70 ideas
14240 | The empty set is something, not nothing! [Oliver/Smiley] |
14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
22246 | A train of reasoning must be treated as all happening simultaneously [Recanati] |
16357 | Mental files are the counterparts of singular terms [Recanati] |
14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
21812 | Being is the product of pure intellect [Plotinus] |
21817 | The One does not exist, but is the source of all existence [Plotinus] |
21824 | The One is a principle which transcends Being [Plotinus] |
21813 | Number determines individual being [Plotinus] |
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] |
5506 | If soul was like body, its parts would be separate, without communication [Plotinus] |
21827 | The movement of Soul is continuous, but we are only aware of the parts of it that are sensed [Plotinus] |
21828 | A person is the whole of their soul [Plotinus] |
21809 | Our soul has the same ideal nature as the oldest god, and is honourable above the body [Plotinus] |
21825 | The soul is outside of all of space, and has no connection to the bodily order [Plotinus] |
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] |
21826 | The Soul reasons about the Right, so there must be some permanent Right about which it reasons [Plotinus] |
6922 | Ecstasy is for the neo-Platonist the highest psychological state of man [Plotinus, by Feuerbach] |
21814 | How can multiple existence arise from the unified One? [Plotinus] |
21815 | Because the One is immobile, it must create by radiation, light the sun producing light [Plotinus] |
21816 | Soul is the logos of Nous, just as Nous is the logos of the One [Plotinus] |
21808 | Soul is author of all of life, and of the stars, and it gives them law and movement [Plotinus] |
21811 | Even the soul is secondary to the Intellectual-Principle [Nous], of which soul is an utterance [Plotinus] |