11 ideas
3338 | Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn] |
Full Idea: Dedekind and Peano define the number series as the series of successors to the number zero, according to five postulates. | |
From: report of Giuseppe Peano (works [1890]) by Simon Blackburn - Oxford Dictionary of Philosophy p.279 |
5897 | 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew] |
Full Idea: 1) 0 is a number; 2) The successor of any number is a number; 3) No two numbers have the same successor; 4) 0 is not the successor of any number; 5) If P is true of 0, and if P is true of any number n and of its successor, P is true of every number. | |
From: report of Giuseppe Peano (works [1890]) by Antony Flew - Pan Dictionary of Philosophy 'Peano' | |
A reaction: Devised by Dedekind and proposed by Peano, these postulates were intended to avoid references to intuition in specifying the natural numbers. I wonder if they could define 'successor' without reference to 'number'. |
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) |
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. |
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. |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |