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Abelson, R. xi, 67, 68, 223 for Dedekind's recursion theorem Ackerman, W. 171, 177, 185, 186, 188, for formalization: 191-192 239 on Godel's incompleteness theorem as a Arbib, M. 243 positive result: 201 Aristotle 38, 136, 151 Bird, R. 241 Bishop, E. 169 Babbage,C.28,29,32,91,220,233 Blumenthal, o. 121 on machines "of the most general on Hilbert's attitude towards for­ kind": 23-24 malism: 75 Baird, A. 31 on Hilbert's opposition to Kronecker Becker, O. 7,70,173 concerning the independence of on the formal structure of intentional geometry from number : 75 consciousness: 158-169 Bohm, D. I, 15 on the phenomenological basis of on mechanism in physics: 2,12 Gentzen's consistency proof: 159- on Laplace's demon: 2, 12-13 160 on the enhancement of mechanism Bell, E. 133, 145, 167 by randomness ("indeterministic Benacerraf, P. 228 mechanism"): 6 Berg,Jan 70 on quantum mechanism: 11 Berg, Jonathan 241 on infinite variety in nature: 12 Berkeley, G. 40,97,99,109 Bohr, N. xiii on finitism in geometry: 71 Boole, G. 79,80,117,135,138 on the limitations of a pure visual Boltzman, L. 5 intelligence in geometry: 107 Bolyai, J. 39, 164, 165 Bernays, P. 10, 72, 97, 120, 139, 147, on the possibility of proving the par­ 160,163,164,165,166,184,191,192, allel postulate in space if not in 197,239,240 the plane: 83 on ideal elements in logic: 124-125 Bolzano, B. 30, 70 on the Richard (Skolem) paradox for on the infinity of propositions: 59-60 axiomatic set theory: 132 Boolos, G. 135, 136 on Hilbert's generalization of the Borel, E. 128,177,238 spatiality of figures: 140-141 Bourbaki, N. 128 on the compatibility of formalism with Bowden, B. V. 32 incompleteness: 162 Bowie, L. 241 on the conflict between optimism and Bradley, F. H. scepticism in Hilbert's mathemati­ on the limitations of logic machines: 26 cal philosophy: 163 Brillouin, L. 5 on the formalist conception of finite­ Broad, C. D. 31,226 ness: 171 Broden, T. 170,202 on the importance of Godel's (first­ Brouwer, L. E. J. 41, 47, 70, 87, 127, order) formalization of the proof 163,211 264 INDEX OF NAMES 265

on proofs as infinite mental objects: 188, 191, 192, 193, 198, 216, 217, 152-153 223,225,244,245 Buck, R. C. 70 on the justification for calling numbers Burks, A. 31,233 free creations of our own mind: Busemann, H. 115 46,49,50 rejects Kronecker's demand for decida­ Cantor, G. 39, 46, 63, 64, 75, 77, 121, bility: 47 129, 158, 159, 176, 178 on the analysis of the number sequence: on the infinity of the mind: 66 48 his powerful objection to Kronecker's discovers in recursion a new and finitism: 73-74 stronger principle than induction: Cardano, G. 110 51-56 Carnap, R. 48,69, 144, 153, 164, 171 on the consistency problem for arith­ Carnot, S. 31 metic: 58 Carroll, L. 108 on the criterion of identity for his Cassirer, E. 5 reflective thoughts: 61-62 Cauchy, A. 72 on the mind's power to create infinite Chaitin, G. 10,32 sets: 63 Chihara, C. 241,243 Dehn, M. 116,164,165 Church, A. 11,46,212,241 Dennett, D. 237 on the difficulty of saying why Gentzen's on the relevance of Church's thesis to consistency proof is not finitary: non-circular psychology in general: 174 219-220 Chwistek, L. 131, 162 Desargues, G. 100, 101, 102, 106, 110 Cohen, P. 117,118,119,163 introduced space intuition into geome­ Coleman, W. 2 try: 101, 110 Contro, W. 163 Descartes, R. 1, 2, 3, 17, 20, 21, 22, 30, Couturat, L. 138 31, 36, 59, 69, 103, 104, 105, 120, criticized Hilbert for not using any 156,247 logical calculus in his work on his proof for the immateriality of mind geometry: 89 . requires the existence of an actually Curry, H. 181, 184,212,239 infinite God: 18,34 on combinatory logic as an analysis of denies self-consciousness to animals: 19 thought and its relation to Hil­ tried to base all philosophy on the bert's mathematics: 182-183 necessary connection between our finite self-consciousness and our Darwin, C. 22 consciousness of an infinite God: Daub, E. 31 33-34 Davis, M. 242 freed algebra from its dependence on on Gode\'s reasons for not advancing spatial dimensions by introducing Church's thesis himself: 203-204 linear multiplication: 99-100 Dedekind, R. xi, 30, 31, 37, 38, 41, 44, held that our bodily and mental vision 59, 64, 65, 66, 67, 68, 69, 70, 72, 74, cannot clearly and distinctly depict 84, 85, 87, 120, 121, 122, 123, 124, more than two dimensions: 100, 128, 130, 133, 137, 139, 141, 148, 110,247 156, 161, 175, 176, 177, 184, 185, Detlefsen, M. 174 266 INDEX OF NAMES

Dewey, J. 164 to its first-order part: 134-135 Dreyfus, H. 164 helped to persuade Hilbert of the value Du Bois-Reymond, E. 76, 119 of symbols in mathematics: 138- Du Bois-Reymond, P. 56,76,77, 119 139 Freudenthal, H. 154, 164 Eddington, A. 32 Friedman, H. 216 Ehrenberg, W. 5,31 Fritz, K. von 64 Einstein, A. 168, 174 Enriques, F. 79 Gassendi, P. 34, 36 Essler, W. 164 Gauss, C. F. 35, 39, 40, 41, 42, 43, 53, Euclid 65,71,82,83,87,88,89,97,98-99, 72, 163 100, 106, 107, 109, 110, 165 Gelemter, H. 92, 93, 96, 109 Gentzen, G. 124, 125, 143, 155, 159, 173, Fano, G. 39 193,194,195,240 Feferman, S. 159,172,194 gave "slippery slope" argument for the Finsler, P. 152, 162, 170, 193, 244, 245 visualizability of the co-induction infinitistic mathematics cannot be justi­ used in his consistency proof: 160 fied without an existence proof for argued that his consistency proof for infinite sets: 68-69 number theory used methods more constructed forinally undecidable sen­ reliable than those formalized in it tences which are true when trans­ despite transcending them: 174 ferred to a "purely conceptual Gibson, A. B. 19,32 realm": 147-149 G6del, K. ix, xi, 9, 14, 16,23,24, 26, 41, his mentalistic incompleteness argument 42,46, 56, 60, 64, 70, 101, 147, 150, posed a prima facie obstacle to 151,161,163,171,176,179,181,188, mechanism which was removed by 189-193,196,198,202,207,208,214, G6del's mechanization of it: 150- 215,217, 235, 240, 242, 243, 244, 245 151 formalized and mechanized diago­ Fraser, A. C. 35, 36, 37 nalization: 193, 231 Frege, G. 44, 45, 60, 89, 117, 120, 124, generalized recursion: 203, 206 137, 144, 163, 164, 167, 168,238 on "miracle" of the closure of recursive defended Dedekind's Gedankenwelt functions under diagonalization: proof by reference te> his objective 219 thoughts: 58-59 recognized Turing's thesis as form of attacked Hilbert's formulation of the mechanism and criticized its finite­ axioms of euclidean geometry: state hypothesis for not respecting 80-82 the dynamic growth of the human argued that their consistency is im­ mind: 222-224 mediate from their truth, and that argued against mechanism in biology: consistency generally can only be 226 proved by an existence construc­ on the unpredictability of the universal tion: 85-87, 134 Turing machine: 233 insisted that the referential intention of Goldfarb, W. 164 signs be declared: 133 Good, I. J. 173 his logic absolute and purely syntactical Gordan, P. 74, 75 with no special recognition given Goodman, N. xii, 143 INDEX OF NAMES 267

Grassman, H. 44, 45, 98 held intuition to be as essential to ge­ Gunderson, K. 32 ometry as logic: 90 critical mathematics studies not just the Hadamard, J. 128 rigor of proofs but the possibilities Hameister, E. 164 for their "purity": 101, 105 Hawkins, D. 12 his belief in the solvability of mathe­ Hegel, G. W. F. 63,64,241 matical problems encouraged by Heidegger, M. 62 the growing success of modern Helm,B.70 mathematics in proving the impos­ Henkin, L. 70,164 sibility of solutions by given limited Herbrand, J. 160,204--205,206 means: 111-119 Hertz, H. 79, 90 replaced Dedekind's Gedankenwelt on theories as logically consistent pic­ with a countable set of symbols and tures of phenomena: 79-80 generalized his "free creation" of Hessenberg, G. 104 numbers to a "creative principle" tried unsuccessfully to construct unde­ for axiomatic mathematics: 120- cidable statements in 1905: 74 123 Hilbert: D. vii, ix, xi, xii, 7, 8, 9,14, 16, on the finiteness of nature: 137 39,42,43, 50, 61, 64, 69, 74, 75, 79- on the finiteness of intuition: 140-143 81,85, 87, 89, 92, 93, 94, 96-98, 102- metamathematics turns mental proofs 104, 106, 108-111, 124-128, 131, 133, into concrete objects of intuition: 134, 138-139, 147, 148, 149, 154-155, 145 156,157,161-163,164-174,175, 176, mathematics can henceforth develop 177,181,182,184-189,191,197,203, through the interplay between 205,216,236,238,240,244,245,246 formal systems and the meta-' saw three historical stages (naive, for­ mathematical study of their con­ mal, critical) in the development of sistency, which will continually a mathematical theory which anti­ generate new axioms and theorems cipate his later distinction between in them; but only metamathe­ its formalization and its meta­ matical truths about provability mathematical study: 76, 144-145 and unprovability are absolute: saw elementary geometry as chance to 145-146 refute Kronecker's exclusion of it follows that completeness is not re­ geometry from pure mathematics quired for these formal systems: on the grounds that it dealt with 146 continuous magnitude and was not on the finiteness of mind and thought: based purely on the concept of 151-153 integer: 77-78 Hobbes, T. ix, 18, 19, 28, 34, 59, 91 his completion of Euclid's axioms all reasoning is only calculation: 20, motivated by desire to complete 22-23 the proof for the independence of Hoering, W. 209 parallel postulate: 82-84 Hofstadter, D. 168,243 held that the axioms of geometry could Holder, O. 98 never hold exactly in nature: 87 Hume, D. 32 but his axioms were as rooted in visual on the impossibility of any image of the intuition as Euclid's: 88 infinite: 33 268 INDEX OF NAMES

saw that geometry fails to demonstrate Laing, R. 9, 10 the infinite divisibility of extension: Lambert, J. H. 39 38 La Mettrie, J. ix, 28, 30, 76, 233 Husser!, E. 30,41,85, 142, 159, 160, 168, man as a machine too complicated to 173 be a priori clearly defined: 20-22 on arithmetic as a spiritual machine: Laplace, P. S. 1,6, 12 25-26 Larmour, J. 4 on the basis of completeness in inten­ Lear, J. 168 tionality: 156-158 Leibniz, G. W. 2, 23, 26, 37, 39, 40, 143 on the absolute necessity of the law of Jiirnefelt, G. 39, 71 continuity for geometry and na­ Jevons, S. 26,27, 115 ture: 38 Lob, M. H. 197 Kac, M. 89,96 Lobachevski, N. 39, 83, 115, 165 Kalmar, L. 189,209,240 Locher, L. 150 Kambartel, F. 164 Locke, J. 59,62,66,69,98 Kanitscheider, B. 69 on the mental power of repetition re­ Kant, I. 37, 39-40, 50, 90, 93, 98, 107, quired for an empiricist account of 139,141,170 infinity: 35-37 Kaufmann, F. 41, 156, 160 Lockwood, M. 68, 223 Keferstein, H. 48, 61, 62 Lodge, O. J. 32, 163 Keyser, J. 62 Lorenzen, P. 118 Kitcher, P. 169, 170 Lucas, J. R. vii, ix, x, 193, 194,229,231, Kleene, S. 46, 56, 172, 179, 204, 206--209, 241 211-214,224,231,240,245 uses truth to distinguish man from sees his recursion theorem as the machine: 197 principal evidence for Church's on predictability of machines: 232. thesis and his extension of it to Lyndon, R. 70-71 partial functions: 215-219 Klein, F. 77, 163 Mahnke, D. 173 Konig, J. 170, 181, 192 Mainzer, K. 239 Kreisel, G. ix, xi, 42, 167, 196, 223, 243 Marquand, A. 26, 27 on proofs as infinite mental objects: Martin-Lof, P. 8 155-156 McCulloch, W. 221 on the mechanistic character of for­ Mehlberg, A. 165 malism and its refutation by Meschkowski, H. 165 GOdel: 194-194 Minsky, M. 220, 228, 242, 243 on the complexity of human thoughts Mises, R. von 6, 10, 119 and computations: 225 Moore, E. F. 243 Kripke, S. 210,211 Morrison, P. 32 Kronecker, L. 41, 43, 47, 54, 57, 75, 76, Morrison, E. 32 77,88, 129, 163,219 Moss, J. M. B. 71 demanded that all mathematical defini­ Mueller, I. 88 tions be decidable: 72-74 MUlier, G. H. 171 Kustaanheimo, P. 39, 69, 71 Myhill, J. 233, 234 INDEX OF NAMES 269

