46 ideas
| 22216 | Phenomenology studies different types of correlation between consciousness and its objects [Husserl, by Bernet] |
| 22217 | Phenomenology aims to validate objects, on the basis of intentional intuitive experience [Husserl, by Bernet] |
| 21217 | Phenomenology needs absolute reflection, without presuppositions [Husserl] |
| 22218 | There can only be a science of fluctuating consciousness if it focuses on stable essences [Husserl, by Bernet] |
| 22219 | Husserl saw transcendental phenomenology as idealist, in its construction of objects [Husserl, by Bernet] |
| 22204 | Start philosophising with no preconceptions, from the intuitively non-theoretical self-given [Husserl] |
| 22207 | Epoché or 'bracketing' is refraining from judgement, even when some truths are certain [Husserl] |
| 22208 | 'Bracketing' means no judgements at all about spatio-temporal existence [Husserl] |
| 22210 | After everything is bracketed, consciousness still has a unique being of its own [Husserl] |
| 22215 | Phenomenology describes consciousness, in the light of pure experiences [Husserl] |
| 22201 | The use of mathematical-style definitions in philosophy is fruitless and harmful [Husserl] |
| 13520 | A 'tautology' must include connectives [Wolf,RS] |
| 13524 | Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS] |
| 13521 | Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS] |
| 13522 | Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS] |
| 13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |
| 13529 | Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS] |
| 13526 | Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS] |
| 13534 | In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS] |
| 13535 | First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS] |
| 13519 | Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS] |
| 13531 | Model theory reveals the structures of mathematics [Wolf,RS] |
| 13532 | Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS] |
| 13533 | First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS] |
| 13537 | An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS] |
| 13539 | The LST Theorem is a serious limitation of first-order logic [Wolf,RS] |
| 13538 | If a theory is complete, only a more powerful language can strengthen it [Wolf,RS] |
| 13525 | Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS] |
| 13530 | An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS] |
| 13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
| 22209 | Our goal is to reveal a new hidden region of Being [Husserl] |
| 22211 | As a thing and its perception are separated, two modes of Being emerge [Husserl] |
| 22202 | The World is all experiencable objects [Husserl] |
| 22213 | Absolute reality is an absurdity [Husserl] |
| 21218 | The sense of anything contingent has a purely apprehensible essence or Eidos [Husserl] |
| 19263 | Imagine an object's properties varying; the ones that won't vary are the essential ones [Husserl, by Vaidya] |
| 21220 | The physical given, unlike the mental given, could be non-existing [Husserl] |
| 22205 | Feelings of self-evidence (and necessity) are just the inventions of theory [Husserl] |
| 21221 | Direct 'seeing' by consciousness is the ultimate rational legitimation [Husserl] |
| 22220 | The phenomena of memory are given in the present, but as being past [Husserl, by Bernet] |
| 22206 | Natural science has become great by just ignoring ancient scepticism [Husserl] |
| 22221 | We know another's mind via bodily expression, while also knowing it is inaccessible [Husserl, by Bernet] |
| 22212 | Pure consciousness is a sealed off system of actual Being [Husserl] |
| 22214 | We never meet the Ego, as part of experience, or as left over from experience [Husserl] |
| 19216 | Propositions (such as 'that dog is barking') only exist if their items exist [Williamson] |
| 22203 | Only facts follow from facts [Husserl] |