Re: Contradiction. Was: Probability
Anna, I wanted to write positively to your posts, procrastinated it though and others took it up. Now I want to reflect to one word, I use differently: *MODEL* There are several 'models', the mathematical (or simple physical) metaphor of a different subject is one, not to mention the pretty women in fashion-shows. I use *model* in the sense of a reductionist cut from the totality aspect for a topical view: the epitom of which is Occams razor. Observing (studying) a topic within chosen boundaries - limitations of our selection by our interest. Of course Bruno's all encompassing arithmetic system can cover for this, too, but I am not for restricting our discussions to the limitations of the present human mind's potential (even if only in an allowance for what we cannot comprehend or imagine). Beyond Brent's yam-y extension. What we don't know or understand or even find possible is not impossible. It is part of 'everything'. I chose to be vague and scientifically agnostic. Have fun in science John Mikes ** On Fri, Nov 7, 2008 at 7:41 PM, Brent Meeker [EMAIL PROTECTED]wrote: A. Wolf wrote: So universes that consisted just of lists of (state_i)(state_i+1)... would exist, where a state might or might not have an implicate time value. Of course, but would something that arbitrary be capable of supporting the kind of self-referential behavior necessary for sapience? Anna Capable of supporting implies some physical laws that connect an environment and sapient beings. In an arbitrary list universe, the occurrence of sapience might be just another arbitrary entry in the list (like Boltzman brains). And what about the rules of inference? Do we consider universes with different rules of inference? Are universes considered contradictory, and hence non-existent, if you can prove X and not-X for some X, or only if you can prove Y for all Y? You see, that's what I like about Bruno's scheme, he assumes a definite mathematical structure (arithmetic) and proposes that everything comes out of it. I think there is still problem avoiding wonderland, but in Tegmark's broader approach the problem is much bigger and all the work has to be done by some anthropic principle (which in it's full generality might be called the Popeye principle - I yam what I yam.). Once you start with all non-contradictory mathematics, you might as well let in the contradictory ones too. The Popeye principle can eliminate them as well. Brent --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
If I may, http://en.wikipedia.org/wiki/Model_theory The basic concept is that every model is composed of a set of elements, a set of n-ary relations between them, a set of constants and symbols, plus a set of axiomatic sentences to define it. It's been a few years since my mathematical logic MSc though -- - Did you ever hear of The Seattle Seven? - Mmm. - That was me... and six other guys. 2008/11/8 John Mikes [EMAIL PROTECTED] Anna, I wanted to write positively to your posts, procrastinated it though and others took it up. Now I want to reflect to one word, I use differently: *MODEL* There are several 'models', the mathematical (or simple physical) metaphor of a different subject is one, not to mention the pretty women in fashion-shows. I use *model* in the sense of a reductionist cut from the totality aspect for a topical view: the epitom of which is Occams razor. Observing (studying) a topic within chosen boundaries - limitations of our selection by our interest. Of course Bruno's all encompassing arithmetic system can cover for this, too, but I am not for restricting our discussions to the limitations of the present human mind's potential (even if only in an allowance for what we cannot comprehend or imagine). Beyond Brent's yam-y extension. What we don't know or understand or even find possible is not impossible. It is part of 'everything'. I chose to be vague and scientifically agnostic. Have fun in science John Mikes ** On Fri, Nov 7, 2008 at 7:41 PM, Brent Meeker [EMAIL PROTECTED]wrote: A. Wolf wrote: So universes that consisted just of lists of (state_i)(state_i+1)... would exist, where a state might or might not have an implicate time value. Of course, but would something that arbitrary be capable of supporting the kind of self-referential behavior necessary for sapience? Anna Capable of supporting implies some physical laws that connect an environment and sapient beings. In an arbitrary list universe, the occurrence of sapience might be just another arbitrary entry in the list (like Boltzman brains). And what about the rules of inference? Do we consider universes with different rules of inference? Are universes considered contradictory, and hence non-existent, if you can prove X and not-X for some X, or only if you can prove Y for all Y? You see, that's what I like about Bruno's scheme, he assumes a definite mathematical structure (arithmetic) and proposes that everything comes out of it. I think there is still problem avoiding wonderland, but in Tegmark's broader approach the problem is much bigger and all the work has to be done by some anthropic principle (which in it's full generality might be called the Popeye principle - I yam what I yam.). Once you start with all non-contradictory mathematics, you might as well let in the contradictory ones too. The Popeye principle can eliminate them as well. Brent --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
I am realizing that I don't have time to get into this. I assume that your use of the word model is equivalent to theory. Er, no. I mean a foundational mathematical model which includes at least one set representative of the multiverse, or at the very least a countable transitive submodel that satisfies the same constraints. I'm using the word model in the specific set-theoretic sense. Anna --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
Capable of supporting implies some physical laws that connect an environment and sapient beings. In an arbitrary list universe, the occurrence of sapience might be just another arbitrary entry in the list (like Boltzman brains). And what about the rules of inference? Do we This is true. What you're describing...a list of states, in a sense...would be a teeny subset of all possible consistent universes, though. It doesn't describe our own universe, for one example: there is no grand clock that ticks down such that the universe can be partitioned into states. :) I'd need to cover relativity to explain why, but the universe isn't sliceable in the way you're suggesting it is. Anna --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
A. Wolf wrote: Capable of supporting implies some physical laws that connect an environment and sapient beings. In an arbitrary list universe, the occurrence of sapience might be just another arbitrary entry in the list (like Boltzman brains). And what about the rules of inference? Do we This is true. What you're describing...a list of states, in a sense...would be a teeny subset of all possible consistent universes, though. It doesn't describe our own universe, for one example: there is no grand clock that ticks down such that the universe can be partitioned into states. :) I'd need to cover relativity to explain why, but the universe isn't sliceable in the way you're suggesting it is. Anna I'm well aware of relativity. But I don't see how you can invoke it when discussing all possible, i.e. non-contradictory, universes. Neither do I see that list of states universes would be a teeny subset of all mathematically consistent universes. On the contrary, it would be very large. It would certainly be much larger than that teeny subset obeying general relativity or Newtonian physics or the standard model of QFT in Minkowski spacetime. Brent --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
I'm well aware of relativity. But I don't see how you can invoke it when discussing all possible, i.e. non-contradictory, universes. Neither do I see that list of states universes would be a teeny subset of all mathematically consistent universes. On the contrary, it would be very large. It would certainly be much larger than that teeny subset obeying general relativity or Newtonian physics or the standard model of QFT in Minkowski spacetime. You said: So universes that consisted just of lists of (state_i)(state_i+1)... would exist, where a state might or might not have an implicate time value. I was trying to express that the universe in which we reside isn't separable into a set of lists of states. It's more mathematically complex than that. Some mathematical models are self-contradictory, and some are not. This is true regardless as to how you formulate a foundation of mathematics, and it forms the basis for understanding and proving mathematical truths. I believe that a mathematical structure complex enough to capture the entire set of events that define a universe must be non-self-contradictory to be a truthful model for that universe. There are mathematical structures which are self-contradictory because they are predicated upon axioms which ultimately contradict themselves; these structures are not well-defined and cannot be a basis for existence. Such a basis would make existence itself ambiguous, because all things would have to exist and not-exist at the same time, and not in the quantum way--with no discernable structure or foundation at all. I'm not certain what you're trying to argue, but it seems like you think that anything you can imagine must have a well-founded mathematical basis...? You can imagine all you like, but it won't bring into being a universe where Godel's incompleteness theorems don't hold, for example. The fundamental things that we know about mathematics itself transcend any particular realization of the universe. Anna --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
A. Wolf wrote: I'm well aware of relativity. But I don't see how you can invoke it when discussing all possible, i.e. non-contradictory, universes. Neither do I see that list of states universes would be a teeny subset of all mathematically consistent universes. On the contrary, it would be very large. It would certainly be much larger than that teeny subset obeying general relativity or Newtonian physics or the standard model of QFT in Minkowski spacetime. You said: So universes that consisted just of lists of (state_i)(state_i+1)... would exist, where a state might or might not have an implicate time value. I was trying to express that the universe in which we reside isn't separable into a set of lists of states. It's more mathematically complex than that. Some mathematical models are self-contradictory, and some are not. This is true regardless as to how you formulate a foundation of mathematics, and it forms the basis for understanding and proving mathematical truths. I believe that a mathematical structure complex enough to capture the entire set of events that define a universe must be non-self-contradictory to be a truthful model for that