Nuel Belnap: Curriculum Vitae

NUEL BELNAP: CURRICULUM VITAE

PRESENT POSITION: Alan Ross Anderson Distinguished Professor of Philosophy, Professor of Sociology, Professor of History and Philosophy of Science, and Professor of the Intelligent Systems Program, University of Pittsburgh.

PERSONAL: born Evanston, Illinois, May 1, 1930.

EDUCATION: B. A., University of Illinois, 1952; M. A., Yale University, 1957; Ph. D., Yale University, 1960.

EMPLOYMENT: Yale University, Department of Philosophy, Instructor, 1958-1960; Assistant Professor, 1960--1963. University of Pittsburgh, Department of Philosophy, Associate Professor, 1963- 1966; Professor, 1966 to date; Professor of Sociology, 1967 to date; Professor of History and Philosophy of Science, 1971 to date; Alan Ross Anderson Lecturer, 1983-84; Alan Ross Anderson Distinguished Professor, 1984 to date; Professor in the Intelligent Systems Program, 1988 to date. University of California at Irvine, Visiting Professor of Philosophy, Winter, 1973. Indiana University, Visiting Oscar R. Ewing Professor of Philosophy, Fall, 1977, Fall, 1978, and Fall, 1979.

PROFESSIONAL ASSOCIATIONS: American Philosophical Association; Associa• tion for Symbolic Logic (Program Committee Chairman, 1961; Executive Com• mittee, 1970--1973; representative to Section L ofthe AAAS, 1974-84; Commit• tee on reviews policy, 1974-1976; Oversight Committee 1988-1989; Nomination Committee 1989); American Association for the Advancement of Science; So• ciety for Exact Philosophy (Vice president, 1971-1974; President, 1974-1976; Program coordinator, 1978; treasurer, 1979-80); Mind Association (U. S. trea• surer, 1974 to date).

FELLOWSHIPS AND PRIZES: Predoctoral: Tew Prize, Yale, 1955; Sterling Junior Fellow, Yale, 1955-1956; Fulbright Fellow, Louvain, Belgium, 1957-1958. Postdoctoral: Morse Research Fellow, 1962-1963; Guggenheim Fellow, 1975- 1976; National Endowment for the Humanities Fellow (declined), 1975- 1976; Center for Advanced Study in the Behavioral Sciences Fellow (partially funded by the National Endowment for the Humanities), 1982-1983; Fellow, American Academy of Arts and Sciences, 1988-.

357 358 NUEL BELNAP: CURRICULUM VITAE

EDITORIAL BOARDS: American Philosophical Quarterly, 1966-1978; Journal of Philosophical Logic, 1970 to date (treasurer, 1970-1976; vice president, 1976- 82; chairman of the Board of Governors, 1982-1988); Notre Dame Journal of Formal Logic, 1970 to date; Philosophy of Science, 1975 to date; StudiaLogica, 1976 to date; Philosophical Research Archives, 1976 to date.

GRANTS, CONSULTANTSHIPS, AND RESEARCH FELLOWSHIPS: Director of a program of Summer Undergraduate Research and Independent Study, sponsored by the National Science Foundation (National Science Foun• dation Grants 11848 and G21871), 1960-63. Consultant, Office of Naval Research (Group Psychology Branch) Contract SAR! Nonr-609(16), "Problem solving and social interaction," 1960-63. Consultant, System Development Corporation, Santa Monica, California, c. 1961-1967. Associate investigator, National Science Foundation Grant No. GS-190, "An investigation of some non-classical systems of mathematical logic," 1963-65. Consultant, University of Pittsburgh Knowledge Availability Center, 1963-66. Senior research associate, Center for the Philosophy of Science, University of Pittsburgh, 1964-1978; Fellow, 1979 to date. Principal investigator, National Science Foundation Grant No. GS-689, "An investigation of some non-classical systems of mathematical logic," 1965-68. Co-designer, under a grant from International Business Machines to the Univer• sity of Pittsburgh, of a course on the use of computers for research in the humanities, 1965-67. Working Group 2.2 (Formal Description of computer languages), International Federation of Information Processors, 1967-1976. Travel to meetings in Vienna (1967), Sardinia (1968), Copenhagen (1968), and Vienna (1969) was supported by the University of Pittsburgh. Senior Research Fellow, Programming Research Group, Oxford University, Hi• lary Term, 1970. Sabbatical from Pittsburgh. Principal investigator, National Science Foundation Grant GS-28478, 1971- 1976. Visiting Fellow, Australian National University, January-March, 1976. Consultant, Westinghouse Research Laboratory, May, 1981. NUELBELNAP:DOCTORALSTUDENTS

Giannoni, Carlos 1966 Conventionalism in logic

Meyer, Robert 1966 Topics in modal and many-valued logics

Dunn, J. Michael 1966 The algebra of intensional logics

Woodruff, Peter 1969 Foundations of three-valued logic

Garson, James 1969 The logics of space and time

Wilson, Kent 1969 Are modal statements really metalinguistic? Grover, Dorothy 1970 Topics in propositional quantification

Manor, Ruth 1971 Conditional forms: Assertion, necessity, obligation, and commands Urquhart, Alasdair 1972 The semantics of entailment

Pottinger, Garrel 1972 A theory of implications

Broido, Jonathan 1974 Generalization of model theoretic notions and the eliminabilityof quantification into modal contexts Vandernat, Arnold 1974 First-order indefinite & generalized semantics for weak systems of strict-implication Birmingham, Robert L. 1976 Law as cases

Helman, Glen 1977 Restricted Lambda Abstraction and the interpretation of some non-classical logics Parks, R. Zane 1977 Studies in philosophical logic & its history

Gupta, Anil 1977 The logic of common nouns: an investigation in quantified modal logic

359 360 NUEL BELNAP: DOCTORAL STUDENTS

Cohen, Daniel 1983 The logic of conditional assertion (Indiana University; J. Michael Dunn, co-director) Horty, John 1986 Some aspects of meaning in non-con• tingent language Garfield, Jay 1986 Cognitive science and the ontology of mind Kremer, Michael 1986 Logic and truth NUEL BELNAP: PUBLICATIONS

Articles (except reprintings) are *'d. Monographs and books are **'d. Unmarked items are abstracts, reviews, reprints, etc.

