15 ideas
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. |
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. |
16422 | The necessity of a proposition concerns reality, not our words or concepts [Stalnaker] |
Full Idea: The necessity or contingency of a proposition has nothing to do with our concepts or the meanings of our words. The possibilities would have been the same even if we had never conceived of them. | |
From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 1) | |
A reaction: This sounds in need of qualification, since some of the propositions will be explicitly about words and concepts. Still, I like this idea. |
16423 | Conceptual possibilities are metaphysical possibilities we can conceive of [Stalnaker] |
Full Idea: Conceptual possibilities are just (metaphysical) possibilities that we can conceive of. | |
From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 1) |
16421 | Critics say there are just an a priori necessary part, and an a posteriori contingent part [Stalnaker] |
Full Idea: Critics say there are no irreducible a posteriori truths. They can be factored into a part that is necessary, but knowable a priori through conceptual analysis, and a part knowable only a posteriori, but contingent. 2-D semantics makes this precise. | |
From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 1) | |
A reaction: [Critics are Sidelle, Jackson and Chalmers] Interesting. If gold is necessarily atomic number 79, or it wouldn't be gold, that sounds like an analytic truth about gold. Discovering the 79 wasn't a discovery of a necessity. Stalnaker rejects this idea. |
16429 | A 'centred' world is an ordered triple of world, individual and time [Stalnaker] |
Full Idea: A 'centred' possible world is an ordered triple consisting of a possible world, an individual in the domain of that world, and a time. | |
From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 2) |
16428 | Meanings aren't in the head, but that is because they are abstract [Stalnaker] |
Full Idea: Meanings ain't in the head. Putnam's famous slogan actually fits Frege's anti-psychologism better than it fits Purnam's and Burge's anti-individualism. The point is that intensions of any kind are abstract objects. | |
From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 2) | |
A reaction: If intensions are abstract, that leaves (for me) the question of what they are abstracted from. I take it that there are specific brain events that are being abstractly characterised. What do we call those? |
16432 | One view says the causal story is built into the description that is the name's content [Stalnaker] |
Full Idea: In 'causal descriptivism' the causal story is built into the description that is the content of the name (and also incorporates a rigidifying operator to ensure that the descriptions that names abbreviate have wide scope). | |
From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 5) | |
A reaction: Not very controversial, I would say, since virtually every fact about the world has a 'causal story' built into it. Must we insist on rigidity in order to have wide scope? |
16430 | Two-D says that a posteriori is primary and contingent, and the necessity is the secondary intension [Stalnaker] |
Full Idea: Two-dimensionalism says the necessity of a statement is constituted by the fact that the secondary intensions is a necessary proposition, and their a posteriori character is constituted by the fact that the associated primary intension is contingent. | |
From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 2) | |
A reaction: This view is found in Sidelle 1989, and then formalised by Jackson and Chalmers. I like metaphysical necessity, but I have some sympathy with the approach. The question must always be 'where does this necessity derive from'? |
16431 | In one view, the secondary intension is metasemantic, about how the thinker relates to the content [Stalnaker] |
Full Idea: On the metasemantic interpretation of the two-dimensional framework, the second dimension is used to represent the metasemantic facts about the relation between a thinker or speaker and the contents of her thoughts or utterances. | |
From: Robert C. Stalnaker (Conceptual truth and metaphysical necessity [2003], 4) | |
A reaction: I'm struggling to think what facts there might be about the relation between myself and the contents of my thoughts. I'm more or less constituted by my thoughts. |
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 |
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. |