43 ideas
13838 | A decent modern definition should always imply a semantics [Hacking] |
14480 | Maybe analytic truths do not require truth-makers, as they place no demands on the world [Thomasson] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
14471 | Analytical entailments arise from combinations of meanings and inference rules [Thomasson] |
10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
14493 | Existence might require playing a role in explanation, or in a causal story, or being composed in some way [Thomasson] |
14491 | Rival ontological claims can both be true, if there are analytic relationships between them [Thomasson] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
14489 | Theories do not avoid commitment to entities by avoiding certain terms or concepts [Thomasson] |
14485 | Ordinary objects may be not indispensable, but they are nearly unavoidable [Thomasson] |
14487 | The simple existence conditions for objects are established by our practices, and are met [Thomasson] |
21651 | It is analytic that if simples are arranged chair-wise, then there is a chair [Thomasson, by Hofweber] |
14467 | Ordinary objects are rejected, to avoid contradictions, or for greater economy in thought [Thomasson] |
14479 | To individuate people we need conventions, but conventions are made up by people [Thomasson] |
14486 | Eliminativists haven't found existence conditions for chairs, beyond those of the word 'chair' [Thomasson] |
14481 | Wherever an object exists, there are intrinsic properties instantiating every modal profile [Thomasson] |
14482 | If the statue and the lump are two objects, they require separate properties, so we could add their masses [Thomasson] |
14483 | Given the similarity of statue and lump, what could possibly ground their modal properties? [Thomasson] |
14476 | Identity claims between objects are only well-formed if the categories are specified [Thomasson] |
14477 | Identical entities must be of the same category, and meet the criteria for the category [Thomasson] |
14478 | Modal Conventionalism says modality is analytic, not intrinsic to the world, and linguistic [Thomasson] |
14466 | A chief task of philosophy is making reflective sense of our common sense worldview [Thomasson] |
14475 | How can causal theories of reference handle nonexistence claims? [Thomasson] |
14474 | Pure causal theories of reference have the 'qua problem', of what sort of things is being referred to [Thomasson] |
14488 | Analyticity is revealed through redundancy, as in 'He bought a house and a building' [Thomasson] |