Truth, Reference and Realism

Index

absolute generality, xxvii–xxx, 52–53, 192–203 abstract objects/entities and Benacerraf’s dilemma, 235–237, 261 fictions as, 37 grasping, xxxii, 235–237, 261. See also apprehension of universals/concepts/ senses inferring the existence of, 241 as mathematics’s subject matter, x, xiii, xviii, xx–xxi neo-Platonic account of, xxxiii, 242– 243, 257–258, 261 numbers and sets as, 37 and self-predication, 244, 247 structures as, 20 See also forms; mathematical objects; tropes; universals abstract particulars. See tropes abstraction, 10, 241, 27n10 acceptance, attitude of, 148–152 alien universals. See uninstantiated universals anscombe, G.e.m., 216 ante rem structuralism, xviii–xix, xxi–xxii, 31–34, 37, 42 ante rem theory of abstract entities, 242, 257 of concepts, 243 of numbers, 242 of structures. see ante rem structuralism of universals, 33, 243–244. See also Plato’s theory of forms; realism: about universals See also Platonism anti-realism and Benacerraf’s dilemma, xvi–xvii, 101 its contrast with realism, xv–xvi about logic, 82, 86–87, 100–101, 120 about logical concepts/senses, xxiii, 120 about mathematical referents, xviii about truth, xvi–xvii, 101 apprehension of universals/concepts/ senses, xxxii–xxxiii, 235–242, 261 of logical concepts/senses, 89–92, [93–94]n15, 102–103, 120 See also grasp aristotle, 33, 235–236, 243–245, 247– 252 arithmetic Benacerraf on, 19 dedekind’s axioms for, 24–25, 28, 36, 42, 56 explaining a priori knowledge of, 110 frege on, 7 if-then-ism about, 40–41 non-standard models of, 28, 38, 67, 186n11 Peano (Pa), 5, 9, 24, 48, 54, 67 second-order, 3n1, 40–41, 46, 186n11 undecidable problems in, and ch, 48, 66 See also natural numbers; truth: arithmetical armstrong, d.m., 243, 252, 255–257, 259 assessment of beliefs and assertions, 229 factual, 258–260 of soundness/validity, 128–133, 137, 155–156, 195–196 of utterances and statements, 220–222 associationism, 237–240 index i4 Truth.indb 265 2011.08.15. 8:57 266 index atomic freedom, rule of, [198–199]n24 axiom of coherence, 28–29 of foundation, 49–50 of infinity shapiro’s, 27–28 Zermelo’s, 15, 37 of replacement, 4, 11, 15–17, 45, 50, 54–55 Tarski’s, of inaccessible cardinals, 51 V=L, 59 axiomatic method, 24, 30, 146 ayer, a.J., xiv, 214–215, 217, 239 Balaguer, m., xx Basic law V, 7, 66 Bealer, G., 212n, 229n21 Belnap, n., xv Benacerraf, P., ix, xxi, 2, 18–20, 63, 67n, 241. See also Benacerraf’s dilemma Benacerraf’s dilemma, x–xi, xx–xxi, 2, 81, 101, 235–236 and apprehension of universals, xxxii, 236–237, 240–241 for logic, xi, xxiv–xxv, xxvii, 77–78, 82, 102, 119–121 and obviousness and compellingness, 121 presuppositions of, xi–xiv as a problem for rational insight theories , 88 responses to, x–xi, xiv–xx about senses, 102, 120 Bernays, P., 10, 12–13, 16–18, 20, 47. See also von neumann-Bernays-Gödel set theory Blackburn, s., xv, xvii, 207, 211–213, 216n, 224 Boghossian, P., 78, 88–90, 97n, 103n, 104n BonJour, l., xx, 82, 88, 106, 111 Boolos, G., 46, 53, [66–67]n21, 68, 201n Borel determinacy, 4–5, 53–54, 67 Bourbaki, n., 22–25, 32 Brouwer, l.e.J., xvii Brown, J., xx Burali-forti paradox, 27, 202 Burge, T., xxiv, 96, 249n Butković, a., 97n camp, J.l., xv cantor, G.f., 11–12, 30n, 47, 58, 61, 65 continuum hypothesis. See continuum hypothesis cardinals, 49–50, 58. See also inaccessible cardinals; large cardinals; mahlo cardinals ; Woodin cardinals carnap, r., xvii, 12, 44, 62 casullo, a., 81 categorical characterizations, 2–3, 34–35, 38–39 of the continuum, 2, 5 of the cumulative hierarchy, 10, 15, 38. See also quasi-categoricity of the euclidean plane, 2–3, 7, 42 of the natural numbers, 2, 32, 36–38, 47 categoricity. See categorical characterizations ; quasi-categoricity causal accounts and conceptualism about logic, 78, 89–90, 107–108 of impressions of validity, 100 of logical beliefs/intuitions, xi, 122 of the meaning of representations, 238–240 of perceptual and of a priori knowledge, 81–82, 109–110. See also causal contact theory of knowledge acquisition causal contact theory of knowledge acquisition, x–xi, xiii, xviii–xix, xxxii, 81, 235–236, 240–241. See also causal accounts; contact/no–contact theory of knowledge acquisition ch. See continuum hypothesis characterizations. See categorical characterizations; unique characterization cherniak-stich program, 111 chisholm, r., 109 circularity of...