71 ideas
| 14179 | The finest branch of wisdom is justice and moderation in ordering states and families [Plato] |
| 6947 | Metaphysics does not rest on facts, but on what we are inclined to believe [Peirce] |
| 18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
| 6937 | Reason aims to discover the unknown by thinking about the known [Peirce] |
| 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] |
| 21492 | Realism is basic to the scientific method [Peirce] |
| 6949 | If someone doubted reality, they would not actually feel dissatisfaction [Peirce] |
| 1607 | Diotima said the Forms are the objects of desire in philosophical discourse [Plato, by Roochnik] |
| 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] |
| 6940 | The feeling of belief shows a habit which will determine our actions [Peirce] |
| 6941 | We are entirely satisfied with a firm belief, even if it is false [Peirce] |
| 6942 | We want true beliefs, but obviously we think our beliefs are true [Peirce] |
| 6943 | A mere question does not stimulate a struggle for belief; there must be a real doubt [Peirce] |
| 174 | True opinion without reason is midway between wisdom and ignorance [Plato] |
| 6598 | We need our beliefs to be determined by some external inhuman permanency [Peirce] |
| 18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
| 6944 | Demonstration does not rest on first principles of reason or sensation, but on freedom from actual doubt [Peirce] |
| 6948 | Doubts should be satisfied by some external permanency upon which thinking has no effect [Peirce] |
| 6945 | Once doubt ceases, there is no point in continuing to argue [Peirce] |
| 180 | We call a person the same throughout life, but all their attributes change [Plato] |
| 181 | Only the gods stay unchanged; we replace our losses with similar acquisitions [Plato] |
| 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] |
| 4026 | Beauty is harmony with what is divine, and ugliness is lack of such harmony [Plato] |
| 172 | Love of ugliness is impossible [Plato] |
| 173 | Beauty and goodness are the same [Plato] |
| 183 | Stage two is the realisation that beauty of soul is of more value than beauty of body [Plato] |
| 184 | Progress goes from physical beauty, to moral beauty, to the beauty of knowledge, and reaches absolute beauty [Plato] |
| 171 | Music is a knowledge of love in the realm of harmony and rhythm [Plato] |
| 176 | Love follows beauty, wisdom is exceptionally beautiful, so love follows wisdom [Plato] |
| 179 | Love is desire for perpetual possession of the good [Plato] |
| 14177 | Love assists men in achieving merit and happiness [Plato] |
| 177 | If a person is good they will automatically become happy [Plato] |
| 14178 | Happiness is secure enjoyment of what is good and beautiful [Plato] |
| 170 | The only slavery which is not dishonourable is slavery to excellence [Plato] |
| 182 | The first step on the right path is the contemplation of physical beauty when young [Plato] |
| 6939 | What is true of one piece of copper is true of another (unlike brass) [Peirce] |
| 6938 | Natural selection might well fill an animal's mind with pleasing thoughts rather than true ones [Peirce] |
| 175 | Gods are not lovers of wisdom, because they are already wise [Plato] |
| 6946 | If death is annihilation, belief in heaven is a cheap pleasure with no disappointment [Peirce] |