Re: SV: Only logic is necessary?
In three different posts, Brent Meeker wrote : I'm not sure that logic in the formal sense can be right or wrong; it's a set of conventions about language and inference. About the only standard I've seen by which a logic or mathematical system could be called wrong is it if it is inconsistent, i.e. the axioms and rules of inference allow everything to be a theorem. I disagree. The main lesson provided by the works of of Tarski and Godel has shown us how far truth and consistency are different. By the second incompleteness theorem: (with PA = Peano Arithmetic Theory) PA + PA is consistent is both consistent and correct PA + PA is not consistent is consistent, but hardly correct! I will come back on this. But if you recall that Consistent(p) = ~B~p, then remember that all the followings are not equivalent from the (1 and 3) point of views of the machines: Bp, Bp p, Bp ~B~p, Bp ~B~p p. (if you prefer: p is provable, p is provable *and* p is true, p is provable and p is consistent, p is provable and p is consistent and p is true. I don't understand assumptions about logic and math? We don't need to make assumptions about them because they are rules we made up to keep us from reaching self-contradictions when making long complex inferences. Logician are interested in correctness, and relative correctness. The whole of model (not modal!) theory concerns those matter. They are rules about propositions and inferences. The propositions may be about an observation like a species that used this kind of reasoning survived more frequently than those who used that kind. I might need logic to make further inferences, but I don't need assumptions about logic to understand it. I agree if you talk of some minimal informal logic, like children seems to develop in their early years. (cf Piaget, for examples). Now concerning the many logics, it is different. There is a continuum of logics ... each having apparently some domain of application. Fields like Categorical Logic provides tools for many logics. Linear logic take into account resources. For example, the following is classically, intuitionisticaly and quantum logically valid: If i have one dollar I can buy a box of cigarets If I have one dollar I can buy a box of matches Thus If I have one dollar I can buy a box of cigarets and I can buy a box of matches. ALL logics, when studied mathematically, are studied in the frame of classical mathematics. You will never find a treatise on Fuzzy logic with a theorem like It is 0,743 true that a fuzzy set A can be represented by a function from A to the real line. (ok a case could be made for intuitionist logic, due to the existence of an intuitionist conception of math). Remember Cooper is talking about reasoning, reaching decisions, and taking actions - not just making truth preserving inferences from axioms. Classical logic applies to declarative, timeless sentences - a pretty narrow domain. ... called Platonia. Narrow? Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only logic is necessary?
Brent Meeker wrote: 1Z wrote: Brent Meeker wrote: You misunderstand population models. It's not a question of what members of a species think or vote for; it's a matter of whether their logic will lead to their survival in the evolutionary biological sense. So the majority can be wrong. Cooper is making valid comments about *something*, but it isn't logic. Logic is what tells us the majority can be wrong Cooper is not talking about logic in the formal sense; he's talking about reasoning, making decisions, acting. This can be wrong in the sense that there is a better (in terms of survival) way of reasoning. If you want to judge what is better in terms of survival, you need to use logic. I'm not sure that logic in the formal sense can be right or wrong; it's a set of conventions about language and inference. About the only standard I've seen by which a logic or mathematical system could be called wrong is it if it is inconsistent, i.e. the axioms and rules of inference allow everything to be a theorem. And since logic isn't wrong by that standard, it is correct. Any judgement made about logic will be made with logic. There is no higher court of appeal. (There are of course various fallacious forms of informal reasoning, but they do not deserve to be called logic). Logic ins't just correct --although it is -- it defines correctness. We have no other ultimate defintion. Logic might be wrong is incoherent. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only logic is necessary?