1955 *1. ''Two components of existence," Ideas, vol. 5 (1955), pp. 21-26.

1958 2. "A modification of Ackermann's 'rigorous implication'" [by A. R. Anderson and NOB] (abstract), Journal of symbolic logic, vol. 23 (1958), pp. 457-458.

1959 *3. "EQ and the first order functional calculus," appendix to Completeness• theorems for the systems E of entailment and EQ of entailment with quan• tification by A. R. Anderson, Technical report No.6, Office of Naval Research (Group Psychology Branch) Contract SAR/Nonr-609(16), New Haven, 1959, pp. 25-27. Also appears in Zeitschriftfilr mathematische Logik, vol. 6 (1960), pp.217-218. *4. "Modalities in Ackermann's 'rigorous implication'" [by A. R. Anderson and NOB], Journal of symbolic logic, vol. 24 (1959), pp. 107-111. 5. "Pure rigorous implication as a 'Sequenzen-kalkiil '" (abstract),Journal of sym• bolic logic, vol. 24 (1959), pp. 282-283. 6. "A proof of the Lowenheim-Skolem theorem" [by A. R. Anderson and NOB] (abstract), Journal of symbolic logic, vol. 24 (1959), pp. 285-286. 7. "Tautological entailments" (abstract), Journal ofsymbolic logic, vol. 24 (1959), p.316. *8. "A simple treatment of truth functions" [by A. R. Anderson and NOB],Journal of symbolic logic, vol. 24 (1959), pp. 301-302. 9. "A simple proof of GOdel's completeness theorem" [by A. R. Anderson and NOB] (abstract), Journal of symbolic logic, vol. 24 (1959), pp. 320--321.

1960 ** 10. A formal analysis of entailment, Technical report No.7, Office of Naval Re• search (Group Psychology Branch) Contract SAR/Nonr-609(16),New Haven, 1960,pp. viii, 107. * 11. "Independent axiom schemata for the pure theory of entailment" [by A. R. Anderson, NDB and J. R. Wallace], Zeitschriftfilr mathematische Logik, vol. 6 (1960), pp. 93-95.

361 362 NUEL BELNAP: PUBLICATIONS

12. Book note: Axiomatic set theory (New York, 1960) by P. Suppes, Review of metaphysics, vol. 14 (1960-61),p. 175. 13. Review of "Existential presuppositions and existential commitments" (Journal ofphilosophy, 1959) by J. Hintikka,Journal of symbolic logic, vol. 25 (1960), p.88. 14. Review of ''Nondesignating singular terms" (Philosophical review, 1959) by H. Leblanc and T. Hailperin, Journal of symbolic logic, vol. 25 (1960), pp. 87-88. 15. Review of ''Towards a theory of definite descriptions" (Analysis, 1959) by J. Hintikka,Journal of symbolic logic, vol. 25 (1960),pp. 88-89. *16. "Entailment and relevance," Journal ofsymbolic logic, vol. 25 (1960),pp. 144- 146. 17. "First degree formulas" (abstract), Journal of symbolic logic, vol. 25 (1960), pp.388-389.

1961 *18. ''First degree entailments" [by A. R. Anderson and NOB], Technical report No. 10, Office of Naval Research (Group Psychology Branch) Contract SARI Nonr-609(16), New Haven, 1961, pp. iv, 35. * 19. "A decision procedure for the system EI- of entailment with negation" [by NOB and J.R. Wallace], Technical report No. 11, Office of Naval Research (Group Psychology Branch), Contract SAR/Nonr-609(16), New Haven, 1961, pp. 31. 20. Book note: Leviathan: a simulation of behavioral systems, to operate dynam• ically on a digital computer (Santa Monica, 1959) by B. K. Rome and S. C. Rome,Review of metaphysics, vol. 15 (1961-62),p. 195. 21. Book note: Formal representation of intentionally structured systems (Santa Monica, 1959) by B. K. Rome and S. C. Rome, Review ofmetaphysics, vol. 15 (1961-62), p. 195. 22. Book note: Markov learning models for multiperson interactions (Stanford, 1960) by P. Suppes andR. C. Atkinson,Review ofmetaphysics, vol. 15 (1961- 62),p.196. *23. ''Enthymemes'' [by A. R. Anderson and NOB], Journal of philosophy, vol. 58 (1961),pp.713-723. *24. ''Tonk, Plonk and Plink," Analysis, vol. 22 (1961-62),pp. 130-134.

1962 *25. ''Tautological entailments" [by A. R. Anderson and NOB], Philosophical stud• ies, vol. 13 (1962), pp. 9-24. *26. "Intuitionism reconsidered" [by H. Leblanc and NOB], Notre Dame journal of formal logic, vol. 3 (1962), pp. 79-82. *27. "The pure calculus of entailment" [by A. R. Anderson and NOB], Journal of symbolic logic, vol. 27 (1962), pp. 19-52.