universe. There are mathematical structures which are self-contradictory because they are predicated upon axioms which ultimately contradict themselves; these structures are not well-defined and cannot be a basis for existence. Such a basis would make existence itself ambiguous, because all things would have to exist and not-exist at the same time, and not in the quantum way--with no discernable structure or foundation at all. I'm not certain what you're trying to argue, but it seems like you think that anything you can imagine must have a well-founded mathematical basis...? So long as it is not self-contradictory I can make it an axiom of a mathematical basis. It may not be very interesting mathematics to postulate: Axiom 1: There is a purple cow momentarily appearing to Anna and then vanishing. but by the standard that everything not self-contradictory is mathematics it's just as good as Peano's. You can imagine all you like, but it won't bring into being a universe where Godel's incompleteness theorems don't hold, for example. The fundamental things that we know about mathematics itself transcend any particular realization of the universe. Anna I'm arguing that all mathematically consistent structures is itself an ill defined concept. A mathematical structure consists of a set of axioms and rules of inference. So I supported my point my giving an example in which the set of axioms is an infinite set of propositions of the form state i obtains at time i where state i can be any set of self-consistent declarative sentences whatsoever. I leave the set of rules of inference empty - so there can be no contradiction inferred between states. Then according to the theory that all mathematically consistent structures are instantiated (everything exists) this set exists and defines a universe just as well as general relativity or quantum field theory (perhaps better since we can't be sure those theories are consistent). Brent --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
So long as it is not self-contradictory I can make it an axiom of a mathematical basis. It may not be very interesting mathematics to postulate: Axiom 1: There is a purple cow momentarily appearing to Anna and then vanishing. I fear this is not an axiom of a mathematical basis. :) The problem with improperly-founded axioms is the same problem encountered with the naive set theory of Frege. You can't ever be certain that a set of axioms isn't self-contradictory. In fact, Frege's unstated Axiom of Unrestricted Comprehension, which roughly states for any property P, there exists a set containing all and only the things that satisfy that property, is self-contradictory by itself. Anna --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
A. Wolf wrote: So long as it is not self-contradictory I can make it an axiom of a mathematical basis. It may not be very interesting mathematics to postulate: Axiom 1: There is a purple cow momentarily appearing to Anna and then vanishing. I fear this is not an axiom of a mathematical basis. :) The problem with improperly-founded axioms is the same problem encountered with the naive set theory of Frege. You can't ever be certain that a set of axioms isn't self-contradictory. I can if there's no rule of inference. Perhaps that's crux. You are requiring that a mathematical structure be a set of axioms *plus* the usual rules of inference for and, or, every, any,...and maybe the axiom of choice too. In fact, Frege's unstated Axiom of Unrestricted Comprehension, which roughly states for any property P, there exists a set containing all and only the things that satisfy that property, is self-contradictory by itself. Well not entirely by itself - one still needs the rules of inference to get to Russell's paradox. But then what is the justification for limiting universes to those which admit the usual rule of inference? And remember that because of Godelian incompleteness an infinite number of axioms can be added even to those universes without running into contradictions. Brent --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
2008/11/9 Brent Meeker [EMAIL PROTECTED]: A. Wolf wrote: I can if there's no rule of inference. Perhaps that's crux. You are requiring that a mathematical structure be a set of axioms *plus* the usual rules of inference for and, or, every, any,...and maybe the axiom of choice too. Rules of inference can be derived from the axioms...it sounds circular but in ZFC all you need are nine axioms and two undefinables (which are set, and the binary relation of membership). You write the axioms using the language of predicate calculus, but that's just a convenience to be able to refer to them. Well not entirely by itself - one still needs the rules of inference to get to Russell's paradox. Not true! The paradox arises from the axioms alone (and it isn't a true paradox, either, in that it doesn't cause a contradiction among the axioms...it simply reveals that certain sets do not exist). The set of all sets cannot exist because it would contradict the Axiom of Extensionality, which says that each set is determined by its elements (something can't both be in a set and not in the same set, in other words). I thought you were citing it as an example of a contradiction - but we digress. What is your objection to the existence of list-universes? Are they not internally consistent mathematical structures? Are you claiming that whatever the list is, rules of inference can be derived (using what process?) and thence they will be found to be inconsistent? Brent Well I reverse the question... Do you think you can still be consistent without being consistent ? If there is no rules of inference or in other words, no rules that ties states... How do you define consistency ? Regards, Quentin -- All those moments will be lost in time, like tears in rain. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
A. Wolf wrote: I can if there's no rule of inference. Perhaps that's crux. You are requiring that a mathematical structure be a set of axioms *plus* the usual rules of inference for and, or, every, any,...and maybe the axiom of choice too. Rules of inference can be derived from the axioms...it sounds circular but in ZFC all you need are nine axioms and two undefinables (which are set, and the binary relation of membership). You write the axioms using the language of predicate calculus, but that's just a convenience to be able to refer to them. Well not entirely by itself - one still needs the rules of inference to get to Russell's paradox. Not true! The paradox arises from the axioms alone (and it isn't a true paradox, either, in that it doesn't cause a contradiction among the axioms...it simply reveals that certain sets do not exist). The set of all sets cannot exist because it would contradict the Axiom of Extensionality, which says that each set is determined by its elements (something can't both be in a set and not in the same set, in other words). I thought you were citing it as an example of a contradiction - but we digress. What is your objection to the existence of list-universes? Are they not internally consistent mathematical structures? Are you claiming that whatever the list is, rules of inference can be derived (using what process?) and thence they will be found to be inconsistent? Brent --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
On Sat, Nov 8, 2008 at 8:41 PM, Quentin Anciaux [EMAIL PROTECTED] wrote:
To infer means there is a process which permits to infer.. if there
is none... then you can't simply infer something.
The process itself arises naturally from the universe of sets
guaranteed by the axioms of set theory. For example, the Axiom of
Union says that the elements of the elements of a set form a set. You
can therefore infer that if the set { { { } }, { { { } } } } exists,
then the set { { }, { { } } } exists. By using the axioms alone,
you can prove and disprove everything in mathematics. The process of
inference comes from the axioms themselves and the undefinable
membership relation.
This is elementary set theory...any basic course in set theory should
cover this.
Anna
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Re: Contradiction. Was: Probability
What is your objection to the existence of list-universes? Are they not internally consistent mathematical structures? Are you claiming that whatever the list is, rules of inference can be derived (using what process?) and thence they will be found to be inconsistent? You're rally confused here. I don't suggest your list-universes are inconsistent; quite the opposite. I thought you brought up the list-universe example as if to say if we look at any universe as a list of states, then how can it be inconsistent. To which I responded with that's not a good example because most universes can't be discretised to a simple list of states. In other words, I can't come up with an simple example of an inconsistent list-of-states-universe, but that doesn't mean all universes are consistent, because most universes aren't like your simplified example. Anna --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
Well by your definition a universe is consistent (the inconsistent ones don't exist). So given a universe we could look at it as a list of states if it could be foliated by some parameter (which we might identify as time). The inconsistent ones don't exist, but an abstract description of some of them does. Certainly not all - but I'm not sure what measure would justify most. Usually when you restrict a set of things by a specific property, almost all sets fail to meet that property. As an obtuse example, almost all natural numbers are larger than any given natural number. This is only true if we provide a measurable domain, though (you can't measure all sets to begin with...too big), so technically I'm wrong the way I said it. For most uncountable domains the above would be true, though. That's not quite what you mean - since you've defined them as consistent they all are. But I understand what you mean; just giving some specification of a universe may very well result in inconsistency and hence failure to actually specify one. Yes. Assuming everything exists in some sense, why do we experience this particular one? If we say just because then the everything hypothesis is empty. To say something more informative we need some measure on universes. And then we a justification for that measure rather than some other. That's an interesting question, but a very different topic. I like to think that the experience of one particular reality is just one tiny facet of a global universal consciousness...that there's no real difference between one consciousness and the next, so to speak. As to the topic that I did bring up, I stand by what I said... I don't think we can assume any universe we can imagine is mathematically consistent just because we can describe it, because mathematics has examples where this isn't the case, and I presume that consistency and existence are the same concept mathematically. Anna --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
