51 ideas
| 5896 | Speak the truth, for this alone deifies man [Pythagoras, by Porphyry] |
| 3051 | Pythagoras discovered the numerical relation of sounds on a string [Pythagoras, by Diog. Laertius] |
| 16357 | Mental files are the counterparts of singular terms [Recanati] |
| 17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
| 10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
| 7485 | For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson] |
| 17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
| 18087 | If x changes by less and less, it must approach a limit [Dedekind] |
| 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] |
| 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] |
| 3053 | Pythagoras taught that virtue is harmony, and health, and universal good, and God [Pythagoras, by Diog. Laertius] |
| 5244 | For Pythagoreans, justice is simply treating all people the same [Pythagoras, by Aristotle] |
| 375 | When musical harmony and rhythm were discovered, similar features were seen in bodily movement [Pythagoras, by Plato] |
| 638 | Pythagoreans define timeliness, justice and marriage in terms of numbers [Pythagoras, by Aristotle] |
| 553 | Pythagoreans think mathematical principles are the principles of all of nature [Pythagoras, by Aristotle] |
| 554 | Pythagoreans say things imitate numbers, but Plato says things participate in numbers [Pythagoras, by Aristotle] |
| 644 | For Pythagoreans the entire universe is made of numbers [Pythagoras, by Aristotle] |
| 7467 | The modern idea of an immortal soul was largely created by Pythagoras [Pythagoras, by Watson] |