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Ideas of Stephen Read, by Text

[British, fl. 2001, Professor at St Andrew's University.]

1994 Formal and Material Consequence
'Logic' p.245 If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter
'Logic' p.245 Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible
'Reduct' p.240 If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence
'Repres' p.243 In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway
'Repres' p.244 Logical connectives contain no information, but just record combination relations between facts
'Repres' p.244 Conditionals are just a shorthand for some proof, leaving out the details
'Suppress' p.242 Maybe arguments are only valid when suppressed premises are all stated - but why?
1995 Thinking About Logic
Ch.1 p.9 A proposition objectifies what a sentence says, as indicative, with secure references
Ch.2 p.35 A theory of logical consequence is a conceptual analysis, and a set of validity techniques
Ch.2 p.39 A logical truth is the conclusion of a valid inference with no premisses
Ch.2 p.41 The non-emptiness of the domain is characteristic of classical logic
Ch.2 p.43 A theory is logically closed, which means infinite premisses
Ch.2 p.43 Compactness does not deny that an inference can have infinitely many premisses
Ch.2 p.43 Compactness is when any consequence of infinite propositions is the consequence of a finite subset
Ch.2 p.44 Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite)
Ch.2 p.44 Compactness makes consequence manageable, but restricts expressive power
Ch.2 p.47 In second-order logic the higher-order variables range over all the properties of the objects
Ch.2 p.47 Although second-order arithmetic is incomplete, it can fully model normal arithmetic
Ch.2 p.49 Second-order arithmetic covers all properties, ensuring categoricity
Ch.2 p.51 A possible world is a determination of the truth-values of all propositions of a domain
Ch.2 p.51 How can modal Platonists know the truth of a modal proposition?
Ch.2 p.52 Knowledge of possible worlds is not causal, but is an ontology entailed by semantics
Ch.2 p.53 Logical consequence isn't just a matter of form; it depends on connections like round-square
Ch.2 p.54 Not all validity is captured in first-order logic
Ch.2 p.54 We should exclude second-order logic, precisely because it captures arithmetic
Ch.2 p.59 Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism'
Ch.2 p.62 Any first-order theory of sets is inadequate
Ch.3 p.66 The standard view of conditionals is that they are truth-functional
Ch.3 p.72 The point of conditionals is to show that one will accept modus ponens
Ch.4 p.101 A haecceity is a set of individual properties, essential to each thing
Ch.4 p.106 Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions)
Ch.4 p.106 Von Neumann numbers are helpful, but don't correctly describe numbers
Ch.4 p.107 The mind abstracts ways things might be, which are nonetheless real
Ch.4 p.117 If worlds are concrete, objects can't be present in more than one, and can only have counterparts
Ch.4 p.118 Equating necessity with truth in every possible world is the S5 conception of necessity
Ch.4 p.118 Equating necessity with informal provability is the S4 conception of necessity
Ch.4 p.118 Necessity is provability in S4, and true in all worlds in S5
Ch.5 p.123 Negative existentials with compositionality make the whole sentence meaningless
Ch.5 p.124 Russell started a whole movement in philosophy by providing an analysis of descriptions
Ch.5 p.125 Quantifiers are second-order predicates
Ch.5 p.133 Same say there are positive, negative and neuter free logics
Ch.5 p.140 A 'supervaluation' gives a proposition consistent truth-value for classical assignments
Ch.5 p.142 Identities and the Indiscernibility of Identicals don't work with supervaluations
Ch.6 p.154 Self-reference paradoxes seem to arise only when falsity is involved
Ch.7 p.178 Would a language without vagueness be usable at all?
Ch.7 p.184 Some people even claim that conditionals do not express propositions
Ch.7 p.189 There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers
Ch.7 p.200 Supervaluations say there is a cut-off somewhere, but at no particular place
Ch.8 p.214 Realisms like the full Comprehension Principle, that all good concepts determine sets
Ch.8 p.236 Infinite cuts and successors seems to suggest an actual infinity there waiting for us
Ch.9 p.229 Semantics must precede proof in higher-order logics, since they are incomplete