In Contradiction

In Contradiction

Volumn , Issue , 2007, Pages 1-352

  Priest, Graham ^a,b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b UNIVERSITY OF ST ANDREWS   (United Kingdom)

Author keywords

Aristotle; Dialetheism; Orthodoxy; True contradictions; Western philosophy

Indexed keywords

EID: 84921952827     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1093/acprof:oso/9780199263301.001.0001     Document Type: Book

References (135)

1. Priest (1993), p. 53.
2. Hegel (1955), p. 460.
3. Restall (2004).
4. See Armour-Garb and Beall (2001);
5. Beall and Armour-Garb (2003);
6. see also Beall (2005).
7. See Priest (2001), sect. 9.7.
8. See Priest (2002), sect. 8.5.
9. Priest, (2005), especially ch. 7.
10. As Shapiro (2004), p. 339
11. Mortensen (2002), sect. 6.
12. Pears (1972), pp. 93-4.
13. For example, Harman (1972);
14. Hacking (1975), ch. 8.
15. They can be found, in effect, in Priest (1982).
16. Priest and Routley (1983), ch. 2, sects. 4, 5.
17. Routley et al. (1982), sect. 1.2.
18. Routley et al. (1982), sect. 1.5.
19. Stalnaker (1968); Lewis (1973).
20. Routley et al. (1982), sect. 2.10.
21. Anderson and Belnap (1975), sect. 5.2.1
22. Routley et al. (1982), sect. 1.4.
23. Priest and Routley (1984)
24. Priest (1980).
25. Routley's DK (Routley et al. 1982, sect. 4.1.
26. Lucas (1961).
27. Dummett (1963), p. 195 of reprint.
28. Wittgenstein (1953, 1956).
29. Wang (1962), ch. 18.
30. Priest (2001), ch. 8.
31. Priest (2002), sect. 8.1.
32. Priest (1995), sect. 10.5.
33. Shapiro (2002), p. 828.
34. Friedman and Meyer (1992).
35. Guest (1969), p. 454.
36. Fuller (1969), pp. 65-6.
37. Fitzgerald (1966), p. 137.
38. Hintikka (1971), p. 102.
39. Schotch and Jennings (1981).
40. Hare (1963), sect. 4.3.
41. Priest and Routley (1983), ch. 4, sect. 3.
42. Boyer (1949), ch. 6.
43. Ilyenkov (1977), chs. 7, 8.
44. Priest (2001), sect. 8.3.
45. Dunn and Restall (2002), p. 10.
46. Dummett (1977), ch. 5, esp. p. 197.
47. Carroll (1895)
48. For details of these and other inconsistent theories in the history of science, see Priest and Routley (1983), ch. 5.
49. This argument can be found, for example, in Popper (1940), pp. 316-17
50. What In Contradiction actually says (p. xv) is 'Dialetheism is outrageous-at least to the spirit of contemporary philosophy.'
51. Priest (1995, 2001, and 2006).
52. Some details of these can be found in Priest and Routley (1983), ch. 4
53. see Davies (1981), pp. 193-201. The theory of truth required for an account of validity is, of course, a different matter.
54. See Davidson (1967), p. 314.
55. Tarski (1936), p. 164 of reprint.
56. One might also note that Davidson himself has rejected the whole notion of conceptual relativism; see Davidson (1973).
57. Davidson (1965). In fact, he claims that it must be finitely axiomatisable. But this seems to me not to be right.
58. Peano (1906) p. 157.
59. See e.g. C. Parsons (1974).
60. Russell and Whitehead (1910), vol. I, Introduction, ch. 2.
61. See e.g. Thompson (1962).
62. For the connection, see Yablo (1982).
63. The point is wittily made by Popper (1954).
64. For some further telling criticisms along the same lines, see Gupta (1982).
65. For references and an excellent discussion, see Burge (1979).
66. This line is taken by, e.g. van Fraassen (1970), Fitch (1964), Kripke (1975).
67. This informal argument, which shows that this position ends up in a tangle, can be made quite precise in terms of an indefinability result which shows that the position is self refuting. See Priest (1987).
68. Against the myopic view that Cantor et al did not initially suppose all conditions to determine sets, see Quine (1973), pp. 102-3.
69. See e.g. Fraenkel, Bar-Hillel, and Levy (1973), pp. 321 ff.
70. See e.g. Shoenfield (1967) pp. 238-9;
71. Devlin (1980) pp. 42-6.
72. In the terms of Lakatos (1976), it is merely the version of "exception barring" called 'strategic withdrawal to a safe domain'.
73. Mayberry (1977), p. 31.
74. See e.g. Feferman (1977), Bell (1981), Fraenkel, Bar-Hillel, and Levy (1973), pp. 143-4.
75. Fraenkel, Bar-Hillel, and Levy (1973), pp. 143-4.
76. Bell (1981), p. 356. Italics original.
77. For a number of the others, see Priest and Routley (1983), ch. 5.
78. Further details of all these matters can be found in Routley (1977).
79. See Routley (1977).
80. See Brady (1989). The proof also shows that the theory is non-trivial even if the variable z is allowed to occur in the formula β in (Abs).
81. e.g., C. Parsons (1971), Kripke (1976), and Priest (1983a ) in which much of the material in this chapter first appeared.
82. This follows the practice of Kripke (1976).
83. Though their success has been over-rated: see Priest (1979b ).
84. See Smart (1963) and Gödel (1947).
85. See Routley (1980), especially ch. 11.
86. As in Gödel (1947).
87. Quine's; see Smart (1963).
88. Wittgenstein makes the points in e.g. his (1956). For references and discussion, see Klenk (1976), pp. 8-18.
89. See Dummett (1977), p. 24.
90. See Fraenkel, Bar-Hillel, and Levy (1973), p. 332 ff.
91. One can also give a generic account of how this kind of truth condition arises. See Quine (1973), sects. 22-8
92. See Quine (1973), pp. 118-20;
93. Kripke (1976), p. 385.
94. Kripke (1976), p. 341; italics original.
95. In terms of Quine's fortunate distinction, expressed in unfortunate language (1953, pp. 130-2), set theory may provide the ontology of mathematics without providing its ideology.
96. See e.g. Steiner (1975), pp. 102-8.
97. See e.g. Williams (1951)
98. Smart (1949).
99. e.g. J. W. Dunn (1927).
100. See e.g. Grünbaum (1967a )
101. Mellor (1984).
102. See e.g. Gold (1966).
103. Hegel (1812), p. 440 of translation.
104. Hegel (1840), vol. I, pp. 273, 273-4 of the translation.
105. Hegel (1830), p. 43 of the translation. The italics are original.
106. See Priest and Routley (1983), ch. 2.
107. Much of the following comes from Priest (1982).
108. See e.g. Hamblin (1969).
109. The idea can be made the basis of systems of tense logic; see Humberstone (1979).
110. Leibniz (1687), p. 351 of translation.
111. See Boyer (1949), p. 256.
112. Leibniz (1687), p. 352 of translation.
113. Leibniz (1687), pp. 352-3 of translation.
114. Hegel (1812), p. 439 of translation.
115. Chomsky (1980), p. 220, notes a similar distinction (and confusion) in grammar.
116. For a fuller discussion of the development of modern logical theory, see Priest (1989a).
117. Tarski (1936), p. 188 of reprint.
118. See Quine (1970), pp. 10-13.
119. Davidson (1967). As usual, I am supposing the language in question not to contain indexicals.
120. Montague (1974), especially ch. 6;
121. Lewis (1972);
122. Routley et al. (1982).
123. See Dummett (1978), especially ch. 14. N.B. also p. xxii.
124. Dummett (1978), p. xxi.
125. Dummett (1973), p. 320.
126. Grice (1957, 1968).
127. As, e.g. in Davies (1981), ch. 1.
128. Dummett (1959a), p. 8 of reprint. Italics original.
129. See Haack (1974), ch. 4.
130. This case is examined in more detail in Priest (1979).
131. See e.g. Haack (1974), pp. 101-2.
132. In fact, the supposition that the sentence is neither true nor false leads to problems of its own. See Mortensen and Priest (1981).
133. The propensity of verificationism to produce dialetheism as well as intuitionism is noted in Papineau (1979), pp. 91-2.
134. Rescher and Brandom (1980), sect. 26.
135. The matter is discussed a little further in Priest (1984), sect. 3.