87 ideas
23027 | Ideals and metaphysics are practical, not imaginative or speculative [Green,TH, by Muirhead] |
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] |
23030 | Truth is a relation to a whole of organised knowledge in the collection of rational minds [Green,TH, by Muirhead] |
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] |
16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
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] |
23044 | All knowledge rests on a fundamental unity between the knower and what is known [Green,TH, by Muirhead] |
18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
23034 | The ultimate test for truth is the systematic interdependence in nature [Green,TH, by Muirhead] |
23029 | Knowledge is secured by the relations between its parts, through differences and identities [Green,TH, by Muirhead] |
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] |
23035 | The good life aims at perfections, or absolute laws, or what is absolutely desirable [Green,TH] |
23032 | What is distinctive of human life is the desire for self-improvement [Green,TH, by Muirhead] |
23033 | Hedonism offers no satisfaction, because what we desire is self-betterment [Green,TH, by Muirhead] |
23046 | States only have full authority if they heed the claims of human fellowship [Green,TH] |
23045 | Politics is compromises, which seem supported by a social contract, but express the will of no one [Green,TH] |
23050 | The ideal is a society in which all citizens are ladies and gentlemen [Green,TH] |
23052 | Enfranchisement is an end in itself; it makes a person moral, and gives a basis for respect [Green,TH] |
23036 | The good is identified by the capacities of its participants [Green,TH, by Muirhead] |
23039 | A true state is only unified and stabilised by acknowledging individuality [Green,TH, by Muirhead] |
23037 | People are improved by egalitarian institutions and habits [Green,TH] |
23051 | Equality also implies liberty, because equality must be of opportunity as well as possessions [Green,TH] |
23043 | All talk of the progress of a nation must reduce to the progress of its individual members [Green,TH] |
23038 | People only develop their personality through co-operation with the social whole [Green,TH, by Muirhead] |
23028 | The highest political efforts express our deeper social spirit [Green,TH, by Muirhead] |
23054 | Communism is wrong because it restricts the freedom of individuals to contribute to the community [Green,TH, by Muirhead] |
23047 | Original common ownership is securing private property, not denying it [Green,TH, by Muirhead] |
23042 | National spirit only exists in the individuals who embody it [Green,TH, by Muirhead] |
23048 | The ground of property ownership is not force but the power to use it for social ends [Green,TH, by Muirhead] |
23049 | Property is needed by all citizens, to empower them to achieve social goods [Green,TH] |
23040 | If something develops, its true nature is embodied in its end [Green,TH] |
23031 | God is the ideal end of the mature mind's final development [Green,TH] |
23041 | God is the realisation of the possibilities of each man's self [Green,TH] |