31 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] |
5745 | Quine says quantified modal logic creates nonsense, bad ontology, and false essentialism [Melia on Quine] |
16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
8789 | Various strategies try to deal with the ontological commitments of second-order logic [Hale/Wright on Quine] |
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] |
16865 | 'Theorems' are both proved, and used in proofs [Frege] |
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] |
16871 | A truth can be an axiom in one system and not in another [Frege] |
16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [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] |
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] |
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] |
9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
12812 | Things have real essences, but we categorise them according to the ideas we receive [Locke] |
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] |
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] |