14 ideas
| 9358 | There are several logics, none of which will ever derive falsehoods from truth [Lewis,CI] |
| Full Idea: The fact is that there are several logics, markedly different, each self-consistent in its own terms and such that whoever, using it, avoids false premises, will never reach a false conclusion. | |
| From: C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.366) | |
| A reaction: As the man who invented modal logic in five different versions, he speaks with some authority. Logicians now debate which version is the best, so how could that be decided? You could avoid false conclusions by never reasoning at all. |
| 9357 | Excluded middle is just our preference for a simplified dichotomy in experience [Lewis,CI] |
| Full Idea: The law of excluded middle formulates our decision that whatever is not designated by a certain term shall be designated by its negative. It declares our purpose to make a complete dichotomy of experience, ..which is only our penchant for simplicity. | |
| From: C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.365) | |
| A reaction: I find this view quite appealing. 'Look, it's either F or it isn't!' is a dogmatic attitude which irritates a lot of people, and appears to be dispensible. Intuitionists in mathematics dispense with the principle, and vagueness threatens it. |
| 21566 | 'Propositional functions' are ambiguous until the variable is given a value [Russell] |
| Full Idea: By a 'propositional function' I mean something which contains a variable x, and expresses a proposition as soon as a value is assigned to x. That is to say, it differs from a proposition solely by the fact that it is ambiguous. | |
| From: Bertrand Russell (The Theory of Logical Types [1910], p.216) | |
| A reaction: This is Frege's notion of a 'concept', as an assertion of a predicate which still lacks a subject. |
| 9364 | Names represent a uniformity in experience, or they name nothing [Lewis,CI] |
| Full Idea: A name must represent some uniformity in experience or it names nothing. | |
| From: C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.368) | |
| A reaction: I like this because, in the quintessentially linguistic debate about the exact logical role of names, it reminds us that names arise because of the way reality is; they are not sui generis private games for logicians. |
| 21567 | 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell] |
| Full Idea: Such a proposition as 'all the judgements made by Epimenedes are true' will only be prima facie capable of truth if all his judgements are of the same order. | |
| From: Bertrand Russell (The Theory of Logical Types [1910], p.227) | |
| A reaction: This is an attempt to use his theory of types to solve the Liar. Tarski's invocation of a meta-language is clearly in the same territory. |
| 23457 | Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell] |
| Full Idea: Russell's theory of types meant that features common to different levels of the hierarchy became uncapturable (since any attempt to capture them would involve a predicate which disobeyed the hierarchy restrictions). | |
| From: comment on Bertrand Russell (The Theory of Logical Types [1910]) by Michael Morris - Guidebook to Wittgenstein's Tractatus 2H | |
| A reaction: I'm not clear whether this is the main reason why type theory was abandoned. Ramsey was an important critic. |
| 21556 | Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey] |
| Full Idea: In Russell's mature 1910 theory of types classes are defined in terms of propositional functions, and functions themselves are regimented by a ramified theory of types mitigated by the axiom of reducibility. | |
| From: report of Bertrand Russell (The Theory of Logical Types [1910]) by Douglas Lackey - Intros to Russell's 'Essays in Analysis' p.133 |
| 21568 | A one-variable function is only 'predicative' if it is one order above its arguments [Russell] |
| Full Idea: We will define a function of one variable as 'predicative' when it is of the next order above that of its arguments, i.e. of the lowest order compatible with its having an argument. | |
| From: Bertrand Russell (The Theory of Logical Types [1910], p.237) | |
| A reaction: 'Predicative' just means it produces a set. This is Russell's strict restriction on which functions are predicative. |
| 9362 | Necessary truths are those we will maintain no matter what [Lewis,CI] |
| Full Idea: Those laws and those laws only have necessary truth which we are prepared to maintain, no matter what. | |
| From: C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.367) | |
| A reaction: This bold and simple claim has famously been torpedoed by a well-known counterexample - that virtually every human being will cling on to the proposition "dogs have at some time existed" no matter what, but it clearly isn't a necessary truth. |
| 9365 | We can maintain a priori principles come what may, but we can also change them [Lewis,CI] |
| Full Idea: The a priori contains principles which can be maintained in the face of all experience, representing the initiative of the mind. But they are subject to alteration on pragmatic grounds, if expanding experience shows their intellectual infelicity. | |
| From: C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.373) | |
| A reaction: [compressed] This simply IS Quine's famous 'web of belief' picture, showing how firmly Quine is in the pragmatist tradition. Lewis treats a priori principles as a pragmatic toolkit, which can be refined to be more effective. Not implausible... |
| 9361 | We have to separate the mathematical from physical phenomena by abstraction [Lewis,CI] |
| Full Idea: Physical processes present us with phenomena in which the purely mathematical has to be separated out by abstraction. | |
| From: C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.367) | |
| A reaction: This is the father of modal logic endorsing traditional abstractionism, it seems. He is also, though, endorsing the view that a priori knowledge is created by us, with pragmatic ends in view. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 9363 | Science seeks classification which will discover laws, essences, and predictions [Lewis,CI] |
| Full Idea: The scientific search is for such classification as will make it possible to correlate appearance and behaviour, to discover law, to penetrate to the "essential nature" of things in order that behaviour may become predictable. | |
| From: C.I. Lewis (A Pragmatic Conception of the A Priori [1923], p.368) | |
| A reaction: Modern scientific essentialists no longer invoke scare quotes, and I think we should talk of the search for the 'mechanisms' which explain behaviour, but Lewis seems to have been sixty years ahead of his time. |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |