8 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. |
| 4055 | It isn't obviously wicked to destroy a potential human being (e.g. an ununited egg and sperm) [Lockwood] |
| Full Idea: A week-old embryo without a brain may be a potential human being, but so are a sperm and an ovum that are about to meet in a dish, and it wouldn't be wicked to keep those apart. | |
| From: Michael Lockwood (When Does a Life Begin? [1985], p.19) | |
| A reaction: Sounds fine, but it may be a slippery slope. Is it acceptable to deny a place at music school to a potentially great musician? |
| 4054 | I may exist before I become a person, just as I exist before I become an adult [Lockwood] |
| Full Idea: It makes perfectly good sense to say that I existed before I became a person, just as I existed before I became an adult, or a philosopher. | |
| From: Michael Lockwood (When Does a Life Begin? [1985], p.13) | |
| A reaction: The word 'I' needs thought here. I was once a non-adult, but was I ever a non-person? 'Person' is not a clear concept, despite what many philosophers since Locke may think. |
| 4056 | If the soul is held to leave the body at brain-death, it should arrive at the time of brain-creation [Lockwood] |
| Full Idea: Any Christian who feels that body and soul go their separate ways at brain death ought in consistency to hold that they come together only at the point when whatever is destroyed at brain death first came into being. | |
| From: Michael Lockwood (When Does a Life Begin? [1985], p.24) | |
| A reaction: Hence Christians probably focus less on brain-death than do doctors and the rest of us. |
| 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 |
| 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. |
| 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. |