105 ideas
18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
224 | When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato] |
232 | Opposites are as unlike as possible [Plato] |
8937 | Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato] |
18819 | The idea that there are unrecognised truths is basic to our concept of truth [Rumfitt] |
19160 | A comprehensive theory of truth probably includes a theory of predication [Davidson] |
19151 | Antirealism about truth prevents its use as an intersubjective standard [Davidson] |
19144 | 'Epistemic' truth depends what rational creatures can verify [Davidson] |
18826 | 'True at a possibility' means necessarily true if what is said had obtained [Rumfitt] |
19148 | There is nothing interesting or instructive for truths to correspond to [Davidson] |
19166 | The Slingshot assumes substitutions give logical equivalence, and thus identical correspondence [Davidson] |
19167 | Two sentences can be rephrased by equivalent substitutions to correspond to the same thing [Davidson] |
19150 | Coherence truth says a consistent set of sentences is true - which ties truth to belief [Davidson] |
19145 | We can explain truth in terms of satisfaction - but also explain satisfaction in terms of truth [Davidson] |
19146 | Satisfaction is a sort of reference, so maybe we can define truth in terms of reference? [Davidson] |
19174 | Axioms spell out sentence satisfaction. With no free variables, all sequences satisfy the truths [Davidson] |
19136 | Many say that Tarski's definitions fail to connect truth to meaning [Davidson] |
19139 | Tarski does not tell us what his various truth predicates have in common [Davidson] |
19147 | Truth is the basic concept, because Convention-T is agreed to fix the truths of a language [Davidson] |
19172 | To define a class of true sentences is to stipulate a possible language [Davidson] |
19153 | Truth is basic and clear, so don't try to replace it with something simpler [Davidson] |
19170 | Tarski is not a disquotationalist, because you can assign truth to a sentence you can't quote [Davidson] |
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] |
19140 | 'Satisfaction' is a generalised form of reference [Davidson] |
18807 | Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt] |
13986 | Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle] |
14150 | Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato] |
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] |
16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
229 | The one was and is and will be and was becoming and is becoming and will become [Plato] |
21821 | Plato's Parmenides has a three-part theory, of Primal One, a One-Many, and a One-and-Many [Plato, by Plotinus] |
221 | Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato] |
19173 | Treating predicates as sets drops the predicate for a new predicate 'is a member of', which is no help [Davidson] |
223 | If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato] |
227 | You must always mean the same thing when you utter the same name [Plato] |
210 | It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato] |
220 | The concept of a master includes the concept of a slave [Plato] |
211 | If admirable things have Forms, maybe everything else does as well [Plato] |
219 | If absolute ideas existed in us, they would cease to be absolute [Plato] |
228 | Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato] |
16151 | Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M] |
215 | If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato] |
212 | The whole idea of each Form must be found in each thing which participates in it [Plato] |
218 | Participation is not by means of similarity, so we are looking for some other method of participation [Plato] |
213 | Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato] |
216 | If things are made alike by participating in something, that thing will be the absolute idea [Plato] |
217 | Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato] |
214 | If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato] |
15851 | Parts must belong to a created thing with a distinct form [Plato] |
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] |
15846 | In Parmenides, if composition is identity, a whole is nothing more than its parts [Plato, by Harte,V] |
15849 | Plato says only a one has parts, and a many does not [Plato, by Harte,V] |
15850 | Anything which has parts must be one thing, and parts are of a one, not of a many [Plato] |
13259 | It seems that the One must be composed of parts, which contradicts its being one [Plato] |
15847 | Two things relate either as same or different, or part of a whole, or the whole of the part [Plato] |
18816 | Metaphysical modalities respect the actual identities of things [Rumfitt] |
18825 | S5 is the logic of logical necessity [Rumfitt] |
18828 | If two possibilities can't share a determiner, they are incompatible [Rumfitt] |
18824 | Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right [Rumfitt] |
19142 | Probability can be constrained by axioms, but that leaves open its truth nature [Davidson] |
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] |
19169 | Predicates are a source of generality in sentences [Davidson] |
19149 | If we reject corresponding 'facts', we should also give up the linked idea of 'representations' [Davidson] |
19163 | You only understand an order if you know what it is to obey it [Davidson] |
19152 | Utterances have the truth conditions intended by the speaker [Davidson] |
18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
19162 | Meaning involves use, but a sentence has many uses, while meaning stays fixed [Davidson] |
19131 | We recognise sentences at once as linguistic units; we then figure out their parts [Davidson] |
19156 | Modern predicates have 'places', and are sentences with singular terms deleted from the places [Davidson] |
19176 | The concept of truth can explain predication [Davidson] |
19133 | If you assign semantics to sentence parts, the sentence fails to compose a whole [Davidson] |
19132 | Top-down semantic analysis must begin with truth, as it is obvious, and explains linguistic usage [Davidson] |
19158 | 'Humanity belongs to Socrates' is about humanity, so it's a different proposition from 'Socrates is human' [Davidson] |
18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt] |
19154 | The principle of charity says an interpreter must assume the logical constants [Davidson] |
19161 | We indicate use of a metaphor by its obvious falseness, or trivial truth [Davidson] |
222 | Only a great person can understand the essence of things, and an even greater person can teach it [Plato] |
225 | The unlimited has no shape and is endless [Plato] |
233 | Some things do not partake of the One [Plato] |
2062 | The only movement possible for the One is in space or in alteration [Plato] |
231 | Everything partakes of the One in some way [Plato] |
234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |