63 ideas
10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
22246 | A train of reasoning must be treated as all happening simultaneously [Recanati] |
10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
16357 | Mental files are the counterparts of singular terms [Recanati] |
10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
10900 | Logically true sentences are true in all structures [Zalabardo] |
10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
16360 | Identity statements are informative if they link separate mental files [Recanati] |
16374 | There is a continuum from acquaintance to description in knowledge, depending on the link [Recanati] |
16354 | Indexicality is closely related to singularity, exploiting our direct relations with things [Recanati] |
18409 | Indexicals apply to singular thought, and mental files have essentially indexical features [Recanati] |
22247 | Indexicality is not just a feature of language; examples show it also occurs in thought [Recanati] |
22248 | How can we communicate indexical thoughts to people not in the right context? [Recanati] |
16371 | Files can be confused, if two files correctly have a single name, or one file has two names [Recanati] |
16373 | Encylopedic files have further epistemic links, beyond the basic one [Recanati] |
16375 | Singular thoughts need a mental file, and an acquaintance relation from file to object [Recanati] |
16377 | Expected acquaintance can create a thought-vehicle file, but without singular content [Recanati] |
16378 | An 'indexed' file marks a file which simulates the mental file of some other person [Recanati] |
16387 | Reference by mental files is Millian, in emphasising acquaintance, rather than satisfaction [Recanati] |
16358 | The reference of a file is fixed by what it relates to, not the information it contains [Recanati] |
16367 | There are transient 'demonstrative' files, habitual 'recognitional' files, cumulative 'encyclopedic' files [Recanati] |
16368 | Files are hierarchical: proto-files, then first-order, then higher-order encyclopedic [Recanati] |
16361 | A mental file treats all of its contents as concerning one object [Recanati] |
22242 | Mental files are concepts, which are either collections or (better) containers [Recanati] |
22243 | The Frege case of believing a thing is both F and not-F is explained by separate mental files [Recanati] |
16370 | A file has a 'nucleus' through its relation to the object, and a 'periphery' of links to other files [Recanati] |
16381 | The content of thought is what is required to understand it (which involves hearers) [Recanati] |
16365 | Mental files are individual concepts (thought constituents) [Recanati] |
16356 | There may be two types of reference in language and thought: descriptive and direct [Recanati] |
16386 | Direct reference is strong Millian (just a tag) or weak Kaplanian (allowing descriptions as well) [Recanati] |
16393 | In super-direct reference, the referent serves as its own vehicle of reference [Recanati] |
16372 | Sense determines reference says same sense/same reference; new reference means new sense [Recanati] |
16388 | We need sense as well as reference, but in a non-descriptive form, and mental files do that [Recanati] |
16359 | Sense is a mental file (not its contents); similar files for Cicero and Tully are two senses [Recanati] |
16355 | Problems with descriptivism are reference by perception, by communications and by indexicals [Recanati] |
16348 | Descriptivism says we mentally relate to objects through their properties [Recanati] |
16384 | Definite descriptions reveal either a predicate (attributive use) or the file it belongs in (referential) [Recanati] |
16352 | A rigid definite description can be attributive, not referential: 'the actual F, whoever he is….' [Recanati] |
22245 | A linguistic expression refers to what its associated mental file refers to [Recanati] |
16353 | Singularity cannot be described, and it needs actual world relations [Recanati] |
16382 | Fregean modes of presentation can be understood as mental files [Recanati] |
16389 | If two people think 'I am tired', they think the same thing, and they think different things [Recanati] |
16363 | Indexicals (like mental files) determine their reference relationally, not by satisfaction [Recanati] |
16364 | Indexical don't refer; only their tokens do [Recanati] |
16351 | In 2-D semantics, reference is determined, then singularity by the truth of a predication [Recanati] |
16350 | Two-D semantics is said to help descriptivism of reference deal with singular objects [Recanati] |
16380 | Russellian propositions are better than Fregean thoughts, by being constant through communication [Recanati] |
22250 | There are speakers' thoughts and hearers' thoughts, but no further thought attached to the utterance [Recanati] |
22249 | The Naive view of communication is that hearers acquire exactly the thoughts of the speaker [Recanati] |
20486 | Only liberty, equality and sympathy can stand up to anti-social people [Kropotkin] |