1 Introduction ................................................. 1
1.1 The problem defined ..................................... 1
1.2 The current state of the debate ......................... 3
1.3 The structure of this work .............................. 6
1.4 Historical reflections ................................. 10
1.5 Relationship to AR&L ................................... 13
1.6 A note on style and substance .......................... 14
2 The Realism Debate .......................................... 15
2.1 The central role of truth .............................. 15
2.2 Five important contentions ............................. 19
2.3 Key theses ............................................. 27
2.4 Superassertibility ..................................... 42
2.5 Semantic anti-realism .................................. 45
2.6 A crescendo of concerns ................................ 50
2.7 Remarks on natural deduction ........................... 55
2.7.1 Arguments and natural deductions ................ 56
2.7.2 Accumulating arguments .......................... 56
2.7.3 Rules of inference .............................. 58
2.7.4 Reductio ad absurdum ............................ 59
2.7.5 Regimenting philosophical arguments ............. 60
2.7.6 A plea for tolerance in matters logical ......... 61
3 Irrealism ................................................... 63
3.1 A survey of various kinds of irrealism ................. 63
3.2 Non-factualist irrealism v. error-theory ............... 67
3.3 Notational preliminaries ............................... 75
3.4 A reductio of semantic irrealism? ...................... 77
3.5 Isolating the basic steps .............................. 77
3.5.1 The first basic step ............................ 77
3.5.2 The second basic step ........................... 79
3.5.3 The third basic step ............................ 79
3.6 Some simple arguments using the basic steps ............ 80
3.7 Evaluating the steps ................................... 82
3.7.1 A stratificationist objection to Boghossian
will not work ................................... 83
3.7.2 Objection to step (I) ........................... 86
3.7.3 Objection to step (II) from a projectivist's
point of view ................................... 86
3.8 Conclusion ............................................. 89
4 Against Meaning Scepticism .................................. 91
4.1 The impact of scepticism about meaning. The stress
between materialist metaphysics and analytic
intuition .............................................. 91
4.2 Theses about content, and some orthogonal issues ....... 93
4.3 What semantic determination thesis does the Kripkean
sceptic try to undermine? .............................. 97
4.4 On past and future applications of rules .............. 100
4.5 The sceptic is a non-factualist ....................... 102
4.6 Kripke's dialectic of reinterpretation ................ 104
4.7 Uniformity of reinterpretation requires globality ..... 108
4.8 Kripkean scepticism compared with Quinean
indeterminacy: the new dogma of post-empiricism ....... 115
4.9 Anti-sceptical responses emphasizing the first-
person case ........................................... 120
4.10 On Goodman's Paradox .................................. 122
4.11 The proper way to meet the sceptical challenge ........ 125
4.12 A parable ............................................. 127
4.13 From dispositional facts to normativity of meaning .... 130
4.13.1 On going wrong: competence v. performance ..... 133
4.13.2 Alleged problems for a dispositional
account: the argument from finitude ........... 137
4.13.3 Alleged problems for a dispositional
account: the argument from error .............. 139
5 Avoiding Strict Finitism ................................... 143
5.1 Knowability in principle .............................. 143
5.2 The strict finitist's worry ........................... 148
5.3 Recognitional capacities and compositionality ......... 150
5.4 Feasible verifiability ................................ 151
5.5 Aspectual recognition: competence as factorizable ..... 152
5.6 Finding the right dispositional conditionals .......... 155
6 The Manifestation Argument is Dead ......................... 159
6.1 A summary by way of introduction ...................... 159
6.2 Decidability, knowability and truth: picturing the
positions ............................................. 161
6.3 Dummett's construal of realist truth, and his
blindness to Gödelian Optimism ........................ 168
6.4 Understanding the dialectic of debate ................. 170
6.5 Bivalence and Decidability ............................ 173
6.6 Manifestationism ...................................... 176
6.6.1 The original 'manifestation challenge' ......... 176
6.6.2 Does Bivalence entail the possibility of
recognition transcendent truth? ................ 180
6.6.3 Dummett's quantifier-switch fallacies .......... 185
6.6.4 Independence results are no help to Dummett .... 190
7 Long Live the Manifestation Argument ....................... 195
7.1 A summary by way of introduction ...................... 195
7.2 A more convincing manifestation argument .............. 196
7.2.1 The problem of undecidable sentences ........... 196
7.2.2 The manifestation requirement made more
precise ........................................ 198
7.2.3 The principle of knowability made more
precise ........................................ 203
7.2.4 The principle of bivalence made more precise ... 205
7.3 Logical relationships among theses; the central
inference ............................................. 206
7.4 Decidability: demurral v. denial ...................... 214
7.5 The undecidability of arithmetic ...................... 216
7.6 Responses to undecidability ........................... 219
7.6.1 The anti-realist's response .................... 219
7.6.2 The realist's response ......................... 221
7.7 Realist reconstruals of manifestation? ................ 224
7.8 The central inference revisited; reconstruals
rejected .............................................. 232
7.9 Rubbing out the wrong pictures ........................ 235
7.9.1 Arguing against M-Realism ...................... 236
7.9.2 Arguing against the Gödelian Optimist .......... 239
8 Truth as Knowable .......................................... 245
8.1 Introduction .......................................... 245
8.2 Rational thinkers ..................................... 247
8.3 On wondering whether .................................. 252
8.4 On knowing every truth ................................ 259
8.5 Diagnosis of the underlying problem ................... 266
8.6 Cartesian contents, and our proposed solution ......... 272
8.7 The failure of the reconstrual strategy ............... 276
8.8 Taking stock .......................................... 278
9 Analyticity and Syntheticity ............................... 281
9.1 Logic and analyticity ................................. 281
9.2 A brief history of the two distinctions ............... 282
9.3 The impact of Gödel's first incompleteness theorem .... 290
9.4 An alternative view ................................... 295
9.5 The wider logic of number ............................. 297
9.6 Necessary existents ................................... 299
9.7 The dogma of existence ................................ 303
10 Finding the right logic .................................... 305
10.1 On rational advocacy of reform ........................ 305
10.2 Systematicity, immediacy, separability and harmony .... 308
10.3 Epistemic gain in logic ............................... 322
10.4 The maxim of narrow analysis .......................... 325
10.5 Non-forfeiture of epistemic gain ...................... 328
10.5.1 The Sub-sequent Constraint ..................... 329
10.5.2 Truth-preservation is not enough ............... 330
10.6 The Principle of Harmony .............................. 332
10.7 The Principle of Extraction for natural deduction
systems ............................................... 337
10.9.1 Uniquely determining rules for the logical
operators ...................................... 338
10.9.2 Intuitionistic Relevant Logic .................. 343
10.9.3 Classical Relevant Logic ....................... 344
10.9.4 Benefits for computational logic ............... 346
10.9.5 On choosing the right relevant logic: the
method summarized .............................. 346
10.9.6 Prosecuting our principles further:
a precondition on rule applications ............ 350
11 Cognitive Significance Regained ............................ 355
11.1 Re-evahtating the problem of cognitive significance ... 355
11.2 Conditions of adequacy on a criterion of cognitive
significance .......................................... 360
11.2.1 Sentences are cognitively significant only
within the context of a theory that makes
them so ........................................ 360
11.2.2 Basic sentences ................................ 361
11.2.3 Metalogical neutrality ......................... 362
11.2.4 Inductive levels, new vocabulary and
extension ...................................... 363
11.2.5 Verifiability and falsifiability ............... 365
11.2.6 The principle of composition, or molecularity .. 366
11.2.7 Constrained extension: higher-level
hypotheses ..................................... 366
11.2.8 A remark on significance via compounding ....... 369
11.2.9 Hempel's compositionality condition ............ 370
11.2.10 The first-order case .......................... 372
11.2.11 The invariance of non-significance under
reformulation ................................. 373
11.3 The formal theory ..................................... 374
11.3.1 Extension ...................................... 374
11.3.2 How sentences depend on the atomic facts
within a model for their truth or falsity ...... 382
11.3.3 Some inductive definitions ..................... 388
11.3.4 Main results ................................... 390
11.4 Comparison with Carnap's account ...................... 393
11.5 Blocking Church-Ullian collapses ...................... 399
12 Defeasibility and Constructive Falsifiability .............. 403
12.1 Rationalism and relativism ............................ 403
12.2 On defeasible empirical claims ........................ 406
12.3 Refutation of empirical theories ...................... 414
12.4 Normal forms for disproofs ............................ 422
12.5 Validity of arguments ................................. 425
12.6 Validity of reductio .................................. 429
12.7 The anti-realist construal of empirical claims that
cannot be proved ...................................... 432
13 Summary and Conclusion ..................................... 435
Bibliography .................................................. 439
Index ......................................................... 449
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