Re: Contradiction. Was: Probability

2008-11-08 Thread John Mikes
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

Re: Contradiction. Was: Probability

2008-11-08 Thread Michael Rosefield
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

Re: Contradiction. Was: Probability

2008-11-08 Thread A. Wolf
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

Re: Contradiction. Was: Probability

2008-11-08 Thread A. Wolf
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.

Re: Contradiction. Was: Probability

2008-11-08 Thread Brent Meeker
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

Re: Contradiction. Was: Probability

2008-11-08 Thread A. Wolf
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.

Re: Contradiction. Was: Probability

2008-11-08 Thread Brent Meeker
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

Re: Contradiction. Was: Probability

2008-11-08 Thread A. Wolf
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

Re: Contradiction. Was: Probability

2008-11-08 Thread Brent Meeker
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

Re: Contradiction. Was: Probability

2008-11-08 Thread A. Wolf
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

Re: Contradiction. Was: Probability

2008-11-08 Thread Quentin Anciaux
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.

Re: Contradiction. Was: Probability

2008-11-08 Thread Brent Meeker
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

Re: Contradiction. Was: Probability

2008-11-08 Thread Quentin Anciaux
Also... a list consisting of A exists and A does not exists is consistent to you ? 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

Re: Contradiction. Was: Probability

2008-11-08 Thread A. Wolf
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.

Re: Contradiction. Was: Probability

2008-11-08 Thread A. Wolf
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

Re: Contradiction. Was: Probability

2008-11-08 Thread A. Wolf
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

Re: Contradiction. Was: Probability

2008-11-08 Thread Brent Meeker
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

Re: Contradiction. Was: Probability

2008-11-08 Thread Brent Meeker
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

Re: Contradiction. Was: Probability

2008-11-08 Thread Brent Meeker
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?

Re: Contradiction. Was: Probability

2008-11-08 Thread Brent Meeker
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

Re: Contradiction. Was: Probability

2008-11-08 Thread Quentin Anciaux
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

Re: Contradiction. Was: Probability

2008-11-07 Thread Tom Caylor
I like this topic. I will think about it a little first. By the way, is your use of blue and red a metaphor for Obama and McCain? ;) Tom On Nov 7, 10:44 am, A. Wolf [EMAIL PROTECTED] wrote: But this begs the question What is EVERYTHING? I would say the class of all mathematical models

Re: Contradiction. Was: Probability

2008-11-07 Thread A. Wolf
On Fri, Nov 7, 2008 at 1:07 PM, Tom Caylor [EMAIL PROTECTED] wrote: I like this topic. I will think about it a little first. By the way, is your use of blue and red a metaphor for Obama and McCain? ;) Wow. :) Subconciously, perhaps in part. But it's mainly because the last pair of

Re: Contradiction. Was: Probability

2008-11-07 Thread Brent Meeker
A. Wolf wrote: But this begs the question What is EVERYTHING? I would say the class of all mathematical models which are not self-contradictory constitutes everything. I'd even go so far as to suggest that's exactly what existence is, in a literal sense: a lack of mathematical

Re: Contradiction. Was: Probability

2008-11-07 Thread A. Wolf
If you don't require some mathematical model of evolution of states determining what happens in a Markovian way (like a Schroedinger eqn for example) then one consistent mathematical model is just a list:... Anna wore a red sweater on 6 Nov 2008, Anna wore a blue sweater on 7 Nov 2008, Anna

Re: Contradiction. Was: Probability

2008-11-07 Thread Brent Meeker
A. Wolf wrote: If you don't require some mathematical model of evolution of states determining what happens in a Markovian way (like a Schroedinger eqn for example) then one consistent mathematical model is just a list:... Anna wore a red sweater on 6 Nov 2008, Anna wore a blue sweater on 7

Re: Contradiction. Was: Probability

2008-11-07 Thread A. Wolf
Does model imply a theory which predicts the evolution of states (possibly probabilistic) so that the state of universe yesterday limits what might exist today? No. Model means a mathematical object. One specific, unchanging, crystalline object you can hold in your hand and look at from a

Re: Contradiction. Was: Probability

2008-11-07 Thread Brent Meeker
A. Wolf wrote: Does model imply a theory which predicts the evolution of states (possibly probabilistic) so that the state of universe yesterday limits what might exist today? No. Model means a mathematical object. One specific, unchanging, crystalline object you can hold in your

Re: Contradiction. Was: Probability

2008-11-07 Thread A. Wolf
But not a logical contradiction. It would just contradict our assumed model of physics, i.e. a nomological contradiction. I realize I can't give a concrete example from physics due to the lack of total human understanding, so it is difficult to get across the exact point. If we presume that

Re: Contradiction. Was: Probability

2008-11-07 Thread Brent Meeker
A. Wolf wrote: But not a logical contradiction. It would just contradict our assumed model of physics, i.e. a nomological contradiction. I realize I can't give a concrete example from physics due to the lack of total human understanding, so it is difficult to get across the exact

Re: Contradiction. Was: Probability

2008-11-07 Thread A. Wolf
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

Re: Contradiction. Was: Probability

2008-11-07 Thread Tom Caylor
On Nov 7, 10:44 am, A. Wolf [EMAIL PROTECTED] wrote: But this begs the question What is EVERYTHING? I would say the class of all mathematical models which are not self-contradictory constitutes everything.  I'd even go so far as to suggest that's exactly what existence is, in a literal

Re: Contradiction. Was: Probability

2008-11-07 Thread Brent Meeker
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