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Ideas of Michael Dummett, by Text

[British, b.1925, Professor at Oxford University. Fellow of New College and All Souls'.]

1959 Truth
p.151 Tarski's truth is like rules for winning games, without saying what 'winning' means
p.231 p.231 To explain a concept, we need its purpose, not just its rules of usage
p.231 p.231 It is part of the concept of truth that we aim at making true statements
p.235 p.235 You can't infer a dog's abstract concepts from its behaviour
p.237 p.237 We must be able to specify truths in a precise language, like winning moves in a game
1960 Presupposition
p.27 p.27 Natural language 'not' doesn't apply to sentences
p.27 p.27 Logic would be more natural if negation only referred to predicates
1970 works
p.15 For anti-realists there are no natural distinctions between objects
p.294 Anti-realism needs an intuitionist logic with no law of excluded middle
1973 Frege Philosophy of Language (2nd ed)
p.36 If a genuine singular term needs a criterion of identity, we must exclude abstract nouns
p.136 Concepts only have a 'functional character', because they map to truth values, not objects
Ch.14 p.50 A realistic view of reference is possible for concrete objects, but not for abstract objects
Ch.14 p.50 Ostension is possible for concreta; abstracta can only be referred to via other objects
Ch.14 p.471 There is a modern philosophical notion of 'object', first introduced by Frege
Ch.14 p.472 We can understand universals by studying predication
Ch.14 p.473 'Nominalism' used to mean denial of universals, but now means denial of abstract objects
Ch.14 p.475 Frege's domain for variables is all objects, but modern interpretations first fix the domain
Ch.14 p.477 The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}}
Ch.14 p.480 We can't say that light is concrete but radio waves abstract
Ch.14 p.481 Concrete objects such as sounds and smells may not be possible objects of ostension
Ch.14 p.484 To associate a cardinal with each set, we need the Axiom of Choice to find a representative
Ch.14 p.485 Abstract objects must have names that fall within the range of some functional expression
Ch.14 p.487 The concrete/abstract distinction seems crude: in which category is the Mistral?
Ch.14 p.491 Abstract objects may not cause changes, but they can be the subject of change
Ch.14 p.494 Abstract objects can never be confronted, and need verbal phrases for reference
Ch.14 p.494 We don't need a sharp concrete/abstract distinction
Ch.14 p.497 The context principle for names rules out a special philosophical sense for 'existence'
Ch.14 p.498 Since abstract objects cannot be picked out, we must rely on identity statements
Ch.14 p.503 The objects we recognise the world as containing depends on the structure of our language
Ch.14 p.507 Intuitionism says that totality of numbers is only potential, but is still determinate
Ch.14 p.508 What matters in mathematics is its objectivity, not the existence of the objects
Ch.14 p.511 Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal
Ch.14 p.511 If we can intuitively apprehend abstract objects, this makes them observable and causally active
1973 The Justification of Deduction
p.67 Deduction is justified by the semantics of its metalanguage
p.292 p.292 Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples
p.294 p.294 In standard views you could replace 'true' and 'false' with mere 0 and 1
p.294 p.294 Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning
p.296 p.296 An explanation is often a deduction, but that may well beg the question
p.305 p.305 Classical two-valued semantics implies that meaning is grasped through truth-conditions
p.305 p.305 Beth trees show semantics for intuitionistic logic, in terms of how truth has been established
p.309 p.309 Holism is not a theory of meaning; it is the denial that a theory of meaning is possible
p.310 p.310 Soundness and completeness proofs test the theory of meaning, rather than the logic theory
p.311 p.311 Philosophy aims to understand the world, through ordinary experience and science
p.313 p.313 A successful proof requires recognition of truth at every step
1973 The philosophical basis of intuitionist logic
p.218 p.218 Meaning as use puts use beyond criticism, and needs a holistic view of language
p.224 p.224 Stating a sentence's truth-conditions is just paraphrasing the sentence
p.225 p.225 If a sentence is effectively undecidable, we can never know its truth conditions
p.246 p.246 Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances
1975 Frege's Distinction of Sense and Reference
p.248 p.248 Holism says all language use is also a change in the rules of language
p.254 p.254 The causal theory of reference can't distinguish just hearing a name from knowing its use
p.256 p.256 Ancient names like 'Obadiah' depend on tradition, not on where the name originated
1977 Elements of Intuitionism
p.336 p.168 For intuitionists it is constructed proofs (which take time) which make statements true
p.57 p.168 Platonists ruin infinity, which is precisely a growing structure which is never completed
1983 Could There Be Unicorns?
1 p.329 It was realised that possible worlds covered all modal logics, if they had a structure
1 p.330 If something is only possible relative to another possibility, the possibility relation is not transitive
1 p.330 Relative possibility one way may be impossible coming back, so it isn't symmetrical
2 p.331 Generalised talk of 'natural kinds' is unfortunate, as they vary too much
2 p.332 Kripke says internal structure fixes species; I say it is genetic affinity and a common descent
4 p.336 To explain generosity in a person, you must understand a generous action
8 p.347 Possible worlds aren't how the world might be, but how a world might be, given some possibility
8 p.348 If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality
8 p.348 In S4 the actual world has a special place
8 p.348 If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system
1991 Frege philosophy of mathematics
p.142 Content is replaceable if identical, so replaceability can't define identity
22 'Quantit' p.279 Addition of quantities is prior to ordering, as shown in cyclic domains like angles
22 'Quantit' p.280 Why should the limit of measurement be points, not intervals?
7 Def 11 p.194 A prime number is one which is measured by a unit alone
7 Def 2 p.194 A number is a multitude composed of units
Ch. 3 p.26 In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical
Ch. 5 p.53 Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1
Ch. 5 p.53 The identity of a number may be fixed by something outside structure - by counting
Ch. 8 p.86 To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too
Ch. 8 p.94 Fregean semantics assumes a domain articulated into individual objects
Ch.10 p.112 Frege was the first to give linguistic answers to non-linguistic questions
Ch.10 p.113 Frege introduced criteria for identity, but thought defining identity was circular
Ch.11 p.134 A contextual definition permits the elimination of the expression by a substitution
Ch.12 p.145 Maybe a concept is 'prior' to another if it can be defined without the second concept
Ch.12 p.145 An argument for conceptual priority is greater simplicity in explanation
Ch.12 p.150 We understand 'there are as many nuts as apples' as easily by pairing them as by counting them
Ch.14 p.173 We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus'
Ch.15 p.181 Abstract objects nowadays are those which are objective but not actual
Ch.15 p.182 It is absurd to deny the Equator, on the grounds that it lacks causal powers
Ch.15 p.187 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object
Ch.15 p.198 Realism is just the application of two-valued semantics to sentences
Ch.16 p.207 Abstract objects need the context principle, since they can't be encountered directly
Ch.16 p.208 Abstract terms are acceptable as long as we know how they function linguistically
Ch.18 p.223 Frege was completing Bolzano's work, of expelling intuition from number theory and analysis
Ch.18 p.224 Set theory isn't part of logic, and why reduce to something more complex?
Ch.18 p.231 Nominalism assumes unmediated mental contact with objects
Ch.18 p.239 The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy
Ch.18 p.240 The existence of abstract objects is a pseudo-problem
1991 The Logical Basis of Metaphysics
p.299 p.4 Classical negation is circular, if it relies on knowing negation-conditions from truth-conditions
1992 Realism and Anti-Realism
p.467 p.467 Metaphysical realists are committed to all unambiguous statements being true or not true
1997 Thought and Reality
1 p.3 We know we can state facts, with true statements
1 p.7 Since 'no bird here' and 'no squirrel here' seem the same, we must talk of 'atomic' facts
1 p.11 To 'abstract from' is a logical process, as opposed to the old mental view
2 p.17 Truth is part of semantics, since valid inference preserves truth
2 p.18 If Presentism is correct, we cannot even say that the present changes
3 p.32 To know the truth-conditions of a sentence, you must already know the meaning
3 p.34 We can't distinguish a proposition from its content
3 p.40 Sentences are the primary semantic units, because they can say something
4 p.47 Language can violate bivalence because of non-referring terms or ill-defined predicates
4 p.50 The theories of meaning and understanding are the only routes to an account of thought
4 p.51 A theory of thought will include propositional attitudes as well as propositions
4 p.52 We could only guess the meanings of 'true' and 'false' when sentences were used
5 p.59 Empirical and a priori knowledge are not distinct, but are extremes of a sliding scale
5 p.62 The law of excluded middle is the logical reflection of the principle of bivalence
5 p.64 'That is red or orange' might be considered true, even though 'that is red' and 'that is orange' were not
5 p.64 A justificationist theory of meaning leads to the rejection of classical logic
5 p.70 Verificationism could be realist, if we imagined the verification by a superhuman power
6 p.77 If truths about the past depend on memories and current evidence, the past will change
6 p.79 Philosophers should not presume reality, but only invoke it when language requires it
8 p.101 We can't make sense of a world not apprehended by a mind
8 p.104 Time is the measure of change, so we can't speak of time before all change
1998 The Philosophy of Mathematics
3.1 p.134 First-order logic concerns objects; second-order adds properties, kinds, relations and functions
3.1 p.136 Logical truths and inference are characterized either syntactically or semantically
5 p.156 Ordinals seem more basic than cardinals, since we count objects in sequence
6.1 p.162 The number 4 has different positions in the naturals and the wholes, with the same structure
7 p.166 ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality
7.1.1 p.168 The main alternative to ZF is one which includes looser classes as well as sets
8.1 p.178 Intuitionists reject excluded middle, not for a third value, but for possibility of proof
2000 Elements of Intuitionism (2nd ed)
p.41 p.199 Mathematical statements and entities that result from an infinite process must lack a truth-value
2001 Truth and the Past
1 p.28 Truth-condition theorists must argue use can only be described by appeal to conditions of truth
2 p.30 Intuitionists rely on the proof of mathematical statements, not their truth
2 p.35 The truth-conditions theory must get agreement on a conception of truth
3 p.52 Verification is not an individual but a collective activity
3 p.52 I no longer think what a statement about the past says is just what can justify it
4 p.60 Surely there is no exact single grain that brings a heap into existence
4 p.69 Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense
5 p.74 The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless
5 p.86 Maybe past (which affects us) and future (which we can affect) are both real
5 p.87 A 'Cambridge Change' is like saying 'the landscape changes as you travel east'
5 p.92 The existence of a universe without sentience or intelligence is an unintelligible fantasy