9 ideas
| 11193 | Understanding begins with the notion of being and essence [Avicenna] |
| Full Idea: Understanding begins with the notion of being and essence. | |
| From: Avicenna (Abu Ibn Sina) (Commentary on the Metaphysics [1022], 1/6), quoted by Thomas Aquinas - De Ente et Essentia (Being and Essence) p.91 | |
| A reaction: I think I might put it that wisdom is only really possible for people who aim to grasp being and essence in some way. I see no prospect of understanding 'being', and even essences may be forever just beyond our grasp. |
| 17879 | Axiomatising set theory makes it all relative [Skolem] |
| Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296) |
| 17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
| Full Idea: Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293) |
| 17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
| Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299) | |
| A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers. |
| 17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
| Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300) |
| 11209 | The simple's whatness is its very self [Avicenna] |
| Full Idea: The simple's whatness is its very self. | |
| From: Avicenna (Abu Ibn Sina) (Commentary on the Metaphysics [1022], 5.5), quoted by Thomas Aquinas - De Ente et Essentia (Being and Essence) p.103 | |
| A reaction: Aquinas endorses this Aristotelian view in Idea 11208. |
| 11204 | The ultimate material of things has the unity of total formlessness [Avicenna] |
| Full Idea: The ultimate material of things has the unity of total formlessness. | |
| From: Avicenna (Abu Ibn Sina) (Commentary on the Metaphysics [1022], 11/12.14), quoted by Thomas Aquinas - De Ente et Essentia (Being and Essence) | |
| A reaction: This remark is not invalidated by developments in modern particle physics. |
| 15036 | An essence can either be universal (in the mind) or singular (in concrete particulars) [Avicenna, by Panaccio] |
| Full Idea: Avicenna's 'indifference of essence' says the essence of certain things can become universal or singular, according to whether it is entertained by the mind (as a universal) or concretely exemplified as a singular thing. One essence can exist in two ways. | |
| From: report of Avicenna (Abu Ibn Sina) (Commentary on the Metaphysics [1022]) by Claude Panaccio - Medieval Problem of Universals 'Sources' | |
| A reaction: This would appear to be a form of nominalism, since in the concrete external world we only have particulars, and it is our mode of thinking (by abstraction?) that generates the universal aspect. I think this is probably right. |
| 2116 | The concept of an existing thing must contain more than the concept of a non-existing thing [Leibniz] |
| Full Idea: There must be more in the concept of a thing which exists than in that of one which does not exist. | |
| From: Gottfried Leibniz (On the Principles of Indiscernibles [1696], p.134) |