Reduction and Elimination in Philosophy and the Sciences

More documents

Recommendations

Info

There can be Causal without Ontological Reducibility of Consciousness? Troubles with Searle’s Account of Reduction — Tárik de Athayde Prata V. Concluding Remarks I think that causal and ontological reduction – in Searle’s conception – is essentially linked and that causal reducibility is incompatible with ontological irreducibility. Because of this, Searle’s theory implies contradictory claims: in some moments he asserts that consciousness and brain processes are identical, in other moments he says that they are different. It seems to me that Jaegwon Kim realizes this inconsistence when he comments Searle’s claim that causal interactions between mental and physical phenomena can be rediscribed at different levels: “Obviously, the redescription strategy is available only to those who accept ‘M=P’, namely reducionist physicalists (Searle of course does not count himself among them).” (KIM, 2005, p. 48). Moreover Searle’s strategy to show that ontological irreducibility is harmless seems to repeat the same mistake, then he suggests that consciousness and brain processes are identical, what is incompatible with his claims about ontological irreducibility (difference). This irreducibility is for me the most troublesome thesis of biological naturalism, and it would be very helpful for the credibility of the theory if this thesis was eliminated. Perhaps Searle should conceive the difference between consciousness and brain processes in another way which is not ontological. 4 Acknowledgments Financed by the DCR-Program in accord of CNPq and FUNCAP foundations (Brazil) concepts of levels of description and of realization implies identity (about realization see footnote 1 above). 4 I am very grateful to Guido Imaguire and Noa Latham for many helpful comments and to Ananda Badaró for the correction of the English. Literature Kim, J. (2005) Physicalism, or something near enough. Princeton; Oxford: Princeton University Press. SCHRÖDER, J. (1992) “Searles Auffassung des Verhältnisses von Geist und Körper und ihre Beziehung zur Identitätstheorie” In: Conceptus XXVI, nr. 66, pp. 97-109 Searle, J. (1980) “Intrinsic Intentionality” In: Behavioral and Brain Sciences 3, pp. 450-6. __________ (1983) Intentionality: an essay in the philosophy of mind. Cambridge: Cambridge University Press. __________ (1992) The Rediscovery of the Mind. Cambridge Mass., London: MIT Press. __________ (1995) “Conciousness, the Brain and the Connection Principle: A Reply” In: Philosophy and phenomenological Research 55(1) pp. 217- 32. __________ (2002a) Consciousness and Language. Cambridge (UK): Cambridge University Press. __________ (2002b) “Why I Am Not a Property Dualist” In: Journal of Consciousness Studies, 9, No 12, pp. 57-64 __________ (2004) Mind: a brief introduction. Oxford: Oxford University Press. 57
Algorithms and Ontology Walter Dean, New York, USA This purpose of this note is to advertise — but not answer — a question which is of significant foundational importance to both mathematics and computer science but which has been largely overlooked within philosophy of mathematics. Succinctly stated it is as follows: 58 (A) Are the mathematical procedures conventionally termed algorithms themselves mathematical objects? 1 I will assume that some general notion of algorithm — i.e. of a practical method for solving a mathematical problem — is already implicit in mathematical practice. This seems reasonable since algorithms for simple arithmetic operations (e.g. the “grade school” long division algorithm) have long been commonplaces of our informal computational practice. Specific algorithms (e.g. Euclid's algorithm) are well known not only because of their antiquity but also because of the ways in which they have contributed to modern mathematics (e.g. in the definition of Euclidean domain or in the proof of Sturm's theorem). Finally, a great many other algorithms have been developed in conjunction with specific subfields of mathematics — e.g. Brent’s method in numerical analysis, Gosper’s algorithm in combinatorics, Strassen’s algorithm in matrix algebra — and will thus be known to specialists in these fields. Mathematicians have traditionally been most interested in applying algorithms to solve mathematical problems such as determining whether a given number is prime or that a function has a root in a given interval. This flags two important observations about the role of algorithms in contemporary mathematics: 1) that many of the individual mathematical statements which we now take ourselves to know (e.g. that certain numbers are prime) have been derived by the application of specific algorithms; and 2) that mathematical interest has generally been focused on the results of applying these methods rather than on the computational properties of the methods themselves. 