1963 28. ''First degree entailments" [by A. R. Anderson and NOB], Mathematische Annalen, vol. 149 (1963), pp. 302-319. A slightly revised version of item 18. NUEL BELNAP: PUBLICATIONS 363

29. Review of Computers and common sense (Columbia University Press, 1961) by M. Taube, Modern uses of logic in law, March 1963, pp. 34-38. *30. "A rule-completeness theorem" [by NDB and R. H. Thomason], Notre Dame journal offormallogic, vol. 4 (1963), pp. 39-43. **31. An analysis of questions: preliminary report, System Development Corpora• tion, Santa Monica, California, 1963, pp. 160. 32. Review of Natural deduction (Wadsworth, 1962) by J. M. Anderson and H. W. Johnstone, Jr., American mathematical monthly, 1963. 33. Review of "The number of classes of invertible boolean functions" (Journal ACM, 1963) by M. A. Harrison, Computing reviews, vol. 4 (1963), p. 138. 34. Review of Truth{unctional logic (The Free Press of Glencoe, New York, 1962) by J. A. Faris, Computing reviews, vol. 4 (1963), p. 229. *35. "On not strengthening intuitionistic logic" [by NDB, H. Leblanc and R. H. Thomason], Notre Dame journal offormallogic, vol. 4 (1963),pp. 313-320. 36. "On not strengthening intuitionistic logic" [by NDB, H. Leblanc and R. H. Thomason] (abstract), read at December 1963 meeting of the Association for Symbolic Logic, Journal of symbolic logic, vol. 28 (1963), p. 297.

1964 37. Review of "A logic of questions and answers" (Philosophy of Science, 1961), Communication: A logical model (The M.I.T. Press, 1963), and "A model for applying information and utility functions" (Philosophy of Science, 1963) by D. Harrah, Journal of symbolic logic, vol. 29 (1964), pp. 136-138.

1965 38. Review of "A measure of subjective information" by R. Wells, Structure of language and its mathematical aspects, Proceedings of symposia in applied mathematics, vol. 12, American Mathematical Society, 1961, pp. 237-244, and "Comments" by J. D. Sable and R. Wells, ibid., pp. 267-268. Journal of symbolic logic, vol. 30 (1965), pp. 244-245. 39. "A decision procedure for the system EI- of entailment with negation" [by NDB and J. R. Wallace], Zeitschriftfur mathematische Logik, vol. 11 (1965), pp. 277-289. A revision of item 19.

1966 40. "Questions, answers, and presuppositions," Journal of philosophy, vol. 63 (1966), pp. 609-611. Abstract of a paper read at the 1966 meeting of the Eastern Division of the American Philosophical Association. 41. Combined review of three articles by B. Sobocinski and six articles by I. Thomas, all on Lewis-like modal logics, Journal of symbolic logic, vol. 31 (1966),pp.498-500. *42. "Intensionally complemented distributive lattices" [by NDB and J. Spencer], Portugaliae Mathematica, vol. 25 (1966), pp. 99-104. 364 NUEL BELNAP: PUBLICATIONS

1967 *43. "Intensional models for first degree formulas," Journal of symbolic logic, vol. 32 (1967), pp. 1-22. 44. "Special cases of the decision problem for entailment and relevant implication," Journal of symbolic logic, vol. 32 (1967), pp. 431~32. Abstract of a paper read at the 1967 meeting of the Association for Symbolic Logic. 45. "Homomorphisms of intentionally complemented distributive lattices" [by J. M. Dunn and NDB] (abstract),Journalof symbolic logic, vol. 32 (1967), p. 446. *46. "Comments on H. Simon's 'The logic of heuristic decision making, '" The logic of decision and action, ed. N. Rescher, University of Pittsburgh Press, 1967, pp.27-31. 47. "Tonk, Plonk and Plink," Philosophical logic, ed. P. F. Strawson, Oxford, 1967, pp. 132-137. A reprinting of item 24.

1968 *48. "Homomorphisms of intensionally complemented distributive lattices" [by J. M. Dunn and NDB], Mathematische annalen, vol. 176 (1968), pp. 28-38. 49. ''Entailment'' [by A. R. Anderson and NOB], Logic and Philosophy, ed. G. Iseminger, New York, 1968, pp. 76-110. A version of item 27, with some revisions, deletions, and additions. Also contains a portion of item 25. *50. ''The substitution interpretation of the quantifiers" [by J. M. Dunn and NDB], Nous, vol. 2 (1968),pp. 177-185. 51. Reviews of three articles by C. A. Meredith and A. N. Prior, one by A. F. Bausch, and one by M. J. Cresswell, Zentralblatt fur Mathematik und ihre Grenzgebiete, vol. 146 (1968), pp. 8-9.

1969 *52. "Aqvist's corrections-accumulating question-sequences," Philosophical logic, ed. J. W. Davis, D. J. Hockney, and W. K. Wilson, Reidel, 1969, pp. 122-134. *53. "Questions: their presuppositions, and how they can fail to arise," The logical way of doing things, ed. K. Lambert, Yale University Press, 1969, pp. 23-37.

1970 *54. ''Every functionally complete m-valued logic has a Post-complete axiomatiza• tion" [by NOB and S. McCall], Notre Dame journal offormal logic, vol. 11 (1970), p. 106. *55. "Conditional assertion and restricted quantification," Nofls, vol. 4 (1970), p. 1- 13. 56. Review of "A propositional logic with subjunctive conditionals" (Journal of symbolic logic, 1962) by R. B. Angell, Journal of symbolic logic, vol. 35 (1970),pp. 4~65.

