10 ideas
| 22764 | Ordinary speech is not exact about what is true; we say we are digging a well before the well exists [Sext.Empiricus] |
| Full Idea: We must allow ordinary speech to use inexact terms, as it does not seek after what is really true but what is supposed to be true. We speak of digging a well or weaving a cloak, but there is no well or cloak when they are being dug or woven. | |
| From: Sextus Empiricus (Against the Logicians (two books) [c.180], II.129) | |
| A reaction: Nice examples. The imprecision is reduced if I say I am creating a well, because that implies something that is not yet complete. If I say I intend to dig a well, is that imprecise because the well does not exist? |
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| Full Idea: Maddy dispenses with pure sets, by sketching a strong set theory in which everything is either a physical object or a set of sets of ...physical objects. Eventually a physiological story of perception will extend to sets of physical objects. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: This doesn't seem to find many supporters, but if we accept the perception of resemblances as innate (as in Hume and Quine), it is isn't adding much to see that we intrinsically see things in groups. |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| Full Idea: Maddy takes a natural number to be a certain property of sui generis sets, the property of having a certain number of members. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990], 3 §2) by Alex Oliver - The Metaphysics of Properties | |
| A reaction: [I believe Maddy has shifted since then] Presumably this will make room for zero and infinities as natural numbers. Personally I want my natural numbers to count things. |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| Full Idea: Maddy says that intuition alone does not support very much mathematics; more importantly, a naturalist cannot accept intuition at face value, but must ask why we are justified in relying on intuition. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: It depends what you mean by 'intuition', but I identify with her second objection, that every faculty must ultimately be subject to criticism, which seems to point to a fairly rationalist view of things. |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| Full Idea: Maddy proposes that we can know (some) mind-independent mathematical truths through knowing about sets, and that we can obtain knowledge of sets through experience. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Carrie Jenkins - Grounding Concepts 6.5 | |
| A reaction: Maddy has since backed off from this, and now tries to merely defend 'objectivity' about sets (2011:114). My amateurish view is that she is overrating the importance of sets, which merely model mathematics. Look at category theory. |
| 22762 | Some properties are inseparable from a thing, such as the length, breadth and depth of a body [Sext.Empiricus] |
| Full Idea: Some properties are inseparable from the things to which they belong - as are length, breadth and depth from bodies, for without their presence it is impossible to perceive Body. | |
| From: Sextus Empiricus (Against the Logicians (two books) [c.180], I.270) | |
| A reaction: For the opposite case he suggests a man running, talking or sleeping. He doesn't mention essential natures, but this is clearly correct. We might say that they are properties which need to be mentioned in a full definition. |
| 22759 | Fools, infants and madmen may speak truly, but do not know [Sext.Empiricus] |
| Full Idea: The fool and the infant and the madman at times say something true, but they do not possess knowledge of the true. | |
| From: Sextus Empiricus (Against the Logicians (two books) [c.180], I.042) | |
| A reaction: This may be correct of someone who is insane, but seems unfair to the fool and the infant. At what age do children begin to know things? If speech was just random nonsense, an accidental truth seems impossible. |
| 22760 | Madmen are reliable reporters of what appears to them [Sext.Empiricus] |
| Full Idea: The madman is a trustworthy criterion of the appearances which occur in madness. | |
| From: Sextus Empiricus (Against the Logicians (two books) [c.180], I.062) | |
| A reaction: It is hard to conceive of an genuinely insane person deliberately misreporting their hallucinations. They are, of course, the sole witness. |
| 22763 | We can only dream of a winged man if we have experienced men and some winged thing [Sext.Empiricus] |
| Full Idea: He who in his sleep dreams of a winged man does not dream so without having seen some winged thing and a man. And in general it is impossible to find in conception anything which one does not possess as known by experience. | |
| From: Sextus Empiricus (Against the Logicians (two books) [c.180], II.058) | |
| A reaction: This precisely David Hume's empiricist account of the formation of concepts. Hume's example is a golden mountain, which he got from Aquinas. How do we dream of faces we have never encountered, or shapes we have never seen? |
| 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. |