, resonance based way. Then humans can come along and describe these regularities in mathematical language. Statements about equivalence (symmetry) and scale (asymmetry).

    So does the number 1 exist? No, not like the world. But the essence of what we mean by one-ness can be found all over the place.

    One is not "necessarily existent" as lifeforms may have never got round to constructing the kind of languages in which 1 has its contextual meaning (being opposed to the many, for a start).

    The one-ness quality would always be out there as a natural regularity of self-organising development. But if say there really was nothingness, then one-ness of that self-organising regularity type also could never have existed as a possibility. Not even in imagination because if nothingness could actually be the case, then self-organising development also gets banned as a consquence. Things (or rather nothings) would have to have that non-feature as well.

    But 1, our name for one-ness, is not a thing that has existence except as a human concept and part of our language system, part of mapping of the territory. So it cannot have an existence/non-existence issue except in this very secondary, epistemic, sense.

    Really, modal realism, modal logic in general, is schoolboy stuff. But like conspiracy theories, it can be amusing how it plays out, the contortions people go through to "believe".
  12. Nov 3, 2009 #11


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    1,2,3 ..ready set go REALITY. The natural numbers and relations created with them (structure, geometry) constitute the ultimate truth.1,2,3.. Is the basic and the Only truth, everything else is derived notion (from the relations). There is no difference between the mathematical language description of the mathematical objects and the objects themselves. The same would be true for the description of physical stuff with mathematical description; they are one and the same. The first argument is many times stronger than the second. You can define any relation between groups of numbers to your heart’s content, let them produce familiar or unfamiliar, apply to our universe or not, make them as exotic as you like, no problem. But you do have to live with consequences of you definitions; they might produce a really weird existence. You can create a universe out of nothing. Just throw random numbers consider that bunch your space, throw other numbers, and make them represent particles’ positions on the previous numbers. There you go; just a taste of what is possible. Check out a realistic (test) universe created that way.
  13. Nov 3, 2009 #12
    The tradition idea of mathematical propositions is that they are descriptive about numbers. For example: The proposition "13 is prime" is about the number 13. To many, the act of saying 13 has the property of being prime means that 13 really exist. Now, you can ask if i belleve in santa claus, becayse "santa claus is fat" is about santa claus, and the statment seems to be describing santa claus. One distinction is that math propositions are objective, while santa might not be objective. The fact that math propositions seem to describe numbers, and the fact that numbers seems to have an objective existence in their own right independent of minds lead us to think they do exist.
  14. Nov 3, 2009 #13


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    Poinit of order, vectorcube: Why do you consistently use "` " instead of "'"?

    i.e. tagmark` s should be tagmark's.

    It makes it very difficult you read your posts.

    Carry on.
  15. Nov 3, 2009 #14
    How are math propositions objective?
  16. Nov 4, 2009 #15


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    Or Tegmark's if we were being picky.
  17. Nov 4, 2009 #16


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    Yet properties of objects are always given their meaning by their contexts. So primeness is a fact about a lack of factors. Every other number has to be considered in case divisors might not have been noticed.

    So on this semiotic consideration, properties as usual are context-dependent rather than purely inherent in objects.

    So objects - even mathematical - only gain their crisp properties, their meaning, from being parts of larger systems. Every event must have a context to be an event.

    And what is with this idea that maths is self-evidently objective? Are you saying it is even the majority view within philosophy of maths? The case needs to be argued. I have already argued for the epistemic case and glad to go futher.
  18. Nov 4, 2009 #17


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    after 10000 years of civilization we are questioning if 1,2,3 ... to be a fact. Really. And we hope to discover the secret of existence!
  19. Nov 4, 2009 #18

    Are you sure it is because it is "difficult"?
  20. Nov 4, 2009 #19
    Example is fermat` s theorm. We now know that the theorm is true( because we have a proof), but conceivably, some alien from outer space would produce a proof that shows that theorm is true. The alien could never show that the theorm is falses even if they want to. Similarly, fermat` s theorm would be true even if fermat never formulated the conjuncture in the first place.
  21. Nov 4, 2009 #20
    properties are represented by predicates, and they are forever tied to their instances.

    For predicate P, there is a object m, so that Pm. Is not clear why Pm is context dependent, or what that even mean.

    The set of natural numbers is a math structure. Tell me the larger context?

    never made any definitive claims at all.
  22. Nov 4, 2009 #21


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    Here is a counterexample to that logic:
    I could say, "The purple elephant in the dream I had last night, had a single tusk".
    This is an objective statement, yet the purple elephant never existed.

    Or more generally, we can imagine anything, even ascribe some objective properties to it, but it still doesn't exist.

    "Santa Claus wears a red suit" would be an objective statement about Santa Claus.
    Last edited: Nov 4, 2009
  23. Nov 4, 2009 #22


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    Not sure I agree.

    Re: the elephant. How can there be an objective statement about something only you can see? It is, by definition, subjective. Same with Santa, it is only agreed upon by the general populace that he wears a red suit. That's not objective.

    How would you go about falsifying such claims?
    Last edited: Nov 4, 2009
  24. Nov 4, 2009 #23
    Well, you can invent a character called santa, and ascribe some properties P to santa.

    The objectivity comes in in math is when people knowns the rules and axioms of say twin primes, and that two mathematicians separated by long distence, and never had any contact with one another can suddenly discovery some new properties about twin primes. No one seem to ascribe any properties to twin primes at all.
  25. Nov 4, 2009 #24


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    Leopold Kronecker said: "The natural numbers come from God, everything else is man's work."
  26. Nov 4, 2009 #25
    well, anti-platonism is a completely consistent view.
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