-
2
-
-
85047893286
-
Model-theoretic logics: Background and aims
-
Barwise and Feferman [1985]
-
Barwise, J. [1985], "Model-theoretic logics: Background and aims," in Barwise and Feferman [1985], 3-23.
-
(1985)
, pp. 3-23
-
-
Barwise, J.1
-
3
-
-
0004153851
-
-
itors, New York, Springer-Verlag. (Extensive treatment of a lot of logics, many of which are intermediate between first-order and second-order. Quite technical, for the most part. Extensive bibliography.)
-
Barwise, J., and S. Feferman (editors) [1985], Model-theoretic logics, New York, Springer-Verlag. (Extensive treatment of a lot of logics, many of which are intermediate between first-order and second-order. Quite technical, for the most part. Extensive bibliography.)
-
(1985)
Model-theoretic logics
-
-
Barwise, J.1
Feferman, S.2
-
4
-
-
0000665713
-
To be is to be a value of a variable (or to be some values of some variables)
-
reprinted in, 331-350. (Initial account of plural quantification.)
-
Boolos, G. [1984], "To be is to be a value of a variable (or to be some values of some variables)," Journal of Philosophy 81, 430-450; reprinted in, 331-350. (Initial account of plural quantification.)
-
(1984)
Journal of Philosophy
, vol.81
, pp. 430-450
-
-
Boolos, G.1
-
5
-
-
0001599661
-
Nominalist Platonism
-
reprinted in, 351-368. (Another defense of plural quantification.)
-
Boolos, G. [1985], "Nominalist Platonism," Philosophical Review 94, 327-344; reprinted in, 351-368. (Another defense of plural quantification.)
-
(1985)
Philosophical Review
, vol.94
, pp. 327-344
-
-
Boolos, G.1
-
7
-
-
0003692125
-
-
Princeton, NJ: Princeton University Press. (Still an excellent introduction to both first-order logic and secondorder logic.)
-
Church, A. [1956], Introduction to mathematical logic, Princeton, NJ: Princeton University Press. (Still an excellent introduction to both first-order logic and secondorder logic.).
-
(1956)
Introduction to mathematical logic
-
-
Church, A.1
-
8
-
-
34248868234
-
Predication versus membership in the distinction between logic as language and logic as calculus
-
reprinted in, 473-508
-
Cocchiarella, N. [1988], "Predication versus membership in the distinction between logic as language and logic as calculus," Synthèse 77, 37-72; reprinted in, 473-508.
-
(1988)
Synthèse
, vol.77
, pp. 37-72
-
-
Cocchiarella, N.1
-
9
-
-
0009282153
-
Categoricity
-
reprinted in, 241-261
-
Corcoran, J. [1980], "Categoricity," History and Philosophy of Logic 1, 187-207; reprinted in, 241-261.
-
(1980)
History and Philosophy of Logic
, vol.1
, pp. 187-207
-
-
Corcoran, J.1
-
10
-
-
84919958942
-
-
Brunswick, Vieweg; translated as The nature and meaning of numbers, in Essays on the theory of numbers, edited by W. W. Beman, New York, Dover Press 1963
-
Dedekind, R. [1888], Was sind und was sollen die Zahlen?, Brunswick, Vieweg; translated as The nature and meaning of numbers, in Essays on the theory of numbers, edited by W. W. Beman, New York, Dover Press, 1963, 31-115.
-
(1888)
Was sind und was sollen die Zahlen?
, pp. 31-115
-
-
Dedekind, R.1
-
11
-
-
0010212569
-
Reply to Wright
-
ited by B. McGuinness and G. Oliveri, Dordrecht, Kluwer Academic Publishers
-
Dummett, M. [1994], "Reply to Wright," in The philosophy of Michael Dummett, edited by B. McGuinness and G. Oliveri, Dordrecht, Kluwer Academic Publishers, 329-338.