Quentin Anciaux wrote: To infer means there is a process which permits to infer.. if there is none... then you can't simply infer something. Right. So you can't infer a contradiction. Brent 2008/11/9 Brent Meeker [EMAIL PROTECTED]: Quentin Anciaux wrote: 2008/11/9 Brent Meeker [EMAIL PROTECTED]: A. Wolf wrote: I can if there's no rule of inference. Perhaps that's crux. You are requiring that a mathematical structure be a set of axioms *plus* the usual rules of inference for and, or, every, any,...and maybe the axiom of choice too. Rules of inference can be derived from the axioms...it sounds circular but in ZFC all you need are nine axioms and two undefinables (which are set, and the binary relation of membership). You write the axioms using the language of predicate calculus, but that's just a convenience to be able to refer to them. Well not entirely by itself - one still needs the rules of inference to get to Russell's paradox. Not true! The paradox arises from the axioms alone (and it isn't a true paradox, either, in that it doesn't cause a contradiction among the axioms...it simply reveals that certain sets do not exist). The set of all sets cannot exist because it would contradict the Axiom of Extensionality, which says that each set is determined by its elements (something can't both be in a set and not in the same set, in other words). I thought you were citing it as an example of a contradiction - but we digress. What is your objection to the existence of list-universes? Are they not internally consistent mathematical structures? Are you claiming that whatever the list is, rules of inference can be derived (using what process?) and thence they will be found to be inconsistent? Brent Well I reverse the question... Do you think you can still be consistent without being consistent ? If there is no rules of inference or in other words, no rules that ties states... How do you define consistency ? A set of propositions is consistent if it is impossible to infer contradiction. Brent --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
Quentin Anciaux wrote: 2008/11/9 Brent Meeker [EMAIL PROTECTED]: A. Wolf wrote: I can if there's no rule of inference. Perhaps that's crux. You are requiring that a mathematical structure be a set of axioms *plus* the usual rules of inference for and, or, every, any,...and maybe the axiom of choice too. Rules of inference can be derived from the axioms...it sounds circular but in ZFC all you need are nine axioms and two undefinables (which are set, and the binary relation of membership). You write the axioms using the language of predicate calculus, but that's just a convenience to be able to refer to them. Well not entirely by itself - one still needs the rules of inference to get to Russell's paradox. Not true! The paradox arises from the axioms alone (and it isn't a true paradox, either, in that it doesn't cause a contradiction among the axioms...it simply reveals that certain sets do not exist). The set of all sets cannot exist because it would contradict the Axiom of Extensionality, which says that each set is determined by its elements (something can't both be in a set and not in the same set, in other words). I thought you were citing it as an example of a contradiction - but we digress. What is your objection to the existence of list-universes? Are they not internally consistent mathematical structures? Are you claiming that whatever the list is, rules of inference can be derived (using what process?) and thence they will be found to be inconsistent? Brent Well I reverse the question... Do you think you can still be consistent without being consistent ? If there is no rules of inference or in other words, no rules that ties states... How do you define consistency ? A set of propositions is consistent if it is impossible to infer contradiction. Brent --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
A. Wolf wrote: What is your objection to the existence of list-universes? Are they not internally consistent mathematical structures? Are you claiming that whatever the list is, rules of inference can be derived (using what process?) and thence they will be found to be inconsistent? You're rally confused here. I doubt it. I don't suggest your list-universes are inconsistent; quite the opposite. I thought you brought up the list-universe example as if to say if we look at any universe as a list of states, then how can it be inconsistent. Well by your definition a universe is consistent (the inconsistent ones don't exist). So given a universe we could look at it as a list of states if it could be foliated by some parameter (which we might identify as time). To which I responded with that's not a good example because most universes can't be discretised to a simple list of states. Certainly not all - but I'm not sure what measure would justify most. In other words, I can't come up with an simple example of an inconsistent list-of-states-universe, but that doesn't mean all universes are consistent, That's not quite what you mean - since you've defined them as consistent they all are. But I understand what you mean; just giving some specification of a universe may very well result in inconsistency and hence failure to actually specify one. because most universes aren't like your simplified example. But the question of measure, what makes up most, is the crux of the question. Assuming everything exists in some sense, why do we experience this particular one? If we say just because then the everything hypothesis is empty. To say something more informative we need some measure on universes. And then we a justification for that measure rather than some other. Brent --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
Quentin Anciaux wrote: Also... a list consisting of A exists and A does not exists is consistent to you ? No, that would be inconsistent. Could I infer A exsits or A does not exists from this list ? If I takes the states separately, there is no contradiction... but If I take the states as following each other (in any order) then there must be a rule that ties those states together... and how could it be a rule if it change at every steps ? I was thinking of lists like A exists at t. and A does not exist at t+1.; so it is explicit that the propositions in the list do not directly contradict each other. In our models of the universe we rely on various regularities which are subsumed under the laws of physics to compare propositions that refer to different spacetime events. But if we're going to contemplate all mathematically consistent universes and try to derive the laws of physics then we have only the laws of logic to relate one proposition to another. I think they are to weak rule out completely arbitrary universes like my list-universe. Maybe by mathematically consistent you mean more than just free of logical contradiction; maybe you mean including ZF or ZFC - that would capture a lot of mathematics. Brent 2008/11/9 Brent Meeker [EMAIL PROTECTED]: Quentin Anciaux wrote: 2008/11/9 Brent Meeker [EMAIL PROTECTED]: A. Wolf wrote: I can if there's no rule of inference. Perhaps that's crux. You are requiring that a mathematical structure be a set of axioms *plus* the usual rules of inference for and, or, every, any,...and maybe the axiom of choice too. Rules of inference can be derived from the axioms...it sounds circular but in ZFC all you need are nine axioms and two undefinables (which are set, and the binary relation of membership). You write the axioms using the language of predicate calculus, but that's just a convenience to be able to refer to them. Well not entirely by itself - one still needs the rules of inference to get to Russell's paradox. Not true! The paradox arises from the axioms alone (and it isn't a true paradox, either, in that it doesn't cause a contradiction among the axioms...it simply reveals that certain sets do not exist). The set of all sets cannot exist because it would contradict the Axiom of Extensionality, which says that each set is determined by its elements (something can't both be in a set and not in the same set, in other words). I thought you were citing it as an example of a contradiction - but we digress. What is your objection to the existence of list-universes? Are they not internally consistent mathematical structures? Are you claiming that whatever the list is, rules of inference can be derived (using what process?) and thence they will be found to be inconsistent? Brent Well I reverse the question... Do you think you can still be consistent without being consistent ? If there is no rules of inference or in other words, no rules that ties states... How do you define consistency ? A set of propositions is consistent if it is impossible to infer contradiction. Brent --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Contradiction. Was: Probability
To infer means there is a process which permits to infer.. if there is none... then you can't simply infer something. 2008/11/9 Brent Meeker [EMAIL PROTECTED]: Quentin Anciaux wrote: 2008/11/9 Brent Meeker [EMAIL PROTECTED]: A. Wolf wrote: I can if there's no rule of inference. Perhaps that's crux. You are requiring that a mathematical structure be a set of axioms *plus* the usual rules of inference for and, or, every, any,...and maybe the axiom of choice too. Rules of inference can be derived from the axioms...it sounds circular but in ZFC all you need are nine axioms and two undefinables (which are set, and the binary relation of membership). You write the axioms using the language of predicate calculus, but that's just a convenience to be able to refer to them. Well not entirely by itself - one still needs the rules of inference to get to Russell's paradox. Not true! The paradox arises from the axioms alone (and it isn't a true paradox, either, in that it doesn't cause a contradiction among the axioms...it simply reveals that certain sets do not exist). The set of all sets cannot exist because it would contradict the Axiom of Extensionality, which says that each set is determined by its elements (something can't both be in a set and not in the same set, in other words). I thought you were citing it as an example of a contradiction - but we digress. What is your objection to the existence of list-universes? Are they not internally consistent mathematical structures? Are you claiming that whatever the list is, rules of inference can be derived (using what process?) and thence they will be found to be inconsistent? Brent Well I reverse the question... Do you think you can still be consistent without being consistent ? If there is no rules of inference or in other words, no rules that ties states... How do you define consistency ? A set of propositions is consistent if it is impossible to infer contradiction. Brent -- All those moments will be lost in time, like tears in rain. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
