Robert:
As you say, logic can be viewed as a game, like chess. You also say that "More great technical innovations result from playing the game of logic than playing these other games." The question then is what is it about logic that leads to more great technical innovations than other games. --John ________________________________________ From: [email protected] [[email protected]] On Behalf Of Robert Howard [[email protected]] Sent: Monday, April 27, 2009 2:13 PM To: 'The Friday Morning Applied Complexity Coffee Group' Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences John: Why is logic valid? For the same reason the rules of chess are valid: by definition. Its validity is presupposed. If you don't like chess, don't play. If you do then you have to play by the agreed rules. Else don't call it chess (or logic). Make a new name for your game. In logic, one begins with a rule that a proposition has exactly one of two values: true or false. Other games, like fuzzy logic, have additional "maybe" values, but we use the adjective "fuzzy" to distinguish these games (or rule sets). Other rules are added to define ways to relate (or compose) propositions in the form of conjunctions, disjunctions, etc; to build up structures. All players agree to the rules and knowledge and science progress. Some people don't like these games, so they don't play. Some people play badly and aren't much fun. Some make mistakes (called fallacies) that are hard to see by other players. Some prefer other rules, like "the highest authority is always right" or "there is no truth; only love". More great technical innovations result from playing the game of logic than playing these other games. John: Why is it useful to put together long strings of logical implications? This is probably a result of trivial observation; nature puts together long strings of related events of cause and effects; e.g. chemical reactions and planetary motions. We are merely recording what we see in the formal language of cause and effect, namely logic. In this case, logic is more of a historian's tool. --Rob Howard -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of John Kennison Sent: Monday, April 27, 2009 5:15 AM To: ForwNThompson; [email protected] Cc: Sean Moody Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences Nick et al, This is a great question, with, I think, two parts. The first part is why is logic valid. I am almost certainly a platonist or worse on this point --it's validity simply seems to be obvious. Can the proposition that logic is valid be supported by any argument that doesn't implicitly use logic? (Okay, even "implicitly" assumes logic). The argument that we evolved to be convinced by logical implications because it is useful for survival suggests that logic is, at least, approximately valid, which is a lot less of a conclusion than what I would want, and which doesn't explain why logic works in modern physics. The other part of the original question is, even if we grant that logic is valid (or at least approximately valid) why is it useful to put together long strings of logical implications? Believing that logical implications are trivially true, I wonder how can long chains of such implications be anything but trivial. (And if we believe that logic is at best approximately true, wouldn't long chains of implications stop being good approximations if each link in the chain is a little inaccurate.) Perhaps Physics somehow restricts itself to a domain where logic works very well. And maybe things like consciousness are simply outside that domain (but I hope not). I wonder if there is there a domain where logic is a useful approximation, but long chains of implications are not useful? Perhaps social analysis? Perhaps philosophy? Perhaps the humanities? Nick, and others,--I'd be curious about what you think on this issue. ---John ________________________________________ From: Nicholas Thompson [[email protected]] Sent: Sunday, April 26, 2009 1:40 PM To: [email protected] Cc: John Kennison; Sean Moody Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences Owen, et al, Well, isn't this part of the broader mystery of why logic should get you anywhere in the study of nature? Isn't logic just a language trick? Why should nature give a fig for the tricks we play with our words? This is all reminding me, for some reason, of the "discovery" of the fact that the differential of the integral is just the original function. There seem to be two sorts of "discovery" in our discourse: One is the discovery of something in nature that we did not already know. The other is the discovery of a new implication in what we have already said that we did not anticipate when we said it. I can see why mathematics can help with the latter sort of "discovery", but have no idea why it should help with the former. In the emergence literature appears the endearing phrase "natural reverence". The early philosophical emergentists believed that one had to accept emergent properties with "natural reverence," since such properties could not be reduced to the properties of their parts. I am deeply ambivalent about natural reverence: one the one hand, I believe that there is no point in being a scientist if you are not prepared to experience some natural reverence. On the other hand, I also believe that natural reverence is the enemy of discovery. Perhaps "natural reverence" is a fleeting pleasure one gets before one gets down to the dirty business of figuring out how things work: too little of it and one would never be inspired; too much of it, and one would never be curious. Nick Nicholas S. Thompson Emeritus Professor of Psychology and Ethology, Clark University ([email protected]<mailto:[email protected]>) http://home.earthlink.net/~nickthompson/naturaldesigns/ ----- Original Message ----- From: Steve Smith<mailto:[email protected]> To: The Friday Morning Applied Complexity Coffee Group<mailto:[email protected]> Sent: 4/26/2009 10:17:16 AM Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences Well said/observed David, I too am a Lakoff/Johnson/Nunez fan in this matter. While I am quite enamored of mathematics and it's fortuitous application to all sorts of phenomenology, Physics being somehow the most "pure" in an ideological sense, I've always been suspicious of the conclusion that "the Universe *is* Mathematics". This discussion also begs the age-old question of whether we are "inventing" or "discovering" mathematics. Similarly, it revisits the question of whether discoveries in mathematics portend discoveries in Physics (or other, "messier" phenomenological observations). - Steve Prof David West wrote: I'm completely of Tegmark's ilk: I assume that means you would also adhere to the sentiment attributed to Einstein: "How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?" Which contains the fallacy, "independent of experience." Thought - and mathematics! - is but a refined metaphor of experience. (following Lakoff) davew A different response, advocated by Physicist Max Tegmark (2007), is that physics is so successfully described by mathematics because the physical world is completely mathematical, isomorphic to a mathematical structure, and that we are simply uncovering this bit by bit. In this interpretation, the various approximations that constitute our current physics theories are successful because simple mathematical structures can provide good approximations of certain aspects of more complex mathematical structures. In other words, our successful theories are not mathematics approximating physics, but mathematics approximating mathematics. -- Owen ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