-
(1994)
The philosophy of Michael Dummett
, pp. 329-338
-
-
Dummett, M.1
-
14
-
-
0003483580
-
-
Halle, Louis Nebert; translated in van, 1-82
-
Frege, G. [1879], Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Halle, Louis Nebert; translated in van, 1-82.
-
(1879)
Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens
-
-
Frege, G.1
-
15
-
-
84919954036
-
The monadic theory of types in the lower-predicate calculus
-
Washington, DC, Institute for Defense Analyses
-
Gilmore, P. [1957], "The monadic theory of types in the lower-predicate calculus," in Summaries of talks presented at the Summer Institute of Symbolic Logic at Cornell, Washington, DC, Institute for Defense Analyses, 309-312.
-
(1957)
Summaries of talks presented at the Summer Institute of Symbolic Logic at Cornell
, pp. 309-312
-
-
Gilmore, P.1
-
16
-
-
0000495135
-
Die Vollständigkeit der Axiome des logischen Funktionenkalkuls
-
translated as "The completeness of the axioms of the functional calculus of logic," in van 582-591
-
Gödel, K. [1930], "Die Vollständigkeit der Axiome des logischen Funktionenkalkuls," Montatshefte für Mathematik und Physik 37, 349-360; translated as "The completeness of the axioms of the functional calculus of logic," in van, 582-591.
-
(1930)
Montatshefte für Mathematik und Physik
, vol.37
, pp. 349-360
-
-
Gödel, K.1
-
17
-
-
34347193348
-
Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I
-
translated as "On formally undecidable propositions of the Principia Mathematica," in van, 596-616
-
Gödel, K. [1931], "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I," Montatshefte für Mathematik und Physik 38, 173-198; translated as "On formally undecidable propositions of the Principia Mathematica," in van, 596-616.
-
(1931)
Montatshefte für Mathematik und Physik
, vol.38
, pp. 173-198
-
-
Gödel, K.1
-
18
-
-
0039605548
-
Steps towards a constructive nominalism
-
Goodman, Nelson, and W.V.O. Quine [1947], "Steps towards a constructive nominalism," Journal of Symbolic Logic 12, 105-122.
-
(1947)
Journal of Symbolic Logic
, vol.12
, pp. 105-122
-
-
Goodman, N.1
Quine, W.V.O.2
-
19
-
-
47549089384
-
Predicative logics
-
ited by D. Gabbay and F. Guenthner, Dordrecht, D. Reidel, (Readable account and defense of ramified type theory.)
-
Hazen, A. [1983], "Predicative logics," in Handbook of philosophical logic, vol. 1, edited by D. Gabbay and F. Guenthner, Dordrecht, D. Reidel, 331-407. (Readable account and defense of ramified type theory.)
-
(1983)
Handbook of philosophical logic
, vol.1
, pp. 331-407
-
-
Hazen, A.1
-
20
-
-
0002785435
-
Completeness in the theory of types
-
Henkin, L. [1950], "Completeness in the theory of types," Journal of Symbolic Logic 15, 81-91.
-
(1950)
Journal of Symbolic Logic
, vol.15
, pp. 81-91
-
-
Henkin, L.1
-
21
-
-
0003879089
-
-
Berlin, Springer; translated as Principles of mathematical logic by L. Hammond, G. Leckie, and F. Steinhardt, New York, Chelsea, 1950. (Historical source. Still quite readable.)
-
Hilbert, D., and W. Ackermann [1928], Grundzüge der theoretischen Logik, Berlin, Springer; translated as Principles of mathematical logic by L. Hammond, G. Leckie, and F. Steinhardt, New York, Chelsea, 1950. (Historical source. Still quite readable.).
