56 ideas
| 18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
| 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] |
| 21812 | Being is the product of pure intellect [Plotinus] |
| 21817 | The One does not exist, but is the source of all existence [Plotinus] |
| 21824 | The One is a principle which transcends Being [Plotinus] |
| 21813 | Number determines individual being [Plotinus] |
| 17945 | Forms are not a theory of universals, but an attempt to explain how predication is possible [Nehamas] |
| 17946 | Only Tallness really is tall, and other inferior tall things merely participate in the tallness [Nehamas] |
| 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] |
| 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] |
| 18821 | Possibilities are like possible worlds, but not fully determinate or complete [Rumfitt] |
| 17944 | 'Episteme' is better translated as 'understanding' than as 'knowledge' [Nehamas] |
| 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] |
| 5506 | If soul was like body, its parts would be separate, without communication [Plotinus] |
| 21827 | The movement of Soul is continuous, but we are only aware of the parts of it that are sensed [Plotinus] |
| 21828 | A person is the whole of their soul [Plotinus] |
| 21809 | Our soul has the same ideal nature as the oldest god, and is honourable above the body [Plotinus] |
| 21825 | The soul is outside of all of space, and has no connection to the bodily order [Plotinus] |
| 18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
| 18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt] |
| 21826 | The Soul reasons about the Right, so there must be some permanent Right about which it reasons [Plotinus] |
| 6922 | Ecstasy is for the neo-Platonist the highest psychological state of man [Plotinus, by Feuerbach] |
| 21814 | How can multiple existence arise from the unified One? [Plotinus] |
| 21816 | Soul is the logos of Nous, just as Nous is the logos of the One [Plotinus] |
| 21815 | Because the One is immobile, it must create by radiation, light the sun producing light [Plotinus] |
| 21808 | Soul is author of all of life, and of the stars, and it gives them law and movement [Plotinus] |
| 21811 | Even the soul is secondary to the Intellectual-Principle [Nous], of which soul is an utterance [Plotinus] |