81 ideas
17240 | Definitions are the first step in philosophy [Hobbes] |
18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
17237 | Definitions of things that are caused must express their manner of generation [Hobbes] |
17239 | Definition is resolution of names into successive genera, and finally the difference [Hobbes] |
17241 | A defined name should not appear in the definition [Hobbes] |
17242 | 'Petitio principii' is reusing the idea to be defined, in disguised words [Hobbes] |
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] |
17245 | A part of a part is a part of a whole [Hobbes] |
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] |
17258 | If we just say one, one, one, one, we don't know where we have got to [Hobbes] |
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] |
17253 | Change is nothing but movement [Hobbes] |
16670 | Accidents are just modes of thinking about bodies [Hobbes] |
16621 | Accidents are not parts of bodies (like blood in a cloth); they have accidents as things have a size [Hobbes] |
16734 | The complete power of an event is just the aggregate of the qualities that produced it [Hobbes] |
17247 | The only generalities or universals are names or signs [Hobbes] |
14960 | Bodies are independent of thought, and coincide with part of space [Hobbes] |
17250 | If you separate the two places of one thing, you will also separate the thing [Hobbes] |
17249 | If you separated two things in the same place, you would also separate the places [Hobbes] |
17248 | If a whole body is moved, its parts must move with it [Hobbes] |
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] |
16790 | A body is always the same, whether the parts are together or dispersed [Hobbes] |
17244 | To make a whole, parts needn't be put together, but can be united in the mind [Hobbes] |
17233 | Particulars contain universal things [Hobbes] |
17246 | Some accidental features are permanent, unless the object perishes [Hobbes] |
17251 | The feature which picks out or names a thing is usually called its 'essence' [Hobbes] |
17257 | It is the same river if it has the same source, no matter what flows in it [Hobbes] |
12853 | Some individuate the ship by unity of matter, and others by unity of form [Hobbes] |
17256 | If a new ship were made of the discarded planks, would two ships be numerically the same? [Hobbes] |
16794 | As an infant, Socrates was not the same body, but he was the same human being [Hobbes] |
17255 | Two bodies differ when (at some time) you can say something of one you can't say of the other [Hobbes] |
18816 | Metaphysical modalities respect the actual identities of things [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] |
16582 | We can imagine a point swelling and contracting - but not how this could be done [Hobbes] |
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] |
17238 | Science aims to show causes and generation of things [Hobbes] |
17260 | Imagination is just weakened sensation [Hobbes] |
19373 | A 'conatus' is an initial motion, experienced by us as desire or aversion [Hobbes, by Arthur,R] |
2948 | Sensation is merely internal motion of the sentient being [Hobbes] |
17261 | Apart from pleasure and pain, the only emotions are appetite and aversion [Hobbes] |
17236 | Words are not for communication, but as marks for remembering what we have learned [Hobbes] |
18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
1554 | Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind] |
18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt] |
16600 | Prime matter is body considered with mere size and extension, and potential [Hobbes] |
17252 | Acting on a body is either creating or destroying a property in it [Hobbes] |
17254 | An effect needs a sufficient and necessary cause [Hobbes] |
17235 | A cause is the complete sum of the features which necessitate the effect [Hobbes] |
17234 | Motion is losing one place and acquiring another [Hobbes] |
17259 | 'Force' is the quantity of movement imposed on something [Hobbes] |
17243 | Past times can't exist anywhere, apart from in our memories [Hobbes] |
1555 | People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus] |
1543 | He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus] |
535 | The gods are just personified human benefits [Prodicus] |