-
(1928)
Grundzüge der theoretischen Logik
-
-
Hilbert, D.1
Ackermann, W.2
-
22
-
-
77957003984
-
Arithmetical truth and hidden higher-order concepts
-
ited by The Paris Logic Group, Amsterdam, North-Holland, 1987
-
Isaacson, D. [1985], "Arithmetical truth and hidden higher-order concepts," in Logic Colloquium 85, edited by The Paris Logic Group, Amsterdam, North-Holland, 1987, 147-169.
-
(1985)
Logic Colloquium
, vol.85
, pp. 147-169
-
-
Isaacson, D.1
-
23
-
-
60949242724
-
A critical appraisal of second-order logic
-
reprinted in 177-196
-
Jané, I. [1993], "A critical appraisal of second-order logic," History and Philosophy of Logic 14, 67-86; reprinted in, 177-196.
-
(1993)
History and Philosophy of Logic
, vol.14
, pp. 67-86
-
-
Jané, I.1
-
24
-
-
77956949740
-
Informal rigour and completeness proofs
-
ited by I. Lakatos, Amsterdam, North-Holland, (Among other things, a multifaceted philosophical defense of the use of higher-order languages in foundational studies. Moderate difficulty.)
-
Kreisel, G. [1967], "Informal rigour and completeness proofs," in Problems in the philosophy of mathematics, edited by I. Lakatos, Amsterdam, North-Holland, 138-186. (Among other things, a multifaceted philosophical defense of the use of higher-order languages in foundational studies. Moderate difficulty.)
-
(1967)
Problems in the philosophy of mathematics
, pp. 138-186
-
-
Kreisel, G.1
-
26
-
-
2442494054
-
Mathematics is megethology
-
3rd ser., 1
-
Lewis, D. [1993], "Mathematics is megethology," Philosophia Mathematica, 3rd ser., 1, 3-23.
-
(1993)
Philosophia Mathematica
, pp. 3-23
-
-
Lewis, D.1
-
27
-
-
0040456170
-
On extensions of elementary logic
-
Lindström, P. [1969], "On extensions of elementary logic," Theoria 35, 1-11.
-
(1969)
Theoria
, vol.35
, pp. 1-11
-
-
Lindström, P.1
-
28
-
-
0000507008
-
Über Möglichkeiten im Relativkalkül
-
translated in van, 228-251
-
Löwenheim, L. [1915], "Über Möglichkeiten im Relativkalkül," Mathematische Annalen 76, 447-479; translated in van, 228-251.
-
(1915)
Mathematische Annalen
, vol.76
, pp. 447-479
-
-
Löwenheim, L.1
-
29
-
-
77956976929
-
Set theory and higher-order logic
-
ited by J. Crossley and M. Dummett, Amsterdam, North-Holland, (Higher-order logic, put to linguistic use. The start of an extensive research program.)
-
Montague, R. [1965], "Set theory and higher-order logic," in Formal systems and recursive functions, edited by J. Crossley and M. Dummett, Amsterdam, North-Holland, 131-148. (Higher-order logic, put to linguistic use. The start of an extensive research program.)
-
(1965)
Formal systems and recursive functions
, pp. 131-148
-
-
Montague, R.1
-
30
-
-
0002242447
-
Beyond first-order logic: The historical interplay between logic and set theory
-
reprinted in 3-45
-
Moore, G.H. [1980], "Beyond first-order logic: The historical interplay between logic and set theory," History and Philosophy of Logic 1, 95-137; reprinted in, 3-45.
-
(1980)
History and Philosophy of Logic
, vol.1
, pp. 95-137
-
-
Moore, G.H.1
-
31
-
-
0008808203
-
The emergence of first-order logic
-
ited by W. Aspray and P. Kitcher, Minnesota Studies in the Philosophy of Science, Minneapolis, University of Minnesota Press
-
Moore, G.H. [1988], "The emergence of first-order logic," in History and philosophy of modern mathematics, edited by W. Aspray and P. Kitcher, Minnesota Studies in the Philosophy of Science, 11, Minneapolis, University of Minnesota Press, 95-135.
