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. |
17783 | A number is not a multitude, but a unified ratio between quantities [Newton] |
Full Idea: By a Number we understand not so much a Multitude of Unities, as the abstracted Ratio of any Quantity to another Quantity of the same Kind, which we take for unity. | |
From: Isaac Newton (Universal Arithmetick [1669]), quoted by John Mayberry - What Required for Foundation for Maths? p.407-2 | |
A reaction: This needs a metaphysics of 'kinds' (since lines can't have ratios with solids). Presumably Newton wants the real numbers to be more basic than the natural numbers. This is the transition from Greek to modern. |
9329 | Justification is coherence with a background system; if irrefutable, it is knowledge [Lehrer] |
Full Idea: Justification is coherence with a background system which, when irrefutable, converts to knowledge. | |
From: Keith Lehrer (Consciousness,Represn, and Knowledge [2006]) | |
A reaction: A problem (as the theory stands here) would be whether you have to be aware that the coherence is irrefutable, which would seem to require a pretty powerful intellect. If one needn't be aware of the irrefutability, how does it help my justification? |
9330 | Generalization seems to be more fundamental to minds than spotting similarities [Lehrer] |
Full Idea: There is a level of generalization we share with other animals in the responses to objects that suggest that generalization is a more fundamental operation of the mind than the observation of similarities. | |
From: Keith Lehrer (Consciousness,Represn, and Knowledge [2006]) | |
A reaction: He derives this from Reid (1785) - Lehrer's hero - who argued against Hume that we couldn't spot similarities if we hadn't already generalized to produce the 'respect' of the similarity. Interesting. I think Reid must be right. |
9328 | All conscious states can be immediately known when attention is directed to them [Lehrer] |
Full Idea: I am inclined to think that all conscious states can be immediately known when attention is directed to them. | |
From: Keith Lehrer (Consciousness,Represn, and Knowledge [2006]) | |
A reaction: This strikes me as a very helpful suggestion, for eliminating lots of problem cases for introspective knowledge which have been triumphally paraded in recent times. It might, though, be tautological, if it is actually a definition of 'conscious states'. |
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). |