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. |
| 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. |
| 18085 | Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy] |
| Full Idea: When the successive absolute values of a variable decrease indefinitely in such a way as to become less than any given quantity, that variable becomes what is called an 'infinitesimal'. Such a variable has zero as its limit. | |
| From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
| A reaction: The creator of the important idea of the limit still talked in terms of infinitesimals. In the next generation the limit took over completely. |
| 18084 | When successive variable values approach a fixed value, that is its 'limit' [Cauchy] |
| Full Idea: When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others. | |
| From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
| A reaction: This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction? |
| 22076 | Being is only perceptible to itself as becoming [Schelling] |
| Full Idea: Being is only perceptible to itself in the state of becoming. | |
| From: Friedrich Schelling (Of Human Freedom [1809], p.403), quoted by Jean-François Courtine - Schelling p.90 | |
| A reaction: Is the Enlightenment the era of Being, and the Romantic era that of Becoming? They like process, fluidity, even chaos. |
| 22074 | We must show that the whole of nature, because it is effective, is grounded in freedom [Schelling] |
| Full Idea: What is required is to show that everything that is effective (nature, the world of things) is grounded in activity, life, freedom. | |
| From: Friedrich Schelling (Of Human Freedom [1809], p.351), quoted by Jean-François Courtine - Schelling | |
| A reaction: I take the ancestor of this view of nature to be the monads of Leibniz, as the active principle in nature. Because this is an idealist view, it starts with the absolute freedom of the Self, and presumably sees nature in its own image. |
| 22075 | Only idealism has given us the genuine concept of freedom [Schelling] |
| Full Idea: Until the discovery of idealism, the genuine concept of freedom has been missing from every modern system, whether it be that of Leibniz or of Spinoza. | |
| From: Friedrich Schelling (Of Human Freedom [1809], p.345), quoted by Jean-François Courtine - Schelling p.87 | |
| A reaction: Spinoza denied free will, and Leibniz fudged it. Evidently more medieval theological accounts were not good enough. I presume Fichte is Schelling's hero, and he seems to see freedom as axiomatic about the Self. |
| 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). |