80 ideas
| 18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
| 5486 | Essentialism says metaphysics can't be done by analysing unreliable language [Ellis] |
| 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] |
| 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] |
| 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] |
| 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] |
| 18802 | In specifying a logical constant, use of that constant is quite unavoidable [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] |
| 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] |
| 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] |
| 5468 | Properties are 'dispositional', or 'categorical' (the latter as 'block' or 'intrinsic' structures) [Ellis, by PG] |
| 5469 | The passive view of nature says categorical properties are basic, but others say dispositions [Ellis] |
| 5456 | Redness is not a property as it is not mind-independent [Ellis] |
| 5481 | Properties have powers; they aren't just ways for logicians to classify objects [Ellis] |
| 5458 | Nearly all fundamental properties of physics are dispositional [Ellis] |
| 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] |
| 5443 | Kripke and others have made essentialism once again respectable [Ellis] |
| 5444 | 'Individual essences' fix a particular individual, and 'kind essences' fix the kind it belongs to [Ellis] |
| 5462 | Essential properties are usually quantitatively determinate [Ellis] |
| 5448 | 'Real essence' makes it what it is; 'nominal essence' makes us categorise it a certain way [Ellis] |
| 5477 | One thing can look like something else, without being the something else [Ellis] |
| 18816 | Metaphysical modalities respect the actual identities of things [Rumfitt] |
| 18825 | S5 is the logic of logical necessity [Rumfitt] |
| 5479 | Scientific essentialists say science should define the limits of the possible [Ellis] |
| 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] |
| 5483 | Essentialists deny possible worlds, and say possibilities are what is compatible with the actual world [Ellis] |
| 5447 | Metaphysical necessities are true in virtue of the essences of things [Ellis] |
| 5476 | Essentialists say natural laws are in a new category: necessary a posteriori [Ellis] |
| 5478 | Imagination tests what is possible for all we know, not true possibility [Ellis] |
| 5482 | Possible worlds realism is only needed to give truth conditions for modals and conditionals [Ellis] |
| 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] |
| 5453 | Essentialists mostly accept the primary/secondary qualities distinction [Ellis] |
| 5466 | Primary qualities are number, figure, size, texture, motion, configuration, impenetrability and (?) mass [Ellis] |
| 18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
| 5485 | Emeralds are naturally green, and only an external force could turn them blue [Ellis] |
| 5484 | Essentialists don't infer from some to all, but from essences to necessary behaviour [Ellis] |
| 18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
| 5457 | Predicates assert properties, values, denials, relations, conventions, existence and fabrications [Ellis, by PG] |
| 18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt] |
| 5488 | Regularity theories of causation cannot give an account of human agency [Ellis] |
| 5489 | Humans have variable dispositions, and also power to change their dispositions [Ellis] |
| 5490 | Essentialism fits in with Darwinism, but not with extreme politics of left or right [Ellis] |
| 541 | Virtue comes more from habit than character [Critias] |
| 5472 | Natural kinds are of objects/substances, or events/processes, or intrinsic natures [Ellis] |
| 5471 | Essentialism says natural kinds are fundamental to nature, and determine the laws [Ellis] |
| 5446 | For essentialists two members of a natural kind must be identical [Ellis] |
| 5480 | The whole of our world is a natural kind, so all worlds like it necessarily have the same laws [Ellis] |
| 5445 | Essentialists regard inanimate objects as genuine causal agents [Ellis] |
| 5463 | Essentialists believe causation is necessary, resulting from dispositions and circumstances [Ellis] |
| 5491 | A general theory of causation is only possible in an area if natural kinds are involved [Ellis] |
| 5442 | For 'passivists' behaviour is imposed on things from outside [Ellis] |
| 5473 | The laws of nature imitate the hierarchy of natural kinds [Ellis] |
| 5474 | Laws of nature tend to describe ideal things, or ideal circumstances [Ellis] |
| 5475 | We must explain the necessity, idealisation, ontology and structure of natural laws [Ellis] |
| 5460 | Causal relations cannot be reduced to regularities, as they could occur just once [Ellis] |
| 5459 | Essentialists say dispositions are basic, rather than supervenient on matter and natural laws [Ellis] |
| 5461 | The essence of uranium is its atomic number and its electron shell [Ellis] |
| 5464 | For essentialists, laws of nature are metaphysically necessary, being based on essences of natural kinds [Ellis] |
| 5487 | Essentialism requires a clear separation of semantics, epistemology and ontology [Ellis] |
| 542 | Fear of the gods was invented to discourage secret sin [Critias] |