50 ideas
| 16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
| 11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
| 16878 | We must be clear about every premise and every law used in a proof [Frege] |
| 16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
| 16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
| 16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
| 1618 | We study bound variables not to know reality, but to know what reality language asserts [Quine] |
| 16865 | 'Theorems' are both proved, and used in proofs [Frege] |
| 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] |
| 16866 | Tracing inference backwards closes in on a small set of axioms and postulates [Frege] |
| 16868 | The essence of mathematics is the kernel of primitive truths on which it rests [Frege] |
| 16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
| 16871 | A truth can be an axiom in one system and not in another [Frege] |
| 16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
| 16864 | If principles are provable, they are theorems; if not, they are axioms [Frege] |
| 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] |
| 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] |
| 9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
| 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] |
| 16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
| 16875 | We use signs to mark receptacles for complex senses [Frege] |
| 16879 | A sign won't gain sense just from being used in sentences with familiar components [Frege] |
| 1619 | There is an attempt to give a verificationist account of meaning, without the error of reducing everything to sensations [Dennett on Quine] |
| 1617 | The word 'meaning' is only useful when talking about significance or about synonymy [Quine] |
| 1609 | I do not believe there is some abstract entity called a 'meaning' which we can 'have' [Quine] |
| 19159 | Quine relates predicates to their objects, by being 'true of' them [Quine, by Davidson] |
| 16873 | Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege] |
| 16872 | A thought is the sense expressed by a sentence, and is what we prove [Frege] |
| 16874 | The parts of a thought map onto the parts of a sentence [Frege] |
| 15998 | Perfect love is not in spite of imperfections; the imperfections must be loved as well [Kierkegaard] |