2000 | "Yes" and "No" |
p.784 | 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table |
II | p.787 | 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter |
III | p.787 | 11212 | The sense of a connective comes from primitively obvious rules of inference |
IV | p.797 | 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence |
2002 | Concepts and Counting |
I | p.43 | 17461 | Some 'how many?' answers are not predications of a concept, like 'how many gallons?' |
III | p.56 | 17462 | A single object must not be counted twice, which needs knowledge of distinctness (negative identity) |
2007 | The Logic of Boundaryless Concepts |
p.13 | p. | 9390 | Logic guides thinking, but it isn't a substitute for it |
p.5 | p. | 9389 | Vague membership of sets is possible if the set is defined by its concept, not its members |
2010 | Logical Necessity |
p.10 | 14532 | A distinctive type of necessity is found in logical consequence |
Intro | p.35 | 12193 | Logical necessity is when 'necessarily A' implies 'not-A is contradictory' |
Intro | p.36 | 12194 | Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' |
Intro | p.36 | 12195 | Soundness in argument varies with context, and may be achieved very informally indeed |
§1 | p.41 | 12198 | Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) |
§2 | p.44 | 12199 | There is a modal element in consequence, in assessing reasoning from suppositions |
§2 | p.44 | 12200 | A logically necessary statement need not be a priori, as it could be unknowable |
§2 | p.46 | 12202 | Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not |
§2 | p.46 | 12201 | We reject deductions by bad consequence, so logical consequence can't be deduction |
§4 | p.60 | 12203 | If a world is a fully determinate way things could have been, can anyone consider such a thing? |
§5 | p.61 | 12204 | The logic of metaphysical necessity is S5 |
2015 | The Boundary Stones of Thought |
1.1 | p.2 | 18798 | It is the second-order part of intuitionistic logic which actually negates some classical theorems |
1.1 | p.3 | 18799 | Intuitionists can accept Double Negation Elimination for decidable propositions |
1.1 | p.4 | 18800 | Introduction rules give deduction conditions, and Elimination says what can be deduced |
1.1 | p.9 | 18802 | In specifying a logical constant, use of that constant is quite unavoidable |
1.1 | p.10 | 18803 | Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables |
1.1 | p.13 | 18804 | The case for classical logic rests on its rules, much more than on the Principle of Bivalence |
1.1 | p.13 | 18805 | Classical logic rules cannot be proved, but various lines of attack can be repelled |
1.2 | p.18 | 18806 | Frege thought traditional categories had psychological and linguistic impurities |
2.3 | p.43 | 18808 | Normal deduction presupposes the Cut Law |
2.3 | p.43 | 18807 | Monotonicity means there is a guarantee, rather than mere inductive support |
2.5 | p.56 | 18809 | Logical truths are just the assumption-free by-products of logical rules |
3.3 | p.74 | 18813 | Logical consequence is a relation that can extended into further statements |
3.3 | p.76 | 18814 | 'Absolute necessity' would have to rest on S5 |
3.3 | p.78 | 18815 | Logic is higher-order laws which can expand the range of any sort of deduction |
3.4 | p.83 | 18816 | Metaphysical modalities respect the actual identities of things |
4.2 | p.99 | 18817 | We understand conditionals, but disagree over their truth-conditions |
5.1 | p.127 | 18819 | The idea that there are unrecognised truths is basic to our concept of truth |
5.2 | p.133 | 18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' |
6 | p.153 | 18821 | Possibilities are like possible worlds, but not fully determinate or complete |
6.2 | p.159 | 18823 | To say there could have been people who don't exist, but deny those possible things, rejects Barcan |
6.4 | p.166 | 18824 | Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right |
6.4 n16 | p.166 | 18825 | S5 is the logic of logical necessity |
6.6 | p.181 | 18826 | 'True at a possibility' means necessarily true if what is said had obtained |
7 | p.184 | 18827 | If truth-tables specify the connectives, classical logic must rely on Bivalence |
7.1 | p.185 | 18828 | If two possibilities can't share a determiner, they are incompatible |
7.1 | p.185 | 18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A |
7.2 | p.196 | 18831 | Medieval logicians said understanding A also involved understanding not-A |
7.2 | p.196 | 18830 | Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic |
7.4 | p.215 | 18834 | Infinitesimals do not stand in a determinate order relation to zero |
7.5 | p.219 | 18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics |
8.4 | p.240 | 18836 | A set may well not consist of its members; the empty set, for example, is a problem |
8.4 | p.241 | 18837 | A set can be determinate, because of its concept, and still have vague membership |
8.5 | p.47 | 18839 | An object that is not clearly red or orange can still be red-or-orange, which sweeps up problem cases |
8.5 | p.245 | 18838 | The extension of a colour is decided by a concept's place in a network of contraries |
8.7 | p.261 | 18840 | When faced with vague statements, Bivalence is not a compelling principle |
9.1 | p.267 | 18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain |
9.2 | p.275 | 18842 | Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set |
9.3 | p.277 | 18843 | The iterated conception of set requires continual increase in axiom strength |
9.6 | p.292 | 18845 | If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom |
9.6 | p.298 | 18846 | Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) |