80 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] |
17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
18803 | Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables [Rumfitt] |
17765 | Propositional language can only relate statements as the same or as different [Walicki] |
17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
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] |
17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
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] |
17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
6548 | Physicalism requires the naturalisation or rejection of set theory [Lycan] |
17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
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] |
17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
18807 | Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt] |
17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
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] |
17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
17754 | Inductive proof depends on the choice of the ordering [Walicki] |
6531 | Institutions are not reducible as types, but they are as tokens [Lycan] |
6532 | Types cannot be reduced, but levels of reduction are varied groupings of the same tokens [Lycan] |
6534 | One location may contain molecules, a metal strip, a key, an opener of doors, and a human tragedy [Lycan] |
6529 | I see the 'role'/'occupant' distinction as fundamental to metaphysics [Lycan] |
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] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
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] |
6549 | I think greenness is a complex microphysical property of green objects [Lycan] |
18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
6543 | Intentionality comes in degrees [Lycan] |
6537 | Teleological views allow for false intentional content, unlike causal and nomological theories [Lycan] |
6546 | Pain is composed of urges, desires, impulses etc, at different levels of abstraction [Lycan] |
6547 | The right 'level' for qualia is uncertain, though top (behaviourism) and bottom (particles) are false [Lycan] |
6527 | If energy in the brain disappears into thin air, this breaches physical conservation laws [Lycan] |
6528 | In lower animals, psychology is continuous with chemistry, and humans are continuous with animals [Lycan] |
6554 | Two behaviourists meet. The first says,"You're fine; how am I?" [Lycan] |
6545 | If functionalism focuses on folk psychology, it ignores lower levels of function [Lycan] |
6541 | Functionalism must not be too abstract to allow inverted spectrum, or so structural that it becomes chauvinistic [Lycan] |
6539 | The distinction between software and hardware is not clear in computing [Lycan] |
6533 | Mental types are a subclass of teleological types at a high level of functional abstraction [Lycan] |
6535 | Teleological characterisations shade off smoothly into brutely physical ones [Lycan] |
6544 | Identity theory is functionalism, but located at the lowest level of abstraction [Lycan] |
6530 | We reduce the mind through homuncular groups, described abstractly by purpose [Lycan] |
6536 | Teleological functionalism helps us to understand psycho-biological laws [Lycan] |
6542 | A Martian may exhibit human-like behaviour while having very different sensations [Lycan] |
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] |
6538 | We need a notion of teleology that comes in degrees [Lycan] |
6551 | 'Physical' means either figuring in physics descriptions, or just located in space-time [Lycan] |