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] |
18815 | Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt] |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
9390 | Logic guides thinking, but it isn't a substitute for it [Rumfitt] |
18805 | Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt] |
18804 | The case for classical logic rests on its rules, much more than on the Principle of Bivalence [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] |
12202 | Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [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] |
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] |
21912 | Fichte, Schelling and Hegel rejected transcendental idealism [Lewis,PB] |
21911 | Fichte, Hegel and Schelling developed versions of Absolute Idealism [Lewis,PB] |
18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
17405 | If a theory can be fudged, so can observations [Scerri] |
17397 | The periodic system is the big counterexample to Kuhn's theory of revolutionary science [Scerri] |
17393 | Scientists eventually seek underlying explanations for every pattern [Scerri] |
17403 | The periodic table suggests accommodation to facts rates above prediction [Scerri] |
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] |
17394 | Natural kinds are what are differentiated by nature, and not just by us [Scerri] |
17421 | If elements are natural kinds, might the groups of the periodic table also be natural kinds? [Scerri] |
17396 | The colour of gold is best explained by relativistic effects due to fast-moving inner-shell electrons [Scerri] |
17420 | The stability of nuclei can be estimated through their binding energy [Scerri] |
17411 | If all elements are multiples of one (of hydrogen), that suggests once again that matter is unified [Scerri] |
17415 | A big chemistry idea is that covalent bonds are shared electrons, not transfer of electrons [Scerri] |
17409 | Does radioactivity show that only physics can explain chemistry? [Scerri] |
17392 | How can poisonous elements survive in the nutritious compound they compose? [Scerri] |
17391 | Periodicity and bonding are the two big ideas in chemistry [Scerri] |
17404 | Chemistry does not work from general principles, but by careful induction from large amounts of data [Scerri] |
17407 | The electron is the main source of chemical properties [Scerri] |
17418 | It is now thought that all the elements have literally evolved from hydrogen [Scerri] |
17398 | 19th C views said elements survived abstractly in compounds, but also as 'material ingredients' [Scerri] |
17395 | Elements were ordered by equivalent weight; later by atomic weight; finally by atomic number [Scerri] |
17417 | To explain the table, quantum mechanics still needs to explain order of shell filling [Scerri] |
17416 | Orthodoxy says the periodic table is explained by quantum mechanics [Scerri] |
17410 | Moseley showed the elements progress in units, and thereby clearly identified the gaps [Scerri] |
17412 | Elements are placed in the table by the number of positive charges - the atomic number [Scerri] |
17406 | Moseley, using X-rays, showed that atomic number ordered better than atomic weight [Scerri] |
17408 | Some suggested basing the new periodic table on isotopes, not elements [Scerri] |
17414 | Pauli explained the electron shells, but not the lengths of the periods in the table [Scerri] |
17413 | Elements in the table are grouped by having the same number of outer-shell electrons [Scerri] |
17419 | Since 99.96% of the universe is hydrogen and helium, the periodic table hardly matters [Scerri] |
17422 | The best classification needs the deepest and most general principles of the atoms [Scerri] |