94 ideas
| 18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
| 9376 | A sentence may simultaneously define a term, and also assert a fact [Boghossian] |
| 18819 | The idea that there are unrecognised truths is basic to our concept of truth [Rumfitt] |
| 18826 | 'True at a possibility' means necessarily true if what is said had obtained [Rumfitt] |
| 6345 | Minimalism is incoherent, as it implies that truth both is and is not a property [Boghossian, by Horwich] |
| 18803 | Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables [Rumfitt] |
| 12204 | The logic of metaphysical necessity is S5 [Rumfitt] |
| 18814 | 'Absolute necessity' would have to rest on S5 [Rumfitt] |
| 18798 | It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt] |
| 18799 | Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt] |
| 18830 | Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt] |
| 18843 | The iterated conception of set requires continual increase in axiom strength [Rumfitt] |
| 18836 | A set may well not consist of its members; the empty set, for example, is a problem [Rumfitt] |
| 18837 | A set can be determinate, because of its concept, and still have vague membership [Rumfitt] |
| 18845 | If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt] |
| 18815 | Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt] |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| 9390 | Logic guides thinking, but it isn't a substitute for it [Rumfitt] |
| 18805 | Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt] |
| 18804 | The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt] |
| 18827 | If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt] |
| 12195 | Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt] |
| 12199 | There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt] |
| 12201 | We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt] |
| 18813 | Logical consequence is a relation that can extended into further statements [Rumfitt] |
| 18808 | Normal deduction presupposes the Cut Law [Rumfitt] |
| 18840 | When faced with vague statements, Bivalence is not a compelling principle [Rumfitt] |
| 12194 | Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt] |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| 18802 | In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt] |
| 12198 | Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt] |
| 18800 | Introduction rules give deduction conditions, and Elimination says what can be deduced [Rumfitt] |
| 9375 | Conventionalism agrees with realists that logic has truth values, but not over the source [Boghossian] |
| 18809 | Logical truths are just the assumption-free by-products of logical rules [Rumfitt] |
| 18807 | Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt] |
| 18842 | Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt] |
| 17462 | A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt] |
| 18834 | Infinitesimals do not stand in a determinate order relation to zero [Rumfitt] |
| 18846 | Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt] |
| 17461 | Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt] |
| 16661 | There are two sorts of category - referring to things, and to circumstances of things [Boethius] |
| 15035 | If universals are not separate, we can isolate them by abstraction [Boethius, by Panaccio] |
| 14665 | We can call the quality of Plato 'Platonity', and say it is a quality which only he possesses [Boethius] |
| 9389 | Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt] |
| 18839 | An object that is not clearly red or orange can still be red-or-orange, which sweeps up problem cases [Rumfitt] |
| 18838 | The extension of a colour is decided by a concept's place in a network of contraries [Rumfitt] |
| 14532 | A distinctive type of necessity is found in logical consequence [Rumfitt, by Hale/Hoffmann,A] |
| 18816 | Metaphysical modalities respect the actual identities of things [Rumfitt] |
| 12193 | Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt] |
| 12200 | A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt] |
| 12202 | Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [Rumfitt] |
| 18825 | S5 is the logic of logical necessity [Rumfitt] |
| 18824 | Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right [Rumfitt] |
| 18828 | If two possibilities can't share a determiner, they are incompatible [Rumfitt] |
| 12203 | If a world is a fully determinate way things could have been, can anyone consider such a thing? [Rumfitt] |
| 18821 | Possibilities are like possible worlds, but not fully determinate or complete [Rumfitt] |
| 18831 | Medieval logicians said understanding A also involved understanding not-A [Rumfitt] |
| 23308 | Reasoning relates to understanding as time does to eternity [Boethius, by Sorabji] |
| 9369 | 'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian] |
| 9367 | The a priori is explained as analytic to avoid a dubious faculty of intuition [Boghossian] |
| 9373 | That logic is a priori because it is analytic resulted from explaining the meaning of logical constants [Boghossian] |
| 9380 | We can't hold a sentence true without evidence if we can't agree which sentence is definitive of it [Boghossian] |
| 9384 | We may have strong a priori beliefs which we pragmatically drop from our best theory [Boghossian] |
| 9374 | If we learn geometry by intuition, how could this faculty have misled us for so long? [Boghossian] |
| 18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
| 5771 | Knowledge of present events doesn't make them necessary, so future events are no different [Boethius] |
| 5767 | Rational natures require free will, in order to have power of judgement [Boethius] |
| 5768 | God's universal foreknowledge seems opposed to free will [Boethius] |
| 5769 | Does foreknowledge cause necessity, or necessity cause foreknowledge? [Boethius] |
| 18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
| 9377 | 'Conceptual role semantics' says terms have meaning from sentences and/or inferences [Boghossian] |
| 9378 | If meaning depends on conceptual role, what properties are needed to do the job? [Boghossian] |
| 9372 | Could expressions have meaning, without two expressions possibly meaning the same? [Boghossian] |
| 17721 | There are no truths in virtue of meaning, but there is knowability in virtue of understanding [Boghossian, by Jenkins] |
| 9368 | Epistemological analyticity: grasp of meaning is justification; metaphysical: truth depends on meaning [Boghossian] |
| 18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt] |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| 5762 | The wicked want goodness, so they would not be wicked if they obtained it [Boethius] |
| 5770 | Rewards and punishments are not deserved if they don't arise from free movement of the mind [Boethius] |
| 5764 | When people fall into wickedness they lose their human nature [Boethius] |
| 5756 | Happiness is a good which once obtained leaves nothing more to be desired [Boethius] |
| 5763 | The bad seek the good through desire, but the good through virtue, which is more natural [Boethius] |
| 5759 | Varied aims cannot be good because they differ, but only become good when they unify [Boethius] |
| 5754 | You can't control someone's free mind, only their body and possessions [Boethius] |
| 16692 | Divine eternity is the all-at-once and complete possession of unending life [Boethius] |
| 5752 | Where does evil come from if there is a god; where does good come from if there isn't? [Boethius] |
| 5757 | God is the supreme good, so no source of goodness could take precedence over God [Boethius] |
| 5758 | God is the good [Boethius] |
| 5760 | The power through which creation remains in existence and motion I call 'God' [Boethius] |
| 5753 | The regular events of this life could never be due to chance [Boethius] |
| 5765 | The reward of the good is to become gods [Boethius] |
| 5761 | God can do anything, but he cannot do evil, so evil must be nothing [Boethius] |
| 5766 | If you could see the plan of Providence, you would not think there was evil anywhere [Boethius] |