1972 *57. "S-P interrogatives," Journal ofphilosophicallogic, vol. 1 (1972),pp. 331-346. 58. "Foreword" to A general interpreted modal calculus by A. Bressan, Yale Uni• versity Press, 1972, pp. xiii-xxv. NUEL BELNAP: PUBLICATIONS 365

1973 *59. "Quantifying in and out of quotes" [by NDB and D. L. Grover], Truth, syntax, and modality, ed. H. Leblanc, North-Holland, 1973, pp. 17-47. *60. "Restricted quantification and conditional assertion," Truth, syntax, and modal• ity, ed. H. Leblanc, North-Holland, 1973, pp. 48-75.

1974 61. "A memorial note on A. R. Anderson," Metaphilosophy, vol. 5 (1974), pp. 73- 75.

1975 *62. "A prosentential theory of truth" [by D. L. Grover, J. L. Camp, Jr. and NDB], Philosophical Studies, vol. 27 (1975), pp. 73-125. 63. "A useful four-valued logic" (abstract), Proceedings 0/ the 1975 International Symposium on Multiple-valuedLogic, eds. N.B. Cocchiarella,J.M. Dunn,G.E. Epstein, and S. Shapiro, available from IEEE Computer Society, Long Beach, California, p. 399. *64. "Grammatical propaedeutic," The logical enterprise, ed. A. R. Anderson, R. B. Marcus, and R. M. Martin, Yale University Press, 1975, pp. 143-165. **65. Entailment: the logic o/relevance and necessity, vol. I [by A. R. Anderson and NDB], Princeton University Press, 1975, pp. xxxii, 542. *66. "Testing matrix claims interactively on a computer," Cirpho, vol. 3 (1975), pp.7-9.

1976 **67. The logic 0/ questions and answers [by NDB and T. B. Steel and with a Bibli• ography of the theory of questions and answers by U. Egli and H. Schleichert], Yale University Press, 1976, pp. vi, 209. *68. "The two property," The relevance logic newsletter, vol. 1 (1976), pp. 173-180. *69. "How a computer should think," Contemporary aspects o/philosophy, ed. G. Ryle, Oriel Press, 1976, pp. 30-55.

1977 70. "Relevant analytic tableaux" [by M. A. McRobbie and NDB] (abstract), The relevance logic newsletter, vol. 2 (1977), pp. 46-49. 71. "Entailment (vol. 1) errata," The relevance logic newsletter, vol. 2 (1977), pp.176-182. *72. "A useful four-valued logic," Modern uses o/multiple-valued logic, ed. J. M. Dunn and G. Epstein, D. Reidel, 1977,pp. 8-37.

1978 *73. "BINDEX: a book indexing system," Scholarly publishing, vol. 9 (1978), pp. 167-170. 74. A reprinting of item 24. Contemporary Philosophical Logic, ed. I. M. Copi and J. A. Gould, St. Martin's Press, pp. 44-48. 366 NUEL BELNAP: PUBLICATIONS

1979 *75. "Rescher's hypothetical reasoning: an amendment," The philosophy 0/ Nicholas Rescher: discussion and replies, ed. E. Sosa, D. Reidel, 1979, pp.19-28. *76. ''Relevant analytic tableaux" [by M. A. McRobbie and NDB], Studia Logica, vol. 38 (1979), pp. 187-200.

1980 *77. "A consecution calculus for positive relevant implication with necessity" [by NDB, A. Gupta, and J. M. Dunn], Journal o/philosophicallogic, vol. 9 (1980), pp. 343-362. (By error the title appeared as "A consecutive.... ") *78. "Modal and relevance logics: 1977," Modern logic-a survey, ed. E. Agazzi, D. Reidel, 1980, pp. 131-151.

1981 79. Photograph: inside dust cover of Mind design, ed. J. Haugeland, Bradford Books, Montgomery, VT, 1981. *80. "Entailment and the disjunctive syllogism" [by NDB and J. M. Dunn], Contem• porary philosophy. A new survey., vol. 1, Martinus Nijhoff, The Hague/Boston/ London,1981,pp.337-366. *81. "Logica docens and relevance," Teaching philosophy, vol. 4 (1981), pp. 419- 427. 82. Russian translation of item 67: Logi/w voprosov i otvetov [by NDB and T. Steel, Jr.], translated by G. E. Krejdlin, edited and with foreword and notes by V. A. Smirnov and V. K. Finn, Progress Publishers (17 Zubovsky Blvd., Moscow 119021), 1981, pp. 288. Also included are translations of items 69 (pp. 208-239) and 72 (pp. 240-267). 83. Russian translation of item 43. Semantika modal' nix i intensional' nix logik, compiled, edited and with an introductory essay by V. A. Smirnov, Progress Publishers (17 Zubovsky Blvd., Moscow 119021), 1981, pp. 325-362. The translation is by A. L. Nikiforov.

