4 ideas
18946 | Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer] |
Full Idea: As speakers of the language, we unreflectively assume that there are nonexistents, and that reference to them is possible. | |
From: Marga Reimer (The Problem of Empty Names [2001], p.499), quoted by Sarah Sawyer - Empty Names 4 | |
A reaction: Sarah Swoyer quotes this as a good solution to the problem of empty names, and I like it. It introduces a two-tier picture of our understanding of the world, as 'unreflective' and 'reflective', but that seems good. We accept numbers 'unreflectively'. |
18465 | An 'equivalence' relation is one which is reflexive, symmetric and transitive [Kunen] |
Full Idea: R is an equivalence relation on A iff R is reflexive, symmetric and transitive on A. | |
From: Kenneth Kunen (The Foundations of Mathematics (2nd ed) [2012], I.7.1) |
21687 | It seems obvious to prefer the simpler of two theories, on grounds of beauty and convenience [Quine] |
Full Idea: It is not to be wondered that theory makers seek simplicity. When two theories are equally defensible on other counts, certainly the simpler of the two is to be preferred on the score of both beauty and convenience. | |
From: Willard Quine (On Simple Theories of a Complex World [1960], p.255) | |
A reaction: A simple application of Ockham's Razor. Quine goes on to nicely deconstruct what is involved in simplicity, and identify a certain amount of dubious prejudice in the concept. |
21688 | There are four suspicious reasons why we prefer simpler theories [Quine] |
Full Idea: We prefer simpler theories through wishful thinking, or a bias which slants the data, or a bias where the simpler hypothesis is more open to confirmation, or simpler hypotheses tolerating wider deviations in score-keeping. | |
From: Willard Quine (On Simple Theories of a Complex World [1960], p.258) | |
A reaction: [a compression of his summary of the paper] Quine is not dismissing our preference for simpler theories, but just very nicely inviting us to focus of aspects about which we should be cautious. |