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A¤  ©  @£nÿý?" dd@ÿÿï€ÿÿÿÿÿÿ  @@``€€ ¼ð´ðP¨)t        C ð¿Àÿpñÿ™f™™€€3f™3™fÿ@ñ÷ð8ó€ó€Ð‚ÿ úgþý4kdkdÀ³Ïý4˜Ièþÿÿÿÿÿúpûppû@ <ý4!d!dgÈ}n¸zn<ý4BdBdgÈ}n¸znúgþý4PdPdÀ³Ïý4˜I ùÿÿˆÿÿÿúpû@ pûp?Ù Ú%OÙ Ú;ð©RóŸ¨$ Reduction without the Structures¡$% ª % Ÿ¨› Robert C. Richardson, Professor of Philosophy College of Arts & Sciences, University of Cincinnati Molecular Cell Physiology, Vrije Universiteit Amsterdam¡Bœ~fþ€fþ€ þª ~    óŸ¨Overview¡ ª  Ÿ¨Ÿ The Appeal of Reduction The Vision of the Structures Thermodynamics and Statistical Mechanics Difficulties with the Structures Reduction with the Dynamics¡h  @Ðÿ,a aƒBa aƒaªÀ )  óŸ¨The Appeal of Reduction ¡eª>  Ÿ¨ì Theoretical: Our science should reflect the hierarchical organization in nature. Empirical: Progress is often realized in theories of greater scope and precision. Methodological: Complexity can yield to decomposition and localization.¡’í@Ðÿa cDc cHcc8caª^      & óŸ¨The Vision of the Structures ¡De eƒe€ª>  Ÿ¨¾Reduction promotes parsimony: (1) in ontological commitments: postulate no entities without necessity; (2) in explanatory principles: explain as much as possible with as little as possible ¡p ¡ @Ðÿaa0aa:aªP        óŸ¨The Vision of the Structures ¡De eƒe€ª>  Ÿ¨Reduction is defined in terms of its structure: (1) Theories are axiomatic systems, including sets of basic laws; (2) Explanation is deductive derivation within a theory; (3) Reduction shows that laws at higher levels are the consequences of more fundamental, lower level, principles. ¡˜0 ï @Ðÿ0!!4!a a-a afaªœ0          óŸ¨The Vision of the Structures ¡De eƒe€ª>  Ÿ¨¬Reduction Requires: (1) compositional identities: specify what entities within the domain of the reduced (or secondary) science consist of in terms of the domain of the reducing, (or primary) science; (2) type identities: identify properties of reduced entities with properties of reducing entities; and (3) explanations: explain laws of the secondary theory (perhaps as corrected) as but special cases of the primary theory.¡Ž ™ @ÐÿaaŸaaYa aiaª†      !   ó Ÿª  Ÿ P ... a reduction is effected when the experimental laws of the secondary science (if it has an adequate theory, its theory as well) are shown to be the logical consequences of the theoretical assumptions (inclusive of the coordinating definitions) of the primary science (Nagel 1961, p. 352). ¡()@Ðÿ(cª‚       ó Ÿ¨2 Thermodynamics and Statistical Mechanics ¡031ee€ª2 Ÿ rMaxwell and Boltzmann Began with  phenomenological laws describing the behavior of gases. Explained as a consequence of statistical laws A conservative extension of Newtonian mechanics¡.º £aª"          óŸ¨2 Thermodynamics and Statistical Mechanics ¡031ee€ª2 Ÿ ´Boyle s Law P*V is constant for constant T the Law of Charles and Gay-Lussac: V*T is constant for a constant P The Boyle-Charles Law: PV = kT The Bernoulli Formula: PV = (2/3)et T is proportional to kinetic energy¡DÛ +‰aiçÿ$aª2+     ó Ÿ¨The Structuralist rendering ¡e€ª$  Ÿ¨8 (1) Gases can be identified with aggregates of particles which lack any internal structure. (2) The particles are of a constant size, and vanishingly small in comparison with the distance between them. (3) The thermal energy of a gas is the aggregate kinetic energy of the particles constituting the gas. ¡*8 @Ðÿ@Ðÿ9aª),    ó Ÿ¨!Difficulties with the Structures ¡D"e eƒe€ª2  Ÿ ~The  New Wave Multiple Realization The Variety of Reductions ¡p?²@uÐÿ’@uÐÿg 3™þe3™þ.aaªN  óŸ The  New Wave ¡eª Ÿ¨ T2 ~~~~> T2* T1 ¡d@Ðÿacaª óŸ The  New Wave ¡eª Ÿ¨Q PV = kT ~~~~~~~~~~~~~> PV = (2/3)et Statistical Mechanics Newtonian Mechanics¡V( * #aiçÿa*aª4.ó Ÿ The  New Wave ¡eª Ÿ  perfect rough failure of mapping isomorphism mapping microreduction  bumpy elimination themodynamics mechanics phlogiston¡$ˆ‰aªh/3óŸ The  New Wave ¡eª Ÿ¨ï Improves on the vision of the Structures Does not require strict derivation Acknowleges a wider range of outcomes Consistent with the Structuralist vision Theories are still formal structures Explanation & Reduction are formal relations ¡”) I * R *aIa*aRaaª*  )   #  ó!Ÿ¨!Difficulties with the Structures ¡D"e eƒe€ª2  Ÿ ~The  New Wave Multiple Realization The Variety of Reductions ¡Š?²@uÐÿ’@uÐÿaag 3™þaaaªN  ó Ÿª  Ÿ¨D... there are two necessary formal conditions for the reduction of the former to the latter: (1) Assumptions of some kind must be introduced which postulate suitable relations between whatever is signified by 'A' and traits represented by theoretical terms already in the primary science. (2) With the help of these additional assumptions, all the laws of the secondary science, including those containing the term 'A,' must be logically derivable from the theoretical premises and their associated coordinating definitions in the primary discipline. (Nagel 1961, pp. 353-354).¡EEaªR$    '  0*' óŸª  Ÿ à If psychology is reducible to neurology, then for every psychological kind predicate there is a coextensive neurological kind predicate, and the generalization which states this coextension is a law. ... What seems increasingly clear is that even if there are such coextensions, they cannot be lawful. For it seems increasingly likely that there are nomologically possible systems other than organisms (viz., automata) which satisfy no neurological predicates at all (Fodor 1975, pp. 17-18). ¡ññª޲   L   I  (  ?      óŸª  Ÿ¨wPhenotype Underlying genotypes Ratio reddish coat color AABB AABb AaBB AaBb 9/16 black coat color AAbb Aabb 3/16 albino coat aaBB aaBb aabb 4/16 Phenotype-Genotype Mappings in the Coat Color of Guinea Pigs Color is a function of genes at at least two loci. At the first locus A is dominant and at the second B is dominant. An individual homozygous for a will be albino. An individual homozygous for b will be black as long as it is not homozygous for a at the first locus. The third column indicates the proportion of each type in the offspring. 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