--- 1Z [EMAIL PROTECTED] wrote: Brent Meeker wrote: (Skip to 1Z's reply) If you want to judge what is better in terms of survival, you need to use logic. And then you may be still wrong, things sometimes occur (in our terms - see below) as illogical or even: counterproductive. Human logic is based on the 'part' of nature (in broadest terms) we so far discovered. Even only the reductionist representation of such. Further epistemic enrichment may change our views (our logic included). BM: I'm not sure that logic in the formal sense can be right or wrong; it's a set of conventions about language and inference. About the only standard I've seen by which a logic or mathematical system could be called wrong is it if it is inconsistent, i.e. the axioms and rules of inference allow everything to be a theorem. Inconsistent towards language and inference and more, all on a certain evolutionary level of human development - as we know AND acknowledge it. In devising future advancement in thinking I would go a bit further than what I've seen. 1Z: And since logic isn't wrong by that standard, it is correct. Any judgement made about logic will be made with logic. There is no higher court of appeal. (There are of course various fallacious forms of informal reasoning, but they do not deserve to be called logic). Wise inter-remark: by that standard. You are entitled to your opinion to call 'logic' whatever you define.. The 'Any judgement' is valid even towards yours. Including what you deem as deserve to be called. - What reminds me of the ongoing stupid debates about the so called (gay) marriage - a 'name' with ONE ancient definition,causing endless problems, while another 'name' or definition would eliminate the controversy. Logic ins't just correct --although it is -- it defines correctness. We have no other ultimate defintion. Logic might be wrong is incoherent. Withuin (BY?) our human logic we define 'correctness' as consistent within (by?) itself. Closing our minds to anything different. John John --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only logic is necessary?
1Z wrote: Brent Meeker wrote: 1Z wrote: Brent Meeker wrote: You misunderstand population models. It's not a question of what members of a species think or vote for; it's a matter of whether their logic will lead to their survival in the evolutionary biological sense. So the majority can be wrong. Cooper is making valid comments about *something*, but it isn't logic. Logic is what tells us the majority can be wrong Cooper is not talking about logic in the formal sense; he's talking about reasoning, making decisions, acting. This can be wrong in the sense that there is a better (in terms of survival) way of reasoning. If you want to judge what is better in terms of survival, you need to use logic. No, you just need to see who survives. Experiment trumps theory. Brent Meeker --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only logic is necessary?
Brent Meeker wrote: 1Z wrote: Brent Meeker wrote: 1Z wrote: Brent Meeker wrote: You misunderstand population models. It's not a question of what members of a species think or vote for; it's a matter of whether their logic will lead to their survival in the evolutionary biological sense. So the majority can be wrong. Cooper is making valid comments about *something*, but it isn't logic. Logic is what tells us the majority can be wrong Cooper is not talking about logic in the formal sense; he's talking about reasoning, making decisions, acting. This can be wrong in the sense that there is a better (in terms of survival) way of reasoning. If you want to judge what is better in terms of survival, you need to use logic. No, you just need to see who survives. Experiment trumps theory. Brent Meeker Presumably Cooper used theory to show why certain types of reasoning are more likely to aid survival, no? Anyway, we still need assumptions about logic and math to make sense of statements about basic experimental observations like the individuals with trait X survived more frequently than those who lacked it. Jesse --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only logic is necessary?
Jesse Mazer wrote: Brent Meeker wrote: 1Z wrote: Brent Meeker wrote: 1Z wrote: Brent Meeker wrote: You misunderstand population models. It's not a question of what members of a species think or vote for; it's a matter of whether their logic will lead to their survival in the evolutionary biological sense. So the majority can be wrong. Cooper is making valid comments about *something*, but it isn't logic. Logic is what tells us the majority can be wrong Cooper is not talking about logic in the formal sense; he's talking about reasoning, making decisions, acting. This can be wrong in the sense that there is a better (in terms of survival) way of reasoning. If you want to judge what is better in terms of survival, you need to use logic. No, you just need to see who survives. Experiment trumps theory. Brent Meeker Presumably Cooper used theory to show why certain types of reasoning are more likely to aid survival, no? Anyway, we still need assumptions about logic and math to make sense of statements about basic experimental observations like the individuals with trait X survived more frequently than those who lacked it. Jesse I don't understand assumptions about logic and math? We don't need to make assumptions about them because they are rules we made up to keep us from reaching self-contradictions when making long complex inferences. They are rules about propositions and inferences. The propositions may be about an observation like a species that used this kind of reasoning survived more frequently than those who used that kind. I might need logic to make further inferences, but I don't need assumptions about logic to understand it. Brent Meeker Brent Meeker --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only logic is necessary?
Brent Meeker: Jesse Mazer wrote: Brent Meeker wrote: 1Z wrote: Brent Meeker wrote: 1Z wrote: Brent Meeker wrote: You misunderstand population models. It's not a question of what members of a species think or vote for; it's a matter of whether their logic will lead to their survival in the evolutionary biological sense. So the majority can be wrong. Cooper is making valid comments about *something*, but it isn't logic. Logic is what tells us the majority can be wrong Cooper is not talking about logic in the formal sense; he's talking about reasoning, making decisions, acting. This can be wrong in the sense that there is a better (in terms of survival) way of reasoning. If you want to judge what is better in terms of survival, you need to use logic. No, you just need to see who survives. Experiment trumps theory. Brent Meeker Presumably Cooper used theory to show why certain types of reasoning are more likely to aid survival, no? Anyway, we still need assumptions about logic and math to make sense of statements about basic experimental observations like the individuals with trait X survived more frequently than those who lacked it. Jesse I don't understand assumptions about logic and math? We don't need to make assumptions about them because they are rules we made up to keep us from reaching self-contradictions when making long complex inferences. Sure, but those rules still qualify as assumptions. For example, it's apparently possible to create paraconsistent logics where self-contradictions are not forbidden in all cases, but this does not entail that every proposition must be judged true--see http://en.wikipedia.org/wiki/Paraconsistent_logic and http://en.wikipedia.org/wiki/Graham_Priest for some more on this. And Cooper (judging from Lennart Nilsson's summary) seems to be saying that the rules of classical logic which we use are somewhat arbitrary, that we need a relativistic evolutionary logic where classical logic only would be justified for certain special classes of problems. Presumably in problems outside these special classes, rules of classical logic could be violated, which I'm guessing wouldimply violating the principle of non-contradiction or at least the law of the excluded middle (unless there are forms of logic which preserve these principles but still differ from classical logic, I'm not sure). They are rules about propositions and inferences. The propositions may be about an observation like a species that used this kind of reasoning survived more frequently than those who used that kind. I might need logic to make further inferences, but I don't need assumptions about logic to understand it. But if there are other versions of logic besides classical logic, then the decision to use classical logic is itself an assumption about logic, just like the decision to use euclidean geometry in a certain problem would be an assumption about geometry, since other non-euclidean forms are known to be possible. Jesse --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only logic is necessary?
Jesse Mazer wrote: Brent Meeker: Jesse Mazer wrote: Brent Meeker wrote: 1Z wrote: Brent Meeker wrote: 1Z wrote: Brent Meeker wrote: You misunderstand population models. It's not a question of what members of a species think or vote for; it's a matter of whether their logic will lead to their survival in the evolutionary biological sense. So the majority can be wrong. Cooper is making valid comments about *something*, but it isn't logic. Logic is what tells us the majority can be wrong Cooper is not talking about logic in the formal sense; he's talking about reasoning, making decisions, acting. This can be wrong in the sense that there is a better (in terms of survival) way of reasoning. If you want to judge what is better in terms of survival, you need to use logic. No, you just need to see who survives. Experiment trumps theory. Brent Meeker Presumably Cooper used theory to show why certain types of reasoning are more likely to aid survival, no? Anyway, we still need assumptions about logic and math to make sense of statements about basic experimental observations like the individuals with trait X survived more frequently than those who lacked it. Jesse I don't understand assumptions about logic and math? We don't need to make assumptions about them because they are rules we made up to keep us from reaching self-contradictions when making long complex inferences. Sure, but those rules still qualify as assumptions. For example, it's apparently possible to create paraconsistent logics where self-contradictions are not forbidden in all cases, but this does not entail that every proposition must be judged true--see http://en.wikipedia.org/wiki/Paraconsistent_logic and http://en.wikipedia.org/wiki/Graham_Priest for some more on this. And Cooper (judging from Lennart Nilsson's summary) seems to be saying that the rules of classical logic which we use are somewhat arbitrary, that we need a relativistic evolutionary logic where classical logic only would be justified for certain special classes of problems. Remember Cooper is talking about reasoning, reaching decisions, and taking actions - not just making truth preserving inferences from axioms. Classical logic applies to declarative, timeless sentences - a pretty narrow domain. Presumably in problems outside these special classes, rules of classical logic could be violated, which I'm guessing wouldimply violating the principle of non-contradiction or at least the law of the excluded middle (unless there are forms of logic which preserve these principles but still differ from classical logic, I'm not sure). They are rules about propositions and inferences. The propositions may be about an observation like a species that used this kind of reasoning survived more frequently than those who used that kind. I might need logic to make further inferences, but I don't need assumptions about logic to understand it. But if there are other versions of logic besides classical logic, then the decision to use classical logic is itself an assumption about logic, just like the decision to use euclidean geometry in a certain problem would be an assumption about geometry, since other non-euclidean forms are known to be possible. Jesse Maybe we're just disagreeing about words. I'd say the decision to use classical logic is an assumption that you're applying it to sentences or propositions where it will work (i.e. declarative, timeless sentences), not an assumption about logic. Same for geometry. I use Euclidean geometry to calculate distances in my backyard, I use spherical geometry to calculate air-miles to nearby airports, I use WGS84 to calculate distance between naval vessels at sea. Brent Meeker --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only logic is necessary?
John M wrote: --- 1Z [EMAIL PROTECTED] wrote: Brent Meeker wrote: (Skip to 1Z's reply) If you want to judge what is better in terms of survival, you need to use logic. And then you may be still wrong, things sometimes occur (in our terms - see below) as illogical or even: counterproductive. So much for the claim: If you use logic, you will never go wrong. I never made that claim. The claim I made was Whatever else you do, you'll be using logic. There is no standpoint outside of logic. No, not even evolutionary theory. Human logic is based on the 'part' of nature (in broadest terms) we so far discovered. Even only the reductionist representation of such. Further epistemic enrichment may change our views (our logic included). Nothing can chnage one part of our logic without using another. X contradicts our logic depends on the idea that contradictions are wrongwhich is logical. Withuin (BY?) our human logic we define 'correctness' as consistent within (by?) itself. Closing our minds to anything different. Relax the rules too far, and you don't just get something different, you get quodlibet -- everything. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
RE: SV: Only logic is necessary?
Lennart Nilsson wrote: No, you have the burden of showing what possible worlds could possibly mean outside a real biological setting. Cooper shows that logical laws are dependent on which population model they refer to. Of course that goes for the notion of possibility also... That sounds incoherent to me...how can you even define population models without assuming various things about math and logic? Do you think the (mathematical) laws of population genetics have some sort of objective existence outside the human mind, but laws of math and logic themselves do not? Jesse --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only logic is necessary?
Lennart Nilsson wrote: No, you have the burden of showing what possible worlds could possibly mean outside a real biological setting. I have shown that; HYPOTHETICAL states-of-affairs which do not contradict any laws KNOWN TO US. Cooper shows that logical laws are dependent on which population model they refer to. I have no doubt that whatver rules can be reverse-engineered from practical problem-solving tend to vary. I doubt that de facto problem-solving defines or constitutes logic. There are psychological tests which show that most people, 80%-90% , get certain logical problems worng. Of course the notion of right and wrong logic that is being appealed to here comes from the textbook, not from the study of populations. If populations defined logic, the majority couldn't be wrong (by textbook logic, anyway). If popular practice defined logic, people wouldn't have to learn logic. Of course that goes for the notion of possibility also... LN -Ursprungligt meddelande- Från: everything-list@googlegroups.com [mailto:[EMAIL PROTECTED] För 1Z Skickat: den 8 juli 2006 22:38 Till: Everything List Ämne: Re: Only logic is necessary? Brent Meeker wrote: Bruno Marchal wrote: Le 05-juil.-06, à 15:55, Lennart Nilsson a écrit : William S. Cooper says: The absolutist outlook has it that if a logic is valid at all it is valid period. A sound logic is completely sound everywhere and for everyone, no exceptions! For absolutist logicians a logical truth is regarded as 'true in all possible worlds', making logical laws constant, timeless and universal. Of course logical laws are true in all logically possible worlds is a (logical) tautology. An X-possible world is just a hypothetical state of affairs that does not contradict X-rules (X is usually logic or physics). Where do the laws of logic come from? he asks the absolutist. Bruno First you have to ask if they could possibly have been different. Then you have to ask what notion of possibility you are appealling to... --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only logic is necessary?
Le 09-juil.-06, à 10:07, Jesse Mazer a écrit : Lennart Nilsson wrote: No, you have the burden of showing what possible worlds could possibly mean outside a real biological setting. Cooper shows that logical laws are dependent on which population model they refer to. Of course that goes for the notion of possibility also... That sounds incoherent to me...how can you even define population models without assuming various things about math and logic? Do you think the (mathematical) laws of population genetics have some sort of objective existence outside the human mind, but laws of math and logic themselves do not? I agree with you. Lennart Nilsson wrote: We use mathematics as a meta-language, just like you kan describe what is said in latin by using italian. That does not make italian logically/evolutionary prior to latin of course. I think you are confusing language and theory. I agree that the language belongs to human inventions, but even and especially in math (and numbers) we use those languages to build theories *about* truth which should be, and mostly are, independent of the choice of the languages. You are defending a conventionalist philosophy of math. I don't think that conventionalism is coherent either with (simple) mathematics or with metamathematics. There is nothing conventional in the distribution of the primes. There is nothing conventional in the fact that the set of total computable function is not recursively enumerable. Etc. It seems to me. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only logic is necessary?
1Z wrote: Lennart Nilsson wrote: No, you have the burden of showing what possible worlds could possibly mean outside a real biological setting. I have shown that; HYPOTHETICAL states-of-affairs which do not contradict any laws KNOWN TO US. Cooper shows that logical laws are dependent on which population model they refer to. I have no doubt that whatver rules can be reverse-engineered from practical problem-solving tend to vary. I doubt that de facto problem-solving defines or constitutes logic. There are psychological tests which show that most people, 80%-90% , get certain logical problems worng. Of course the notion of right and wrong logic that is being appealed to here comes from the textbook, not from the study of populations. If populations defined logic, the majority couldn't be wrong (by textbook logic, anyway). You misunderstand population models. It's not a question of what members of a species think or vote for; it's a matter of whether their logic will lead to their survival in the evolutionary biological sense. So the majority can be wrong. Brent Meeker Brent Meeker --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only logic is necessary?
Brent Meeker wrote: You misunderstand population models. It's not a question of what members of a species think or vote for; it's a matter of whether their logic will lead to their survival in the evolutionary biological sense. So the majority can be wrong. Cooper is making valid comments about *something*, but it isn't logic. Logic is what tells us the majority can be wrong --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only logic is necessary?
1Z wrote: Brent Meeker wrote: You misunderstand population models. It's not a question of what members of a species think or vote for; it's a matter of whether their logic will lead to their survival in the evolutionary biological sense. So the majority can be wrong. Cooper is making valid comments about *something*, but it isn't logic. Logic is what tells us the majority can be wrong Cooper is not talking about logic in the formal sense; he's talking about reasoning, making decisions, acting. This can be wrong in the sense that there is a better (in terms of survival) way of reasoning. I'm not sure that logic in the formal sense can be right or wrong; it's a set of conventions about language and inference. About the only standard I've seen by which a logic or mathematical system could be called wrong is it if it is inconsistent, i.e. the axioms and rules of inference allow everything to be a theorem. Brent Meeker --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only logic is necessary?
Brent Meeker wrote: 1Z wrote: Brent Meeker wrote: You misunderstand population models. It's not a question of what members of a species think or vote for; it's a matter of whether their logic will lead to their survival in the evolutionary biological sense. So the majority can be wrong. Cooper is making valid comments about *something*, but it isn't logic. Logic is what tells us the majority can be wrong Cooper is not talking about logic in the formal sense; he's talking about reasoning, making decisions, acting. This can be wrong in the sense that there is a better (in terms of survival) way of reasoning. I'm not sure that logic in the formal sense can be right or wrong; it's a set of conventions about language and inference. About the only standard I've seen by which a logic or mathematical system could be called wrong is it if it is inconsistent, i.e. the axioms and rules of inference allow everything to be a theorem. If this is all that Cooper is talking about, I probably wouldn't have any objection to it--but Lennart Nilsson seemed to be making much stronger claims about the contingency of logic itself based on his interpretation of Cooper. Jesse --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
Re: SV: Only logic is necessary?
Le 06-juil.-06, à 21:49, Lennart Nilsson a écrit : x-tad-biggerBruno;/x-tad-bigger x-tad-biggerAccording to Cooper classical analysis is plain bad biology, /x-tad-bigger ? x-tad-biggerand not a matter of subjective judgement or philosophical preferens (such as taking atithmetical truth for granted). /x-tad-bigger ?? x-tad-biggerI think this is where he would say your whole castle in the sky tumbles, and that has nothing to do with trying to find a fault in your argument /x-tad-biggerx-tad-biggerJ /x-tad-bigger ??? I don't understand what you are trying to say at all. Perhaps you could elaborate? What do you or Cooper mean by classical analysis is bad biology? Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~--~~~~--~~--~--~---