2 The situation is quite different in contemporary computer science. In this context, algorithms are regarded as abstract objects in their own right whose properties may be directly studied and compared. This is evident from the sort of language used to describe individual algorithms, of which the following observations are typical: I) Individual algorithms are referred to by proper names — e.g. “Euclid's algorithm”, MERGESORT, 1 Although it appears that this question has not been systematically investigated by philosophers, the technical proposals of (Moschovakis 1998) and (Gurevich 1999) both seek to establish positive solutions. However, both of these approaches arguably fall victim to the problem of “computational artifacts” which is discussed below. 2 This is not, of course, to say that properties of algorithms are completely ignored by mathematicians. For in particular, it is acknowledged that prior to claiming that the fact that the application of an algorithm A to a value a yields b as output is a proof that the value of a function f at a is equal to b, A must be proven correct with respect to f -- i.e. it must be shown that ∀x[f(x) = A(x)]. Such proofs generally proceed by constructing a mathematical model M of A -- i.e. a purely mathematical representation of its mode of operation. The availability of such representations might be taken to suggest that mathematical practice is already committed to some version of (A). However, since mathematicians are not generally interested in the computational properties of individual algorithms (e.g. their running time), they will generally accept correctness proofs based on models M which only weakly reflect the operation of the algorithms which they are introduced to represent. HEAPSORT, etc. II) Such names are used to predicate computational properties directly of individual algorithms — e.g. “MERGESORT” has running-time O(nlog2(n)).” III) General results are stated using quantifiers ranging over algorithms — e.g. “There is a polynomial time algorithm for primality”, “If P ≠ NP, then there is no polynomial time algorithm for deciding propositional satisfiability”, “There is no comparison sorting algorithm with running-time less than O(nlog2(n)).” If we apply conventional standards of ontological commitment to I)-III), we are led to the conclusion that computer science is committed to regarding algorithms realistically — i.e. as forming a class of objects to which algorithmic names (such as those in I)) refer, and over which quantifiers (such as those in III)) range. To get an impression of what is at stake in our interpretation of such claims, it will be useful to consider the developments which led to the adoption of the idiom exemplified by I)-III). Statements of this sort are characteristic of a field known as algorithmic analysis which was established in the late 1950s by (Knuth 1973). Knuth proposed a means of measuring and comparing the efficiency of algorithms in terms of their so-called big-O running-time complexity — i.e. the asymptotic rate of growth of the number of steps O(tA(|x|)) it takes algorithm A to return a value on an input x as a function of its size. The development of this theory was motivated by the dual observations that i) there exist intuitively distinct algorithms A1 and A2 which compute the same function but which differ in their asymptotic running-time and ii) the relative efficiency of A1 and A2 in practice is often invariant with respect to how they are implemented relative to a particular formal model of computation M (e.g. as RAM machines). The first of these observations illustrates that within computer science, algorithms are treated intensionally. This is to say that an algorithm A is generally not identified with the function fA it computes, but rather with a procedure or method whose operation induces this function. That algorithms are indeed individuated in this manner may be illustrated by observing that a computational predicate like “A has running-time O(t(|x|))” creates a context in which the substitution of names for algorithms which compute the same function need not preserve truth value. 3 The second observation records the fact that it is conventional to treat algorithms as the intrinsic bearers of asymptotic complexity theoretic properties. For not only is it often difficult to reason mathematically about the complexity of an algorithm if we are forced to work with a particular mathematical representation (e.g. RAM machine), but the combinatorial features of such representations often turn out to be irrelevant for comparing the behavior of different algorithms in practice. These observations shed some light on why it is useful to adopt an idiom which treats algorithms as 3 For instance, it does not follow from the fact that 1) MERGESORT has running-time O(|x|log2(|x|)), and 2) that MERGESORT and SELECTIONSORT compute the same function that 3) SELECTIONSORT has running-time O(|x|log2(|x|)).
Page 1 and 2:
31 Alexander Hieke Hannes Leitgeb H
Page 3 and 4:
Reduktion und Elimination in Philos
Page 5 and 6:
Distributors Die Österreichische L
Page 7 and 8: 6 Inhalt / Contents Wittgenstein me
Page 9 and 10: 8 Inhalt / Contents The Evolution o
Page 12 and 13: Formal Mechanisms for Reduction in
Page 14 and 15: 4. Property language and theoretica
Page 16 and 17: imperatives, or commands in the for
Page 18 and 19: Referential Practice and the Lure o
Page 20 and 21: The Augustinian account confuses mo
Page 22 and 23: hurried to fix it on the page. The
Page 24 and 25: The Essence (?) of Color, According
Page 26 and 27: Literature Austin, James 1980 “Wi
Page 28 and 29: Wittgenstein’s Externalism - Gett
Page 30 and 31: Informal Reduction E.P. Brandon, Ca
Page 32 and 33: An Anti-Reductionist Argument Based
Page 34 and 35: An Anti-Reductionist Argument Based
Page 36 and 37: Did I Do It? -Yeah, You Did! Wittge
Page 38 and 39: Literature Did I Do It? -Yeah, You
Page 40 and 41: tween the two approaches. The task
Page 42 and 43: On Two Recent Defenses of The Simpl
Page 44 and 45: On Two Recent Defenses of The Simpl
Page 46 and 47: Queen Victoria’s Dying Thoughts T
Page 48 and 49: Diagonalization. The Liar Paradox,
Page 50 and 51: Proof: Given a function ƒ from con
Page 52 and 53: that I am sure that it is true that
Page 54 and 55: experiencing something as a red pen
Page 56 and 57: There can be Causal without Ontolog
Page 60 and 61: objects. But they also leave unansw
Page 62 and 63: The Knower Paradox and the Quantifi
Page 64 and 65: The Knower Paradox and the Quantifi
Page 66 and 67: lent. It also implies that an inven
Page 68 and 69: The Scapegoat Theory of Causality M
Page 70 and 71: We may have evolved a specialized c
Page 72 and 73: easoning have their source in the l
Page 74 and 75: Wittgenstein on Frazer and Explanat
Page 76 and 77: genstein 1993, p. 143). In order to
Page 78 and 79: an adequate syntactic analysis of o
Page 80 and 81: Wittgenstein meets ÖGS: Wovon man
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
Page 106 and 107: Betrachtung ontologischer Fragen, M
Page 108 and 109:
The decisive consequences of this a
Page 110 and 111:
Benacerraf and Bad Company (An Atta
Page 112 and 113:
offer a solution to the bad company
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
Page 122 and 123:
mental properties, for instance, or
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 130 and 131:
All in all, we have seen that reduc
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
Page 160 and 161:
Zwischen Humes Gesetz und „Sollen
Page 162 and 163:
Page 164 and 165:
Assessing Humean Supervenience Amir
Page 166 and 167:
determination thesis; it fails as a
Page 168 and 169:
Aus der obigen Definition folgt, da
Page 170 and 171:
Ding-Ontology of Aristotle vs. Sach
Page 172 and 173:
Ding-Ontology of Aristotle vs. Sach
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,
Page 180 and 181:
A with distinguished subset Z of te
Page 182 and 183:
A Metaphysically Moderate Version o
Page 184 and 185:
Literature Balashov, Yuri 2002 ''Wh
Page 186 and 187:
“In der Frage liegt ein Fehler”
Page 188 and 189:
Problems with Psychophysical Identi
Page 190 and 191:
identity theory, or as a predecesso
Page 192 and 193:
of the world. It only matters that
Page 194 and 195:
Four Anti-reductionist Dogmas in th
Page 196 and 197:
Four Anti-reductionist Dogmas in th
Page 198 and 199:
notion of time and requires that so
Page 200 and 201:
Some Remarks on Wittgenstein and Ty
Page 202 and 203:
Some Remarks on Wittgenstein and Ty
Page 204 and 205:
concrete particulars can be subject
Page 206 and 207:
phenomenal concept of experiencing
Page 208 and 209:
Metaphorische Bedeutung als virtus
Page 210 and 211:
speaker is then attaching a special
Page 212 and 213:
„Vom Weißdorn und vom Propheten
Page 214 and 215:
„Die Einheit hören“ - Einige
Page 216 and 217:
„Die Einheit hören“ - Einige
Page 218 and 219:
S4) the necessity of arithmetic is
Page 220 and 221:
Getting out from Inside: Why the Cl
Page 222 and 223:
Dispensing with Particulars: Unders
Page 224 and 225:
Literature Dispensing with Particul
Page 226 and 227:
Reichenbach’s Concept of Logical
Page 228 and 229:
Defining Ontological Naturalism Mar
Page 230 and 231:
Literature Jackson, Frank 1986. “
Page 232 and 233:
properties are located. This proces
Page 234 and 235:
‘our conceptual scheme’ “is c
Page 236 and 237:
Properties and Reduction between Me
Page 238 and 239:
Does this mean that metaphysics sho
Page 240 and 241:
do not pick out pain in a system by
Page 242 and 243:
The Writing of Nietzsche and Wittge
Page 244 and 245:
his teachings. He coincides with hi
Page 246 and 247:
sense of a proposition without firs
Page 248 and 249:
Naturalistic Ethics: A Logical Posi
Page 250 and 251:
Literature Kant, Immanuel 2006 Crit
Page 252 and 253:
What we now require is a bridge the
Page 254 and 255:
Species, Variability, and Integrati
Page 256 and 257:
could mention the many sorts of iso
Page 258 and 259:
to work this way. Classic examples
Page 260 and 261:
The Key Problems of KC Matteo Pleba
Page 262 and 263:
have embraced the myth of prose: it
Page 264 and 265:
5. Prior’s Problem As Patrick Bla
Page 266 and 267:
Reductionism in Axiology: the Case
Page 268 and 269:
developing of cancer tissue in huma
Page 270 and 271:
(2) One-way Nagelian bridge princip
Page 272 and 273:
Rethinking the Modal Argument again
Page 274 and 275:
Rethinking the Modal Argument again
Page 276 and 277:
that we are to find the features we
Page 278 and 279:
Atypical Rational Agency Paul Raymo
Page 280 and 281:
Literature Anscombe, G. E. M. 1957
Page 282 and 283:
situation bieten sich keine Kriteri
Page 284 and 285:
Two Reductions of ‘rule’ Dana R
Page 286 and 287:
one that could take place, but does
Page 288 and 289:
physics is not able to make, since
Page 290 and 291:
Wittgenstein’s Attitudes Fabien S
Page 292 and 293:
view of logic, in accordance with h
Page 294 and 295:
Warum man auf transzendentalphiloso
Page 296 and 297:
Making the Mind Higher-Level Elizab
Page 298 and 299:
Literature Churchland, P. M. (1995)
Page 300 and 301:
Page 302 and 303:
Mental Causation: A Lesson from Act
Page 304 and 305:
Again, this is mistaken. Non-reduct
Page 306 and 307:
auf alle Arten von kontingenten Pro
Page 308 and 309:
Reduction, Sets, and Properties Ben
Page 310 and 311:
Literature Egan, Andy (2004): ‘Se
Page 312 and 313:
there is a tension between evaluati
Page 314 and 315:
The Elimination of Meaning in Compu
Page 316 and 317:
sufficient to explain all of the em
Page 318 and 319:
that 'A' and 'A' could never be tok
Page 320 and 321:
the necktie sense) can differ in wh
Page 322 and 323:
Supervenience and ‘Should’ Arto
Page 324 and 325:
word 'norm' can be thought to expre
Page 326 and 327:
Rule-following as Coordination: A G
Page 328 and 329:
vast majority are bent: gruesome, g
Page 330 and 331:
human life, the violent condition o
Page 332 and 333:
A Division in Mind. The Misconceive
Page 334 and 335:
A Division in Mind. The Misconceive
Page 336 and 337:
could then deduce (1c) and conclude
Page 338 and 339:
Neutral Monism. A Miraculous, Incoh
Page 340 and 341:
Neutral Monism. A Miraculous, Incoh
Page 342 and 343:
A somewhat Eliminativist Proposal a
Page 344 and 345:
Impliziert der intentionale Redukti
Page 346 and 347:
Impliziert der intentionale Redukti
Page 348 and 349:
Structure of the Paradoxes, Structu
Page 350 and 351:
Structure of the Paradoxes, Structu
Page 352 and 353:
that he was working on a translatio
Page 354 and 355:
Objects of Perception, Objects of S
Page 356 and 357:
Objects of Perception, Objects of S
Page 358 and 359:
Let us take the example of the hypo
Page 360 and 361:
Reducing Sets to Modalities Rafał
Page 362 and 363:
variables ai that (under an interpr
Page 364 and 365:
Are Lamarckian Explanations Fully R
Page 366 and 367:
A Note on Tractatus 5.521 Nuno Vent
Page 368 and 369:
And he goes on saying, referring to
Page 370 and 371:
The Place of Theory Reduction in th
Page 372 and 373:
Ethik als irreduzibles Supervenienz
Page 374 and 375:
unabhängig von denen ihrer Mitglie
Page 376 and 377:
Das ‘schwierige Problem’ des Be
Page 378 and 379:
The Supervenience Argument, Levels,
Page 380 and 381:
The Supervenience Argument, Levels,
Page 382 and 383:
their relations both to the physica
Page 384 and 385:
On the Characterization of Objects
Page 386 and 387:
On the Characterization of Objects
Page 388 and 389:
The Functional Unity of Special Sci
Page 390 and 391:
size, location, temporal characteri
Page 392 and 393:
Transcendental Philosophy and Mind-
Page 394 and 395:
From Topology to Logic. The Neural
Page 396 and 397:
From Topology to Logic. The Neural
Page 398 and 399:
The Calculus of Inductive Construct
Page 400 and 401:
The Four-Color Theorem, Testimony a
Page 402 and 403:
experience. Of course, a detailed a
Page 404 and 405:
Clearly x = y → x = ext y holds,
Page 406 and 407:
Intentional Fundamentalism Petri Yl
Page 408 and 409:
The second dimension to be consider
Page 410 and 411:
The very existence of the special s
Page 412 and 413:
Heil, J. (1999), “Multiple Realiz
Page 414 and 415:
independent of what is the fact, fa
Page 416 and 417:
415
Page 418:
Publications of the Austrian Ludwig
show all

Reduction and Elimination in Philosophy and the Sciences

Create successful ePaper yourself

Delete template?

Save as template?