Re: [Fis] Reply to Ted Goranson: levels of description
John Collier wrote on 6/10/06: At 05:35 PM 6/10/2006, Stanley N. Salthe wrote: John said: > Hmm. You should read Barwise and Seligman, Information Flow... ... It depends what you mean by logic. The issue is too complicated to get into here and now, but the simple answer is that there is no non-arbitrary distinction between mathematics and logic. Exactly the same reasons apply to the limits of both, and the only way to get one more powerful than the other is to apply a double standard for proofs and/or acceptability. Thank you, John. Good insight. I sponsored a workshop on a topic near to this, during which Barwise said much the same thing. It seems to me that mathematics and logic are siblings, perhaps cojoined. I suppose there are other siblings not so human-friendly, used by natural objects. Information seems to be the light by which we might see them by their shadows. I'm not surprised that most physicists want to ontologically flatten everything into a QM-described truth. What does surprise me is that no one has mentioned the inconvenient fact that gravity, that most prevalent force in physics, is notably unfriendly to QM. Best, Ted -- __ Ted Goranson Sirius-Beta ___ fis mailing list fis@listas.unizar.es http://webmail.unizar.es/mailman/listinfo/fis
Re: [Fis] Reply to Ted Goranson: levels of description
At 05:35 PM 6/10/2006, Stanley N. Salthe wrote: John said: > Hmm. You should read Barwise and Seligman, Information Flow: the logic of >distributed Systems. Very important for understanding Quantum Information. >Also, I assume that you are familiar with algorithmic complexity theory, >which is certainly rigourous, Minimum Description Length (Rissanen) and >Minimum Message Length (Wallace and Dowe) methods that apply Kolomogorov >and Chaitin's ideas very rigourously. If you don't like the computational >approaches for some reason, then you might want to look at Ingarden et al, >(1997) Information Dynamics and Open Systems (Dordrecht: Kluwer). They >show how probability can be derived from Boolean structures, which are >based on the fundamental notion of information theory, that of making a >binary distinction. So probability is based in information theory, not the >other way around (there are other ways to show this, but I take the >Ingarden et al approach as conclusive -- Chaitin and Kolmogorov and >various commentators have observed the same thing). If you think about the >standard foundations of probability theory, whether Bayesian subjective >approaches or various objective approaches (frequency approaches fail for >a number of reasons -- so they are out, but could be a counterexample to >what I say next), then you will see that making distinctions and/or the >idea of information present but not accessible are the grounds for >probability theory. Information theory is the more fundamental notion, >logically, it is more general, but includes probability theory as a >special case. Information can be defined directly in terms of distinctions >alone; probability cannot. We need to construct a measure to do that. So, I ask a follow-up question: Would the greater generality of information theory with respect to probability theory imply something concerning the even more general question of whether or not logic is more general than mathematics? Some seem to think that Goedel showed the opposite. It depends what you mean by logic. The issue is too complicated to get into here and now, but the simple answer is that there is no non-arbitrary distinction between mathematics and logic. Exactly the same reasons apply to the limits of both, and the only way to get one more powerful than the other is to apply a double standard for proofs and/or acceptability. So the answer, briefly, is that Goedel showed no such thing, either way you take it, if you do not apply a double standard for evidence. John -- Professor John Collier [EMAIL PROTECTED] Philosophy and Ethics, University of KwaZulu-Natal, Durban 4041 South Africa T: +27 (31) 260 3248 / 260 2292 F: +27 (31) 260 3031 http://www.nu.ac.za/undphil/collier/index.html ___ fis mailing list fis@listas.unizar.es http://webmail.unizar.es/mailman/listinfo/fis
Re: [Fis] Reply to Ted Goranson: levels of description
John said: > Hmm. You should read Barwise and Seligman, Information Flow: the logic of >distributed Systems. Very important for understanding Quantum Information. >Also, I assume that you are familiar with algorithmic complexity theory, >which is certainly rigourous, Minimum Description Length (Rissanen) and >Minimum Message Length (Wallace and Dowe) methods that apply Kolomogorov >and Chaitin's ideas very rigourously. If you don't like the computational >approaches for some reason, then you might want to look at Ingarden et al, >(1997) Information Dynamics and Open Systems (Dordrecht: Kluwer). They >show how probability can be derived from Boolean structures, which are >based on the fundamental notion of information theory, that of making a >binary distinction. So probability is based in information theory, not the >other way around (there are other ways to show this, but I take the >Ingarden et al approach as conclusive -- Chaitin and Kolmogorov and >various commentators have observed the same thing). If you think about the >standard foundations of probability theory, whether Bayesian subjective >approaches or various objective approaches (frequency approaches fail for >a number of reasons -- so they are out, but could be a counterexample to >what I say next), then you will see that making distinctions and/or the >idea of information present but not accessible are the grounds for >probability theory. Information theory is the more fundamental notion, >logically, it is more general, but includes probability theory as a >special case. Information can be defined directly in terms of distinctions >alone; probability cannot. We need to construct a measure to do that. So, I ask a follow-up question: Would the greater generality of information theory with respect to probability theory imply something concerning the even more general question of whether or not logic is more general than mathematics? Some seem to think that Goedel showed the opposite. STAN ___ fis mailing list fis@listas.unizar.es http://webmail.unizar.es/mailman/listinfo/fis
Re: [Fis] Reply to Ted Goranson: levels of description
With respect to definitions of information (Shannon, Von Neumann, Kolmogorov, etc.) there is the completely opposite approach of Michael Leyton. He defines information as causal explanation. This is very powerful because it is driven by a meaning-making system, i.e., a cognitive system. With respect to quantitative issues, his work uses his group-theoretic methods based on levels of wreath-product sequences. The wreath products come from structural characterizations of intelligent causal explanation. best Jim Johnson - Original Message - From: John Collier To: FIS Sent: Saturday, June 10, 2006 2:22 PM Subject: Re: [Fis] Reply to Ted Goranson: levels of description At 08:20 AM 6/7/2006, Andrei Khrennikov wrote: My comment:Yes, >> deeply about the nature of information>>This is the crucial point. But as I know there are only two ways todefine information rigorously, classical Shannon information, andquantum von Neumann information. In fact, all my discussion was aboutthe possibility (if it would be possible at all) to reduce the secondone to the first one.I understood that very often people speak about information in someheuristic sense, but we are not able to proceed rigorously with amathematical definition of information. And I know only definitionswhich are based on different kinds of entropy and hence probability.Hmm. You should read Barwise and Seligman, Information Flow: the logic of distributed Systems. Very important for understanding Quantum Information. Also, I assume that you are familiar with algorithmic complexity theory, which is certainly rigourous, Minimum Description Length (Rissanen) and Minimum Message Length (Wallace and Dowe) methods that apply Kolomogorov and Chaitin's ideas very rigourously. If you don't like the computational approaches for some reason, then you might want to look at Ingarden et al, (1997) Information Dynamics and Open Systems (Dordrecht: Kluwer). They show how probability can be derived from Boolean structures, which are based on the fundamental notion of information theory, that of making a binary distinction. So probability is based in information theory, not the other way around (there are other ways to show this, but I take the Ingarden et al approach as conclusive -- Chaitin and Kolmogorov and various commentators have observed the same thing). If you think about the standard foundations of probability theory, whether Bayesian subjective approaches or various objective approaches (frequency approaches fail for a number of reasons -- so they are out, but could be a counterexample to what I say next), then you will see that making distinctions and/or the idea of information present but not accessible are the grounds for probability theory. Information theory is the more fundamental notion, logically, it is more general, but includes probability theory as a special case. Information can be defined directly in terms of distinctions alone; probability cannot. We need to construct a measure to do that.John Professor John Collier [EMAIL PROTECTED]Philosophy and Ethics, University of KwaZulu-Natal, Durban 4041 South AfricaT: +27 (31) 260 3248 / 260 2292 F: +27 (31) 260 3031http://www.nu.ac.za/undphil/collier/index.html ___fis mailing listfis@listas.unizar.eshttp://webmail.unizar.es/mailman/listinfo/fis ___ fis mailing list fis@listas.unizar.es http://webmail.unizar.es/mailman/listinfo/fis
Re: [Fis] Reply to Ted Goranson: levels of description
At 08:20 AM 6/7/2006, Andrei Khrennikov wrote: My comment: Yes, >> deeply about the nature of information>> This is the crucial point. But as I know there are only two ways to define information rigorously, classical Shannon information, and quantum von Neumann information. In fact, all my discussion was about the possibility (if it would be possible at all) to reduce the second one to the first one. I understood that very often people speak about information in some heuristic sense, but we are not able to proceed rigorously with a mathematical definition of information. And I know only definitions which are based on different kinds of entropy and hence probability. Hmm. You should read Barwise and Seligman, Information Flow: the logic of distributed Systems. Very important for understanding Quantum Information. Also, I assume that you are familiar with algorithmic complexity theory, which is certainly rigourous, Minimum Description Length (Rissanen) and Minimum Message Length (Wallace and Dowe) methods that apply Kolomogorov and Chaitin's ideas very rigourously. If you don't like the computational approaches for some reason, then you might want to look at Ingarden et al, (1997) Information Dynamics and Open Systems (Dordrecht: Kluwer). They show how probability can be derived from Boolean structures, which are based on the fundamental notion of information theory, that of making a binary distinction. So probability is based in information theory, not the other way around (there are other ways to show this, but I take the Ingarden et al approach as conclusive -- Chaitin and Kolmogorov and various commentators have observed the same thing). If you think about the standard foundations of probability theory, whether Bayesian subjective approaches or various objective approaches (frequency approaches fail for a number of reasons -- so they are out, but could be a counterexample to what I say next), then you will see that making distinctions and/or the idea of information present but not accessible are the grounds for probability theory. Information theory is the more fundamental notion, logically, it is more general, but includes probability theory as a special case. Information can be defined directly in terms of distinctions alone; probability cannot. We need to construct a measure to do that. John Professor John Collier [EMAIL PROTECTED] Philosophy and Ethics, University of KwaZulu-Natal, Durban 4041 South Africa T: +27 (31) 260 3248 / 260 2292 F: +27 (31) 260 3031 http://www.nu.ac.za/undphil/collier/index.html ___ fis mailing list fis@listas.unizar.es http://webmail.unizar.es/mailman/listinfo/fis
[Fis] Reply to Ted Goranson: levels of description
Dear collegues, This is a part of my discussion with Ted Goranson. In the previous Email to the FIS- list Ted Goranson wrote: >> >> Any number of such ontological layers are >> >> possible and I suppose as system scale increases >> >> (physical, chemical, biological and so on...) new >> >> ones are added, possibly with constant semantic >> >> distance. >> >> The point here is as stated at the beginning, >> >> that ontological precedence is key in >> >> unwrapping how QM and information inform each >> >> other, if I can use such a reflexive notion. My reply to him: >> >In the orthodox copenhagen interpretation, the main problem is that it is strongly forbidden to consider onthological levels. There is only one level -- level of observations. If you want go beyond this layer, you go by definition beyond science. >> >Andrei His reply to me: >> No, my friend, I go beyond Copenhagen, for certain. But modern >> thought on the nature of modeling (including theoretical models) >> separates out representational issues, perhaps in layers, from >> natural behavior. Science is about understanding, at least as I see >> it. My letter was one which addresses the understanding of >> understanding where QM seems inadequate and FIS interests (at least >> as the group was originally defined) are centered. My comment: >Here I agree QM with the Copenhagen interpreation is really #end of the >road of physics (see Karl Popper, Quantum Theory and the Schism in Physics.) His reply to me (continuation): >> But the online discussion as it is developing seems not to worry too >> deeply about the nature of information, so perhaps I leave the letter as a marker for a future discussion. My comment: Yes, >> deeply about the nature of information>> This is the crucial point. But as I know there are only two ways to define information rigorously, classical Shannon information, and quantum von Neumann information. In fact, all my discussion was about the possibility (if it would be possible at all) to reduce the second one to the first one. I understood that very often people speak about information in some heuristic sense, but we are not able to proceed rigorously with a mathematical definition of information. And I know only definitions which are based on different kinds of entropy and hence probability. Andrei ___ fis mailing list fis@listas.unizar.es http://webmail.unizar.es/mailman/listinfo/fis
