111 ideas
| 18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
| 13395 | If an analysis shows the features of a concept, it doesn't seem to 'reduce' the concept [Jubien] |
| 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] |
| 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] |
| 9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
| 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] |
| 13378 | It is a mistake to think that the logic developed for mathematics can clarify language and philosophy [Jubien] |
| 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] |
| 13402 | We only grasp a name if we know whether to apply it when the bearer changes [Jubien] |
| 13405 | The baptiser picks the bearer of a name, but social use decides the category [Jubien] |
| 13399 | Examples show that ordinary proper names are not rigid designators [Jubien] |
| 13398 | We could make a contingent description into a rigid and necessary one by adding 'actual' to it [Jubien] |
| 11115 | 'All horses' either picks out the horses, or the things which are horses [Jubien] |
| 13392 | Philosophers reduce complex English kind-quantifiers to the simplistic first-order quantifier [Jubien] |
| 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] |
| 18809 | Logical truths are just the assumption-free by-products of logical rules [Rumfitt] |
| 9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
| 18807 | Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt] |
| 9965 | There couldn't just be one number, such as 17 [Jubien] |
| 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] |
| 9966 | The subject-matter of (pure) mathematics is abstract structure [Jubien] |
| 9962 | How can pure abstract entities give models to serve as interpretations? [Jubien] |
| 9963 | If we all intuited mathematical objects, platonism would be agreed [Jubien] |
| 9964 | Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien] |
| 13404 | To exist necessarily is to have an essence whose own essence must be instantiated [Jubien] |
| 13386 | If objects are just conventional, there is no ontological distinction between stuff and things [Jubien] |
| 13403 | The category of Venus is not 'object', or even 'planet', but a particular class of good-sized object [Jubien] |
| 11116 | Being a physical object is our most fundamental category [Jubien] |
| 9969 | The empty set is the purest abstract object [Jubien] |
| 13375 | The idea that every entity must have identity conditions is an unfortunate misunderstanding [Jubien] |
| 11117 | Haecceities implausibly have no qualities [Jubien] |
| 13393 | Any entity has the unique property of being that specific entity [Jubien] |
| 13388 | It is incoherent to think that a given entity depends on its kind for its existence [Jubien] |
| 13384 | Objects need conventions for their matter, their temporal possibility, and their spatial possibility [Jubien] |
| 13385 | Basically, the world doesn't have ready-made 'objects'; we carve objects any way we like [Jubien] |
| 13383 | If the statue is loved and the clay hated, that is about the object first qua statue, then qua clay [Jubien] |
| 13400 | If one entity is an object, a statue, and some clay, these come apart in at least three ways [Jubien] |
| 13401 | The idea of coincident objects is a last resort, as it is opposed to commonsense naturalism [Jubien] |
| 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] |
| 13380 | Parts seem to matter when it is just an object, but not matter when it is a kind of object [Jubien] |
| 13376 | We should not regard essentialism as just nontrivial de re necessity [Jubien] |
| 13381 | Thinking of them as 'ships' the repaired ship is the original, but as 'objects' the reassembly is the original [Jubien] |
| 13382 | Rearranging the planks as a ship is confusing; we'd say it was the same 'object' with a different arrangement [Jubien] |
| 13379 | If two objects are indiscernible across spacetime, how could we decide whether or not they are the same? [Jubien] |
| 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] |
| 13394 | Entailment does not result from mutual necessity; mutual necessity ensures entailment [Jubien] |
| 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] |
| 11119 | De re necessity is just de dicto necessity about object-essences [Jubien] |
| 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] |
| 13391 | Modality concerns relations among platonic properties [Jubien] |
| 13374 | To analyse modality, we must give accounts of objects, properties and relations [Jubien] |
| 11118 | Modal propositions transcend the concrete, but not the actual [Jubien] |
| 11108 | Your properties, not some other world, decide your possibilities [Jubien] |
| 11111 | Modal truths are facts about parts of this world, not about remote maximal entities [Jubien] |
| 11105 | We have no idea how many 'possible worlds' there might be [Jubien] |
| 11109 | If other worlds exist, then they are scattered parts of the actual world [Jubien] |
| 11106 | If all possible worlds just happened to include stars, their existence would be necessary [Jubien] |
| 11107 | If there are no other possible worlds, do we then exist necessarily? [Jubien] |
| 11112 | Possible worlds just give parallel contingencies, with no explanation at all of necessity [Jubien] |
| 11113 | Worlds don't explain necessity; we use necessity to decide on possible worlds [Jubien] |
| 13389 | The love of possible worlds is part of the dream that technical logic solves philosophical problems [Jubien] |
| 13390 | Possible worlds don't explain necessity, because they are a bunch of parallel contingencies [Jubien] |
| 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] |
| 11110 | We mustn't confuse a similar person with the same person [Jubien] |
| 18831 | Medieval logicians said understanding A also involved understanding not-A [Rumfitt] |
| 18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
| 13396 | Analysing mental concepts points to 'inclusionism' - that mental phenomena are part of the physical [Jubien] |
| 18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
| 13377 | First-order logic tilts in favour of the direct reference theory, in its use of constants for objects [Jubien] |
| 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] |
| 7346 | Jeremiah implied a link between weakness and goodness, and the evil of the state [Jeremiah, by Johnson,P] |
| 22920 | Do I not fill heaven and earth? saith the Lord [Jeremiah] |
| 22089 | Am I a God afar off, and not a God close at hand? [Jeremiah] |