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Ideas of Ian Rumfitt, by Text

[British, fl. 2014, Pupil of Dummett. At University College, Oxford. Then Professor at Birkbeck, then Birmingham.]

2000 "Yes" and "No"
p.784 Standardly 'and' and 'but' are held to have the same sense by having the same truth table
II p.787 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter
III p.787 The sense of a connective comes from primitively obvious rules of inference
IV p.797 We learn 'not' along with affirmation, by learning to either affirm or deny a sentence
2002 Concepts and Counting
I p.43 Some 'how many?' answers are not predications of a concept, like 'how many gallons?'
III p.56 A single object must not be counted twice, which needs knowledge of distinctness (negative identity)
2007 The Logic of Boundaryless Concepts
p.13 p. Logic guides thinking, but it isn't a substitute for it
p.5 p. Vague membership of sets is possible if the set is defined by its concept, not its members
2010 Logical Necessity
p.10 A distinctive type of necessity is found in logical consequence
Intro p.35 Logical necessity is when 'necessarily A' implies 'not-A is contradictory'
Intro p.36 Soundness in argument varies with context, and may be achieved very informally indeed
Intro p.36 Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B'
1 p.41 Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths)
2 p.44 There is a modal element in consequence, in assessing reasoning from suppositions
2 p.44 A logically necessary statement need not be a priori, as it could be unknowable
2 p.46 Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not
2 p.46 We reject deductions by bad consequence, so logical consequence can't be deduction
4 p.60 If a world is a fully determinate way things could have been, can anyone consider such a thing?
5 p.61 The logic of metaphysical necessity is S5
2015 The Boundary Stones of Thought
1.1 p.2 It is the second-order part of intuitionistic logic which actually negates some classical theorems
1.1 p.3 Intuitionists can accept Double Negation Elimination for decidable propositions
1.1 p.4 Introduction rules give deduction conditions, and Elimination says what can be deduced
1.1 p.9 In specifying a logical constant, use of that constant is quite unavoidable
1.1 p.10 Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables
1.1 p.13 Classical logic rules cannot be proved, but various lines of attack can be repelled
1.1 p.13 The case for classical logic rests on its rules, much more than on the Principle of Bivalence
1.2 p.18 Frege thought traditional categories had psychological and linguistic impurities
2.3 p.43 Normal deduction presupposes the Cut Law
2.3 p.43 Monotonicity means there is a guarantee, rather than mere inductive support
2.5 p.56 Logical truths are just the assumption-free by-products of logical rules
3.3 p.74 Logical consequence is a relation that can extended into further statements
3.3 p.76 'Absolute necessity' would have to rest on S5
3.3 p.78 Logic is higher-order laws which can expand the range of any sort of deduction
3.4 p.83 Metaphysical modalities respect the actual identities of things
4.2 p.99 We understand conditionals, but disagree over their truth-conditions
5.1 p.127 The idea that there are unrecognised truths is basic to our concept of truth
5.2 p.133 In English 'evidence' is a mass term, qualified by 'little' and 'more'
6 p.153 Possibilities are like possible worlds, but not fully determinate or complete
6.2 p.159 To say there could have been people who don't exist, but deny those possible things, rejects Barcan
6.4 p.166 Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right
6.4 n16 p.166 S5 is the logic of logical necessity
6.6 p.181 'True at a possibility' means necessarily true if what is said had obtained
7 p.184 If truth-tables specify the connectives, classical logic must rely on Bivalence
7.1 p.185 If two possibilities can't share a determiner, they are incompatible
7.1 p.185 The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A
7.2 p.196 Medieval logicians said understanding A also involved understanding not-A
7.2 p.196 Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic
7.4 p.215 Infinitesimals do not stand in a determinate order relation to zero
7.5 p.219 Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics
8.4 p.240 A set may well not consist of its members; the empty set, for example, is a problem
8.4 p.241 A set can be determinate, because of its concept, and still have vague membership
8.5 p.47 An object that is not clearly red or orange can still be red-or-orange, which sweeps up problem cases
8.5 p.245 The extension of a colour is decided by a concept's place in a network of contraries
8.7 p.261 When faced with vague statements, Bivalence is not a compelling principle
9.1 p.267 Categoricity implies that Dedekind has characterised the numbers, because it has one domain
9.2 p.275 Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set
9.3 p.277 The iterated conception of set requires continual increase in axiom strength
9.6 p.292 If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom
9.6 p.298 Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry)