Index

Abductive inference, 98 Availability theory, 140 Abstractness, platonic vs. nonplatonic, Avenarius, R., 4 192 Acknowledging the predicament, 55, Basic Laws of Arithmetic (Frege), 32 69–71 Begriffsschrift (Frege), xii, 32, 120, 207, AI 229 strong, 102–106, 108 Belnap, N., 252n18 weak, 103, 105, 108 Benacerraf, P., xxi, 2, 22–25, 71, Analytic inferences, 225 155–156, 182–191, 193, 199–200 Analyticity, 36–37 Benacerraf dilemma Analytic necessity, 197 extended, 184 Analytic philosophy, xx, 1, 3 original, 182–184 Alice, 158–159, 185 Block, N., 93 Antinaturalism, 14–21 Bolzano, B., 5 Antiperceptualism, 186, 189, 191–200 Bonjour, L., 188 Antipsychologism, 14–21 Boole, G., xi–xiii, 25, 31–32, 115–116, Antirealism, 185, 188–189 131, 204–205, 216 Anti-supernaturalism, 9 Braine, M., 130 Aphasias, 86, 106–107 Brentano, F., 1, 4 A priori–a posteriori, xii, 272n20, Broca’s area, 106 273n24 Byrne, R., 135 Apriority of protologic, 29, 44–45, 109, 201 Carnap, R., 36–37, 54, 59–61, 65, 186, Aristotle, xi, xiii–xv, 31–32, 124 210–211, 226–227 Arnaud, P., xii, 204–205 Carroll, L. (Charles Dodgson), 54–59, Artificial intelligence. See AI 61–62, 65, 69, 78, 158, 223 Art of Thinking (Arnaud and Nicole), Carruthers, P., 111 xii Categorical normativity. See Aspects of the Theory of Syntax Normativity, categorical (Chomsky), 86 Causation, 23, 189–190, 242n62 Autism, 112 Central processes, 89, 100–102, 109 310 Index

Chalmers, D., 12, 98, 277–278n78 Darwinian evolution, 97, 142–143 Cheng, P., 141 Davidson, D., 110, 173 Cherniak, C., 146, 270n88 Dedekind, R., 36 Chinese brain argument, 106–107 Dedicated cognitive capacity, 88, 101 Chinese nation argument, 93 Deduction, intuitive vs. rote, 199 Chinese room argument, 103–104 Deferred ostension, 187, 190 Chomsky, N., xi, xiii, xxi, 25–26, 30, De Morgan, A., 218 46–52, 78–79, 83–87, 90, 98, “Deny the doctrine, change the subject” 109–111, 121, 128–130, 133, 172, argument, 42, 181 209, 250n57, 250n60 Descartes, R., 78, 98, 110, 134, 174, Church-Turing thesis, 102. See also 176, 224–226, 229, 282n57 Turing computability; Turing Deviant logic, xii, 40–41, 234n12, machines 246n34. See also Nonclassical logic Circular argument, 31 Deviant Logic (Haack), 40 Classical logic, xii, xx, 29, 35–36, Dialetheic logic, xii, 41, 223–224, 40–46, 122, 148, 216, 222, 231, 234n14 233n10 Diehard classicism (about logic), 41–43, Cogito, 224–225 133, 222 Cognitive creativity, 86–88, 102 Diehard nonclassicism (about logic), Cognitive faculties, 79–80 41–43, 122, 133 Cognitive generativity, 86, 102 Discourse on Method (Descartes), 224 Cognitive productivity. See Cognitive Domain-specific cognitive capacities, creativity 88–89, 101 Cognitive relativism, 5, 8, 29, 238n18 Dretske, F., 187–188 Cognitive science, xx, 82, 231 Dualism, 262n56 Cognitivism, xii. See also Logical Dummett, M., 3, 22, 54, 66–69, cognitivism 253n21, 253n22, 253n24 Cognitivist existential predicament, 136, 147–148, 200 Early modern conceptions of ourselves, Cognitivist solution to the logocentric 113–114 predicament, 74 Einstein, A., 98 Cohen, L. J., 117, 128–129 Elementary logic. See Classical logic Competence, 263n6 Embodied rationalism, 13, 283–284n72 Connectionism, 260n38 Empirical psychology, 7, 52 Consequence. See Logical consequence Empiricism, 8, 10, 29, 84–85, 186, Constructivism, 79, 85–88, 107, 109 188–189 Conventionalism, 60–68, 185, 188–189, Encapsulated cognitive capacities, 89, 210–213 101 Copi, I., 219 Enquiry Concerning Human Cosmides, L., 142, 227 Understanding (Hume), 160 Cox, G. R., 125 Epigenesis of pure reason, 86–87 Craik, K., 135 E pluribus unum problem, xx, 29–52, Creativity. See Productivity 75, 77, 115, 122, 133, 138 Index 311

Erdmann, B., 5 Henle, M., 123, 130 Ethics of logic, 201–231 Herbart, J., 5 Euler diagrams, 136 Heuristics-and-biases theory, 139–146, Evans, J., 126 226 Evnine, S., 254n33 Hilbert, D., 58, 60, 244n7 Extensions of classical logic, xii, 40–41, Holyoak, K., 141 148, 233n11 Human interest postulates, 211 Hume, D., xvii, 84, 115, 160, 163, 164, Fallacies, 217–220 167, 170, 186, 228 Fast cognitive capacities, 88, 101 Husserl, E., xii, xix, 1–9, 14, 20, 24, Fictionalism, 185, 188 27, 205, 206–209, 238n20 Field, H., 185, 189 Fluent aphasia, 106–107 I-language, 90 Fodor, J., xi, xiii, 26, 78–80, 88, 90–91, I-logic, 51, 251n67 94, 110, 121 Imagination Folk psychology, 82 linguistic, 175 Foot, P., 210–212 logical, 35, 192–195, 199–200 Formalism, 244n7 Incompleteness theorems. See Gödel, K. Formal logic, 30–32 Indeterminacy of translation, 161 Form of life, 180 Indexicality, 145 Foundations of Arithmetic (Frege), 7 Indirect perceptualism, 188, 190–191 Frankfurt, H., 281n36 Inductive logic, 30–31 Free logic, 41 Inference-tickets, 57, 63, 65, 207 Frege, G., xii, xix, 1–9, 14, 21, 24, 27, Inference to the best explanation, 52, 98 31–32, 36–37, 81, 90, 116, 174, 182, Inferential role theory of logical con- 204–206, 208, 229, 238–239n29 stants, 63–65, 133–134, 156, Freud, S., 115 168–170 Informal logic, 31 Garden path sentences, 220 Informational encapsulation, 26, Generativity, 249n52 100–101, 132 Genetic logic, 120–122 Informational promiscuity, 100–102, 107 Gentzen, G., 54, 63, 65, 131, 133, 206 Innatism, 79, 83–85, 96–99, 107, 109, Geuss, R., 228 134, 138, 258–259n27 Gödel, K., 36, 38–40, 134, 187, 235n23 Inscrutability of reference, 161 Goodman, N., 66, 70, 161 Intensional logic, 31 Griggs, R. A., 125 Intentionalism. See Representationalism Groundlessness of logic, 55, 69–72, 74–75 Intentionality, 80–82, 256n9 Intuition, 171–182 Haack, S., 1, 28, 54, 66, 68–70, vs. deduction, 174–175 246–247n35, 247n41, 253n23, 253n24 logical (see Logical intuition) Hale, B., 39, 186 mathematical (see Mathematical Harman, G., xxii, 202, 220–223 intuition) Hegel, G. W. F., xvii Intuitionist logic, 41 312 Index

Intuition-of, 173 Law of noncontradiction, 31, 41–42, Intuition-that, 173 243–244n3 Investigation of the Laws of Thought Lawrence, D. H., 115 (Boole), xii, 32, 120 Laws of thought, 4, 25–26, 78, 110, 204 “Investigations into Logical Deduction” Leibniz, G. W., 5, 31 (Gentzen), 63 Lewis, C. I., 20, 33, 35, 40–41, 156 Irrationalism, 124–130, 146–147, 150, Liar paradox, 36, 38–39 154, 226 Lingua mentis (mental language). See Language of thought Jackendoff, R., 86 Linguistic competence, 78, 121, James, W., 116–120, 122–123 128–129, 250n55 Jäsche Logic (Kant), xii Lipps, T., 5 Johnson-Laird, P., 116, 135, 193–194 Logical animals, 77–78, 201, 215 Justification, 44 Logical bad faith, 166 Justificational holism, 255n37 Logical cognitivism, xix, 3, 24–29, “The Justification of Deduction” 46–47, 52–53, 75, 77, 115, 156, 180, (Dummett), 66 202, 209, 213, 230 “The Justification of Deduction” Logical communitarianism, 69–71 (Haack), 68 Logical competence, 51 Justification of deduction problem, 54, Logical consequence, xv, 27, 133–34, 66–69 214–215, 231, 234n17 Logical expressivism, 70–71, 186, 188–189 Kahneman, D., 116, 140 Logical form, 51 Kant, I., xi–xiii, xvii, xx, xxi, 1, 5, Logical intuition, 156–157, 170–182, 25–26, 31, 37, 45, 85–87, 110, 115, 168, 197–201 131, 204–205, 208–214, 217, 230, Logical knowledge, 155–200 231, 236n32 Logical necessity, 158, 195–197 Kantian constructivism in ethics, 212 Logical nihilism, 227, 230 Katz, J., 186, 189 Logical nonfactualism. See Logical Kim, J., 11 expressivism Kirk, R., 111 Logical possibility, 196, 225 Kosslyn, S., 193–194 Logical pragmatism, 70–71 Kripke, S., 41, 98, 156, 158–168, 178 Logical prudentialism, 69, 71 Kripkenstein, 161, 163–168, 170. See Logical psychologism, xii, xix–xx, 1–29, also Rule following paradox 75, 115–116, 206–208, 222 Kusch, M., 5 Logical structuralism, 156, 191–192, 199–200 Language of thought (LOT), 26, 47, 78, Logical Syntax of Language (Carnap), 80, 90–92, 94–96, 107–110, 151, 213 54, 59–61, 210 L’art de penser (art of thinking), 204 Logical truth, 61–63, 225 Law of bivalence, 31, 41, 243–244n3 Logic faculty thesis, xiii, 3, 25–26, 28, Law of excluded middle, 31, 41, 46–53, 73–75, 77, 107–108, 115, 243–244n3 154, 157, 168, 200–202, 230 Index 313

Logicism, 36, 40 Modal downsizing, 8, 29 Logic-liberated-animals, xxii Modality, xv Logic of thought, 51, 107–110, Modes of presentation (MOPs), 81, 93 132–133, 135, 154, 213–214, 226 Modularity, 25, 79, 88–90, 100–102, Logic-oriented conception of human 107, 109, 131–132, 259n30 rationality, xviii, 77–78, 113–115, Monty Python’s Flying Circus, 156, 201–202 115–116, 152 Logocentric predicament, 53–75, 115, Mooney, C., 88 157, 211 Mooney faces, 88 Lotze, H., 5 Moore, G. E., 2, 14–18, 20, 24, 27 Lowe, E. J., 136 “Morality as a System of Hypothetical Imperatives” (Foot), 210 Mach, E., 5 Moral science conception of logic, Machine functionalism, 26, 103, 205–206, 231 243n74 Mr. Spock, 215 Macnamara, J., 130, 266n37 Multiple embodiability, xviii, 25, 52 Mad Hatter, 78 Manktelow, K.I., 126 Nagel, T., 281n36 Many-valued logic, 41 Nativism. See Innatism Mathematical intuition, 23 Natorp, P., 5 Mathematical logic, 3, 32–35 Naturalistic fallacy, 2, 15–17 “Mathematical Truth” (Benacerraf), 182 Natural logic, 51, 251n68 Meditations on First Philosophy “The Nature of Judgement” (Moore), 15 (Descartes), 224, 229 Necker cube, 89, 219 Mein Kampf, 229 Negation, 165–166, 180–182, 225 Meinong, A., 41 Negativity, 165–166, 180–182 Mentalese. See Language of thought Neo-Fregeanism, 39 Mental language. See Language of Neo-Kantianism, 9, 13 thought Neo-Nietzscheanism, xii, 224, Mental Logic, 131–135, 138, 145 226–231 Mental logic theory, xxi, 130–136, Nicole, J., xii, 204–205 145–146, 151, 266–267n45, 267n46 Nietzsche, F., 226, 227–229 Mental models theory, 135–140, 145, Noncausal perceptualism, 187, 190–191 267n51 Nonclassical logic, 40–46, 73, Metalogic, 61 216, 231 Metalogical principles of protologic, Noncontact causal perceptualism, 187, 45–46 189, 191 Metaphysical necessity, 196–197, Nonepistemic perception, 187, 190 234–235n21, 278n79 Nonformal logic, 30–31 Mill, J. S., xii, 5, 13, 186, 204, 208 Normativity Millikan, R. G., 223 categorical, xii, 202–205, 208–215, 231 Milton, J., 227 hypothetical, 203, 208 Minimal rationality theory, 146–150 Nye, A., 201, 205–206, 226, 229 314 Index

