86 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] |
| 12204 | The logic of metaphysical necessity is S5 [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] |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| 18815 | Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt] |
| 9390 | Logic guides thinking, but it isn't a substitute for it [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] |
| 12195 | Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt] |
| 12199 | There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt] |
| 12201 | We reject deductions by bad consequence, so logical consequence can't be deduction [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] |
| 12194 | Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt] |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| 18802 | In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt] |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| 12198 | Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [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] |
| 17462 | A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [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] |
| 17461 | Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt] |
| 9389 | Vague membership of sets is possible if the set is defined by its concept, not its members [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] |
| 14532 | A distinctive type of necessity is found in logical consequence [Rumfitt, by Hale/Hoffmann,A] |
| 18816 | Metaphysical modalities respect the actual identities of things [Rumfitt] |
| 12193 | Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt] |
| 12200 | A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt] |
| 18825 | S5 is the logic of logical necessity [Rumfitt] |
| 12202 | Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [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] |
| 12203 | If a world is a fully determinate way things could have been, can anyone consider such a thing? [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] |
| 18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
| 17472 | Thick mechanisms map whole reactions, and thin mechanism chart the steps [Weisberg/Needham/Hendry] |
| 17471 | Using mechanisms as explanatory schemes began in chemistry [Weisberg/Needham/Hendry] |
| 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] |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| 23110 | Human injustice is not a permanent feature of communities [Rawls] |
| 15676 | Rawls defends the priority of right over good [Rawls, by Finlayson] |
| 4123 | A fair arrangement is one that parties can agree to without knowing how it will benefit them personally [Rawls, by Williams,B] |
| 21051 | Check your rationality by thinking of your opinion pronounced by the supreme court [Rawls] |
| 3279 | Utilitarianism inappropriately scales up the individual willingness to make sacrifices [Rawls, by Nagel] |
| 22406 | The maximisation of happiness must be done fairly [Rawls, by Smart] |
| 21137 | Rawls rejected cosmopolitanism because it doesn't respect the autonomy of 'peoples' [Rawls, by Shorten] |
| 3280 | Why does the rational agreement of the 'Original Position' in Rawls make it right? [Nagel on Rawls] |
| 20552 | The original position models the idea that citizens start as free and equal [Rawls, by Swift] |
| 18636 | Choose justice principles in ignorance of your own social situation [Rawls] |
| 18631 | All desirable social features should be equal, unless inequality favours the disadvantaged [Rawls] |
| 21119 | Power is only legitimate if it is reasonable for free equal citizens to endorse the constitution [Rawls] |
| 20538 | Utilitarians lump persons together; Rawls somewhat separates them; Nozick wholly separates them [Swift on Rawls] |
| 9277 | Rawls's account of justice relies on conventional fairness, avoiding all moral controversy [Gray on Rawls] |
| 23420 | In a pluralist society we can't expect a community united around one conception of the good [Rawls] |
| 20527 | Liberty Principle: everyone has an equal right to liberties, if compatible with others' liberties [Rawls] |
| 21018 | The social contract has problems with future generations, national boundaries, disabilities and animals [Rawls, by Nussbaum] |
| 21041 | Justice concerns not natural distributions, or our born location, but what we do about them [Rawls] |
| 23583 | If an aggression is unjust, the constraints on how it is fought are much stricter [Rawls] |
| 17465 | Lavoisier's elements included four types of earth [Weisberg/Needham/Hendry] |
| 17468 | Over 100,000,000 compounds have been discovered or synthesised [Weisberg/Needham/Hendry] |
| 17470 | Water molecules dissociate, and form large polymers, explaining its properties [Weisberg/Needham/Hendry] |
| 17473 | It is unlikely that chemistry will ever be reduced to physics [Weisberg/Needham/Hendry] |
| 17474 | Quantum theory won't tell us which structure a set of atoms will form [Weisberg/Needham/Hendry] |
| 17475 | For temperature to be mean kinetic energy, a state of equilibrium is also required [Weisberg/Needham/Hendry] |
| 17469 | 'H2O' just gives the element proportions, not the microstructure [Weisberg/Needham/Hendry] |
| 17467 | Isotopes (such as those of hydrogen) can vary in their rates of chemical reaction [Weisberg/Needham/Hendry] |
| 17466 | Mendeleev systematised the elements, and also gave an account of their nature [Weisberg/Needham/Hendry] |