1982 *84. "Questions and answers in Montague grammar," Processes, beliefs, and ques• tions, ed. S. Peters and E. Saarinen, D. Reidel, 1982, pp. 165-198. 85. Reprintingsofitems 26 and 35. Existence, truth and provability by H. Leblanc, State University of New York Press, Albany, 1982, pp. 385-389 and pp. 390- 396. *86. "Display logic," Journal ofphilosophical logic, vol. 11 (1982),pp. 375-417. *87. "Gupta's rule of revision theory of truth," Journal ofphilosophicallogic, vol. 11 (1982), pp. 103-116. *88. "Approaches to the semantics of questions in natural language (II)," Philosoph• ical essays dedicated to Lennart Aqvist on his fiftieth birthday, ed. T. Pauli, University ofUppsala, Sweden, 1982, pp. 16-33. NUEL BELNAP: PUBLICATIONS 367

1983 *89. "Approaches to the semantics of questions in natural language (I)," Meaning. use. and interpretation of language, ed. R. Bauerle, C. Schwarze, and A. von Stechow, Walter de Gruyter, 1983, pp. 22-29. *90. "Symbolization trees," unit 25 of Understanding symbolic logic by V. Klenk, Prentice-Hall, 1983, pp. 402-411. 91. "Display logic" (abstract), Journal of symbolic logic, vol. 48 (1983), p. 907.

1984 *92. "Proof tableau formulations of some first-order relevant ortho-Iogics" [by M. A. McRobbie and NDB], Bulletin of the section of logic, Polish Academy of Sciences, Institute of Philosophy and Sociology, vol. 13 (1984), pp. 233-240.

1986 93. "Approaches to the semantics of questions in natural language: part I," From models to modules: studies in cognitive science from the McGill Workshops, eds. I. Gopnik and M. Gopnik, Ablex Publishing Corporation, Norwood, NJ, 1986, pp. 257-284. In spite of the agreement of this title with that of item 89, this is essentially a reprinting of a combination of items 88 and 89.

1987 *94. "A note on extension, intension, and truth," [by A. Gupta and NDB] Journal ofphilosophy,pp. 168-174,1987. 95. "Foreword" to Imperatives by C. L. Hamblin, Basil Blackwell, 1987. 96. German translation of item 62. Der Wahrheitsbegriff: Neue Erkliirungs• versuche. Edited by L. B. Puntel. (Darmstadt: Wissenschaftliche Buchge• sellschaft), 1987. The translation is by I. Dumitriv and V. Winko.

1988 *97. "Seeing to it that: a canonical form for agentives" [by NDB and M. Perloff], Theoria, vol. 54 (1988)pp. 175-199. INDEX OF NAMES

Abdali, S. K. 229 Brodie, M. 281 Achinstein, P. 356 Broome, J. 353 Ackermann, W. 62, 75-6 Brouwer, L. E. J. 177 Aczel, P. 116, 120, 122 Butler, J. 36, 38 Akmajian, A. 32 Anderson, A. R. 61-2, 75-7, 83-4, Camp, J. 4,17,19 95, 97, 106-7, 109, 111, 117, Campell, R. 329, 343 135, 149, 154, 231, 247, 265 Care, N. 103, 109 Appiah, A. 129, 132 Carnap, R. 315, 325 Aquinas, T. 89 Chandrasekhar, S. 343, 327 Aquist, L. 154 Chellas, B. 194 Asquith, P. 356 Cherniak, C. 98, 100-1, 109 Chihara, C. 34, 47 Bacon, F. 343 Chomsky, N. 98 Baker, C. 32 Chrysippus 97 Barendregt, 229 H.P. Church, A. 62, 76, 229, 245, 269 Barwise, J. 113,117,122 Cody, A. 133 Bayes, T. 290, 299 Cohen, D. 124, 127-8, 132 Bealer, G. 245, 265 Cohen, L. J. 283,296-9 Belnap, N. 1, 4, 9, 17, 19, 31-2, Coleridge, S. T. 97 49-52, 61-2, 75-7, 83-4, 95, Cresswell, M. J. 133, 136, 138, 97, 104, 106-7, 109, 111, 117, 150-1, 154 127-9, 132, 135, 148-9, 154- Curry, H. B. 41, 47, 74, 76, 229, 5, 175, 177, 183-5, 187, 194, 231-3, 239-43, 247, 265, 271- 215-6 2, 280-1, 283, 307-8, 325, 345 Benacerraf, P. 181, 194, 197-8, Dowty, D. R. 154 201-2 Duhem, P. 327, 343 Beth, E. W. 307, 325 Dummett, M. 1, 179, 182, 194 Bishop, E. 177 Dunn, J. M. 77-80, 82-5, 92, 94-5, Blanshard, B. 77, 86, 92, 95 97, 107, 109, 154, 175, 271-2, Blok, W. 189 281, 307-8 Bolles, R. 99, 109 Bonotto, C. 247,265 Earman, J. 356 Bosanquet, B. 81, 95 Ellis, B. 346, 356 Bowie, L. 107 Esakia,1. 187, 194 Brachman, R. 267, 279, 281 Etchemendy, J.112-4, 116-7, Brady, R. 132 121-2 Brandom, R. 11, 17, 47 Euclid 124, 126 Bressan, A. 265 Ewing, A. C. 81-2,95