O’Brien, D. P., 130, 145 Principia Ethica (Moore), 2, 15 O’Neill, O., 212–213 Principia Mathematica (Whitehead and One True Logic, 26, 41, 43, 222 Russell), 31, 35, 38, 54, 120 Open question argument, 16–17 Principle of Tolerance, 211, 226 Overton, W., 130 Principles of Psychology (James), 118 Prior, A. N., 54, 63–65, 69, 252n15, Paraconsistent logic, xii, 41, 234n13 252n16 Paradise Lost (Milton), 227 Private language argument (PLA) Paradox of classes, 36–38, 237n15 (Wittgenstein), 160 Paratactic approach to logical intuition- Productivity, 249n52 that, 172–173 Prolegomena to Pure Logic (Husserl), 5, Parsons, C., 173–174, 188 205–206 Peano, G., 36, 38, 134 Property-identity criteria, 16–17, Peirce, C. S., 136, 225–226, 229 241n50, 241n56 Permission schema, 142–143 Prosopagnosia, 89 Phenomenology of intuition, 177–178 Protologic, xii, xviii, xxi–xxii, 30, 40, Philo and Stoic logic, 31 43–46, 48, 50–53, 73–74, 77, Philosophical Investigations 108–110, 112–113, 116, 133, (Wittgenstein), xx, 159, 160–161 149–153, 201, 209, 213–215, 217, Philosophie der Arithmetik (Husserl), 4 222–223, 230–231 Phrase-structure grammar, 249n51 Protological competence theory, xxi, Physicalism, 9–10, 239n32 116, 149–154 Physical necessity, 196 Psycholinguistics, xxi, 25–26, 30, Piaget, J., 116–118, 120–124, 130 47–52 Piagetian logic, 120–122, 124 Psychological logicism, 116 Piagetian stages of cognitive develop- Psychologism. See Logical psychologism ment, 120–121 Psychology from an Empirical Plato, 227, 229 Standpoint (Brentano), 4 Platonism Psychology of reasoning, 26, 115–154, logical, xx, 2, 21–27, 29, 184 200 mathematical, 22, 183–184 Pure logic, 7, 116 Plus–quus, 161–163. See also Rule-fol- Putnam, H., 70 lowing paradox Pylyshyn, Z., 194 Port Royal logicians, 204 Postmodern conceptions of ourselves, Quine, W. V. O., xi, xiii, 9, 13, 25, 37, 113–114 41–44, 54, 59, 61–64, 69–71, 85, Poverty-of-the-stimulus argument, 161, 181–182, 186–188, 211, 83–85, 97, 108, 257n18 239n30, 252n13 Pragmatic reasoning schemas theory, 140–143 Rational anthropology, xx Presuppositional arguments, 72–73 Rationalism, 124–130, 135, 139, and transcendental arguments, 255n39 146–147, 150, 154 Index 315

