32 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] |
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] |
14329 | Some dispositional properties (such as mental ones) may have no categorical base [Price,HH] |
9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
19696 | There are reasons 'for which' a belief is held, reasons 'why' it is believed, and reasons 'to' believe it [Neta] |
19697 | The basing relation of a reason to a belief should both support and explain the belief [Neta] |
9032 | Before we can abstract from an instance of violet, we must first recognise it [Price,HH] |
9035 | If judgement of a characteristic is possible, that part of abstraction must be complete [Price,HH] |
9034 | There may be degrees of abstraction which allow recognition by signs, without full concepts [Price,HH] |
9036 | There is pre-verbal sign-based abstraction, as when ice actually looks cold [Price,HH] |
9037 | Intelligent behaviour, even in animals, has something abstract about it [Price,HH] |
9033 | Recognition must precede the acquisition of basic concepts, so it is the fundamental intellectual process [Price,HH] |
16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
16875 | We use signs to mark receptacles for complex senses [Frege] |
9030 | Abstractions can be interpreted dispositionally, as the ability to recognise or imagine an item [Price,HH] |
9029 | If ideas have to be images, then abstract ideas become a paradoxical problem [Price,HH] |
9031 | The basic concepts of conceptual cognition are acquired by direct abstraction from instances [Price,HH] |
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] |