63 ideas
20455 | Philosophy really got started as the rival mode of discourse to tragedy [Critchley] |
20446 | Philosophy begins in disappointment, notably in religion and politics [Critchley] |
6848 | Humour is practically enacted philosophy [Critchley] |
6847 | Humour can give a phenomenological account of existence, and point to change [Critchley] |
7068 | If infatuation with science leads to bad scientism, its rejection leads to obscurantism [Critchley] |
6844 | Scientism is the view that everything can be explained causally through scientific method [Critchley] |
20449 | Science gives us an excessively theoretical view of life [Critchley] |
7075 | To meet the division in our life, try the Subject, Nature, Spirit, Will, Power, Praxis, Unconscious, or Being [Critchley] |
7069 | The French keep returning, to Hegel or Nietzsche or Marx [Critchley] |
6835 | German idealism aimed to find a unifying principle for Kant's various dualisms [Critchley] |
6837 | Since Hegel, continental philosophy has been linked with social and historical enquiry. [Critchley] |
6836 | Continental philosophy fights the threatened nihilism in the critique of reason [Critchley] |
6838 | Continental philosophy is based on critique, praxis and emancipation [Critchley] |
6845 | Continental philosophy has a bad tendency to offer 'one big thing' to explain everything [Critchley] |
6846 | Phenomenology is a technique of redescription which clarifies our social world [Critchley] |
20448 | Phenomenology uncovers and redescribes the pre-theoretical layer of life [Critchley] |
22520 | You can't reason someone out of an irrational opinion [Swift] |
9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
9701 | A 'relation' is a set of ordered pairs [Enderton] |
9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
20454 | Wallace Stevens is the greatest philosophical poet of the twentieth century in English [Critchley] |
20456 | Interesting art is always organised around ethical demands [Critchley] |
20447 | The problems is not justifying ethics, but motivating it. Why should a self seek its good? [Critchley] |
7067 | Food first, then ethics [Critchley] |
6843 | Perceiving meaninglessness is an achievement, which can transform daily life [Critchley] |
20452 | Anarchism used to be libertarian (especially for sexuality), but now concerns responsibility [Critchley] |
20450 | The state, law, bureaucracy and capital are limitations on life, so I prefer federalist anarchism [Critchley] |
20451 | Belief that humans are wicked leads to authoritarian politics [Critchley] |