8 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. |
| 13501 | De Morgan found inferences involving relations, which eluded Aristotle's syllogistic [De Morgan, by Hart,WD] |
| Full Idea: There was a prejudice against relations (in favour of properties) but De Morgan and others that impeccable inferences turn on relations and elude Aristotle's syllogistic. Thus: All horses are animals. Hence, all heads of horses are heads of animals. | |
| From: report of Augustus De Morgan (On the Syllogism IV [1859]) by William D. Hart - The Evolution of Logic 4 | |
| A reaction: This is actually an early example of modern analytic philosophy in action. You start with the inferences, and then work back to the ontology and the definition of concepts. But in pinning down such concepts, do we miss their full meaning? |
| 17744 | De Morgan started the study of relations and their properties [De Morgan, by Walicki] |
| Full Idea: De Morgan started the sustained interest in the study of relations and their properties. | |
| From: report of Augustus De Morgan (On the Syllogism IV [1859]) by Michal Walicki - Introduction to Mathematical Logic History D.1.1 |
| 10486 | If we are rebuilding our ship at sea, we should jettison some cargo [Boolos on Neurath] |
| Full Idea: If we are sailors rebuilding our ship plank by plank on the open sea, then I know of some cargo we might want to jettison. | |
| From: comment on Otto Neurath (Protocol Sentences [1932]) by George Boolos - Must We Believe in Set Theory? p.128 | |
| A reaction: This may just be an assertion of Ockham's Razor, but the interest is that the Neurath image demands internal standards of economy etc, whereas reality itself seems to be a right mess. |
| 8485 | We must always rebuild our ship on the open sea; we can't reconstruct it properly in dry-dock [Neurath] |
| Full Idea: We are like sailors who must rebuild their ship out on the open sea, never able to dismantle it in a dry-dock and reconstruct it there out of the best materials. | |
| From: Otto Neurath (Protocol Sentences [1932]), quoted by Alex Orenstein - W.V. Quine Ch.8 | |
| A reaction: This is the classic statement of the anti-foundationalist picture of knowledge. It is often quoted by Quine. A tricky issue. I have a lot of sympathy with Bonjour's rationalist foundationalism. |
| 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). |