369 370 INDEX OF NAMES

Fahlman, S. 281 Heyting, A. 177-8, 180, 182, Feferman, S. 47 187-92 Feys, R. 74, 76,229 Hilbert, D. 83 Field, H. 1, 17 Hindley, J. R. 74, 76, 229 Fine, K. 154, 347, 356 Hintikka, J. 86, 95, 99-100, 103, Fischer, P. C. 76 109, 307 Fitch, F. B. 183-4, 190, 194 Holland, M. 80 Fogelin, R. J. 187,194 Hopcroft, J. E. 76 Fomin, S. V. 343 Horty, J. F. 267-8, 281 Forbes, G. B. 89-90, 95 Horwich, P. 1, 17,328,343 Howard, W. 74, 76 Gaal, S. A. 351,356 Humberstone, L. 187 Gabbay, D. 133 Hume, D. 305 Gaifman, H. 347-8, 356 Huygens, C. 327, 343 Gardner, H. 32 Garfield, J. 98, 109 Israel, D. 267, 279, 281 Garson, J. 175 Geach, P. 20 Jacobs, B. 115, 117, 122 Gentzen, G. 43, 180, 184, 194, 271, Jeffrey, R. 347, 356 281, 308 Jennings, R. 178, 194 Giambrone, S. 74 Giere, R. N. 328, 343 Kamp, H. 133, 154, 347, 356 Godel, K. 111, 180, 187, 194, 283 Kanger, S. 120, 122 Goguen, J. 154 Kant, I. 283 Goldblatt, R. 187, 194 Kaplan, D. 112, 122 Goldstein, I. 281 Kapus, J. 1 Goodman, N. 124, 132, 186-90, Karp, R. M. 75-6 194, 295 Kasher, A. 154 Grice, H. P. 137, 154 Keenan, E. L. 356 Grover, D. 4-5, 11, 14-5, 17, 19, Keynes, J. M. 304, 328, 343 21, 23, 26, 31-2 Kleene, S. C. 229 Guenthner, F. 154 Kolmogorov, A. N. 343 Gupta, A. 1, 8, 17, 19, 27,31, 43, Kornblith, H. 98, 109 49, 52, 77, 86 Kreisel, G. 114 Kremer, M. 47 Halmos, P. R. 343 Kripke, S. 5, 8, 17,33-4,37-9,42, Hannaway, O. 356 46-7, 61-2, 75-6, 82, 84, 86, Harman, G. 98, 100-2, 104, 109, 89-90, 92-3, 95, 187-8, 194 353 Kuhn, T. S. 327, 343 Harper, W. 356 K vart, I. 124, 132 Hayes, P. 270, 281 Henkin, L. 307, 325 Lakatos, I. 125-7, 132, 328, 343 Heny, F. 32 Lakoff, G. 28, 32 Herbrand, J. 180 Leblanc, H. 84, 95, 183-4, 194, Herzberger, H. 49, 57 307-8, 325 INDEX OF NAMES 371

Leeds, S. 1-3, 10, 17 Prior, A. N. 21 Levi, I. 347,356 Putnam, H. 1, 182, 186, 194 Lewis, D. 29, 32, 87-8, 95, 124-9, 131-2, 343 Quine W. V. O. 2-3, 7, 9-10, 13, Lewis, C. 1. 290, 295 15, 17, 82, 95, 98, 177, 183, Lewy, C. 95 197-8, 201, 203, 207,245, 265, 307 Mackie, J. L. 124, 132 Macnamara, J. 98, 109 Ramsey, F. P. 1,21-2,34,47 Maher, P. 343 Redhead, M. 328, 343 Maksimova, L. 83, 95 Reichenbach, H. 178, 283, 295-7, Manor, R. 133, 154 299-300 Marcus, R. B. 82, 95 Rescher, N. 154, 356 Martin, R. L. 47, 49, 356 Richardson, A. 31 Mayr, E. 62, 67-9, 76 Richardson, J. 31 McAloon, K. 62, 75-6 Roberts, R. 281 McCawley, J. D. 28, 32, 155, 175 Robinson, A. 187, 194 McRobbie, M. A. 61, 75-76 Roeper, P. 325 Meyer A. 62, 67-9, 76, 229 Rosenberg, A. L. 76 Meyer R. K. 61, 63, 74, 76, 82, 84, Rosenbloom, P.C. 229 95, 97, 107, 109, 130-2, 307, Rosenkrantz, R. D. 328, 343 325 Ross, L. 104, 109 Mill, J. S. 328, 343 Rosser, J. B. 229 Miller, R. E. 75-6 Routley, R. 63, 76, 125, 130-2 Minsky, M. 267, 281 Rudin, W. 343 Monk, D. 265 Russell, B. 34, 47, 288 Moore, G. E. 83, 95 Myhill, J. 183-4,194 Sandewall, E. 267, 281 Mylopoulos, J. 281 Sanford, D. H. 154 Schmide, J. 281 Nelson, D. 177, 194 Schmolze, J. 267, 281 Nisbett, R. 104, 109 Schnelle, H. S. 32 Schutte, K. 307, 325 Ong, W. J. 32 Scott, O. 223 Segerberg, K. 187 Parsons, T. 82-3, 95 Seldin, J. P. 74, 76, 229 Parsons, C. 187, 194,245,265 Sellars, W. 10, 295 Pascal, B. 299 Sextus Empiricus 97 Peirce, C. S. 304, 327, 343 Shapiro, S. 186-90, 195 Perlmutter, D. 32 Simon, H. 99, 109 Perloff, M. 231, 239 Skyrms, B. 31, 343, 356 Peters, S. 133 Smith, C. A. B. 347, 356 Plumwood, V. 132 Smorynski, C. 195 Popper, K. R. 325, 327-8, 343 Smullyan, R. 170,174-5,309 Pottinger, G. 229 Soames, S. 1-3,7, 10, 17, 32 372 INDEX OF NAMES

Spielman, S. 347,356 Wittgenstein, L. 124, 132, 199-200, Stalnaker, R. C. 86, 95 207 Statman, R. 74, 76 Strawson, P. F. 15, 22 Zanardo, A. 247 Stubbs, M. 32 Zanotti, M. 347,356 Suppe, F. 356 Suppes, P. 347,356

