smiller@ral.rpi.edu (Scott Miller) (03/23/90)
In article <492e6ff2.1a4d7@cicada.engin.umich.edu> zarnuk@caen.engin.umich.edu (Paul Steven Mccarthy) writes: >(Chris Malcolm) writes: >>In chess it is not possible to checkmate a king with _only_ two knights. >>If you regard this as a property of reality how is it a consequence of >>the laws of physics? > >I am a Reductionist. These kinds of reductions are terribly tedious, but >the basic format is: > > The given property is a consequence of the rules of the game. > The rules of the game are the consequence of human perceptions > of pleasure. > Human perceptions of pleasure are the consequence of human > nuero-chemistry > Human nuero-chemistry is the consequence of the laws of chemistry. > The laws of chemistry are the consequence of the laws of physics. > It seems to me that Paul could have avoided a weak response by properly defining the scope of reductionism, thereby showing that it does not apply to the chess question. "Truth", as far as I can tell, is a property of a proposition within the context of a formal system. A proposition is true if it is provable within the system. The proposition does not necessarily have any meaning (or interpretation) in any other system. Thus, for example, the proposition "a king cannot be checkmated with just two knights" is true within the system of definitions and rules called chess, but it does not have any bearing on "the real world" because chess is not meant to be a model of the real world. You may object, "What about physical truths, such as the conservation of energy, or the speed of light being the absolute speed limit?" Well, first of all, the propositions that the universe has these respective properties are always subject to doubt, despite our constant confirmation of them. Secondly, these and all other "universal truths" are propositions, composed of symbols, simply by the fact that they are communicated in symbolic form. (Is it possible to communicate in nonsymbolic form?) To analyze the truth of these statements, you must provide a formal system of axioms and inference rules in which there exist interpretations for these statements. I submit, therefore, that "P is true in the real (physical) world" should be defined as "P is provable in a formal system S which is a model of reality". By model I mean a system which is consistent and complete with respect to whatever it is modelling. All scientists are trying to build models of the particular domains they are exploring, e.g., physics, biology, chemistry, and maybe even psychology. The essence of the reductionist thesis, in these terms, is that a formal system which models the domain of physics can, given the proper definitions, simulate the systems which model all other domains of reality. (Sort of a Church-Turing thesis for physics!) None of this has anything to do with chess. One thing bothers me about the discussion of models above: the observation that, if a model of physics could exist, I think it would probably be powerful enough to generate arithmetic, which would imply that the model cannot exist, because a model is consistent _and_ complete. It follows that we can never know the truth, the whole truth, and nothing but the truth about physics, but I suppose that's not saying anything new. I could be wrong about a model of physics generating arithmetic. However, the real problem is that the definition of "truth in the real world" must be modified to account for the possibility that a model cannot exist. That is, "P is true in W" might be redefined as "If there exists a system S which models W, then P is a theorem in S." A better definition might be P is true in W iff there exists a system S consistent with W such that P is a theorem in S This is all fine and dandy, but it still leaves my definition of reductionism utterly meaningless if a model of physics is a logical impossibility. It also leaves truth unanalyzable w.r.t. the real world, since we can never know if a given formal system is consistent with a system we did not create. Nevertheless, this definition does answer the chess question. If any of you netters discover a glaring example of naivete in this article, please edify me. Scott Miller -- Scott A. Miller bitnet: smiller@ral.rpi.edu (for now) "!Cuidado, hay llamas!"