7 ideas
17809 | Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel] |
Full Idea: Usually Gödel's incompleteness theorems are taken as showing a limitation on the syntactic approach to an understanding of the concept of infinity. | |
From: Georg Kreisel (Hilbert's Programme [1958], 05) |
17810 | The study of mathematical foundations needs new non-mathematical concepts [Kreisel] |
Full Idea: It is necessary to use non-mathematical concepts, i.e. concepts lacking the precision which permit mathematical manipulation, for a significant approach to foundations. We currently have no concepts of this kind which we can take seriously. | |
From: Georg Kreisel (Hilbert's Programme [1958], 06) | |
A reaction: Music to the ears of any philosopher of mathematics, because it means they are not yet out of a job. |
1757 | The Electra: she knows this man, but not that he is her brother [Eucleides, by Diog. Laertius] |
Full Idea: The 'Electra': Electra knows that Orestes is her brother, but not that this man is Orestes, so she knows and does not know her brother simultaneously. | |
From: report of Eucleides (fragments/reports [c.410 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Eu.4 | |
A reaction: Hence we distinguish 'know of', 'know that' and 'know how'. Hence Russell makes 'knowledge by acquaintance' fundamental, and descriptions come later. |
20328 | A thing is only seen as art in an 'artworld', which has a theory and a history [Danto] |
Full Idea: To see something as art requires something the eye cannot descry - an atmosphere of artistic theory, a knowledge of the history of art: an artworld. | |
From: Arthur C. Danto (The Artworld [1964], II) | |
A reaction: The editors of the volume call this a revolutionary remark, followed up by Danto and George Dickie with a social and institutional account of art. Danto's key example is Warhol's Brillo pads - art in a gallery, cleaning material in a shop. |
20441 | An ordinary object can be a work of art, but only if some theory of art supports it [Danto] |
Full Idea: What in the end makes the difference between a Brillo box and a work of art consisting of a Brillo box is a certain theory of art. It is the theory that takes it up into the world of art, and keeps it from collapsing into the real object which it is. | |
From: Arthur C. Danto (The Artworld [1964], p.581), quoted by Sondra Bacharach - Arthur C. Danto | |
A reaction: It is hard to describe Duchamp's original claim that the urinal was an artwork as a 'theory'. It is a mere rebellious assertion. |
3028 | The chief good is unity, sometimes seen as prudence, or God, or intellect [Eucleides] |
Full Idea: The chief good is unity, which is known by several names, for at one time people call it prudence, at another time God, at another intellect, and so on. | |
From: Eucleides (fragments/reports [c.410 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 02.9.2 | |
A reaction: So the chief good is what unites and focuses our moral actions. Kant calls that 'the will'. |
17811 | The natural conception of points ducks the problem of naming or constructing each point [Kreisel] |
Full Idea: In analysis, the most natural conception of a point ignores the matter of naming the point, i.e. how the real number is represented or by what constructions the point is reached from given points. | |
From: Georg Kreisel (Hilbert's Programme [1958], 13) | |
A reaction: This problem has bothered me. There are formal ways of constructing real numbers, but they don't seem to result in a name for each one. |