Nagel, E. 193 theories: 126-128 Nathanson, S. 67 asserted the denumerability of our Nelson, R. J. 246 Gedankenwelt and rejected Can­ Neumann, J. von 2,31, 160,233,243 tor's proof on non-denumerable on the meaning of "meaningless' for­ sets: 129 malisms: 143 Post, E. x, 175, 222, 242 accepts without proof in 1927 the unde­ on the generality of incompleteness cidability of mathematics: 146-147 (Turing's thesis): 222 Newman, J. R. 193 on the invalidity of the incompleteness Newton, I. 168 argument against mechanism: 229 on the mechanization of those creative O'Connor, D. J. 37 processes of which we can become "completely conscious" (axiom of Pappus 107-109, 110, 111 reducibility for finite operations) Parikh, R. 243 229 Parsons, C. 170 Prenowitz, W. 88 Pascal, B. 1, 20, 22, 23 Proclus 40, 107, 108, 110 Pasch, M. 78, 89 on the status of Euclid's plane: 98-99 Pattee, H. H. 16, 17 on the emancipation of geometry from Peirce, C. S. 30, 52, 53, 64, 96 pictures in the imagination: 99 critique of logic machines and psy­ Putnam, H. 193, 194 chologism: 26-28 did not appreciate the generality of Quine, W. V. O. 167, 173,225-226 Babbage's analytical engine: 28 on the synthetic character of logic: 29 Rabin, M. O. 167 on optical diagrams and their use to Raggio, A. R. 139, 154, 168-169 prove Desargues' theorem: 93-95 Ramsey, F. 60 Peter, R. 189,239 Rautenberg, W. 165 Pitts, W. 221 Reid, C. 163 Plato 87 Resnick, M. D. 164, 174 Pogorelov, A. V. 115 Richard, J. 56, 129 Poincare, H. 11-12, 32, 54, 55, 59, 91, Riemann, B. 75, 78,115 96, 98, 110, 125, 130, 131, 137, 139, Rogers, H. 178,181,197,216,233 165, 166-167, 175,247 Rosenbloom, P. 154 his explanation of the synthetic char­ Royce, J. 63-64 acter of induction is just Locke's Russell, B. 62-63, 71, 89, 104, 124, 135, power of repetition of mental acts: 142 37 claimed that Hilbert had made ge­ Saville, H. 164 ometry accessible to blind mecha­ Schonfinkel, M. 181,183,212 nisms: 89,90,97 Schor, D. 102-103 held induction incapable of being Schutte, K. 155 denied: 126 Schwabhauser, W. 165 held the axiomatic method to be sterile Schwarz, H. A. 74, 75 as long as applied only to complete Scott, D. 201, 203 270 INDEX OF NAMES

Shoenfield, J. R. 154, 171, 172 gained by simply increasing the Siefkes, D. 240 number of symbols: 225 Singh, J. 243 his imitation game involves more than Skinner, B. F. 237 crude simulation: 236-237 Skolem, T. 46,58,131, 132, 185,240 Turner, M. 242 Smart, J. J. C. 173 Smith, D. 32 van Heijenoort, J. 135, 167-168 Stadt, G. von 28,29, 93, 97 Vartanian, A. 32 Stackel, P. 164 Veblen, O. 39, 164, 173 Steen, S. W. P. 239 Veronese, G. 70 Stein, H. 164 Steiner, H. G. 70, 164 Wang,H. 70,118-119,158,224,242 Stenlund, S. 239 reports on Godel's belief in Hilbert's Stolz, O. 39 solvability thesis: 112-113 Strong, H. R. 241 on Turing's finite-state hypothesis: 221 Struik, D. 174 report's on Godel's critique of Turing's Sturm, C. 43, 72, 73, 105 finite-state hypothesis: 222-223 Szilard, L. xi, 4, 5, 8, 9 Webb, J. C. 241 Weierstrass, K. 72, 73, 74 Takeuti, G. 174,242 Weizenbaum, J. 247 Tannery, J. 128 Weston, T. 117 Tarski, A. 43, 60, 105, 106, 144, 147, Weyl, H. 47, 81, 118, 142, 160, 167, 168 165, 197, 200 199 Tharp, L. 164 on isomorphism as a boundary of Thomas, W. J. 241 scientific thought: 50 Trachtenbrot, B. A. 171 the first to apply the Richard's paradox Troelstra, A. S. 241 to axiomatic set theory: 131 Turing, A. M. ix, xi, 7, 8, 16,17,26,29, argued that incompleteness theorem 159, 172, 219, 222, 223, 224, 228, shows that we cannot completely 230, 232, 235, 236 formalize our number concept: 198 on his finite-state hypothesis for the Wiener, H. 105 human computer: 8,221 Wiener, N. ix, 7-8 begged the question of machine orig­ Wigner, E. 243 inality: 28 Wilkes, M. V. 32 circumvented the problem of getting Wilson, E. B. 124 a machine to understand natural Wittgenstein, L. 142,153,156, 160 language: 220 claimed that the effect of more com­ Zermelo, E. 130, 131, 132,241 plicated states of mind can be INDEX OF SUBJECTS

Ackerman function: 177, 185, 186, 188 202 raised problem of most general re­ in geometry: 42, 65, 77, 78, 80-84, cursions: 188 88-89,97-109, 116, 118-119, 120 Algebra: 43, 72, 74, 76, 78, 79, 86, 88, in physics: 116, 139-140 99, 100, 103-104, 105, 1l0, 112, 165, in set theory: 117, 118, 121, 130, 131, 176,200 132 Algorithm: 43, 44, 54, 75, 76, 180 Analytic,geometry: see geometry Babbage's thesis: 24, 220 Analytical engine: 23, 24, 27, 28, 29, 43 Berkeley's Intelligence: 107, 109 Arithmetic: 22-23, 24-25, 38, 40, 43-45, Brentano's thesis: 156 46-49, 51-52, 57, 82, 84, 87, 92, 98, 105, 116, 120, 121, 123, 126-127, Cantor's curse: 73-74,76, 187 130, 140, 184-187, 191, 199-200, 266 Categorical systems: 49, 84,123,124,128 algorithmic conception of: 44, 202-203 Church's theorem: 114,201 deductive conception of: 44, 49, 123, Church's thesis: vii, x, xi, 49, 114, 122, 124, 202-203 180, 188--189, 190, 195, 198, 200, a stain on geometry: 77-78, 98, 104, 203, 206, 208-212, 215-218, 219- 105 222, 224, 240, 241, 243, 245, 246; see versus geometry: 38, 40, 42, 92, 247 also Kleene's thesis, Turing's thesis Arithmetization: 181, 187, 188, 192, 203, as form of mechanism: vi, x, 220, 222, 206,207,208 224-225 Axiom(s): xi, 31, 44, 80, 81, 82, 83, 84, evidence for: 211-212 88, 89, 93, 96, 97, 122, 124, 126, 142, intuitionistic critique of: 163, 209-211, 157,166 223-225, 241 of Archimedes: 39, 65, 78, 84, 85, 98, Kleene's arguments for: 215-219, 224 104, 116, 207 Combinatory logic: 181-184, 212-213, of congruence: 39, 69, 83, 101, 105, 239 107-109, 115 and Hilbert's metamathematics: 182- of continuity: 38-40, 65, 69, 77, 78, 183,239 83, 84, 98, 105, 109 and problem of effectiveness: 212-213 of infinity: xi, 38, 62-63, 66, 68, 118, as an analysis of thought: 182 130,246 Compactness: 135-137 of parallels: see parallel postulate as clarification of potential infinity: of power-sets: 117, 118 135-136 of space: 83, 91, 92, 94-95, 96, 97, 99, Completeness: 40, 41-42, 44, 46, 47, 49, 101, 102-103, 106, 110, 165 50, 82-85, 102, 105, 113, 117, 123, Axiomatic method: 42, 44-45, 97, 115- 126, 134, 135, 139, 146, 157, 158, 116, 120, 122, 126, 128, 142, 175, 160-162, 165, 167, 183, 189, 190, 200--201 199, 200, 229, 244; see also Voll­ in arithmetic: 42, 44-45, 121, 122-123, stiindigkeitsaxiom 126--127, 176, 184-185, 191, 201- experimental: 162,191,201 271 272 INDEX OF SUBJECTS

