11 ideas
| 7068 | If infatuation with science leads to bad scientism, its rejection leads to obscurantism [Critchley] |
| Full Idea: If what is mistaken in much contemporary philosophy is its infatuation with science, which leads to scientism, then the equally mistaken rejection of science leads to obscurantism. | |
| From: Simon Critchley (Continental Philosophy - V. Short Intro [2001], Ch.1) | |
| A reaction: Clearly a balance has to be struck. I take philosophy to be a quite separate discipline from science, but it is crucial that philosophy respects the physical facts, and scientists are the experts there. Scientists are philosophers' most valued servants. |
| 7075 | To meet the division in our life, try the Subject, Nature, Spirit, Will, Power, Praxis, Unconscious, or Being [Critchley] |
| Full Idea: Against the Kantian division of a priori and empirical, Fichte offered activity of the subject, Schelling offered natural force, Hegel offered Spirit, Schopenhauer the Will, Nietzsche power, Marx praxis, Freud the unconscious, and Heidegger offered Being. | |
| From: Simon Critchley (Continental Philosophy - V. Short Intro [2001]) | |
| A reaction: The whole of Continental Philosophy summarised in a sentence. Fichte and Schopenhauer seem to point to existentialism, Schelling gives evolutionary teleology, Marx abandons philosophy, the others are up the creek. |
| 7069 | The French keep returning, to Hegel or Nietzsche or Marx [Critchley] |
| Full Idea: French philosophy since the 1930s might be described as a series of returns: to Hegel (in Kojève and early Sartre), to Nietzsche (in Foucault and Deleuze), or to Marx (in Althusser). | |
| From: Simon Critchley (Continental Philosophy - V. Short Intro [2001], Ch.2) | |
| A reaction: An interesting map. The question might be why they return to those three, rather than (say) Hume or Leibniz. If the choice of which one you return to a matter of 'taste' (as Nietzsche would have it)? |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 22293 | Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter] |
| Full Idea: Hilbert proposed to circuvent the paradoxes by means of the doctrine (already proposed by Poincaré) that in mathematics consistency entails existence. | |
| From: report of David Hilbert (On the Concept of Number [1900], p.183) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 19 'Exist' | |
| A reaction: Interesting. Hilbert's idea has struck me as weird, but it makes sense if its main motive is to block the paradoxes. Roughly, the idea is 'it exists if it isn't paradoxical'. A low bar for existence (but then it is only in mathematics!). |
| 7067 | Food first, then ethics [Critchley] |
| Full Idea: Food first, then ethics. | |
| From: Simon Critchley (Continental Philosophy - V. Short Intro [2001], 8857) | |
| A reaction: This is not a dismissal of philosophy, but a key fact which ethical philosophers must face up to. See Mr Doolittle's speech in Shaw's 'Pygmalion. It connects to the debate c.1610 about whether one is entitled to grab someone's plank to avoid drowning. |