89 ideas
| 3348 | If phenomenology is deprived of the synthetic a priori, it is reduced to literature [Benardete,JA on Husserl] |
| 15570 | Phenomenology is the science of essences - necessary universal structures for art, representation etc. [Husserl, by Polt] |
| 7614 | Bracketing subtracts entailments about external reality from beliefs [Husserl, by Putnam] |
| 6893 | Phenomenology aims to describe experience directly, rather than by its origins or causes [Husserl, by Mautner] |
| 22216 | Phenomenology studies different types of correlation between consciousness and its objects [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] |
| 22217 | Phenomenology aims to validate objects, on the basis of intentional intuitive experience [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] |
| 10073 | There cannot be a set theory which is complete [Smith,P] |
| 10616 | Second-order arithmetic can prove new sentences of first-order [Smith,P] |
| 21222 | Logicians presuppose a world, and ignore logic/world connections, so their logic is impure [Husserl, by Velarde-Mayol] |
| 21223 | Phenomenology grounds logic in subjective experience [Husserl, by Velarde-Mayol] |
| 17699 | Variables are auxiliary notions, and not part of the 'eternal' essence of logic [Schönfinkel] |
| 10075 | A 'partial function' maps only some elements to another set [Smith,P] |
| 10074 | A 'total function' maps every element to one element in another set [Smith,P] |
| 10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
| 10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
| 10605 | Two functions are the same if they have the same extension [Smith,P] |
| 10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
| 10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
| 10602 | A 'natural deduction system' has no axioms but many rules [Smith,P] |
| 10613 | No nice theory can define truth for its own language [Smith,P] |
| 10078 | An 'injective' ('one-to-one') function creates a distinct output element from each original [Smith,P] |
| 10077 | A 'surjective' ('onto') function creates every element of the output set [Smith,P] |
| 10079 | A 'bijective' function has one-to-one correspondence in both directions [Smith,P] |
| 10070 | If everything that a theory proves is true, then it is 'sound' [Smith,P] |
| 10086 | Soundness is true axioms and a truth-preserving proof system [Smith,P] |
| 10596 | A theory is 'sound' iff every theorem is true (usually from true axioms and truth-preservation) [Smith,P] |
| 10598 | A theory is 'negation complete' if it proves all sentences or their negation [Smith,P] |
| 10597 | 'Complete' applies both to whole logics, and to theories within them [Smith,P] |
| 10069 | A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P] |
| 10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
| 10080 | 'Effective' means simple, unintuitive, independent, controlled, dumb, and terminating [Smith,P] |
| 10087 | A theory is 'decidable' if all of its sentences could be mechanically proved [Smith,P] |
| 10088 | Any consistent, axiomatized, negation-complete formal theory is decidable [Smith,P] |
| 10081 | A set is 'enumerable' is all of its elements can result from a natural number function [Smith,P] |
| 10083 | A set is 'effectively enumerable' if a computer could eventually list every member [Smith,P] |
| 10084 | A finite set of finitely specifiable objects is always effectively enumerable (e.g. primes) [Smith,P] |
| 10085 | The set of ordered pairs of natural numbers <i,j> is effectively enumerable [Smith,P] |
| 10601 | The thorems of a nice arithmetic can be enumerated, but not the truths (so they're diffferent) [Smith,P] |
| 10600 | Being 'expressible' depends on language; being 'capture/represented' depends on axioms and proof system [Smith,P] |
| 10599 | For primes we write (x not= 1 ∧ ∀u∀v(u x v = x → (u = 1 ∨ v = 1))) [Smith,P] |
| 10610 | The reals contain the naturals, but the theory of reals doesn't contain the theory of naturals [Smith,P] |
| 9837 | 0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett] |
| 9576 | Multiplicity in general is just one and one and one, etc. [Husserl] |
| 17444 | Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck] |
| 10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
| 21224 | Pure mathematics is the relations between all possible objects, and is thus formal ontology [Husserl, by Velarde-Mayol] |
| 10618 | All numbers are related to zero by the ancestral of the successor relation [Smith,P] |
| 10608 | The number of Fs is the 'successor' of the Gs if there is a single F that isn't G [Smith,P] |
| 10849 | Baby arithmetic covers addition and multiplication, but no general facts about numbers [Smith,P] |
| 10850 | Baby Arithmetic is complete, but not very expressive [Smith,P] |
| 10851 | Robinson Arithmetic 'Q' has basic axioms, quantifiers and first-order logic [Smith,P] |
| 10852 | Robinson Arithmetic (Q) is not negation complete [Smith,P] |
| 10068 | Natural numbers have zero, unique successors, unending, no circling back, and no strays [Smith,P] |
| 10603 | The logic of arithmetic must quantify over properties of numbers to handle induction [Smith,P] |
| 10848 | Multiplication only generates incompleteness if combined with addition and successor [Smith,P] |
| 10604 | Incompleteness results in arithmetic from combining addition and successor with multiplication [Smith,P] |
| 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] |
| 21226 | Husserl sees the ego as a monad, unifying presence, sense and intentional acts [Husserl, by Velarde-Mayol] |
| 22202 | The World is all experiencable objects [Husserl] |
| 22213 | Absolute reality is an absurdity [Husserl] |
| 10617 | The 'ancestral' of a relation is a new relation which creates a long chain of the original relation [Smith,P] |
| 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] |
| 21216 | Husserl says we have intellectual intuitions (of categories), as well as of the senses [Husserl, by Velarde-Mayol] |
| 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] |
| 21228 | Husserl's monads (egos) communicate, through acts of empathy. [Husserl, by Velarde-Mayol] |
| 22212 | Pure consciousness is a sealed off system of actual Being [Husserl] |
| 9575 | Husserl identifies a positive mental act of unification, and a negative mental act for differences [Husserl, by Frege] |
| 21225 | The psychological ego is worldly, and the pure ego follows transcendental reduction [Husserl, by Velarde-Mayol] |
| 22214 | We never meet the Ego, as part of experience, or as left over from experience [Husserl] |
| 21214 | We clarify concepts (e.g. numbers) by determining their psychological origin [Husserl, by Velarde-Mayol] |
| 9819 | Psychologism blunders in focusing on concept-formation instead of delineating the concepts [Dummett on Husserl] |
| 9851 | Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them [Dummett on Husserl] |
| 22203 | Only facts follow from facts [Husserl] |