9 ideas
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
| A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
| 19370 | 'Blind thought' is reasoning without recognition of the ingredients of the reasoning [Leibniz, by Arthur,R] |
| Full Idea: Leibniz invented the concept of 'blind thought' - reasoning by a manipulation of characters without being able to recognise what each character stands for. | |
| From: report of Gottfried Leibniz (Towards a Universal Characteristic [1677]) by Richard T.W. Arthur - Leibniz |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
| From: Ian Rumfitt ("Yes" and "No" [2000]) | |
| A reaction: This is the standard view which Rumfitt sets out to challenge. |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
| A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
| 19391 | We can assign a characteristic number to every single object [Leibniz] |
| Full Idea: The true principle is that we can assign to every object its determined characteristic number. | |
| From: Gottfried Leibniz (Towards a Universal Characteristic [1677], p.18) | |
| A reaction: I add this as a predecessor of Gödel numbering. It is part of Leibniz's huge plan for a Universal Characteristic, to map reality numerically, and then calculate the truths about it. Gödel seems to allow metaphysics to be done mathematically. |
| 19390 | Everything is subsumed under number, which is a metaphysical statics of the universe, revealing powers [Leibniz] |
| Full Idea: There is nothing which is not subsumable under number; number is therefore a fundamental metaphysical form, and arithmetic a sort of statics of the universe, in which the powers of things are revealed. | |
| From: Gottfried Leibniz (Towards a Universal Characteristic [1677], p.17) | |
| A reaction: I take numbers to be a highly generalised and idealised description of an aspect of reality (seen as mainly constituted by countable substances). Seeing reality as processes doesn't lead us to number. So I like this idea. |
| 16635 | Incorporeal substances are powers or forces [Descartes, by Pasnau] |
| Full Idea: In one of his last letters Descartes describes incorporeal substances as 'powers or forces'. | |
| From: report of René Descartes (Two letters on mind [1649], Feb 1649) by Robert Pasnau - Metaphysical Themes 1274-1671 08.4 | |
| A reaction: Only a glimmer, but I really like this idea. (Ellis flirts with it somewhere). Minds are deeply and intrinsically active things. Try ceasing to think for five minutes. Apparently 12th century Cistercian authors were keen on the idea. |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
| A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
| 16684 | Impenetrability only belongs to the essence of extension [Descartes] |
| Full Idea: It is demonstrated that impenetrability belongs to the essence of extension and not to the essence of any other thing. | |
| From: René Descartes (Two letters on mind [1649], More, Apr 1649), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 15.5 | |
| A reaction: I'm not sure that I understand how pure extension can be impenetrable. |