61 ideas
22438 | Philosophy is largely concerned with finding the minimum that science could get by with [Quine] |
18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
22436 | Logicians don't paraphrase logic into language, because they think in the symbolic language [Quine] |
22431 | Good algorithms and theories need many occurrences of just a few elements [Quine] |
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] |
22435 | The logician's '→' does not mean the English if-then [Quine] |
18814 | 'Absolute necessity' would have to rest on S5 [Rumfitt] |
22433 | It is important that the quantification over temporal entities is timeless [Quine] |
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] |
22437 | Logical languages are rooted in ordinary language, and that connection must be kept [Quine] |
18840 | When faced with vague statements, Bivalence is not a compelling principle [Rumfitt] |
22434 | Reduction to logical forms first simplifies idioms and grammar, then finds a single reading of it [Quine] |
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] |
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] |
22432 | Normally conditionals have no truth value; it is the consequent which has a conditional truth value [Quine] |
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] |
22430 | If we understand a statement, we know the circumstances of its truth [Quine] |
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] |
6248 | Reason is too slow and doubtful to guide all actions, which need external and moral senses [Hutcheson] |
6238 | We approve of actions by a superior moral sense [Hutcheson] |
6239 | We dislike a traitor, even if they give us great benefit [Hutcheson] |
6240 | The moral sense is not an innate idea, but an ability to approve or disapprove in a disinterested way [Hutcheson] |
6242 | We cannot choose our moral feelings, otherwise bribery could affect them [Hutcheson] |
6247 | Everyone feels uneasy when seeing others in pain, unless the others are evil [Hutcheson] |
6244 | Human nature seems incapable of universal malice, except what results from self-love [Hutcheson] |
6243 | As death approaches, why do we still care about family, friends or country? [Hutcheson] |
6246 | My action is not made good by a good effect, if I did not foresee and intend it [Hutcheson] |
6241 | Contempt of danger is just madness if it is not in some worthy cause [Hutcheson] |
6245 | That action is best, which procures the greatest happiness for the greatest number [Hutcheson] |
6251 | The loss of perfect rights causes misery, but the loss of imperfect rights reduces social good [Hutcheson] |
13713 | Quine holds time to be 'space-like': past objects are as real as spatially remote ones [Quine, by Sider] |
6250 | We say God is good if we think everything he does aims at the happiness of his creatures [Hutcheson] |
6249 | If goodness is constituted by God's will, it is a tautology to say God's will is good [Hutcheson] |