10 ideas
| 17833 | The first-order ZF axiomatisation is highly non-categorical [Hallett,M] |
| Full Idea: The first-order Sermelo-Fraenkel axiomatisation is highly non-categorical. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1213) |
| 17834 | Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M] |
| Full Idea: The non-categoricity of the axioms which Zermelo demonstrates reveals an incompleteness of a sort, ....for this seems to show that there will always be a set (indeed, an unending sequence) that the basic axioms are incapable of revealing to be sets. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1215) | |
| A reaction: Hallett says the incompleteness concerning Zermelo was the (transfinitely) indefinite iterability of the power set operation (which is what drives the 'iterative conception' of sets). |
| 17837 | Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M] |
| Full Idea: Unlike earlier writers (such as Fraenkel), Zermelo clearly allows that there might be ur-elements (that is, objects other than the empty set, which have no members). Indeed he sees in this the possibility of widespread application of set-theory. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217) |
| 17836 | The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M] |
| Full Idea: In 1938, Gödel showed that ZF plus the General Continuum Hypothesis is consistent if ZF is. Cohen showed that ZF and not-GCH is also consistent if ZF is, which finally shows that neither GCH nor ¬GCH can be proved from ZF itself. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217) |
| 14759 | A thing is simply a long event, linked by qualities, and spatio-temporal unity [Broad] |
| Full Idea: A thing is simply a long event, throughout the course of which there is either qualitative similarity or continuous qualitative change, together with a characteristic spatio-temporal unity. | |
| From: C.D. Broad (Scientific Thought [1923], 10 'Duration') | |
| A reaction: At least he is trying to give some sort of principle that links the stages of the event together. |
| 11842 | If short-lived happenings like car crashes are 'events', why not long-lived events like Dover Cliffs? [Broad] |
| Full Idea: We call a lightning flash or a motor accident an event, but refuse to apply this to the cliffs of Dover. ...But quantitative differences (of time) give no good grounds for calling one bit of history an event, and refusing the name to another bit. | |
| From: C.D. Broad (Scientific Thought [1923], p.54), quoted by David Wiggins - Sameness and Substance Renewed 2.3 n13 | |
| A reaction: Wiggins calls this proposal a 'terrible absurdity', but it seems to me to demand attention. There is a case to be made for a 'process' to be the fundamental category of our ontology, with stable physical objects seen in that light. |
| 16764 | The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus] |
| Full Idea: Every accident of a living thing, as well as all its organs and temperaments and its dispositions are conserved by the soul. We see this from experience, since when that soul recedes, all these dissolve and become corrupted. | |
| From: Franciscus Toletus (Commentary on 'De Anima' [1572], II.1.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.5 | |
| A reaction: A nice example of observing a phenemonon, but not being able to observe the dependence relation the right way round. Compare Descartes in Idea 16763. |
| 8160 | The present and past exist, but the future does not [Broad, by Dummett] |
| Full Idea: Not only the present but also the past exist, but the future (so long as it is the future) does not. | |
| From: report of C.D. Broad (Scientific Thought [1923]) by Michael Dummett - Thought and Reality 1 | |
| A reaction: This is quite appealing, and seems right if you believe that every truth has a truthmaker, and that there are no truths about the future. And yet the whole misery of people dying is that they cease to exist. |
| 14609 | We could say present and past exist, but not future, so that each event adds to the total history [Broad] |
| Full Idea: One theory accepts the reality of the present and the past, but holds that the future is simply nothing at all. Nothing has happened to the present by becoming past except that fresh slices of existence have been added to the total history of the world. | |
| From: C.D. Broad (Scientific Thought [1923], II) | |
| A reaction: This is now known as Broad's 'Growing Block' view of time. It is tempting to say that neither past nor future exist, but it seems undeniable that statements about the past can be wholly true, unlike those about the future. |
| 22933 | We imagine the present as a spotlight, moving across events from past to future [Broad] |
| Full Idea: We imagine presentness moving, like the spot of light from a policeman's bulls eye traversing the fronts of houses in a street. What is illuminated is present, what was illuminated is past, and what is not yet illuminated is the future. | |
| From: C.D. Broad (Scientific Thought [1923], II) | |
| A reaction: This is the 'moving spotlight' compromise theory, which retains the B-series eternal sequence of ordered events, but adds the A-series privileged present moment. Le Poidevin says Broad represents time twice over. |