9 ideas
18198 | Mathematics is part of science; transfinite mathematics I take as mostly uninterpreted [Quine] |
Full Idea: The mathematics wanted for use in empirical sciences is for me on a par with the rest of science. Transfinite ramifications are on the same footing as simplifications, but anything further is on a par rather with uninterpreted systems, | |
From: Willard Quine (Review of Parsons (1983) [1984], p.788), quoted by Penelope Maddy - Naturalism in Mathematics II.2 | |
A reaction: The word 'uninterpreted' is the interesting one. Would mathematicians object if the philosophers graciously allowed them to continue with their transfinite work, as long as they signed something to say it was uninterpreted? |
19269 | 'Quus' means the same as 'plus' if the ingredients are less than 57; otherwise it just produces 5 [Kripke] |
Full Idea: I will define 'quus' by x-quus-y = x + y, if x, y < 57, and otherwise it equals 5. Who is to say that this is not the function I previously meant by '+'? | |
From: Saul A. Kripke (Wittgenstein on Rules and Private Language [1982], 2) | |
A reaction: Kripke's famous example, to illustrate the big new scepticism introduced by Wittgenstein's questions about the rationality of following a rule. I suspect that you have to delve into psychology to understand rule-following, rather than logic. |
19271 | No rule can be fully explained [Kripke] |
Full Idea: Every explanation of a rule could conceivably be misunderstood. | |
From: Saul A. Kripke (Wittgenstein on Rules and Private Language [1982], 3) | |
A reaction: This is Kripke's summary of what he takes to be Wittgenstein's scepticism about rules. |
7305 | Kripke's Wittgenstein says meaning 'vanishes into thin air' [Kripke, by Miller,A] |
Full Idea: Quine and Kripke's Wittgenstein attempt to argue that there are no facts about meaning, that the notion of meaning, as Kripke puts it, 'vanishes into thin air'. | |
From: report of Saul A. Kripke (Wittgenstein on Rules and Private Language [1982]) by Alexander Miller - Philosophy of Language Pref | |
A reaction: A tempting solution to the problem. If, though, it is possible for someone to say something that is self-evidently meaningless, or to accuse someone of speaking (deep down) without meaning, then that needs explaining. |
19270 | If you ask what is in your mind for following the addition rule, meaning just seems to vanish [Kripke] |
Full Idea: What can there be in my mind that I make use of when I follow a general rule to add in the future? It seems that the entire idea of meaning vanishes into thin air. | |
From: Saul A. Kripke (Wittgenstein on Rules and Private Language [1982], 2) | |
A reaction: Introspection probably isn't the best way to investigate the phenomenon of meaning. Indeed it seems rather old-fashioned and Cartesian. Kripke says, though, that seeking 'tacit' rules is even worse [end of note 22]. |
11076 | Community implies assertability-conditions rather than truth-conditions semantics [Kripke, by Hanna] |
Full Idea: If we take account of the fact that a speaker is in a community, then we must adopt an assertability-conditions semantics (based on what is legitimately assertible), and reject truth-conditional semantics (based on correspondence to the facts). | |
From: report of Saul A. Kripke (Wittgenstein on Rules and Private Language [1982]) by Robert Hanna - Rationality and Logic 6.1 | |
A reaction: [Part of Hanna's full summary of Kripke's argument] This sounds wrong to me. There are conditions where it is agreed that a lie should be told. Two people can be guilty of the same malapropism. |
11075 | The sceptical rule-following paradox is the basis of the private language argument [Kripke, by Hanna] |
Full Idea: Kripke argues that the 'rule-following paradox' is essential to the more controversial private language argument, and introduces a radically new form of scepticism. | |
From: report of Saul A. Kripke (Wittgenstein on Rules and Private Language [1982]) by Robert Hanna - Rationality and Logic 6.1 | |
A reaction: It certainly seems that Kripke is right to emphasise the separateness of the two, as the paradox is quite persuasive, but the private language argument seems less so. |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
Full Idea: Archelaus was the first person to say that the universe is boundless. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |