6 ideas
| 6408 | Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling] |
| Full Idea: In order to deduce the theorems of mathematics from purely logical axioms, Russell had to add three new axioms to those of standards logic, which were: the axiom of infinity, the axiom of choice, and the axiom of reducibility. | |
| From: A.C. Grayling (Russell [1996], Ch.2) | |
| A reaction: The third one was adopted to avoid his 'barber' paradox, but many thinkers do not accept it. The interesting question is why anyone would 'accept' or 'reject' an axiom. |
| 13128 | 'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins] |
| Full Idea: 'Ultimate sortals' are said to be non-subordinated, disjoint from one another, and uniquely paired with each object. Because of this, the ultimate sortal cannot be a satisfactory explication of the notion of an ontological category. | |
| From: comment on David Wiggins (Identity and Spatio-Temporal Continuity [1971], p.75) by Jan Westerhoff - Ontological Categories §26 | |
| A reaction: My strong intuitions are that Wiggins is plain wrong, and Westerhoff gives the most promising reasons for my intuition. The simplest point is that objects can obviously belong to more than one category. |
| 6414 | Two propositions might seem self-evident, but contradict one another [Grayling] |
| Full Idea: Two propositions might contradict each other despite appearing self-evident when considered separately. | |
| From: A.C. Grayling (Russell [1996], Ch.2) | |
| A reaction: Russell's proposal (Idea 5416) is important here, that self-evidence comes in degrees. If self-evidence was all-or-nothing, Grayling's point would be a major problem, but it isn't. Bonjour explores the idea more fully (e.g. Idea 3704) |
| 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. |
| 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? |