59 ideas
| 3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
| 15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
| 3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
| 22246 | A train of reasoning must be treated as all happening simultaneously [Recanati] |
| 16357 | Mental files are the counterparts of singular terms [Recanati] |
| 13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
| 22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
| 12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
| 18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
| 18180 | Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann] |
| 15925 | Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine] |
| 13672 | All the axioms for mathematics presuppose set theory [Neumann] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 22808 | Liberalism is minimal government, or individual rights, or equality [Avineri/De-Shalit] |
| 22803 | Can individualist theories justify an obligation to fight in a war? [Avineri/De-Shalit] |
| 22804 | Autonomy is better achieved within a community [Avineri/De-Shalit] |
| 22806 | Communitarians avoid oppression for the common good, by means of small mediating communities [Avineri/De-Shalit] |
| 22807 | If our values are given to us by society then we have no grounds to criticise them [Avineri/De-Shalit] |