Tappenden, J. 347,356 Tarski, A. 2-3, 8-10,13-15,17, 34-6, 47, 111 Thayer, J. 301 Theseus 93 Thistlewaite, P. B. 61, 75-6 Thomason, R. 86, 95, 133, 183-5, 194,268,280-1 Thomason, S. K. 154 Touretzky, D. 267, 273, 280-1 Trotsky, 1. 296 Turing, A. 229 Turner, D. 229

Ullmann, J. D. 76 Urquhart, A. 76, 154 van Benthem, J. F. A. K. 133, 154 van Dalen, D. 161, 175 van Fraassen, B. C. 128, 132, 135, 154, 177-8, 195,307, 347, 356 Veblen, T. 284 Vendler, Z. 138, 154 Vinci, T. 329, 343

Wallace, J. R. 61, 76 Weaver, G. 324 Wegener, I. 73, 76 Whewell, W. 327, 343 Whitehead, A. N. 288 Williams, M. 1,3, 10,17 Williams, B. 103, 109 Williams, P. 347, 356 Wilson, C. 77, 81, 95 Winston, P. 281 Wisdom, W. A. 325 INDEX OF SUBJECTS a-conversion 210, 212, 214 calculi of combinators 215-6 ,B-contraction 214 canonical modal logics 169 ,B-conversion 215 canonical model 156, 158, 168 ,B-normal form 209 categoricity 156-8, 167 ,B-normal209 causation, 88 ,B-redex 214 chance 330-1, 335 ,B-reduction 215 change of bindings 214 7]-conversion 210, 224 change of mind 100 A-calculus, 74, 215-6 choice 231, 243, 239 multivariate 209 Church-Rosser Property 209, 217, ordinary 209 223-4 strict 74 classical logic 100 , 103, 156 typed 74 classical models 167 AI-calculus 74 classical prejudice 105 w-rule 114, 121 classical semantics 160-1 combinator, 209, 216 accessibility relation 168 rudimentary 217 accomodation 327 combinators, Ackermann function 75 basic 215 actual state of affairs 243-4 Curry-style theory of 220 adequate for 158 IISII combinatory logic 215-6, 218 anaphora 19-21, 26 combinatory model 227 Anti-Butler 36-8, 45 complete deductive system 112 anti-foundation axiom AFA 116, 120 complete for IISII 158 applicator 219 complete partial orderings 227 assertibility 123, 124, 127-9 completeness 155, 158-9, 164, 173-4 Bach-Peters sentences 28 Completeness Theorem, Kanger's Barcan Principle 188, 191-2 120 belief revision 101, 106 complex 211 belief-pollution 100 complexity 353-4 believing relation 247 complexity theory 65 Berry's Paradox 34, 42 component 308 Beth model 191-2 conditional, 123-31 bracket abstraction 209, 215, categorizity of 160 219-21 classical vs relevant interpreta• branch points 232, 238 tion of 105 branched spaces, 234 conditional assertion 127-31 topology of 233 conditionalization 351-5

373 374 INDEX OF SUBJECTS conditionals, subjunctive 106, 125, disjunctive syllogism, 97, 100-7 129 admissibility of 105, 107 confirmation 327 doubled path 236 conjunction 156 durations 134 conservative extension 46, 155 dynamic logic 149 consistency, 111-3 for 11811158 E 82-3, 95 in the standard sense 320, 324 entailment 83, 86 instantial 320, 323-4 Entscheidungsproblem 186 of valuation 157 environment model 225-6 constitutive inferences 101 epistemic hostility 99-101, 104-8 constructible falsity 177 epistemic hospitality 107 constructive proof 178-9 epistemological holism 199, 201 continuous functions 228 epistemology of reasoning 102 contraposition 156, 165, 167 essential predication, 83 converSIOn, asymmetric 89 algebraic treatment of 221 essential property 77, 82, 89 Curry-style axiomatization of essentialness of origins 92 210 Etchemendy's Problem 111, 114-6, counter machine 66 120 counterfactuaI123-31, 289 Eval 225, 227 counterpossible 123-31 event sentences 134 currying 226 evidence 104 cut 44-5 evidentiary mechanism 304 excluded middle 294 database logic 115, 117 expectation 355 database model 119 expectation value 346 wellfounded 120 exponential space complete 65 databases, non-hierarchical 115 exponential space hard 65 de dicto 86-7 extension of relations 119 de re 86-7 external relations 79-80 decision problem 61 Extraposition 23 deductive systems 121 default rules 267 factual constraints on our reason- defeasible information 267 ing 98 defeasible inheritance 267, 273 fallible 104 definite description 41-2, 77, 85, feasible inference 98, 101 87, 91-2 figure 353-5 denotation 33-43,45-6 Finitism 180 deontic logic 186-8 first-order language of number the• descriptive psychology 101 ory 113 disjunction, 104, 107 Fitch's Basic Logic 183 ambiguity of 106 fixed point, 36-43,46 elimination 104 intrinsic 38 introduction 100, 104, 108 largest intrinsic 38, 43 INDEX OF SUBJECTS 375

minimal 37-8, 41-3 instantaneous descriptions 66 fixed-point combinators 210,223 intended model 156 four-valued interpretations 165 internal relation 77, 80, 83,89 four-valued logic 156 intrinsic properties 77 frame 226 intrinsicality, world global 88 free logic 39 world local 88 free variables 212 intuitionistic logic, 156, 161, 164 Fregean semantics 245 S4 semantics 164 functional programming languages semantics 161-4 218 intuitionistic negation 163 fusion 62, 64 FV 212 judgement 345 justification 104, 106 gaps 39-40 justified beliefs 104 generate 218-20 Gentzen's Hauptsatz 184 knowledge 106 grammar 123 Kripke's Lemma 61,75 grounded 38 lambda calculus, see A-calculus Hausdorff spaces 234 Liar Paradox 33-4, 36, 46, 137 heterological paradox 34 linguistic ability 98 Hilbert's program 180 log-lin reducible 65 holist argument for platonism 197 logic in epistemology and psychol• human reasoning 98, 100, 103 ogy 98 hyper-intensionality axiom 246 logical consequence, 111-3 hyper-quasi-extension 246, 251 truth value account of 307 Logical Implication Principle 102 ideal reasoner 103-4 Logical Inconsistency Principle 102 idealization 99-101,103 logical truth 111-3 imperfect agent 103 logical truth, truth-value account imperfection with rationality 101 of 307 inconsistency 100 lower cut 233 indicative 129 lower cut branched space 237 indicator 346, 354 indirect proof 100 Markov's Principle 179 indiscernibility of identicals 78, 81, mathematical confirmation 204 85-6 mathematical object 197-9, 201-2, inference 101 205-8 inference ticket 106 mathematical platonism 197-9, 201 infinitely extendible 324 metalinguistic 200 infon 119 method of generating hypotheses inheritance, 269 329 strict 270 Meyer-Dunn argument 97 inheritance networks 267 minimal consistency condition 100 instant-based model 134 minimal inference condition 100 376 INDEX OF SUBJECTS minimal rationality 100, 103 probability, 345 modal logic 156, 168, 186-91 absolute 308 model 63 conditional 330 non-standard 155 function 310, 315-6, 318, 320, of a rule 155, 157 323-4 of a system 157 of a set 308, 324 standard 157 proforms of laziness 26 model theory 112 pronoun, 19-21, 24, 26 modular completeness 156, 158-9, laziness 20, 25 168 quantification 20-1 modularity 156 proof, modus ponens 105, 108, 294 in the instantial sense 320 monads 81 in the standard sense 319 monotonicity 37-41 proof-theory 112, 123, 127, 130 morality 103 property (e) 215 propositional attitudes 100 natural interpretation 156, 160-1, propositional content 21, 25-7 164, 174 prosentence, 4-6, 9, 11, 13-5, natural semantics 156, 164, 172-4 19-23, 26-8 naturalized epistemology 98, 100, of laziness 21, 23, 27 103 of quantification 21-3 necessary a posteriori 86 pseudo-relational relevant property negation, 162-3 89 categoricity of 162 psychological architecture 104 negative interpretation 179-83 psychological theory 103 networks 268 pure logic 107 Nixon diamond 273 nonassertiveness 128-9 quantification, 156 normal form 184-6, 223 non-vacuous 318 normative content 103 objectual interpretation 156, normative epistemology 98-9 171,173 normative theory of rationality 103 vacuous 309-10, 317 quantified modal logic 173 ontological commitment 174 quantifier-height 309 operator-complexity 309 quantum logic 177-8, 186 quasi-sense 246 parallel processing 73 questions 345 path 235, 268 quotation 34, 41, 46 path connected 235 Petri net 75 R 82-6 possible worlds 292 RD 84-5 pragmatics 123, 127 random variable 346 prediction 327 range of choice 243 predictivist thesis 327 rank 309 prime extension 167 rationality 97,99-100, 103, 105-7 INDEX OF SUBJECTS 377 reachability tree 75 statement, 309 reasoning 103, 107 atomic 308, 315 recursive functions 210, 223 static logic 148 redex 209 strict implication 82 reductio 124, 131 stripping 24 reduction, 214 strongly path connected 236 strong 216 structural rules 156, 162 weak 216 subnector 41 reference 33-5, 40 substatement, 308-9, 316, 324 relevance 107 atomic 308 relevance logic 97-9, 103-5, 156, substitution 212-3, 309 165-6 substitution interpretation 156, four valued interpretation of 171,173,307 167 supervaluation 39, 43, 135, 156,347 relevant implication 78, 82-3, 86 Surprize Exam Paradox 137 relevant interpretation of disjunction 97 Tl -spaces 235 relevant Peano arithmetic 82 tautological entailments 135 relevant property of a pair 79-80 temporal interval 134 relevant pseudo-relational property temporal reference 134 79-81 term model 226 relevant relation 78-81 term structure 210 relevant relational property 79 three-valued logic, 37, 39 reliability 332-5 strong Kleene 39-40, 45 representational semantics 113 weak Kleene representational system 30 39-40, 45 representor 347-8, 353 Thue system 67 retract 225 topological space 233 Richard's Paradox 34 tree 231 rigid designator 84-7, 90, 92 truth, 1, 33-44, 46 Russell's Paradox 91 correspondence theory of 200, 206 S484 deflationary analysis of 1 S584 disquotational theory of 1 satisfaction 33-4 prosentential theory of 1, 4, seeing to it that (stit) 231, 239 19-25, 27-31 semantic ascent 2 redundancy theory of 21-2 semantics 123, 125-30, 158 revision theory of 49 semi-Thue system 63 truth-conditions 127, 129 semifactual 124 truth-value assignment 307, 320 semigroup presentations 67 truth-value semantics 307 sentential interpretation 173-4 Turing machine, off-line 65 sequent-calculus 43 Tweety triangle 274 sound deductive system 112 stability, revision theory of 49-60 upper cut 233, 239 378 INDEX OF SUBJECTS validity, preservation of 155, 158 Vague Expectation (VEX) 349-53 vague probability 347 vagueness 347 valuation 157, 225 valuation-set 146 variable binding 212, 218 word problem for commutative semigroups 62