16 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) |
| 23664 | Powers are quite distinct and simple, and so cannot be defined [Reid] |
| Full Idea: Power is a thing so much of its own kind, and so simple in its nature, as to admit of no logical definition. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 1) | |
| A reaction: True. And this makes Powers ideally suited for the role of primitives in a metaphysics of nature. |
| 23669 | Thinkers say that matter has intrinsic powers, but is also passive and acted upon [Reid] |
| Full Idea: Those philosophers who attribute to matter the power of gravitation, and other active powers, teach us, at the same time, that matter is a substance altogether inert, and merely passive; …that those powers are impressed on it by some external cause. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 6) | |
| A reaction: This shows the dilemma of the period, when 'laws of nature' were imposed on passive matter by God, and yet gravity and magnetism appeared as inherent properties of matter. |
| 23666 | It is obvious that there could not be a power without a subject which possesses it [Reid] |
| Full Idea: It is evident that a power is a quality, and cannot exist without a subject to which it belongs. That power may exist without any being or subject to which that power may be attributed, is an absurdity, shocking to every man of common understanding. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 1) | |
| A reaction: This is understandble in the 18th C, when free-floating powers were inconceivable, but now that we have fields and plasmas and whatnot, we can't rule out pure powers as basic. However, I incline to agree with Reid. Matter is active. |
| 23665 | Consciousness is the power of mind to know itself, and minds are grounded in powers [Reid] |
| Full Idea: Consciousness is that power of the mind by which it has an immediate knowledge of its own operations. …Every operation of the mind is the exertion of some power of the mind. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 1) | |
| A reaction: I strongly favour this account of the mind and consciousness in terms of powers, because they give the best basis for their dynamic nature, and seem to be primitives which terminate all of our explanations. Science identifies the powers for us. |
| 23668 | Our own nature attributes free determinations to our own will [Reid] |
| Full Idea: Every man is led by nature to attribute to himself the free determination of his own will, and to believe those events to be in his power which depend upon his will. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 5) | |
| A reaction: I'm happy to say we are all responsible for those actions which are caused by the conscious decisions of our own will (our mental decision mechanisms), but personally I would drop the word 'free', which adds nothing. We are not 'ultimately' responsible. |
| 20051 | Reid said that agent causation is a unique type of causation [Reid, by Stout,R] |
| Full Idea: Thomas Reid said that an agent's causing something involves a fundamentally different kind of causation from inanimate causing. | |
| From: report of Thomas Reid (Essays on Active Powers 1: Active power [1788]) by Rowland Stout - Action 4 'Agent' | |
| A reaction: I'm afraid the great philosopher of common sense got it wrong on this one. Introducing a new type of causation into our account of nature is crazy. |
| 8383 | Day and night are constantly conjoined, but they don't cause one another [Reid, by Crane] |
| Full Idea: A famous example of Thomas Reid: day regularly follows night, and night regularly follows day. There is therefore a constant conjunction between night and day. But day does not cause night, nor does night cause day. | |
| From: report of Thomas Reid (Essays on Active Powers 1: Active power [1788]) by Tim Crane - Causation 1.2.2 | |
| A reaction: Not a fatal objection to Hume, of course, because in the complex real world there are huge numbers of nested constant conjunctions. Night and the rotation of the Earth are conjoined. But how do you tell which constant conjunctions are causal? |
| 23667 | Regular events don't imply a cause, without an innate conviction of universal causation [Reid] |
| Full Idea: A train of events following one another ever so regularly, could never lead us to the notion of a cause, if we had not, from our constitution, a conviction of the necessity of a cause for every event. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 5) | |
| A reaction: Presumably a theist like Reid must assume that the actions of God are freely chosen, rather than necessities. It's hard to see why this principle should be innate in us, and hard to see why it must thereby be true. A bit Kantian, this idea. |
| 23670 | Scientists don't know the cause of magnetism, and only discover its regulations [Reid] |
| Full Idea: A Newtonian philosopher …confesses his ignorance of the true cause of magnetic motion, and thinks that his business, as a philosopher, is only to find from experiment the laws by which it is regulated in all cases. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 6) | |
| A reaction: Since there is a 'true cause', that implies that the laws don't actively 'regulate' the magnetism, but only describe its regularity, which I think is the correct view of laws. |
| 23671 | Laws are rules for effects, but these need a cause; rules of navigation don't navigate [Reid] |
| Full Idea: The laws of nature are the rules according to which the effects are produced; but there must be a cause which operates according to these rules. The rules of navigation never navigated a ship. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 6) | |
| A reaction: Very nice. No enquirer should be satisfied with merely discovering patterns; the point is to explain the patterns. |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |