58 ideas
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| 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] |
| 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] |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| 16357 | Mental files are the counterparts of singular terms [Recanati] |
| 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] |
| 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] |
| 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] |
| 16360 | Identity statements are informative if they link separate mental files [Recanati] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 16374 | There is a continuum from acquaintance to description in knowledge, depending on the link [Recanati] |
| 18409 | Indexicals apply to singular thought, and mental files have essentially indexical features [Recanati] |
| 16354 | Indexicality is closely related to singularity, exploiting our direct relations with things [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] |
| 16361 | A mental file treats all of its contents as concerning one object [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] |
| 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] |
| 16393 | In super-direct reference, the referent serves as its own vehicle of reference [Recanati] |
| 16386 | Direct reference is strong Millian (just a tag) or weak Kaplanian (allowing descriptions as well) [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] |
| 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] |
| 1466 | Claims about God don't seem to claim or deny anything tangible, so evidence is irrelevant [Flew, by PG] |
| 1465 | You can't claim a patch of land is tended by a 'gardener' if there is no evidence, and all counter-evidence is rejected [Flew, by PG] |
| 1467 | Religious people seem unwilling to accept any evidence that God does not love us, so their claim is unfalsifiable [Flew, by PG] |