Reduction and Elimination in Philosophy and the Sciences

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could mention the many sorts of isolating barriers (Section 3) that prevent gene flow between distinct species (Wilson et al. forthcoming). Despite its apparent plausibility, the goal of this section is to present an objection against HPC theory. The properties in the cluster F can be either intrinsic or relational. According to the conceptual argument against essentialism (Section 2), no intrinsic property may count as necessary for membership in a species. But the same argument is also effective against Boyd’s finite disjunction of intrinsic properties. 4 For if Okasha is right, there is no boundary on the variation of individual traits among the members of a species. Thus, if the cluster F contains intrinsic properties, then given the rejection of essentialism F could not exclude any phenotypic or genotypic trait. If it did exclude such a trait, F would entail that not having a certain property is necessary for membership in a species. But this consequence cannot be right because F would then not single out individual species. To make this clear, consider an example. Suppose an unbounded disjunction of intrinsic properties P1 v P2 v … and objects a and b both containing P1 and P2. Are they both members of the same species? As the disjunction is unbounded, the disjunction by itself cannot decide this question. Therefore, if we accept the conceptual argument against essentialism, F cannot contain intrinsic properties and so F can only contain relational properties. Now let us move to the second kind of homeostasis (Homeostasis-II). As mentioned earlier, isolating barriers between species seem to count as Homeostasis-II. An important feature about isolating barriers is that they are evolved characters between two species – e.g., courtship. Since isolating barriers are evolved characters, they are analogous to phenotypic/genotypic traits: they not only can vary through time, but also there is no boundary to such variation. In contrast, non-interbreeding caused by geographic separation is not considered as an isolating barrier because it is not an evolved character (Ridley 2004: 355). 4 See Ereshefsky and Matthen (2005), p. 9. Species, Variability, and Integration — Makmiller Pedroso But if the previous paragraph is correct, we can extend the argument used above against Homeostasis-II. A finite disjunction of isolating barriers cannot single out a species. Otherwise, we would have to accept that there is some a priori impediment to how isolating barriers between two species can evolve. Hence, species cannot be distinguished via Homeostasis-II. I have drawn two conclusions so far: (i) F can only contain relational properties; and (ii) species cannot be distinguished via Homeostasis-II. Because of (i) and (ii) it follows that, if species are HPC kinds, then they are a cluster of relational properties where some of these properties induce the presence of others (thereby, intrinsic properties and Homeostasis-II are both excluded). If I am right about this, when applied to species, HPC theory collapses into a theory that is no more explanatory than the species concepts themselves. Boyd’s theory can only state that some relational property such as interbreeding with con-specifics induces other relational property like belonging to the same gene pool as. So, although the notions of homeostatic mechanisms or cluster of cooccurring properties seem to carry some additional explanatory power, I tried to show above that these notions are irrelevant to comprehending what a species is.* Literature Boyd, R. 1991 “Realism, Anti-foundationalism, and the Enthusiasm for Natural Kinds” Philosophical Studies 61: 127-48. Boyd, R. 1999 “Homeostasis, Species, and Higher Taxa”, R. A. Wilson (ed.), Species: New Interdisciplinary Essays. Cambridge: MIT Press, 141-85. Ehrlich, P. and P. Raven (1969) “Differentiation of Populations” Science 165: 1228-32. Ereshefsky, M. 2001 The Poverty of Linnaean Hierarchy Cambridge: Cambridge University Press. * Special thanks to Travis Dumsday for his helpful comments. 255
Limiting Frequencies in Scientific Reductions Wolfgang Pietsch, Munich, Germany 1. Introduction Limiting frequencies have been largely discredited in the philosophical discussions on the interpretation of probability. A crucial reason is that frequency interpretations are usually classified as objective accounts of probability which stands in obvious contrast to the non-empirical notion of infinite frequencies. In this essay I will argue that notwithstanding these conceptual difficulties, limiting frequencies are an indispensable tool in theory reductions. Section two will be concerned with a classification of reduction according to its methodological role: This role can be ontological, i.e. concerned with unifying phenomena that were originally thought to be of different nature. Or reduction can have an epistemological function in making a theory simpler and thereby better applicable – e.g. when the general theory of relativity is simplified to Newton's theory of gravitation, which suffices to treat most phenomena concerned with the motion of planets. In Section three an important case of such an epistemological reduction is examined, which will be termed statistical reduction.. In statistical reductions the concepts of the higher-level theory necessarily involve a large amount of entities of the lower-level theory. Therefore the probability calculus is essential for this type of reduction. Furthermore, it turns out that such reductions usually require the limit of an infinite number of lower-level entities, i.e. limiting or infinite frequencies. Finally, Section four will discuss how probability in statistical reductions should be interpreted. The described use of limiting frequencies generally calls for further research into the conceptual difficulties of this notion: Can the limit be empirically justified by means of certain averaging procedures, e.g. time or ensemble averages? What is the relation between such different types of averages? Are there subjective and epistemic elements involved and if so, which role do they play? Due to their indispensable role in theory reduction, infinite frequencies cannot simply be dismissed, as often happens in philosophical discussions on probability. 2. Reduction as an Epistemological Enterprise There has long been the sense that reduction comes in two different kinds, although the dividing line has been drawn in several quite different ways. Ernest Nagel (1974) distinguished homogeneous from inhomogeneous reductions: In the former, all concepts of the reduced theory are already contained in the reducing theory. In the later, the reduced theory employs additional concepts beyond those of the reducing theory, which leads to the need to establish bridge laws between these new concepts and the reducing theory. Another way, in which a distinction has been made, is between interlevel and intralevel reductions. Interlevel reductions concern theories on different levels of fundamentality – for example chemistry and physics – while intralevel reductions refer to the same level, for example the relation between Newton's theory of gravity and the general theory of relativity. When the reduced theory is not eliminated in favor of the reducing theory – which is mostly 256 the case in interlevel reductions – one speaks of synchronic reductions. When the reduced theory is given up after a successful reduction, this is called a diachronic reduction. In what follows we will adopt a classification that somewhat differs from these suggestions. We will distinguish two types according to the function of the reduction: (i) reduction as an ontological enterprise and (ii) reduction as an epistemological enterprise 1 . As with the other distinctions this is not meant to suggest, that one can always unambiguously classify a reduction as one of these cases. Rather, we always deal with a mixture, where each of the types is more or less clearly present. (i) In ontological reductions, phenomena that were originally thought to be quite different in nature are traced back to the same mechanism. Examples for this type are the derivation of optics from electrodynamics or the unification of Galileo's law of falling bodies and Kepler's laws for the planetary motion within the general framework of Newton's theory of gravity. Usually, these are intralevel and diachronic reductions, where the original theories do not survive. (ii) Reduction as an epistemological enterprise deals with those cases where considerable simplification is required in order to apply theories in a specific context. Examples for this type are the reduction of thermodynamics to manyparticle mechanics or the reduction of macro- to microeconomics. These epistemological reductions need not always be fully worked out. In many cases only certain elements of the higher-level theory can actually be reduced to concepts of the lower-level theory, i.e. there are emergent aspects in the higher-level theory – at least for the time being. Most epistemological reductions are 'imperfect' in this way: the reduction of psychology to neuroscience, of biology to chemistry, or of chemistry to physics. Usually these reductions are interlevel reductions, but not always: a counterexample is the reduction of geometrical optics to wave optics. Since the different theories in an epistemological reduction each retain their significance in particular contexts, mostly both theories are kept, i.e. the reduction is synchronic. For the rest of the paper, the focus will be on reduction as an epistemological enterprise. Whenever a theory is simplified in order to make it better applicable, this can in principle be interpreted as a reduction of a simpler framework to a more complicated and general one. Two important types can be further distinguished, that I will call (a) parametric and (b) statistical reduction. This classification is not necessarily exhaustive, one can well imagine other types of simplification. (a) In parametric reduction the limit of a parameter of the reducing theory is taken in order to make the equations mathematically better manageable. This type is often said to be typical for reduction in physics (Nickles 1973, Batterman 2002) and indeed many physical reductions seem 1 The distinction between the ontological and epistemological role of reduction is certainly not novel (compare e.g. Hoyningen-Huene 2007, 181-183). However, there are subtle differences between our treatment and that in the literature.
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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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Wittgenstein meets ÖGS: Wovon man
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Wittgenstein meets ÖGS: Wovon man
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3. Der Elementarsatz wird als Relat
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Literatur Glock, Hans Johann 2006
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Explaining the Brain: Ruthless Redu
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Occam’s Razor in the Theory of Th
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Literature Campbell, Donald T. 1987
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Die Nichtreduzierbarkeit der klassi
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Literatur Die Nichtreduzierbarkeit
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Let T I be the minimal theory of tr
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Does Bradley’s Regress Support No
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(3) Mutatis mutandis, realism has t
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Zeitliche Ontologie und zeitliche R
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Betrachtung ontologischer Fragen, M
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The decisive consequences of this a
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Benacerraf and Bad Company (An Atta
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offer a solution to the bad company
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Literature Benacerraf, Paul 1965
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"PA" by using "PA* ", at least at t
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Hard Naturalism and its Puzzles Ren
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The Mind-Body-Problem and Score-Kee
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mental properties, for instance, or
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kommt es zu einem gravierenden Miss
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Reduction Revisited: The Ontologica
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4. Conclusion Reduction Revisited:
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All in all, we have seen that reduc
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Physicalism Without the A Priori Pa
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Literature Cartwright, Nancy 1999:
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Wittgensteins Projektionsmethode al
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Schlussbemerkungen Wittgensteins Pr
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intentional states requires functio
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Relating Theories. Models and Struc
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Literature Relating Theories. Model
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e invoked in response to the questi
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Do Brains Think? Christopher Humphr
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4. Conclusion So do brains think or
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How Metaphors Alter the World-Pictu
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The Modal Supervenience of the Conc
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Literature van der Auwera, Johan an
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3. The Determination of Form by Syn
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Zwischen Humes Gesetz und „Sollen
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Zwischen Humes Gesetz und „Sollen
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Assessing Humean Supervenience Amir
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determination thesis; it fails as a
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Aus der obigen Definition folgt, da
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Ding-Ontology of Aristotle vs. Sach
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Ding-Ontology of Aristotle vs. Sach
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How do Moral Principles Figure in M
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“Downward Causation”: Emergent,
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“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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Page 276 and 277: that we are to find the features we
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Page 290 and 291: Wittgenstein’s Attitudes Fabien S
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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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