16 ideas
| 21945 | Foucault originally felt that liberating reason had become an instrument of domination [Foucault, by Gutting] |
| Full Idea: In early work Foucault writes in opposition to the Enlightenment. ..The reason that was supposed to liberate us has itself become the primary instrument of our domination. ..His heroisation of the mad aims to set up an alternative to the regime of reason. | |
| From: report of Michel Foucault (works [1978]) by Gary Gutting - Foucault: a very short introduction 7 | |
| A reaction: Adorno and Horkheimer are cited as background. I hear Spinoza turning in his grave, because right reason could never be an instrument of domination. |
| 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) |
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| Full Idea: One of Hilbert's aims in 'The Foundations of Geometry' was to eliminate number [as measure of lengths and angles] from geometry. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: Presumably this would particularly have to include the elimination of ratios (rather than actual specific lengths). |
| 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] |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| Full Idea: Hilbert's geometrical axioms were existential in character, asserting the existence of certain geometrical objects (points and lines). Euclid's postulates do not assert the existence of anything; they assert the possibility of certain constructions. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Charles Chihara - A Structural Account of Mathematics 01.1 | |
| A reaction: Chihara says geometry was originally understood modally, but came to be understood existentially. It seems extraordinary to me that philosophers of mathematics can have become more platonist over the centuries. |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| Full Idea: In his formal investigation of Euclidean geometry, Hilbert uncovered congruence axioms that implicitly played a role in Euclid's proofs but were not explicitly recognised. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 2 | |
| A reaction: The writers are offering this as a good example of the benefits of a precise and formal approach to foundational questions. It's hard to disagree, but dispiriting if you need a PhD in maths before you can start doing philosophy. |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| Full Idea: Hilbert's formulation of the Euclidean theory is of special interest because (besides being rigorously axiomatised) it does not employ the real numbers in the axioms. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Hartry Field - Science without Numbers 3 | |
| A reaction: Notice that this job was done by Hilbert, and not by the fictionalist Hartry Field. |
| 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) |
| 21942 | Foucault challenges knowledge in psychology and sociology, not in the basic sciences [Foucault, by Gutting] |
| Full Idea: Foucault's project is to question quite specific claims to cognitive authority, made by many psychologists and social scientists. He has not problems with other domains, such as mathematics and the basic sciences. | |
| From: report of Michel Foucault (works [1978]) by Gary Gutting - Foucault: a very short introduction 5 | |
| A reaction: Nowadays we describe his target as Epistemic Injustice (see book of that title by Miranda Fricker). |
| 21941 | Unlike Marxists, Foucault explains thought internally, without deference to conscious ideas [Foucault, by Gutting] |
| Full Idea: Unlike Marxists, Foucault's project is to offer an internal account of human thinking, without assuming a privileged status for the conscious content of that thought. | |
| From: report of Michel Foucault (works [1978]) by Gary Gutting - Foucault: a very short introduction 4 | |
| A reaction: His project is historical. Personally I resent anyone who claims to understand my thought better than I do. I suppose my intellectual duty is to read Foucault, and see (honestly) whether his project applies to me. |
| 21939 | The author function of any text is a plurality of selves [Foucault, by Gutting] |
| Full Idea: Foucault maintains that for any 'authored' text a plurality of selves fulfils the author function. | |
| From: report of Michel Foucault (works [1978]) by Gary Gutting - Foucault: a very short introduction 2 | |
| A reaction: This is a completely different concept of a 'self' from the one normally found in this database. I would call it the sociological concept of self, as something changing with context. So how many selves is 'Jane Austen'? |
| 21940 | Nature is not the basis of rights, but the willingness to risk death in asserting them [Foucault] |
| Full Idea: The decision 'to prefer the risk of death to the certainty of having to obey' is the 'last anchor point' for any assertion of rights, 'one more solid and closer to the experience than "natural rights"'. | |
| From: Michel Foucault (works [1978], EW III:449) | |
| A reaction: I recall a group of Afrikaan men going to face certain death, rather than give up apartheid. |
| 21116 | Power is used to create identities and ways of life for other people [Foucault, by Shorten] |
| Full Idea: For Foucault power is less about repressing people or issuing commands, and more about producing identities and ways of living. | |
| From: report of Michel Foucault (works [1978]) by Andrew Shorten - Contemporary Political Theory 01 | |
| A reaction: I take this to be the culmination of the Hegelian view of a person, as largely created by social circumstances rather than by biology. I'm beginning to think that Foucault may be a very important philosopher - although elusive. |