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. |
| 21681 | Given all true atomic propositions, in theory every other truth can thereby be deduced [Russell] |
| Full Idea: Given all true atomic propositions, together with the fact that they are all, every other true proposition can theoretically be deduced by logical methods. | |
| From: Bertrand Russell (Intro to 2nd ed of Principia Mathematica [1925], p.xv) | |
| A reaction: This is evidently his strongest statement of the ideal underlying logical atomism. The atoms were initially sense-date, but then became atomic propositions saying an object has a property. |
| 21386 | We should accept as explanations all the plausible ways in which something could come about [Epicurus] |
| Full Idea: The phases of the Moon could happen in all the ways [at least four] which the phenomena in our experience suggest for the explanation of this kind of thing - as long as one is not so enamoured of unique explanations as to groundlessly reject the others. | |
| From: Epicurus (Letter to Pythocles [c.292 BCE], 94) | |
| A reaction: Very interesting, for IBE. While you want to embrace the 'best', it is irrational to reject all of the other candidates, simply because you want a single explanation, if there are no good grounds for the rejection. |
| 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). |
| 14051 | A cosmos is a collection of stars and an earth, with some sort of boundary, movement and shape [Epicurus] |
| Full Idea: A cosmos is a circumscribed portion of the heavens containing stars and an earth; it is separated from the unlimited, with a boundary which is rare or dense; it is revolving or stationary; it is round or triangular, or some shape. All these are possible. | |
| From: Epicurus (Letter to Pythocles [c.292 BCE], 88) | |
| A reaction: Notice that there seem to exist the 'heavens' which extend beyond the cosmos. See Idea 14036, saying that there are many other cosmoi in the heavens. |
| 1828 | God does not intervene in heavenly movements, but is beyond all action and perfectly happy [Epicurus] |
| Full Idea: Let us beware of making the Deity interpose in heavenly movements, for that being we ought to suppose exempt from all occupation and perfectly happy. | |
| From: Epicurus (Letter to Pythocles [c.292 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 10.25 |