-
(1988)
History and philosophy of modern mathematics
, vol.11
, pp. 95-135
-
-
Moore, G.H.1
-
32
-
-
26444493149
-
On the ontological significance of the Löwenheim-Skolem theorem
-
ited by M. White, Philadelphia, American Philosophical Society, also in Contemporary readings in logical theory, edited by I. Copi and J. Gould, New York, Macmillan, 1967 40-54
-
Myhill, J. [1951], "On the ontological significance of the Löwenheim-Skolem theorem," in Academic freedom, logic and religion, edited by M. White, Philadelphia, American Philosophical Society, 57-70; also in Contemporary readings in logical theory, edited by I. Copi and J. Gould, New York, Macmillan, 1967, 40-54.
-
(1951)
Academic freedom, logic and religion
, pp. 57-70
-
-
Myhill, J.1
-
33
-
-
0003778554
-
-
Turin, Bucca, translated in van
-
Peano, G. [1889], Arithmetices principia, nova methodo exposita, Turin, Bucca, translated in van, 85-97.
-
(1889)
Arithmetices principia, nova methodo exposita
, pp. 85-97
-
-
Peano, G.1
-
34
-
-
80053390870
-
Whitehead and the rise of modern logic
-
ited by P. A. Schilpp, New York, Tudor
-
Quine, W.V.O. [1941], "Whitehead and the rise of modern logic," in The philosophy of Alfred North Whitehead, edited by P. A. Schilpp, New York, Tudor, 127-163.
-
(1941)
The philosophy of Alfred North Whitehead
, pp. 127-163
-
-
Quine, W.V.O.1
-
35
-
-
0004242804
-
-
2nd ed., Cambridge, MA, Harvard University Press. (Argument against second-order logic, especially ch. 5.)
-
Quine, W.V.O. [1986], Philosophy of logic, 2nd ed., Cambridge, MA, Harvard University Press. (Argument against second-order logic, especially ch. 5.).
-
(1986)
Philosophy of logic
-
-
Quine, W.V.O.1
-
36
-
-
0012484995
-
Nominalism through de-Nominalization
-
Rayo, A., and S. Yablo [2001], "Nominalism through de-Nominalization," Noûs 35, 74-92.
-
(2001)
Noûs
, vol.35
, pp. 74-92
-
-
Rayo, A.1
Yablo, S.2
-
37
-
-
0041156247
-
Second-order logic still wild
-
Resnik, M. [1988], "Second-order logic still wild," Journal of Philosophy 85, 75-87.
-
(1988)
Journal of Philosophy
, vol.85
, pp. 75-87
-
-
Resnik, M.1
-
38
-
-
0013424925
-
-
New York, Oxford University Press. (Extensive development of and justification for higher-order logic. Philosophical, mathematical, and historical treatment. Most of the book requires some background in logic. Extensive bibliography.)
-
Shapiro, S. [1991], Foundations without foundationalism: A case for second-order logic, New York, Oxford University Press. (Extensive development of and justification for higher-order logic. Philosophical, mathematical, and historical treatment. Most of the book requires some background in logic. Extensive bibliography.)
-
(1991)
Foundations without foundationalism: A case for second-order logic
-
-
Shapiro, S.1
-
39
-
-
0040486703
-
Modality and ontology
-
Shapiro, S. [1993], "Modality and ontology," Mind 102, 455-481.
-
(1993)
Mind
, vol.102
, pp. 455-481
-
-
Shapiro, S.1
-
41
-
-
33746782356
-
Logical consequence: Models and modality
-
ited by M. Schirn, Oxford, Oxford University Press
-
Shapiro, S. [1998], "Logical consequence: Models and modality," in The philosophy of mathematics today, edited by M. Schirn, Oxford, Oxford University Press, 131-156.
-
(1998)
The philosophy of mathematics today
, pp. 131-156
-
-
Shapiro, S.1
-
42
-
-
3843149133
-
Do not claim too much: Second-order logic and first-order logic
-
3rd ser., (Reply to some of the critics of.)
-
Shapiro, S. [1999], "Do not claim too much: Second-order logic and first-order logic," Philosophia Mathematica, 3rd ser., 7, 42-64. (Reply to some of the critics of.)
-
(1999)
Philosophia Mathematica
, vol.7
, pp. 42-64
-
-
Shapiro, S.1
-
43
-
-
33750925679
-
Systems between first-order logic and second-order logics
-
2nd ed., edited by D.M. Gabbay and F. Geunthner, Dordrecht, Kluwer Academic Publishers
-
Shapiro, S. [2001], "Systems between first-order logic and second-order logics," in Handbook of philosophical logic, vol. 1, 2nd ed., edited by D.M. Gabbay and F. Geunthner, Dordrecht, Kluwer Academic Publishers, 131-187.
-
(2001)
Handbook of philosophical logic
, vol.1
, pp. 131-187
-
-
Shapiro, S.1
-
44
-
-
0002362693
-
Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre
-
Helsinki, Akademiska Bokhandeln, 217-232; translated as "Some remarks on axiomatized set theory" in van
-
Skolem, T. [1922], "Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre," in Matematikerkongressen i Helsingfors den 4-7 Juli 1922, Helsinki, Akademiska Bokhandeln, 217-232; translated as "Some remarks on axiomatized set theory" in van, 291-301.
-
(1922)
Matematikerkongressen i Helsingfors den 4-7 Juli
, vol.1922
, pp. 291-301
-
-
Skolem, T.1
-
45
-
-
0009888176
-
A philosophical letter of Alfred Tarski
-
ited by Morton White
-
Tarski, A. [1987], "A philosophical letter of Alfred Tarski," edited by Morton White, Journal of Philosophy 84, 28-32.
-
(1987)
Journal of Philosophy
, vol.84
, pp. 28-32
-
-
Tarski, A.1
-
46
-
-
34250397602
-
Which logic is the right logic?
-
reprinted in 47-67
-
Tharp, L. [1975], "Which logic is the right logic?," Synthèse 31, 1-31; reprinted in, 47-67.
-
(1975)
Synthèse
, vol.31
, pp. 1-31
-
-
Tharp, L.1
-
47
-
-
4043088321
-
-
itor, Cambridge, MA, Harvard University Press. (Collection of many original papers in logic, translated into English. Includes works by Frege, Peano, Dedekind, Cantor, Hilbert, Russell, Zermelo, Löwenheim, Skolem, Weyl, Ackermann, von Neumann, Bernays, and Gödel.)
-
Van Heijenoort, J. (editor) [1967], From Frege to Gödel, Cambridge, MA, Harvard University Press. (Collection of many original papers in logic, translated into English. Includes works by Frege, Peano, Dedekind, Cantor, Hilbert, Russell, Zermelo, Löwenheim, Skolem, Weyl, Ackermann, von Neumann, Bernays, and Gödel.)
-
(1967)
From Frege to Gödel
-
-
Van Heijenoort, J.1
-
50
-
-
34250387166
-
Kreisel, the continuum hypothesis and second-order set theory
-
reprinted in 385-402
-
Weston, T. [1976], "Kreisel, the continuum hypothesis and second-order set theory," Journal of Philosophical Logic 5, 281-298; reprinted in, 385-402.
-
(1976)
Journal of Philosophical Logic
, vol.5
, pp. 281-298
-
-
Weston, T.1
-
51
-
-
0004169601
-
-
vol. 1, Cambridge, Cambridge University Press
-
Whitehead, A.N., and B. Russell [1910], Principia mathematica, vol. 1, Cambridge, Cambridge University Press.
-
(1910)
Principia mathematica
-
-
Whitehead, A.N.1
Russell, B.2
|