of mental creations: 35,40-42,46, 161 as existence proof for infinite sets: 30, of phenomenological consciousness: 58-63, 64-66, 67, 68, 69, 156, 223, 158-159 244 theorem: 116, 138 Hilbert's replacement of by symbols: Computability: 16, 197, 198, 211; see 61, 121-122, 139 also effective (methods) Dedekind's recursion theorem: 51-57, Consistency: 14,38,46,57,58,61,63,66, 70, 175, 176, 177, 184, 185, 186, 188, 75, 79-80, 82, 84, 85, 86, 87, 116, 192,216-217,238,244 120, 121, 122, 123, 124-125, 134,136, and intuition of effectiveness: 54-57 137,139-140,144,146,147,155,160, fallacies in proof: 53-55 162, 169, 174, 188, 191, 193-194, stronger than induction principle: 54- 195, 211, 222, 242 57 and scepticism about continuity: 120, Dedekind's thesis: 49-50, 57, 216, 244 165-166 Desargues' theorem: 28, 40, 83, 93-96, as criterion for existence: 85-87, 116, 97,101-102,103-104,105, 106, 110, 134, 137-138 115, 246, 247 phenomenological basis of: 158-160 and Godel-sentences: 101-102 Continuity: 11, 12, 32, 36, 38-40, 65, 69, and Hilbert's later program: 101, 104- 72, 77, 78, 83-84, 90, 98, 101, 104, 105 105, 106, 109, 115, 11'6, 120, 164, 165, as basis of linear perspective: 100-101, 166, 201-202; see also axioms of 102-103 continuity, continuum as geometric basis for number and elimination of: 39, 43, 77-78, 98, 104- algebra: 103-104 106, 116, 120, 165-166 as logical content of spatial intuition relation to spatial intuition: 106, 109- in plane: 102-103 110, 164 as qualitative criterion of straightness: scepticism about: 32, 39, 69, 77-78,90, 115 118-119, 120, 163 difficulty of machine-proof of: 28, Continuum: 73, 77, 119, 120, 129 95-96, 97, 101,246 hypothesis: 116, 117-118, 119 evident to spatial intuition: 83, 94, 95, 96,97 Decidability: x, xi, 41, 42, 43, 70, 72, 73, Descartes' demon: 3, 13, 17, 18-19 74, 114, 128, 139, 144, 161, 197, Diagonalization: 8, 22, 56, 74, 127, 132, 198,209,215; see also Entscheidungs­ 148-149,178-181,185,192-193,205, problem 208-209, 214-215, 230-231, 239, of mental creations: 41-42, 69-70 240, 241, 244 Dedekind's Gedankenwelt: 58-59,61, and existence of recursive functions: 63, 66, 69, 121-122, 128-129, 130, 57, 179-180,212,214 148,156,223,225,245 formalization of: 192-193, 208 and denumerabiIity: 128-129, 167 mechanization of: 151,231 and Frege's objective thoughts: 30, 58-59,139 Effective (methods): x, xi, 5, 6, 7, 8, 9, 10, and idealism: 63-64 11, 15, 16, 17, 26,43,46, 55, 56, 57, and problem of consistency: 58, 61, 72-74,75-76,114,115,128,129,151, 121-122 163,172,175,176,177,185,188,197, and propositions: 60, 61 198, 200, 202, 205, 208, 209, 215, INDEX OF SUBJECTS 273

218-219,223,224,230,232 as excessive use of formulas and sym­ functions: 175, 176, 177-180, 185, 188, bois: 75, 138-139 204-205,208,218,219 Hilbert's: 7, 50, 77, 78, 80-82, 87, 97, gambling system: 5, 6, 16 101, 102-104, 115-116, 119, 121- human versus mechanically effective: 123. 124-125, 127-128, 137, 140- xi, 223-225, 228 141, 142-145, 153-154, 162-163 mechanization of: x, xi, 151, 163, 210, Formalization: 7, 84-85, 89, 90, 97, 115- 245 116, 124-125, 126, 130, 138-139, (V-rule: 155, 171, 172 143-145, 162, 174, 192-193,208 prediction: 11, 14,232-233 Effectiveness: 26, 54, 55, 56, 57, 175, 176, Geometry: x, 38, 39-40, 42, 43, 44, 62, 177, 180-181, 204, 210, 211, 213. 64-65, 69, 71, 72, 76, 77-79, 80-85, 216, 219, 230, 244 87,88-111,112, 115, 116, 117, 118- intuition of: 54, 55, 56, 57, 177, 180, 119, 120, 124, 125, 126, 128, 137, 188, 211, 213 140-141, 143, 146, 156, 158, 164, paradox of: 178, 208, 241 165,166,201,202,207,244,246,247 Entscheidungsproblem: 7-8, 29, 85, 114- analytic: 78,99-100,103-104, 110, 120, 115,147,189,190,206 247 and, Hilbert's program: x, 90,101,104- Finitism: xi-xii, 2, 7,12, 13,21,26,30,33, 105, 109-110, 124-125, 140-142, 39-40,68-69,71,73,75,105,129,137, 143, 146, 165 140, 141-142, 145, 152-154, 155, 160, and logicism: 103-104 165, 170, 171, 173-174, 177, 185, 187, and visual intuition: 88, 89, 90, 97,100, 194,221,222-223,225,236,237 107 and denumerable formalisms: 142 euclidean: 39, 62, 64-65, 71, 80, 82-83, as critique of the infinite: xi-xii, 34-38, 87, 88-89, 92-93, 98-99, 105-110, 58-63, 65-66, 67-69, 98, 118, 135- 118-119, 128, 141, 158, 165, 201- 137, 153-154 202 Berkeley's: 71 finite: 39-40, 69, 71, 98,165 Hilbert's: 7, 69, 105, 120-122,137,140, machine: 92-93, 96, 97, 101, 106, 109, 141-142, 145, 152-154, 155, 161, 111 170,171, 187, 194,236 non-euclidean: 39, 71, 82-83, 87, 97- Kronecker's: 73-74 98, 115, 126, 165 only euclidean planimetry compatible physical: 78, 81, 87, 165, 174 with: 165 "standing next to" euclidean (Hilbert's Formalism: 7, 10, 20-21, 50, ,75-76, 77- fourth problem) 79, 80-81, 82, 84, 86, 103-104, 105, GOdel machines: 214-215, 234, 235, 245; 116--117, 124-125, 127-128, 133-134, see also Kleene's recursion theorem 137-138, 142, 143-144, 147, 162-163, Godel's completeness theorem: 116, 135, 171,192-193,199 138,189-190,206 and isomorphism: 50, 80-81, 117, 128 supports Hilbert's solvability thesis: and mechanical models: 79 116, 138 and mechanism: ix, x, 7-8, 141-142, Godel's fixed-point theorem: 61, 192- 152, 163, 194 193,196--197,200,213,214,229,234 as critique of model concept: 137-138 and Dedekind's proof for infinite sets: as democracy among models: 79 61 274 INDEX OF SUBJECTS

