5 ideas
15927 | Definition just needs negation, known variables, conjunction, disjunction, substitution and quantification [Weyl, by Lavine] |
Full Idea: For mathematics, Weyl arrived (by 1917) at a satisfactory list of definition principles: negation, identification of variables, conjunction, disjunction, substitution of constants, and existential quantification over the domain. | |
From: report of Hermann Weyl (works [1917]) by Shaughan Lavine - Understanding the Infinite V.3 | |
A reaction: Lavine summarises this as 'first-order logic with parameters'. |
17945 | Forms are not a theory of universals, but an attempt to explain how predication is possible [Nehamas] |
Full Idea: The theory of Forms is not a theory of universals but a first attempt to explain how predication, the application of a single term to many objects - now considered one of the most elementary operations of language - is possible. | |
From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xxvii) |
17946 | Only Tallness really is tall, and other inferior tall things merely participate in the tallness [Nehamas] |
Full Idea: Only Tallness and nothing else really is tall; everything else merely participates in the Forms and, being excluded from the realm of Being, belongs to the inferior world of Becoming. | |
From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xxviii) | |
A reaction: This is just as weird as the normal view (and puzzle of participation), but at least it makes more sense of 'metachein' (partaking). |
17944 | 'Episteme' is better translated as 'understanding' than as 'knowledge' [Nehamas] |
Full Idea: The Greek 'episteme' is usually translated as 'knowledge' but, I argue, closer to our notion of understanding. | |
From: Alexander Nehamas (Introduction to 'Virtues of Authenticity' [1999], p.xvi) | |
A reaction: He agrees with Julia Annas on this. I take it to be crucial. See the first sentence of Aristotle's 'Metaphysics'. It is explanation which leads to understanding. |
23224 | That all matter thinks is absurd, and would make each part of our bodies a distinct self-consciousness [Bentley] |
Full Idea: [Belief in thinking matter] leads to monstrous absurdities. …Every stock and stone would be a percipient and rational creature. …every single Atom of our bodies would be a distinct Animal, endued with self-consciousness and personal sensation of its own. | |
From: Richard Bentley (Matter and Motion Cannot Think [1692], p.14-15), quoted by Matthew Cobb - The Idea of the Brain 2 | |
A reaction: Sounds correct, though presumably panpsychists don't think the flickers of consciousness in my toenails and hair constitute full-blown persons. I can't imagine what awareness is being claimed for my toenails. |