6 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. |
17622 | We come to believe mathematical propositions via their grounding in the structure [Burge] |
Full Idea: A deeper justification for believing in [mathematical] propositions [apart from pragmatism] lies in finding their place in a logicist proof structure, by understanding the grounds within this structure that support them. | |
From: Tyler Burge (Frege on Knowing the Foundations [1998], 3) | |
A reaction: This generalises to doubting something until you see what grounds it. |
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). |
23565 | Our obedience to the king erases any crimes we commit for him [Shakespeare] |
Full Idea: We know enough if we know we are the king's men. Our obedience to the king wipes the crime of it out of us. | |
From: William Shakespeare (Henry V [1599]), quoted by Michael Walzer - Just and Unjust Wars 03 | |
A reaction: He is referring to the slaughter of the French servants behind the lines at Agincourt. A classic expression of 'I was just obeying orders', which was rejected at Nurnberg in 1946. Depends on the seriousness of the crime. |