59 ideas
18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
2653 | If the parts of the universe are subject to the law of nature, the whole universe must also be subject to it [Cicero] |
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] |
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] |
8840 | There are five possible responses to the problem of infinite regress in justification [Cleve] |
18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
8841 | Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve] |
2628 | Why would mind mix with matter if it didn't need it? [Cicero] |
18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
20814 | Eloquence educates, exhorts, comforts, distracts and unites us, and raises us from savagery [Cicero] |
18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt] |
2640 | We have the death penalty, but still have thousands of robbers [Cicero] |
2652 | Some regard nature simply as an irrational force that imparts movement [Cicero] |
2645 | Why shouldn't the gods fear their own destruction? [Cicero] |
2627 | I wonder whether loss of reverence for the gods would mean the end of all virtue [Cicero] |
2651 | God doesn't obey the laws of nature; they are subject to the law of God [Cicero] |
2634 | It seems clear to me that we have an innate idea of the divine [Cicero] |
2636 | Many primitive people know nothing of the gods [Cicero] |
2650 | If a person cannot feel the power of God when looking at the stars, they are probably incapable of feeling [Cicero] |
2655 | If the barbarians of Britain saw a complex machine, they would be baffled, but would know it was designed [Cicero] |
2656 | Chance is no more likely to create the world than spilling lots of letters is likely to create a famous poem [Cicero] |
2647 | It is obvious from order that someone is in charge, as when we visit a gymnasium [Cicero] |
2657 | If everything with regular movement and order is divine, then recurrent illnesses must be divine [Cicero] |
2638 | Either the gods are identical, or one is more beautiful than another [Cicero] |
2635 | The gods are happy, so virtuous, so rational, so must have human shape [Cicero] |
2641 | Why believe in gods if you have never seen them? [Cicero] |
2659 | The lists of good men who have suffered and bad men who have prospered are endless [Cicero] |
2658 | The gods blame men for having vices, but they could have given us enough reason to avoid them [Cicero] |