display all the ideas for this combination of philosophers
11 ideas
| 8375 | 'Necessary' is a predicate of a propositional function, saying it is true for all values of its argument [Russell] |
| Full Idea: 'Necessary' is a predicate of a propositional function, meaning that it is true for all possible values of its argument or arguments. Thus 'If x is a man, x is mortal' is necessary, because it is true for any possible value of x. | |
| From: Bertrand Russell (On the Notion of Cause [1912], p.175) | |
| A reaction: This is presumably the intermediate definition of necessity, prior to modern talk of possible worlds. Since it is a predicate about functions, it is presumably a metalinguistic concept, like the semantic concept of truth. |
| 6099 | Modal terms are properties of propositional functions, not of propositions [Russell] |
| Full Idea: Traditional philosophy discusses 'necessary', 'possible' and 'impossible' as properties of propositions, whereas in fact they are properties of propositional functions; propositions are only true or false. | |
| From: Bertrand Russell (The Philosophy of Logical Atomism [1918], §V) | |
| A reaction: I am unclear how a truth could be known to be necessary if it is full of variables. 'x is human' seems to have no modality, but 'Socrates is human' could well be necessary. I like McGinn's rather adverbial account of modality. |
| 16490 | Some facts about experience feel like logical necessities [Russell] |
| Full Idea: The impossibility of seeing two colours simultaneously in a given direction feels like a logical impossibility. | |
| From: Bertrand Russell (Human Knowledge: its scope and limits [1948], 9) | |
| A reaction: I presume all necessities feel equally necessary. If we distinguish necessities by what gives rise to them (a view I favour) then how strong they 'feel' will be irrelevant. We can see why Russell is puzzled by the phenomenon, though. |
| 22308 | Only the actual exists, so possibilities always reduce to actuality after full analysis [Russell] |
| Full Idea: Possibility always marks insufficient analysis: when analysis is completed, only the actual can be relevant, for the simple reason that there is only the actual, and that the mere possibility is nothing. | |
| From: Bertrand Russell (Papers of 1913 [1913], VII.26), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 42 'Logic' | |
| A reaction: Quine agreed with Russell on this. You won't get far in life if you deny possibilities. The answer is to recognise that the actual is dynamic, and not passive. |
| 21533 | Contingency arises from tensed verbs changing the propositions to which they refer [Russell] |
| Full Idea: Contingency derives from the fact that a sentence containing a verb in the present tense - or sometimes in the past or the future - changes its meaning continually as the present changes, and stands for different propositions at different times. | |
| From: Bertrand Russell (Meinong on Complexes and Assumptions [1904], p.26) | |
| A reaction: This immediately strikes me as a bad example of the linguistic approach to philosophy. As if we (like any animal) didn't have an apprehension prior to any language that most parts of experience are capable of change. |
| 19142 | Probability can be constrained by axioms, but that leaves open its truth nature [Davidson] |
| Full Idea: Kolmogorov's axiomatisation of probability puts clear constraints on the concept of probability, but leaves open whether probability is further characterised as relative frequency, degree of belief, or something else. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: Davidson cites this to show the limitations of axiomatic approaches to any topic (e.g. sets, truth, arithmetic). The item in question must be treated as a 'primitive'. This always has the feeling of second-best. |
| 12197 | Inferring q from p only needs p to be true, and 'not-p or q' to be true [Russell] |
| Full Idea: In order that it be valid to infer q from p, it is only necessary that p should be true and that the proposition 'not-p or q' should be true. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XIV) | |
| A reaction: Rumfitt points out that this approach to logical consequences is a denial of any modal aspect, such as 'logical necessity'. Russell observes that for a good inference you must know the disjunction as a whole. Could disjunction be modal?... |
| 14450 | All forms of implication are expressible as truth-functions [Russell] |
| Full Idea: There is no need to admit as a fundamental notion any form of implication not expressible as a truth-function. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XIV) | |
| A reaction: Note that this is from a book about 'mathematical' philosophy. Nevertheless, it seems to have the form of a universal credo for Russell. He wasn't talking about conditionals here. Maybe conditionals are not implications (in isolation, that is). |
| 22303 | It makes no sense to say that a true proposition could have been false [Russell] |
| Full Idea: There seems to be no true proposition of which it makes sense to say that it might have been false. One might as well say that redness might have been a taste and not a colour. | |
| From: Bertrand Russell (The Principles of Mathematics [1903], §430), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 29 'Analy' | |
| A reaction: Few thinkers agree with this rejection of counterfactuals. It seems to rely on Moore's idea that true propositions are facts. It also sounds deterministic. Does 'he is standing' mean he couldn't have been sitting (at t)? |
| 5400 | In any possible world we feel that two and two would be four [Russell] |
| Full Idea: In any possible world we feel that two and two would be four. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: Thinking of necessity in terms of possible worlds is not a new invention, but then Russell was a keen fan of Leibniz. Suppose there were no world at all, and only one truth, namely that two and two make five? (No, I can't make sense of that!) |
| 14460 | If something is true in all possible worlds then it is logically necessary [Russell] |
| Full Idea: Saying that the axiom of reducibility is logically necessary is what would be meant by saying that it is true in all possible worlds. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVII) | |
| A reaction: This striking remark is a nice bridge between Leibniz (about whom Russell wrote a book) and Kripke. |