and truth-predicate: 196-197,234 and ongm of completeness problem: Godel's incompleteness theorem: vii, ix, 84-85 x, xii, 9, 14, 24, 42, 101-102, 112- 113, 119, 126-127, 147, 150-151, Incompleteness: 10, 32, 35, 50, 116-117, 161-162, 163, 170, 171, 190, 191, 132,162, 171, 172, 201-203, 209, 229 192-193, 195, 196, 206, 208, 212, Independence: 38, 63, 83, 101, 112, 115, 215,217,228,231,240,245,246 116, 117, 118,119,126,195,245-246 anticipations of: 78, 147-151, 202, 222, and solvability of mathematical prob­ 229 lems: 115-119 as protection for Church's thesis: 9, importance of for formalist episte­ 206,208,212,231-232,240,245 mology: 245-246 as support for formalism: 126-127, 146- Induction: 37, 40, 45, 47, 49, 51, 52-54, 147,162-163,196,235 55,56,57,98,105,123,125,126-127, as support for mechanism: 9, 151, 193, 153-155, 170, 171, 174, 177, 184, 231,232-233,235,245 191,199,208-209,218,242 used against formalism: 194-195 as synthetic a priori: 37, 125, 126 used against mechanism: 112-113, 119, cannot produce an infinite set: 53, 55 193-196, 229-231 weaker than recursion: 52-56 Godel's second theorem: 14, 160, 173- Infinite: xi, 7, 12, 15, 21, 24, 28, 30, 33- 174, 193-194, 222 38, 40, 47, 48, 53, 55, 57-59, 62-69, Godel-sentences: x, xi, 101-102, 151, 90, 97, 98, 118-119, 120, 130, 135- 173,192-193,196,202,230,245,246 137, 142, 150, 151, 152, 153-156, 157-158,170,175, 186-187, 198,200, Hertz's picture principle: 79-80, 87, 90 209,222-223,225,244 Hilbert's demon: xi, 7-9,11,14,96 actual: 34,35,37,136-137 Hilbert's proof-description thesis: 122, divisibility: 34, 36, 38-39, 71, 98 181, 192 . induction: 153-155, 171, 172, 209 Hilbert's Schnittpunktsatze theorem: 85, mental obligation to produce: 36-37 105, 106, 146, 165 mental obligation to comprehend: 34- as prototype for later program: 105, 146 35,40 Hilbert's solvability thesis: 14, 76, 111- mind (states of): 63-64, 66-68, 222- 119,138,161-162,168,169 223,225, 244 Hilbert's versus Godel's reasons for nature: 12, 13, 15,30 believing: 112-113 potential: 15, 28, 34, 135-136 Hilbert's Streckenrechnung: 78, 90, 104, proofs: 145, 149-150, 152-153, 155, 141 156,170-171 and numerals as subject of arithmetic: structures: 118-119 90, 141 Intelligence: I, 4, 5, 89, 154, 219-220, as formalistic treatment of number 235,237,247 fields: 78, 103-104 artificial: 5, 97, 109, 111, 219-220, based on Desargues' theorem: 103-104 235,247 based on Pascal's theorem: 78, 104 Intentionality: 67, 156, 157, 158-160 Hilbert's Vollstandigkeitsaxiom: 83-84, and completeness: 157, 158, 160-161 85, 137, 164 and infinity: 142, 156, 157, 158 and existence of non-euclidean space: Intuition: 38, 44, 46, 48, 56, 78, 80, 82, 83 87, 88, 89, 90, 91-93, 94-95, 96, 97, INDEX OF SUBJECTS 275

98-100, 101, 102-103, 107, 109-111, Logic: 26--27, 29, 37, 44, 46, 58, 61, 70- 116, 140-142, 143, 196, 197, 198, 71,84-85,88,89,106,116,117,121, 247; see also effectiveness 123-125,134-137,148,161,164, 181, in arithmetic: 196,197,198 182,189,190,198,201 of finiteness: 55 as laws of thought: 46, 58, 61, 85 pure: 38,98 first-order: 85, 105-106, 117, 123, 131, spatial: 44, 46, 78, 87, 90, 94-95, 97, 134-137,164, 189,201 98-100,102-103,107,109,111,247 machines: 26--28,29,89, 125-126, 138 visual: 88,89,93,97, 107 Peirce's critique of logic machines: Isomorphism: 47, 49, 50, 51, 70, 80-81, 26--29 82, 84, 117, 123, 128, 161, 164, 191, 193,216; see aslo categorical systems Machine(s): x, xi, 1-11, 14-31, 89, 90, as formalistic limit on mathematical 91-93,95-96,97, 103, 106, 109, 110, thought: 50,80-81,117,128 111,112,113,125-126,138,141,142, as justification of Dedekind's thesis: 49, 146, 150, 151, 154, 155, 156, 166, 216 173, 193, 197, 199-200,209,214-215, finitization of: 50, 123, 161, 191, 193, 218-238, 241-247 216 evolution of concept of: 1-3 logical limitations on: xi, 16--17 Kleene's recursion theorem: 171, 172, self-reproduction: 22, 233, 243 173,212-213,214,215-219,233-235. thermodynamic limitations on: 3, 9-10, 243,245 16--17 and Godel's fixed-point theorem: 214- universal: 1,8--11,14, 15,23,28,214, 215,234 228-229,233-234 and machine self-reference: 214-215, unpredictability: 9-11, 14, 29, 232- 234-235 233, 237, 245 and machine self-reproduction: 233, vision: 91-92, 96-97, 110-111, 247 243 Maxwell's demon: xi, 3-9, 14, 15, 31 as evidence for Church-Kleene theses: Mechanism: ix, x, 1-7, 11-13, 15, 17- 215-219 31,57,67,89,91,92,93,96-97, 110- as existence theorem for recursive III, 113, 125, 138-139, 146--147, functions: 214,217-219 150-151,156,173,193-196,200,203, as existence theorem for Turing ma­ 210, 220, 222, 223, 225, 226, 228, chines: 218, 233-235 229,232-233,235-238,244-247 as fundamental "limitative" theorem: and exorcism of demons: 12, 13, 17 215,234 and finitism: 2, 12-13,21, 30, 31, 222- Kleene's thesis: 218-219, 223-224 223, 225, 236-237 and human versus mechanical effec- Cartesian: I, 2, 17, 19 tiveness: 223-224 Hobbes': 19-20,22-23,28 Konig's thesis: 181,192 in arithmetic: 22-26, 193-194, 199, Kripke schema: 210, 211, 241 200, 247 Kronecker's decidability demand: 72-74, in geometry: 89,90,91,92,93,95,96, 185 97, 106, f09, Ill, 125, 247 indeterministic: 6, II, 12 Laplace's demon: I, 2, 10, II, 12, 13, La Mettrie's: 20-22, 28, 30, 76, 233, 14,15,119 245 276 INDEX OF SUBJECTS

Turing's: 219-225, 236-238 Psychologism: 26-27,28,29,30 Metamathematics: 77,101, 1l1,127, 131, refuted by mechanization of logic: 139, 142, 144, 145, 146, 153, 154, 26-28 162,. 163, 175, 178, 180, 182, 196, Peirce's arguments against: 26-28 203; see also Church's thesis, com­ pleteness, consistency, decidability, Randomness: 5,6, 10, 11, 12, 14, 16, 17. Godel's incompleteness theorem, 31 undecidability, Hilbert's solvability and incompleteness theorem: 10 thesis enhances mechanism: 6, ll, 12 Recursive functions: 44-46, 51-52, 123, Number: 35, 36, 40-41, 42, 46, 47, 49, 176, 177, 185-189, 191-192,203-208, 50,66,67-68,77-78,84,98,102,104. 211-219, 244, 245; see also Dede­ 105, 109, 120-121, 126, 129, 135, kind's recursion theorem, Kleene's 141, 142, 160, 161, 196, 198-200; recursion theorem see also Dedekind's thesis Godel-Herbrand: 204-206 as mental creation: 40,41,58 Kleene: 206-208 not unformalizable as such: 198-200 of the "most general kind"': J88, 189. 204 Paradox(es): 63, 120, 121,122, 128, 129, partial: 57,179,208,213-214,215,217. 130, 131, 132, 139, 147, 151, 178. 218-2J9,223-225 184, 197, 208, 241, 244 Cantor's: 121, 122 Spatial intuition: 44, 46, 78. 87. 88, 90, of effectiveness: 178, 208, 241 94-95, 97, 98, 99, 100, 102. 103, 107, of finite definability: 147-150 109, HJ, 165,247: see also Berkeley's ofliar: 197 Int~lIigence, perspective paradoxical combinators: 184, 239 as intuition of planes in space: 94-95 Pythagorean: 71 Descartes' restriction of "mental vi­ Richard's: 129-132, 151,241 sion"' to plane: 100, 1 10 Russell's: 63, 121, 122, 130. 184. 212 Hilbert's generalization of: 140-141 Parallel postulate: 38, 42, 62, 65, 69. Hilbert's "logical analysis" of: 87-88, 71, 83, 99, 100, 102, 110, 112, 118- 94-95, 97, 101, 102-103, 106-107, 119, 164,246 109-111 and continuum hypothesis: 118-119 Hilbert's "mnemonic symbols" of: 90. and problem of completeness: 82-83 141,142, J43, 247 stronger than its 'equivalents' in the not required by Euclid's planimetry in absence of continuity: 165 the presence of number, 109 Pascal's theorem: 40, 85, 104, 105 Peirce's "optical diagrams" of: 93, 95 and commutativity of field multiplica- possible for machines: 91-92,96. III. tion: 104 . 247 and Hilbert's program: 104-105 Substitution: 56-57, 179, J80, 181-184, Perspective: 7, 91-92, 94, 96, 100, 101. 192,214,238 102,110 arithmetization of: J92. 214 and machine vision: 91-92, 96 effectiveness of: J 81 and spatial intuition in geometry: 94- operates on symbols: 181 95, 100 Symbols: 16,22,28,61. 62, 89, 90. 121- Post's axiom of reducibility: x, 229 122, 138-139, 140, 141, 142-143, INDEX OF SUBJECTS 277

146, 148, 170, 181,247 101,·102,1\9,134,135,148,149,151, and problem of consistency: 61, 121- 171, 196, 197,201,234 122 and consistency: 85-86 mnemonic versus meaningless: 142- cannot distinguish man from machine: 143 197 permanence of rejected on physical semantics: 91, 93, 142-144, 147, 165, grounds: 16 197,247 spatiality of: 140--141, 142 Tarski's criterion for: 60, 197, 234 thought as manipulation of: 22 versus provability by limited means: 101, 1I9 Tarski's completeness theorem for ge­ Turing's theorem: 8,230,232 ometry: 43, 105, 165 Turing's thesis: vii, x:i, 8, 15, 16, 17, 24, Thales' theorem: 93, 106, 107, 108, 109, 30, 31. 42, 219-225, 229, 230, 231, 110, 1I1, 1I6 232, 242, 245; see also Babbage's Pappus' proof of discovered by geome­ thesis try machine: 109, 1I1 as form of mechanism: 9, 31, 220, 222, presupposes space in the absence of 224--225,229 number or continuity: 109 finite-state hypothesis: 8,221, 222, 225 Truth: 26, 27, 60, 61, 70, 80, 85, 86, 87, GDdel's critique of: 222-224 SYNTHESE LIBRARY

Studies in Epistemology, Logic, Methodology, and Philosophy of Science

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Editors: DONALD DAVIDSON (University of Chicago) GABRIEL NUCHELMANS (University of Leyden) WESLEY C. SALMON (University of Arizona)

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Boston Studies in the Philosophy of Science, Volume II. 1965. II. Evert W. Beth, Mathematical Thought. An Introduction to the Philosophy of Mathematics. 1965. 12. Evert W. Beth and Jean Piaget, Mathematical Epistemology and Psychology. 1966. 13. Guido Kung, Ontology and the Logistic Analysis of Language. An Enquiry into the Contemporary Views on Universals. 1967. 14. Robert S. Cohen and Marx W. Wartofsky (eds.), Proceedings of the Boston Collo­ quium for the Philosophy of Science 1964-1966. In Memory of Norwood Russell Hanson. Boston Studies in the Philosophy of Science, Volume III. 1967. 15. C. D. Broad, Induction, Probability, and Causation. Selected Papers. 1968. 16. Gunther Patzig, Aristotle's Theory of the Syllogism. A Logical-Philosophical Study of Book A of the Prior Analytics. 1968. 17. Nicholas Rescher, Topics in Philosophical Logic. 1968. 18. Robert S. Cohen and Marx W. Wartofsky (eds.), Proceedings of the Boston Collo­ quium for the Philosophy of Science 1966-1968. Boston Studies in the Philosophy of Science, Volume IV. 1969. 19. Robert S. Cohen and Marx W. Wartofsky (eds.), Proceedings of the Boston Collo­ quium for the Philosophy of Science 1966-1968. Boston Studks in the Philosophy of Science, Volume V. 1969. 20. J. W. Davis, D. J. Hockney, and W. K. Wilson (eds.), Philosophical Logic. 1969. 21. D. Davidson and J. Hintikka (eds.), Words and Objections. Essays on the Work of W. V. Quine. 1969. 22. Patrick Suppes, Studie.s in the Methodology OlId Foundations of Science. Selected Papers from 1911 to 1969. 1969. 23. Jaakko Hintikka, Models for Modalities. Selected Essays. 1969. 24. Nicholas Rescher et al. (eds.), Essays in Honor of Carl G. Hempel. A Tribute on the Occasion of His Sixty-Fifth Birthday. 1969. 25. P. V. Tavanec (ed.), Problems of the Logic of Scientific Knowledge. 1969. 26. Marshall Swain (ed.), Induction, Acceptance, and Rational Belief 1970. 27. Robert S. Cohen and Raymond J. Seeger (eds.), Ernst Mach: Physicist and Philos­ opher. Boston Studies in the Philosophy of Science, Volume VI. 1970: 28. Jaakko Hintikka and Patrick Suppes, Information and Inference. 1970. 29. Karel Lambert, Philosophical Problems in Logic. Some Recent Developments. 1970. 30. Rolf A. Eberle, Nominalistic Systems. 1970. 31. Paul Weingartner and Gerhard Zecha (eds.), Induction, Physics, and Ethics. 1970. 32. Evert W. Beth, Aspects of Modern Logic. 1970. 33. Risto Hilpinen (ed.), Deontic Logic: Introductory and Systematic Readings. 1971. 34. Jean-Louis Krivine, Introduction to Axiomatic Set Theory. 1971. 35. Joseph D. Sneed, The Logical Sstructure of Mathematical Physics. 1971. 36. Carl R. Kordig, The Justification of Scientific Change. 1971. 37. Milk Capek, Bergson and Modem PhysiCS. Boston Studies in the Philosophy of Science, Volume VII. 1971. 38. Norwood Russell Hanson, What I Do Not Believe, and Other Essays (ed. by Stephen Toulmin and Harry Woolf). 1971. 39. Roger C. Buck and Robert S. Cohen (eds.), PSA 1970. In Memory of Rudolf (omap. Boston Studies in the Philosophy of Science, Volume VIII. 1971. 40. Donald Davidson and Gilbert Harman (eds.), Semantics of Natural Language. 1972. 41. Yehoshua Bar-Hillel (ed.), Pragmatics of Natural Languages. 1971. 42. Soren Stcnlund, Combinators, X- Terms and Proof Theory. 1972. 43. Martin Strauss, Modem Physics and Its Philosophy. Selected Papers in the Logic, History, and Philosophy of Science. 1972. 44. Mario Bunge, Method, Model and Matter. 1973. 45. Mario Bunge, Philosophy of Physics. 1973. 46. A. A. Zinov'ev, Foundations of the Logical Theory of Scientific Knowledge (Complex Logic). (Revised and enlarged English edition with an appendix by G. A. Smirnov, E. A. Sidorenka, A. M. Fedina, and L. A. Bobrova.) Boston Studies in the Philosophy of Science, Volume IX. 1973. 47. Ladislav Tondl, Scientific Procedures. Boston Studies in the Philosophy of Science, Volume X. 1973. 48. Norwood Russell Hanson, Constellations and Conjectures (ed. by Willard C. Humphreys, Jr.). 1973. 49. K. J. J. Hintikka, J. M. E. Moravcsik, and P. Suppes (eds.),Approaches to Natural Language. 1973. 50. Mario Bunge (ed.), Exact Philosophy - Problems, Tools, and Goals. 1973. 51. Radu J. Bogdan and Ilkka Niiniluoto (eds.), Logic, Language, and Probability. 1973. 52. Glenn Pearce and Patrick Maynard (eds.), Conceptual Change. 1973. 53. Ilkka Niiniluoto and Raimo Tuome\a, Theoretical Concepts and Hypothetico­ Inductive Inference. 1973. 54. Roland Fraisse, Course of Mathematical Logic - Volume 1: Relation and Logical Formula. 1973. 55. Adolf Griinbaum, Philosophical Problems of Space and Time. (Second, enlarged edition.) Boston Studies in the Philosophy of Science, Volume XII. 1973. 56. Patrick Suppes (ed.), Space, Time, and Geometry. 1973. 57. Hans Ke\sen, Essays in Legal and Moral Philosophy (selected and introduced by Ota Weinberger). 1973. 58. R. J. Seeger and Robert S. Cohen (eds.), Philosophical Foundations of Science. Boston Studies in the Philosophy of Science, Volume XI. 1974. 59. Robert S. Cohen and Marx W. Wartofsky (eds.), Logical and Epistemological Studies in Contemporary Physics. Boston Studies in the Philosophy of Science, Volume XIII. 1973. 60. Robert S. Cohen and Marx W. Wartofsky (eds.), Methodological and Historical Essays in the Natural and Social Sciences. Proceedings of the Boston Colloquium for the Philosophy of Science 1969-1972. Boston Studies in the Philosophy of Science, Volume XIV. 1974. 61. Robert S. Cohen, J. J. Stachel, and Marx W. Wartofsky (eds.), For Dirk Struik. Scientific, Historical and Political Essays in Honor of Dirk J. Struik. Boston Studies in the Philosophy of Science, Volume XV. 1974. 62. Kazimierz Ajdukiewicz, Pragmatic Logic (trans\. from the Polish by Olgierd Wojtasiewicz). 1974. 63. Soren Stenlund (ed.), Logical Theory and Semantic Analysis. Essays Dedicated to Stig Kanger on His Fiftieth Birthday. 1974. 64. Kenneth F. Schaffner and Robert S. Cohen (eds.), Proceedings of the 1972 Biennial Meeting, Philosophy of Science Association. Boston Studies in the Philosophy of Science, Volume XX. 1974. 65. Henry E. Kyburg, Jr., The Logical Foundations of Statistical Inference. 1974. 66. Marjorie Grene, The Understanding of Nature. Essays in the Philosophy of Biology. Boston Studies in the Philosophy of Science, Volume XXIII. 1974. 67. Jan M. Broekman,Structuralism: Moscow, Prague, Paris. 1974. 68. Norman Geschwind, Selected Papers on Language and the Brain. Boston Studies in the Philosophy of Science, Volume XVI. 1974. 69. Roland Fraisse, Course of Mathematical Logic - Volume 2: Model Theory. 1974. 70. Andrzej Grzegorczyk, An Outline of Mathematical Logic. Fundamental Results and Notions Explained with All Details. 1974. 71. Franz von Kutschera, Philosophy of Language. 1975. 72. Juha Manninen and Raimo Tuomela (eds.), Essays on Explanation and Under­ standing. Studies in the Foundations of Humanities and Social Sciences. 1976. 73. Jaakko Hintikka (ed.), Rudolf Carnap, Logical Empiricist. Materials and Perspec­ tives. 1975. 74. Milic Capek (ed.), The Concepts of Space and Time. Their Structure and Their Development. Boston Studies in the Philosophy of Science, Volume XXII. 1976. 75. Jaakko Hintikka and Unto Remes, The Method of Analysis. Its Geometrical Origin and Its General Significance. Boston Studies in the Philosophy of Science, Volume XXV. 1974. 76. John Emery Murdoch and Edith Dudley Sylla, The Cultural Context of Medieval Learning. Boston Studies in the Philosophy of Science, Volume XXVI. 1975. 77. Stefan Amsterdamski, Between Experience and Metaphysics. Philosophical Problems of the Evolution of Science. Boston Studies in the Philosophy of Science, Volume XXXV. 1975. 78. Patrick Suppes (ed.), Logic and Probability in Quantum Mechanics. 1976. 79. Hermann von Helmholtz: Epistemological Writings. The Paul Hertz/Moritz Schlick Centenary Edition of 1921 with Notes and Commentary by the Editors. (Newly translated by Malcolm F. Lowe. Edited, with an Introduction and Bibliography, by Robert S. Cohen and Yehuda Elkana.) Boston Studies in the Philosophy of Science, Volume XXXV II. 1977. 80. Joseph Agassi, Science in Flux. Boston Studies in the Philosophy of Science, Volume XXVIII. 1975. 81. Sandra G. Harding (ed.), Can Theories Be R~futed? Essays on the Duhem-Quine Thesis. 1976. 82. Stefan Nowak, Methodology of Sociological Research. General Problems. 1977. 83. Jean Piaget, Jean-Blaise Grize, Alina Szeminska, and Vinh Bang, Epistemology and Psychology of Functions. 1977. 84. Marjorie Grene and Everett Mendelsohn (eds.), Topics in the Philosophy of Biology. Boston Studies in the Philosophy of Science, Volume XXVII. 1976. 85. E. Fischbein, The Intuitive Sources of Probabilistic Thinking in Children. 1975. 86. Ernest W. Adams, The Logic of Conditionals. An Application of Probability to Deductive Logic. 1975. 87. Marian Przelecki and Ryszard Wojcicki (eds.), Twenty-Five Years of Logical Methodology in Poland. 1977. 88. J. Topolski, The Methodology of History .. 1976. 89. A. Kasher (ed.), Language in Focus: Foundations, Methods and Systems. Essays Dedicated to Yehoshua Bar-Hillel. Boston Studies in the Philosophy of Science, Volume XLIII. 1976. 90. Jaakko Hintikka, The Intentions of Intentionality and Other New Models for Modalities. 1975. 91. Wolfgang Stegmiiller, Collected Papers on Epistemology, Philosophy of Science and History of Philosophy. 2 Volumes. 1977. 92. Dov M. Gabbay, Investigations in Modal and Tense Logics with Applications to Problems in Philosophy and Linguistics. 1976. 93. Radu J. Bogdan, LocalInduction. 1976. 94. Stefan Nowak, Understanding and Prediction. Essays in the Methodology of Social and Behavioral Theories. 1976. 95. Peter Mittelstaedt, Philosophical Problems of -Modern Physics. Boston Studies in the Philosophy of Science, Volume XVIII. 1976. 96. Gerald Holton and William Blanpied (eds.), Science and Its Public: The Changing Relationship. Boston Studies in the Philosophy of Science, Volume XXXIII. 1976. 97. Myles Brand and Douglas Walton (eds.), Action Theory. 1976. 98. Paul Gochet, Outline of a Nominalist Theory of Proposition. An Essay in the Theory of Meaning. 1980. 99. R. S. Cohen, P. K. Feyerabend, and M. W. Wartofsky (eds.), Essays in Memory of Imre Lakatos. Boston Studies in the Philosophy of Science, Volume XXXIX. 1976. 100. R. S. Cohen and J. J. Stachel (eds.), Selected Papers of Leon Rosenfeld. Boston Studies in the Philosophy of Science, Volume XXI. 1978. 101. R. S. Cohen, C. A. Hooker, A. C. Michalos, and J. W. van Evra (eds.), PSA 19'14: Proceedings of the 1974 Biennial Meeting of the Philosophy of Science Association. Boston Studies in the Philosophy of Science, Volume XXXII. 1976. 102. Yehuda Fried and Joseph Agassi, Paranoia: A Study in Diagnosis. Boston Studies in the Philosophy of Science, Volume L.1976. 103. Marian Przelecki, Klemens Szaniawski, and Ryszard Wojcicki (eds.), Formal Methods in the Methodology of Empirical Sciences. 1976. 104. John M. Vickers, Belief and Probability. 1976. 105. Kurt H. Wolff, Surrender and Catch: Experience and Inquiry Today. Boston Studies in the Philosophy of Science, Volume LI. 1976. 106. Karel Kosik, Dialectics of the Concrete. Boston Studies in the Philosophy of Science, Volume LII. 1976. 107. Nelson Goodman, The Structure of Appearance. (Third edition.) Boston Studies in the Philosophy of Science, Volume LIII. 1977. 108. Jerzy Giedymin (ed.), Kazimierz Ajdukiewicz: The Scientific World-Perspective and Other Essays, 1931-1963. 1978. 109. Robert L. Causey, Unity of Science. 1977. 110. Richard E. Grandy, Advanced Logic for Applications. 1977. 111. Robert P. McArthur, Tense Logic. 1976. 112. Lars Lindahl, Position and Change. A Study in Law and Logic. 1977. 113. Raimo Tuomela, Dispositions. 1978. 114 Herbert A. Simon, Models of Discovery and Other Topics in the Methods ofScience. Boston Studies in the Philosophy of Science, Volume LlV. 1977. 115. Roger D. Rosenkrantz, Inference, Method and Decision. 1977. 116. Raimo Tuomela, Human Action and Its Explanation. A Study on the Philosophical Foundations of Psychology. 1977. 117. Morris Lazerowitz, The Language of Philosophy. Freud and Wittgenstein. Boston Studies in the Philosophy of Science, Volume LV. 1977. 118. Stanislaw Lesniewski, Collected Works (ed. by S. J. Surma, J. T. J. Srzednicki, and D. I. Barnett, with an annotated bibliography by V. Frederick Rickey). 1980. (Forthcoming.) 119. Jerzy Pelc, Semiotics in Poland, 1894-1969. 1978. 120. Ingmar Porn, Action Theory and Social Science. Some Formal Models. 1977. 121. Joseph Margolis, Persons and Minds. The Prospects of Nonreductive Materialism_ Boston Studies in the Philosophy of Science, Volume LVII. 1977. 122. Jaakko Hintikka, Ilkka Niiniluoto, and Esa Saarinen (eds.), Essays on Mathematical and Philosophical Logic. 1978. 123. Theo A. F. Kuipers, Studies in Inductive Probability and Rational Expectation. 1978. 124. Esa Saarinen, Risto Hilpinen, I1kka Niiniluoto, and Merrill Provence Hintikka (eds.), Essays in Honour of Jaakko Hintikka on the Occasion of His Fiftieth Birth­ day. 1978. 125 Gerard Radnitzky and Gunnar Andersson (eds.), Progress and Rationality in Science. Boston Studies in the Philosophy of Science, Volume LVIII. 1978. 126. Peter Mittelstaedt, Quantum Logic. 1978. 127. Kenneth A. Bowen, Model Theory for Modal Logic. Kripke Models for Modal Predicate Calculi. 1978. 128. Howard Alexander Bursen, Dismantling the Memory Machine. A Philosophical Investigation of Machine Theories of Memory. 1978. 129. Marx W. Wartofsky, Models: Representation and the Scientific Understanding. Boston Studies in the Philosophy of Science, Volume XLVIII. 1979. 130. Don Ihde, Technics and Praxis. A Philosophy of Technology. Boston Studies in the Philosophy of Science, Volume XXIV. 1978. 131. Jerzy J. Wiatr (ed.), Polish Essays in the Methodology of the Social Sciences. Boston Studies in the Philosophy of Science, Volume XXIX. 1979. 132. Wesley C. Salmon (ed.), Hans Reichenbach: Logical Empiricist. 1979. 133. Peter Bieri, Rolf-P. Horstmann, and Lorenz KrUger (eds.), Transcendental Argu­ ments in Science. Essays in Epistemology. 1979. 134. Mihailo Markovic and Gajo Petrovic (eds.), Praxis. Yugoslav Essays in the Philoso­ phy and Methodology of the Social Sciences. Boston Studies in the Philosophy of Science, Volume XXXVI. 1979. 135. Ryszard Wojcicki, Topics in the Formal Methodology of Empirical Sciences. 1979. 136. Gerard Radnitzky and Gunnar Andersson (eds.), The Structure and Development of Science. Boston Studies in the Philosophy of Science, Volume LIX. 1979. 137. Judson Chambers Webb, Mechanism, Mentalism, and Metamathematics. An Essay on Finit(sm. 1980. 138. D. F. Gustafson and B. L. Tapscott (eds.), Body, Mind, and Method. Essays in Honor of Virgil C. Aldrich. 1979. 139. Leszek Nowak, The Structure of Idealization. Towards a Systematic Interpretation of the Marxian Idea of Science. 1979. 140. Chaim Perelman, The New Rhetoric and the Humanities. Essays on Rhetoric and Its Applications. 1979. 141. Wlodzimierz Rabinowicz, Universalizability. A Study in Morals and Metaphysics. 1979. 142. Chaim Perelman, Justice, Law, and Argument. Essays on Moral and Legal Reason­ ing. 1980. 143. S. Kanger and S. Ohman (eds.), Philosophy and Grammar. Papers on the Occasion of the Quincentennial of Uppsala University, Sweden. 1980. 144. Tadeusz Pawlowski, Concept Formation in the Humanities and the Social Sciences. 1980. 145. Iaakko Hintikka and David Gruender (eds.), Theory Change, Ancient Axiomatics, and Galileo 's Methodology. Proceedings of the 1978 Pisa Conference on the History and Philosophy of Science. 1980. (Forthcoming.) 146. Iaakko Hintikka and David Gruender (eds.), Probabilistic Thinking, Thermo­ dynamics, and the Interaction of the History and Philosophy of Science. Proceed­ ings of the 1978 Pisa Conference on the History and Philosophy of Science. 1980. (Forthcoming.) 147. Uwe Monnich, Aspects of Philosophical Logic. 1980. (Forthcoming.) 148. Dov M. Gabbay, Semantical Investigations in Heyting's Intuitionistic Logic. 1981. (Forthcoming.) 149. Evandro Agazzi, Modern Logic - A Survey. Historical, Philosophical, and Mathe­ matical Aspects of Modern Logic and its Applications. 1980. (Forthcoming.) 150. A. F. Parker-Rhodes, The Theory of Indistinguishables. A Search for Explanatory Principles below the Level ofPhysics. 1981. (Forthcoming.)