86 ideas
| 18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
| 14092 | Philosophers are often too fussy about words, dismissing perfectly useful ordinary terms [Rosen] |
| 14100 | Figuring in the definition of a thing doesn't make it a part of that thing [Rosen] |
| 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] |
| 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] |
| 18851 | Pairing (with Extensionality) guarantees an infinity of sets, just from a single element [Rosen] |
| 18845 | If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt] |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| 18815 | Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt] |
| 9390 | Logic guides thinking, but it isn't a substitute for it [Rumfitt] |
| 18804 | The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt] |
| 18805 | Classical logic rules cannot be proved, but various lines of attack can be repelled [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] |
| 18802 | In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt] |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [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] |
| 18809 | Logical truths are just the assumption-free by-products of logical rules [Rumfitt] |
| 14096 | Explanations fail to be monotonic [Rosen] |
| 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] |
| 14097 | Things could be true 'in virtue of' others as relations between truths, or between truths and items [Rosen] |
| 14095 | Facts are structures of worldly items, rather like sentences, individuated by their ingredients [Rosen] |
| 14093 | An 'intrinsic' property is one that depends on a thing and its parts, and not on its relations [Rosen] |
| 8915 | How we refer to abstractions is much less clear than how we refer to other things [Rosen] |
| 18852 | A Meinongian principle might say that there is an object for any modest class of properties [Rosen] |
| 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] |
| 18849 | Metaphysical necessity is absolute and universal; metaphysical possibility is very tolerant [Rosen] |
| 18850 | 'Metaphysical' modality is the one that makes the necessity or contingency of laws of nature interesting [Rosen] |
| 18858 | Sets, universals and aggregates may be metaphysically necessary in one sense, but not another [Rosen] |
| 14094 | The excellent notion of metaphysical 'necessity' cannot be defined [Rosen] |
| 18857 | Standard Metaphysical Necessity: P holds wherever the actual form of the world holds [Rosen] |
| 18856 | Non-Standard Metaphysical Necessity: when ¬P is incompatible with the nature of things [Rosen] |
| 18816 | Metaphysical modalities respect the actual identities of things [Rumfitt] |
| 18848 | Something may be necessary because of logic, but is that therefore a special sort of necessity? [Rosen] |
| 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] |
| 18825 | S5 is the logic of logical necessity [Rumfitt] |
| 12202 | Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [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] |
| 18855 | Combinatorial theories of possibility assume the principles of combination don't change across worlds [Rosen] |
| 14101 | Are necessary truths rooted in essences, or also in basic grounding laws? [Rosen] |
| 18853 | A proposition is 'correctly' conceivable if an ominiscient being could conceive it [Rosen] |
| 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] |
| 18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
| 5692 | Introspection is not perception, because there are no extra qualities apart from the mental events themselves [Rosenthal] |
| 8917 | The Way of Abstraction used to say an abstraction is an idea that was formed by abstracting [Rosen] |
| 8912 | Nowadays abstractions are defined as non-spatial, causally inert things [Rosen] |
| 8913 | Chess may be abstract, but it has existed in specific space and time [Rosen] |
| 8914 | Sets are said to be abstract and non-spatial, but a set of books can be on a shelf [Rosen] |
| 8916 | Conflating abstractions with either sets or universals is a big claim, needing a big defence [Rosen] |
| 8918 | Functional terms can pick out abstractions by asserting an equivalence relation [Rosen] |
| 8919 | Abstraction by equivalence relationships might prove that a train is an abstract entity [Rosen] |
| 18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
| 14099 | 'Bachelor' consists in or reduces to 'unmarried' male, but not the other way around [Rosen] |
| 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] |
| 18854 | The MRL view says laws are the theorems of the simplest and strongest account of the world [Rosen] |
| 14098 | An acid is just a proton donor [Rosen] |