12 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. |
| 16039 | Supervenience: No A-difference without a B-difference [Bennett,K] |
| Full Idea: The slogan for supervenience might be 'there cannot be an A-difference without a B-difference'. …(qualifying as a 'perfect forgery' would be an example). | |
| From: Karen Bennett (Supervenience [2011], Intro) | |
| A reaction: The key point about supervenience is that it is one-way. Presumably 'tracking' would be a better single word for it than 'dependence', which implies some sort of causal power. Supervenience describes, but doesn't attempt to explain. |
| 16043 | Supervenience is non-symmetric - sometimes it's symmetric, and sometimes it's one-way [Bennett,K] |
| Full Idea: Supervenience is neither symmetric nor asymmetric; it is non-symmetric. Sometimes it holds symmetrically. …And sometimes it holds asymmetrically. | |
| From: Karen Bennett (Supervenience [2011], §3.2) | |
| A reaction: I think of supervenience as 'tracking'. Stalkers track victims; married couples track one another. Beauty tracks statues, but statues don't seem to track beauty. I take so-called mind-brain supervenience to be two-way, not one-way. |
| 16047 | Weak supervenience is in one world, strong supervenience in all possible worlds [Bennett,K] |
| Full Idea: Weak supervenience says there is no possible world that contains individuals that are B-indiscernible but A-discernible. Strong supervenience entails the same even if they are in different possible worlds. | |
| From: Karen Bennett (Supervenience [2011], §4.1) | |
| A reaction: In other words (I presume), in simple language, the weak version says they happen supervene, the strong version says they have to supervene. |
| 16040 | Aesthetics, morality and mind supervene on the physical? Modal on non-modal? General on particular? [Bennett,K] |
| Full Idea: It has been claimed that aesthetic, moral and mental properties supervene upon physical properties, …and that modal truths supervene on non-modal ones, and that general truths supervene on particular ones. | |
| From: Karen Bennett (Supervenience [2011], Intro) | |
| A reaction: I am attracted to the last bit. I am bewildered by people who try to derive particular truths from general ones, such as deriving physical behaviour from laws, or the nature of some creature simply from its species. Only some tigers are man-eaters. |
| 16044 | Some entailments do not involve supervenience, as when brotherhood entails siblinghood [Bennett,K] |
| Full Idea: Some entailments do not suffice for supervenience. Being a brother entails being a sibling, but being a sibling does not supervene on being a brother. Sarah has a sister and Jack in an only child. Sarah, unlike Jack, is a sibling; neither is a brother. | |
| From: Karen Bennett (Supervenience [2011], §3.2) | |
| A reaction: The whole point of supervenience, I take it, is to label a relation of tracking, while offering no explanation of the tracking. Entailment would be a rather powerful explanation, as would a dog's being tied to a cart. |
| 16046 | Reduction requires supervenience, but does supervenience suffice for reduction? [Bennett,K] |
| Full Idea: Everyone agrees that reduction requires supervenience, …but the more interesting issue is whether supervenience suffices for reduction. | |
| From: Karen Bennett (Supervenience [2011], §3.3) | |
| A reaction: I think we should assume that there is a reason for every genuine case of supervenience (i.e. there are no cases of eternal or ubiquitious coincidence). One-way causation seems to give supervenience without reduction. |
| 16049 | Definitions of physicalism are compatible with a necessary God [Bennett,K] |
| Full Idea: All definitions of physicalism are compatible with the existence of a necessarily existing God. | |
| From: Karen Bennett (Supervenience [2011], 5.4) | |
| A reaction: All the definitions seem to depend on all the facts covarying with the physical facts, so anything which is invariant (such as divine or platonic entities) will stand outside the definition. Physicalism is more like a credo about all facts whatever. |
| 16042 | The metaphysically and logically possible worlds are the same, so they are the same strength [Bennett,K] |
| Full Idea: Metaphysical necessity is just as strong as logical necessity in that the space of metaphysical possibility is exactly the same as the space of logical possibility: the logically possible worlds = the metaphysically possible worlds. | |
| From: Karen Bennett (Supervenience [2011], §3.1) | |
| A reaction: I think this is wrong. To be the 'same strength' there would also have to be the same number of logical as metaphysical truths, and I presume that is not the case. There are far more logical than metaphysical possibilities. |
| 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) |
| 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. |