37 ideas
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 5745 | Quine says quantified modal logic creates nonsense, bad ontology, and false essentialism [Melia on Quine] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 7548 | Classes, grouped by a convenient property, are logical constructions [Russell] |
| 8789 | Various strategies try to deal with the ontological commitments of second-order logic [Hale/Wright on Quine] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 16966 | Philosophers tend to distinguish broad 'being' from narrower 'existence' - but I reject that [Quine] |
| 16965 | All we have of general existence is what existential quantifiers express [Quine] |
| 7545 | Visible things are physical and external, but only exist when viewed [Russell] |
| 16963 | Existence is implied by the quantifiers, not by the constants [Quine] |
| 16964 | Theories are committed to objects of which some of its predicates must be true [Quine] |
| 4216 | Express a theory in first-order predicate logic; its ontology is the types of bound variable needed for truth [Quine, by Lowe] |
| 18966 | Ontological commitment of theories only arise if they are classically quantified [Quine] |
| 14490 | You can be implicitly committed to something without quantifying over it [Thomasson on Quine] |
| 16961 | In formal terms, a category is the range of some style of variables [Quine] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 7553 | Sense-data are purely physical [Russell] |
| 7549 | If my body literally lost its mind, the object seen when I see a flash would still exist [Russell] |
| 7546 | A man is a succession of momentary men, bound by continuity and causation [Russell] |
| 7550 | We could probably, in principle, infer minds from brains, and brains from minds [Russell] |
| 7547 | Matter requires a division into time-corpuscles as well as space-corpuscles [Russell] |
| 7551 | Matter is a logical construction [Russell] |
| 7552 | Six dimensions are needed for a particular, three within its own space, and three to locate that space [Russell] |