37 ideas
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
1618 | We study bound variables not to know reality, but to know what reality language asserts [Quine] |
8455 | Canonical notation needs quantification, variables and predicates, but not names [Quine, by Orenstein] |
8456 | Quine extended Russell's defining away of definite descriptions, to also define away names [Quine, by Orenstein] |
1611 | Names can be converted to descriptions, and Russell showed how to eliminate those [Quine] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
1613 | Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine] |
1616 | Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine] |
1615 | Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine] |
1614 | Conceptualism holds that there are universals but they are mind-made [Quine] |
10241 | For Quine, there is only one way to exist [Quine, by Shapiro] |
4064 | The idea of a thing and the idea of existence are two sides of the same coin [Quine, by Crane] |
19277 | Quine rests existence on bound variables, because he thinks singular terms can be analysed away [Quine, by Hale] |
12210 | Quine's ontology is wrong; his question is scientific, and his answer is partly philosophical [Fine,K on Quine] |
8496 | What actually exists does not, of course, depend on language [Quine] |
1610 | To be is to be the value of a variable, which amounts to being in the range of reference of a pronoun [Quine] |
8459 | Fictional quantification has no ontology, so we study ontology through scientific theories [Quine, by Orenstein] |
8497 | An ontology is like a scientific theory; we accept the simplest scheme that fits disorderly experiences [Quine] |
16261 | If commitment rests on first-order logic, we obviously lose the ontology concerning predication [Maudlin on Quine] |
7698 | If to be is to be the value of a variable, we must already know the values available [Jacquette on Quine] |
3291 | Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel] |
1612 | Realism, conceptualism and nominalism in medieval universals reappear in maths as logicism, intuitionism and formalism [Quine] |
15402 | There is no entity called 'redness', and that some things are red is ultimate and irreducible [Quine] |
4443 | Quine has argued that predicates do not have any ontological commitment [Quine, by Armstrong] |
8498 | Treating scattered sensations as single objects simplifies our understanding of experience [Quine] |
8856 | Quine's indispensability argument said arguments for abstracta were a posteriori [Quine, by Yablo] |
12443 | Can an unactualized possible have self-identity, and be distinct from other possibles? [Quine] |
18209 | We can never translate our whole language of objects into phenomenalism [Quine] |
1619 | There is an attempt to give a verificationist account of meaning, without the error of reducing everything to sensations [Dennett on Quine] |
1609 | I do not believe there is some abstract entity called a 'meaning' which we can 'have' [Quine] |
1617 | The word 'meaning' is only useful when talking about significance or about synonymy [Quine] |
19159 | Quine relates predicates to their objects, by being 'true of' them [Quine, by Davidson] |
3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |