55 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] |
| 23634 | Accepting the existence of anything presupposes the notion of existence [Reid] |
| 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] |
| 18831 | Medieval logicians said understanding A also involved understanding not-A [Rumfitt] |
| 23635 | Truths are self-evident to sensible persons who understand them clearly without prejudice [Reid] |
| 6230 | If the soul were a tabula rasa, with no innate ideas, there could be no moral goodness or justice [Cudworth] |
| 7631 | Sensation is not committed to any external object, but perception is [Reid] |
| 23637 | Primary qualities are the object of mathematics [Reid] |
| 23638 | Secondary qualities conjure up, and are confused with, the sensations which produce them [Reid] |
| 23639 | It is unclear whether a toothache is in the mind or in the tooth, but the word has a single meaning [Reid] |
| 6228 | Senses cannot judge one another, so what judges senses cannot be a sense, but must be superior [Cudworth] |
| 6492 | Reid is seen as the main direct realist of the eighteenth century [Reid, by Robinson,H] |
| 23641 | People dislike believing without evidence, and try to avoid it [Reid] |
| 18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
| 23642 | If non-rational evidence reaches us, it is reason which then makes use of it [Reid] |
| 6229 | Sense is fixed in the material form, and so can't grasp abstract universals [Cudworth] |
| 23640 | Only mature minds can distinguish the qualities of a body [Reid] |
| 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] |
| 6227 | Keeping promises and contracts is an obligation of natural justice [Cudworth] |
| 6225 | Obligation to obey all positive laws is older than all laws [Cudworth] |
| 6224 | An omnipotent will cannot make two things equal or alike if they aren't [Cudworth] |
| 6223 | If the will and pleasure of God controls justice, then anything wicked or unjust would become good if God commanded it [Cudworth] |
| 6226 | The requirement that God must be obeyed must precede any authority of God's commands [Cudworth] |