Reduction and Elimination in Philosophy and the Sciences

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All in all, we have seen that reduction via deduction has no interesting examples because intertheoretic relations typically are no deductions but comparisons between both mathematical structure and terms differing completely in its usage. So, if we want to define a relation of reduction we cannot rely on deduction. Having in mind that in our investigation we are looking for a concept of reduction that is able to support claims of reductionism, one of the most interesting answers to that problem is that of (Schaffner 1967). For him a theory is not reduced to another if their laws are logically deduced, but if it is possible to deduce a new corrected theory from the reducing one which is formulated in the latter’s vocabulary and strongly analogous to the original one to be reduced. In a similar manner, reduction is defined in (Hooker 1981), and recently in (Bickle 1998) as the so called new wave reduction, which is a result of merging Schaffner’s and Hooker’s concept of analogy with the structuralistic approach to physical theories, as e.g. (Endicott 2001) points out. Let us have a closer look at these concepts. At first, Schaffner’s definition rests on a very vague and not clearly defined “strong analogue”-relation between the original theory to be reduced and a “corrected theory” deduced from the reducing one. This relation can surely be made more precise within the structuralistic approach: As stated in (Moulines 1984), a reduction in structuralistic terms yields a “mathematical relationship between two sets of structures” within a “scheme of reduction” which “does not require semantic predicate-by-predicate connections nor deducibility of statements” (l. c., p. 54-55). So this approach delivers indeed a very sophisticated concept of comparing theories that avoids the difficulties of a concept based on deduction, but can on the other hand be nothing but a comparing relation between both concepts and laws. Moreover, this account yields a comparison between two independent theories in such a way, that “we could have a reductive relationship between two theories that are completely alien to each other” (ibid.). Such a comparing relation now substantiates only reductionistic claims, if it is a comparison between concrete explanations as in our simple case above, but that seems not to be the case if the theories involved are more complex as we will see below considering general relativity. A topological comparison in the sense of (Scheibe 1999), which is possible also between theories “that are completely alien to each other”, doesn’t make any theory superfluous and hence cannot on its own support reductionistic claims. It is much easier to establish a mathematical-conceptual comparing relation between two theories than to show that the one can explain the phenomena which are typically explained by the other. Now, if it is possible to deduce a “corrected theory” from a reducing one, this would show that the latter is able to cope with the phenomena described by the theory to be reduced. However, comparing relations can be established between theories without deducing a corrected theory or explaining phenomena, and there are indeed theories (as general relativity) not permitting such a deduction or explanation despite being comparable to another one (for instance to Newton’s theory of gravitation) – hence the Schaffner-Hooker-Bickle account of reduction seems not to be adequate. Reduction and Reductionism in Physics — Rico Gutschmidt Guided from these observations, I’d like to propose the following two definitions. First it seems to be appropriate to call most of the intertheoretic relations in physics a relation of compatibility: One actually can compare two independent theories with each other and mostly such comparisons show that the involved theories are via approximate derivation and related concepts compatible to each other. This term doesn’t evoke any reductionistic claim and isn’t meant to do so. If we want to find, secondly, a definition of a relation of reduction in such a way that a reduced theory is in principle superfluous, it seems that we have to refresh an idea of (Kemeny and Oppenheim 1956). Their definition of reduction is based on the explanation of phenomena (“observable data” in their terms, cf. p.13): Any phenomenon explainable by means of the theory to be reduced must be explainable by the reducing theory. If, furthermore, the explanations of the reducing theory are in a sense better and if the theories involved are compatible and therefore in a way related to each other, it seems legitimate to say that the one is reduced to the other. A theory reduced in this sense is indeed superfluous: “Their” phenomena are explained better by another theory, to which it is compatible (and there is no need to go a long way round via “corrected theories”). This is now surely the case e.g. for Galileo’s law of falling bodies or Kepler’s laws of planetary motion but not for Newton’s theory of gravitation: We will now see that we have “only” compatibility here. The reason is that in spite of having comparable laws as shown e.g. in (Misner et al. 1973) or (Scheibe 1999), there are many phenomena explained by Newtonian physics but not by general relativity, because no one solved the field equations for them. While the twobody problem is directly solved by Newton’s law, it has (and as a matter of fact can have) only numerical solutions within general relativity. And while the orbits of the planets can be described as geodesics within the Schwarzschild solution, their interaction as described by Newtonian physics is not yet explained by general relativity for there are no solutions of the field equations for moving gravitational sources. Similarly, there are no general relativistic explanations for complex formations as star clusters or spiral galaxies either, while they can too be handled with Newtonian physics. It is surely possible to claim that one will find relativistic explanations of these phenomena one day, but because of the difficult and abstract character of the field equations in contrast to the high applicability of Newton’s theory we can also put the possibility of such explanations in question. And indeed, as a matter of fact numerical simulations of such phenomena on the basis of the field equations depend due to their complex structure on the heuristic help of Newton’s law of gravitation (within the so-called post-Newtonian approximation). Therefore, Newton’s law of gravitation can be improved by general relativity, but is not superfluous – it is in our terms not reduced to general relativity despite compatibility. 129
Literature Bickle, John 1998 Psychoneural Reduction: The New Wave, Cambridge, MA: MIT Press. Endicott, Ronald 2001 “Post-Structuralist Angst-Critical Notice: John Bickle, Psychoneural Reduction: The New Wave”, Philosophy of Science 68(3), 377-393. Feyerabend, Paul 1962 “Explanation, Reduction, and Empiricism”, in: H. Feigl and G. Maxwell (eds.), Scientific Explanation, Space, and Time, Minneapolis: University of Minnesota Press, 28-97. Hooker, Clifford A. 1981 “Towards a General Theory of Reduction. Part I-III”, Dialogue 20, 38-59, 201-236, 496-529. Kemeny, John and Oppenheim, Paul 1956 “On Reduction”, Philosophical Studies 7, 6-19. 130 Reduction and Reductionism in Physics — Rico Gutschmidt Misner, Charles W., Thorne, Kip S., and Wheeler, John A. 1973 Gravitation, New York: W.H. Freeman and Company. Moulines, C. Ulises 1984 “Ontological Reduction in the Natural Sciences”, in: Wolfgang Balzer, David A. Pearce and Heinz- Jürgen Schmidt (eds.), Reduction in Science: Structure, Examples, Philosophical Problems, Dordrecht: Reidel, 51-70. Nagel, Ernest 1961 The Structure of Science: Problems in the Logic of Explanation, New York: Harcourt. Schaffner, Kenneth F. 1967 “Approaches to Reduction”, Philosophy of Science 34, 137-147. Scheibe, Erhard 1999 Die Reduktion physikalischer Theorien Ein Beitrag zur Einheit der Physik Teil II: Inkommensurabilität und Grenzfallreduktion, Berlin: Springer.
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31 Alexander Hieke Hannes Leitgeb H
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Reduktion und Elimination in Philos
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Distributors Die Österreichische L
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6 Inhalt / Contents Wittgenstein me
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8 Inhalt / Contents The Evolution o
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Formal Mechanisms for Reduction in
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4. Property language and theoretica
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imperatives, or commands in the for
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Referential Practice and the Lure o
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The Augustinian account confuses mo
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hurried to fix it on the page. The
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The Essence (?) of Color, According
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Literature Austin, James 1980 “Wi
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Wittgenstein’s Externalism - Gett
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Informal Reduction E.P. Brandon, Ca
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An Anti-Reductionist Argument Based
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An Anti-Reductionist Argument Based
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Did I Do It? -Yeah, You Did! Wittge
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Literature Did I Do It? -Yeah, You
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tween the two approaches. The task
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On Two Recent Defenses of The Simpl
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On Two Recent Defenses of The Simpl
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Queen Victoria’s Dying Thoughts T
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Diagonalization. The Liar Paradox,
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Proof: Given a function ƒ from con
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that I am sure that it is true that
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experiencing something as a red pen
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There can be Causal without Ontolog
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There can be Causal without Ontolog
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objects. But they also leave unansw
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The Knower Paradox and the Quantifi
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The Knower Paradox and the Quantifi
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lent. It also implies that an inven
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The Scapegoat Theory of Causality M
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We may have evolved a specialized c
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easoning have their source in the l
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Wittgenstein on Frazer and Explanat
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genstein 1993, p. 143). In order to
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an adequate syntactic analysis of o
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Page 82 and 83: Wittgenstein meets ÖGS: Wovon man
Page 84 and 85: 3. Der Elementarsatz wird als Relat
Page 86 and 87: Literatur Glock, Hans Johann 2006
Page 88 and 89: Explaining the Brain: Ruthless Redu
Page 90 and 91: Occam’s Razor in the Theory of Th
Page 92 and 93: Literature Campbell, Donald T. 1987
Page 94 and 95: Die Nichtreduzierbarkeit der klassi
Page 96 and 97: Literatur Die Nichtreduzierbarkeit
Page 98 and 99: Let T I be the minimal theory of tr
Page 100 and 101: Does Bradley’s Regress Support No
Page 102 and 103: (3) Mutatis mutandis, realism has t
Page 104 and 105: Zeitliche Ontologie und zeitliche R
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Page 108 and 109: The decisive consequences of this a
Page 110 and 111: Benacerraf and Bad Company (An Atta
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Page 114 and 115: Literature Benacerraf, Paul 1965
Page 116 and 117: "PA" by using "PA* ", at least at t
Page 118 and 119: Hard Naturalism and its Puzzles Ren
Page 120 and 121: The Mind-Body-Problem and Score-Kee
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Page 124 and 125: kommt es zu einem gravierenden Miss
Page 126 and 127: Reduction Revisited: The Ontologica
Page 128 and 129: 4. Conclusion Reduction Revisited:
Page 132 and 133: Physicalism Without the A Priori Pa
Page 134 and 135: Literature Cartwright, Nancy 1999:
Page 136 and 137: Wittgensteins Projektionsmethode al
Page 138 and 139: Schlussbemerkungen Wittgensteins Pr
Page 140 and 141: intentional states requires functio
Page 142 and 143: Relating Theories. Models and Struc
Page 144 and 145: Literature Relating Theories. Model
Page 146 and 147: e invoked in response to the questi
Page 148 and 149: Do Brains Think? Christopher Humphr
Page 150 and 151: 4. Conclusion So do brains think or
Page 152 and 153: How Metaphors Alter the World-Pictu
Page 154 and 155: The Modal Supervenience of the Conc
Page 156 and 157: Literature van der Auwera, Johan an
Page 158 and 159: 3. The Determination of Form by Syn
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Page 162 and 163: Zwischen Humes Gesetz und „Sollen
Page 164 and 165: Assessing Humean Supervenience Amir
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Page 168 and 169: Aus der obigen Definition folgt, da
Page 170 and 171: Ding-Ontology of Aristotle vs. Sach
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Page 174 and 175: How do Moral Principles Figure in M
Page 176 and 177: “Downward Causation”: Emergent,
Page 178 and 179: “Downward Causation”: Emergent,
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A with distinguished subset Z of te
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A Metaphysically Moderate Version o
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Literature Balashov, Yuri 2002 ''Wh
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“In der Frage liegt ein Fehler”
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Problems with Psychophysical Identi
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identity theory, or as a predecesso
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of the world. It only matters that
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Four Anti-reductionist Dogmas in th
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Four Anti-reductionist Dogmas in th
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notion of time and requires that so
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Some Remarks on Wittgenstein and Ty
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Some Remarks on Wittgenstein and Ty
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concrete particulars can be subject
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phenomenal concept of experiencing
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Metaphorische Bedeutung als virtus
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speaker is then attaching a special
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„Vom Weißdorn und vom Propheten
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„Die Einheit hören“ - Einige
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„Die Einheit hören“ - Einige
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S4) the necessity of arithmetic is
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Getting out from Inside: Why the Cl
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Dispensing with Particulars: Unders
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Literature Dispensing with Particul
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Reichenbach’s Concept of Logical
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Defining Ontological Naturalism Mar
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Literature Jackson, Frank 1986. “
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properties are located. This proces
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‘our conceptual scheme’ “is c
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Properties and Reduction between Me
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Does this mean that metaphysics sho
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do not pick out pain in a system by
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The Writing of Nietzsche and Wittge
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his teachings. He coincides with hi
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sense of a proposition without firs
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Naturalistic Ethics: A Logical Posi
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Literature Kant, Immanuel 2006 Crit
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What we now require is a bridge the
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Species, Variability, and Integrati
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could mention the many sorts of iso
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to work this way. Classic examples
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The Key Problems of KC Matteo Pleba
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have embraced the myth of prose: it
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5. Prior’s Problem As Patrick Bla
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Reductionism in Axiology: the Case
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developing of cancer tissue in huma
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(2) One-way Nagelian bridge princip
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Rethinking the Modal Argument again
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Rethinking the Modal Argument again
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that we are to find the features we
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Atypical Rational Agency Paul Raymo
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Literature Anscombe, G. E. M. 1957
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situation bieten sich keine Kriteri
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Two Reductions of ‘rule’ Dana R
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one that could take place, but does
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physics is not able to make, since
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Wittgenstein’s Attitudes Fabien S
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view of logic, in accordance with h
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Warum man auf transzendentalphiloso
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Making the Mind Higher-Level Elizab
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Literature Churchland, P. M. (1995)
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Zwischen Humes Gesetz und „Sollen
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Mental Causation: A Lesson from Act
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Again, this is mistaken. Non-reduct
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auf alle Arten von kontingenten Pro
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Reduction, Sets, and Properties Ben
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Literature Egan, Andy (2004): ‘Se
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there is a tension between evaluati
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The Elimination of Meaning in Compu
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sufficient to explain all of the em
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that 'A' and 'A' could never be tok
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the necktie sense) can differ in wh
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Supervenience and ‘Should’ Arto
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word 'norm' can be thought to expre
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Rule-following as Coordination: A G
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vast majority are bent: gruesome, g
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human life, the violent condition o
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A Division in Mind. The Misconceive
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A Division in Mind. The Misconceive
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could then deduce (1c) and conclude
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Neutral Monism. A Miraculous, Incoh
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Neutral Monism. A Miraculous, Incoh
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A somewhat Eliminativist Proposal a
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Impliziert der intentionale Redukti
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Impliziert der intentionale Redukti
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Structure of the Paradoxes, Structu
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Structure of the Paradoxes, Structu
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that he was working on a translatio
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Objects of Perception, Objects of S
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Objects of Perception, Objects of S
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Let us take the example of the hypo
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Reducing Sets to Modalities Rafał
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variables ai that (under an interpr
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Are Lamarckian Explanations Fully R
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A Note on Tractatus 5.521 Nuno Vent
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And he goes on saying, referring to
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The Place of Theory Reduction in th
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Ethik als irreduzibles Supervenienz
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unabhängig von denen ihrer Mitglie
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Das ‘schwierige Problem’ des Be
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The Supervenience Argument, Levels,
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The Supervenience Argument, Levels,
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their relations both to the physica
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On the Characterization of Objects
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On the Characterization of Objects
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The Functional Unity of Special Sci
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size, location, temporal characteri
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Transcendental Philosophy and Mind-
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From Topology to Logic. The Neural
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From Topology to Logic. The Neural
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The Calculus of Inductive Construct
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The Four-Color Theorem, Testimony a
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experience. Of course, a detailed a
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Clearly x = y → x = ext y holds,
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Intentional Fundamentalism Petri Yl
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The second dimension to be consider
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The very existence of the special s
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Heil, J. (1999), “Multiple Realiz
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independent of what is the fact, fa
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415
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