Rationality, xv–xviii, 26–27, 77–78, Scientific naturalism, xii, xx, 1–2, 9–14, 110–115, 117, 122–130, 153–154, 18–21, 27, 29, 52, 71, 99, 157, 207, 209, 235n24, 264n8, 270n88 236n31 Rawls, J., 212 Scientism, 9 Raz, J., 201 Searle, J., 102–106 Realism, 156 Second-order logic, 40 Reasoning tests, 100, 116–117, Selection task, 125–128, 141–147, 122–154, 270n91 152–153, 219 Red Queen, 158–159, 185 Self-evidence, 35 Reduction Sells, S. B., 123 explanatory, 6–7, 52, 157 Semantic holism, 67, 70 ontological, 7 Semantic realism, 71 Referential opacity, 81 S4 modal logic, 20 Referential transparency, 81 Shapiro, S., 29, 44 Refined cognitivist model of the mind, Sheer logic, 25–26, 44, 242n69 92–107. See also Standard cognitivist Sheffer, H., 54–55, 69 model of the mind Shepard, R., 155, 193 Reflective equilibrium, xvii, 235n25 Signs, vs. symbols, 34–35, 92–94 “The Refutation of Idealism” (Moore), Sigwart, C., 5 15 Smiley, T., 57–58 Relevance logic, 41 Sober, E., xii Remarks on the Foundations of Social contract schemas theory, 140, Mathematics (Wittgenstein), 165, 179 142–146 Remarks on the Philosophy of Spencer, H., 5 Psychology (Wittgenstein), 179 Stalnaker, R., 111 Representationalism, 79–82, 107, 109 Standard cognitivist model of the mind, Republic, 229 xxi, 78–92, 146. See also Refined Rips, L., 125 standard cognitivist model of the Rule-based semantics, 159 mind Rule following paradox (RFP), 158–168 Stein, E., 129 Rules for the Direction of the Mind Stevenson, C., 252n18 (Descartes), 174, 224 Stich, S., 115, 129 Rules of etiquette, and moral rules, 210 Structuralism, 271n8 “The Runabout Inference Ticket” (Prior), Superlogic, 29, 44 63 Supervenience, 7, 10–12, 19–21, 52, 63, Russell, B., 32, 36–38, 60, 216–217 105, 239–240n36, 240n37 Ryle, G., 57, 207 Survey of Symbolic Logic (Lewis), 33, 40 Syllogism, xi, xiii–xv, 31, 118, 120 Satan, 227 Symbolic logic, 3, 32–35, 218 Schmogic, 181 Symbols, vs. signs, 34–35, 92–94 Science-forming faculty (SFF), 98 Syntax languages, 61 Science of logic, xiii–xv, 231 System of Logic (Mill), xii, 9 316 Index

Tarski, A., 21, 35–36, 39–40, 60, 71, Wernicke’s aphasia. See Fluent 168, 182 aphasia Theory of mind module, 112 Wernicke’s area, 106 “Thoughts” (Frege), 21 Wetherick, N., 130 Thrasymachus, 227 “What Numbers Could Not Be” Three-valued logic, 41 (Benacerraf), 182 Through the Looking-Glass (Carroll), “What the Tortoise Said to Achilles” 158, 228 (Carroll), 55 Tonk, 64 Whitehead, A. N., 32 Topic bias (of logic), 8, 29 White Queen, 223, 228 Topic neutrality (of logic), 188 White-queenism, 223–231 Tourette’s syndrome, 106 White queen psychology, 223–224 Tractatus Logico-Philosophicus Wilkins, M. C., 123 (Wittgenstein), xix, 34–35, 54, 59–60 Williams, B., 228 Traité de logique (Piaget), 120 Will to truth, 226 Transcendental psychology, xxi. See also Wittgenstein, L., xix, xxi, 34–37, 54, Kant, I. 59–60, 69–70, 155–170, 176–180, Treatise of Human Nature (Hume), 160 157, 186, 216–217 Truth tables, 136 Wittgenstein on Rules and Private Truth-value gluts, 41, 222 Language (Kripke), 160 Turing computability, 87, 90–91, Woodworth, R. S., 123 102–103 Word and Object (Quine), 85 Turing machines, 82, 103 Words of Power (Nye), 228 Tversky, A., 117, 140 Wright, C., 39, 186 Two-dimensional semantics, 277–278n78 Wundt, W., 5

Unconstrained pluralism (about logic), Yablo, S., 185 41–43 Universal grammar (UG), 44, 48–51, 78, 109–110, 121–122, 209, 249–250n53 Unrevisability, 44–45

Van Heijenoort, J., 3 Venn diagrams, 136 Visual illusions, 219–220 Von Humboldt, W., 86–87

Warmbröd, K., 248–249n48 Wason, P., 100, 116, 125, 127, 132, 147, 153, 219 Weininger, O., 201, 205–206, 217