82 ideas
| 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] |
| 13252 | Some truths have true negations [Beall/Restall] |
| 13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
| 13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
| 13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
| 13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
| 13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
| 13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
| 13254 | A doesn't imply A - that would be circular [Beall/Restall] |
| 13255 | Relevant logic may reject transitivity [Beall/Restall] |
| 13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| 13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
| 13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
| 13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
| 13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| 13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
| 13253 | There are several different consequence relations [Beall/Restall] |
| 13240 | A sentence follows from others if they always model it [Beall/Restall] |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| 13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
| 13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| 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] |
| 13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
| 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] |
| 13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
| 13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
| 13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |
| 22203 | Only facts follow from facts [Husserl] |