57 ideas
19342 | Reason avoids multiplying hypotheses or principles [Leibniz] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
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] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
1613 | Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
1616 | Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
1615 | Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
1614 | Conceptualism holds that there are universals but they are mind-made [Quine] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
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] |
12711 | The immediate cause of movements is more real [than geometry] [Leibniz] |
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] |
19349 | The complete notion of a substance implies all of its predicates or attributes [Leibniz] |
7558 | Substances mirror God or the universe, each from its own viewpoint [Leibniz] |
16761 | Forms are of no value in physics, but are indispensable in metaphysics [Leibniz] |
13088 | Subjects include predicates, so full understanding of subjects reveals all the predicates [Leibniz] |
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] |
13085 | Leibniz is some form of haecceitist [Leibniz, by Cover/O'Leary-Hawthorne] |
18209 | We can never translate our whole language of objects into phenomenalism [Quine] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
5024 | Knowledge doesn't just come from the senses; we know the self, substance, identity, being etc. [Leibniz] |
5027 | If a person's memories became totally those of the King of China, he would be the King of China [Leibniz] |
5023 | Future contingent events are certain, because God foresees them, but that doesn't make them necessary [Leibniz] |
2119 | People argue for God's free will, but it isn't needed if God acts in perfection following supreme reason [Leibniz] |
5025 | Mind and body can't influence one another, but God wouldn't intervene in the daily routine [Leibniz] |
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] |
5026 | Animals lack morality because they lack self-reflection [Leibniz] |