1994 | Formal and Material Consequence |
'Logic' | p.245 | 14188 | Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible |
'Logic' | p.245 | 14187 | If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter |
'Reduct' | p.240 | 14182 | If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence |
'Repres' | p.243 | 14184 | In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway |
'Repres' | p.244 | 14186 | Logical connectives contain no information, but just record combination relations between facts |
'Repres' | p.244 | 14185 | Conditionals are just a shorthand for some proof, leaving out the details |
'Suppress' | p.242 | 14183 | Maybe arguments are only valid when suppressed premises are all stated - but why? |
1995 | Thinking About Logic |
Ch.1 | p.9 | 10966 | A proposition objectifies what a sentence says, as indicative, with secure references |
Ch.2 | p.35 | 10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques |
Ch.2 | p.39 | 10971 | A logical truth is the conclusion of a valid inference with no premisses |
Ch.2 | p.41 | 10972 | The non-emptiness of the domain is characteristic of classical logic |
Ch.2 | p.43 | 10973 | A theory is logically closed, which means infinite premisses |
Ch.2 | p.43 | 10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset |
Ch.2 | p.43 | 10975 | Compactness does not deny that an inference can have infinitely many premisses |
Ch.2 | p.44 | 10976 | Compactness makes consequence manageable, but restricts expressive power |
Ch.2 | p.44 | 10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) |
Ch.2 | p.47 | 10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic |
Ch.2 | p.47 | 10978 | In second-order logic the higher-order variables range over all the properties of the objects |
Ch.2 | p.49 | 10980 | Second-order arithmetic covers all properties, ensuring categoricity |
Ch.2 | p.51 | 10981 | A possible world is a determination of the truth-values of all propositions of a domain |
Ch.2 | p.51 | 10982 | How can modal Platonists know the truth of a modal proposition? |
Ch.2 | p.52 | 10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics |
Ch.2 | p.53 | 10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square |
Ch.2 | p.54 | 10986 | Not all validity is captured in first-order logic |
Ch.2 | p.54 | 10985 | We should exclude second-order logic, precisely because it captures arithmetic |
Ch.2 | p.59 | 10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' |
Ch.2 | p.62 | 10988 | Any first-order theory of sets is inadequate |
Ch.3 | p.66 | 10989 | The standard view of conditionals is that they are truth-functional |
Ch.3 | p.72 | 10992 | The point of conditionals is to show that one will accept modus ponens |
Ch.4 | p.101 | 10995 | A haecceity is a set of individual properties, essential to each thing |
Ch.4 | p.106 | 10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) |
Ch.4 | p.106 | 10997 | Von Neumann numbers are helpful, but don't correctly describe numbers |
Ch.4 | p.107 | 10998 | The mind abstracts ways things might be, which are nonetheless real |
Ch.4 | p.117 | 11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts |
Ch.4 | p.118 | 11001 | Equating necessity with truth in every possible world is the S5 conception of necessity |
Ch.4 | p.118 | 11002 | Equating necessity with informal provability is the S4 conception of necessity |
Ch.4 | p.118 | 11004 | Necessity is provability in S4, and true in all worlds in S5 |
Ch.5 | p.123 | 11005 | Negative existentials with compositionality make the whole sentence meaningless |
Ch.5 | p.124 | 11006 | Russell started a whole movement in philosophy by providing an analysis of descriptions |
Ch.5 | p.125 | 11007 | Quantifiers are second-order predicates |
Ch.5 | p.133 | 11011 | Same say there are positive, negative and neuter free logics |
Ch.5 | p.140 | 11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments |
Ch.5 | p.142 | 11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations |
Ch.6 | p.154 | 11014 | Self-reference paradoxes seem to arise only when falsity is involved |
Ch.7 | p.178 | 11016 | Would a language without vagueness be usable at all? |
Ch.7 | p.184 | 11017 | Some people even claim that conditionals do not express propositions |
Ch.7 | p.189 | 11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers |
Ch.7 | p.200 | 11019 | Supervaluations say there is a cut-off somewhere, but at no particular place |
Ch.8 | p.214 | 11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets |
Ch.8 | p.236 | 11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us |
Ch.9 | p.229 | 11024 | Semantics must precede proof in higher-order logics, since they are incomplete |