3 ideas
17699 | Variables are auxiliary notions, and not part of the 'eternal' essence of logic [Schönfinkel] |
Full Idea: A variable in a proposition of logic ....has the status of a mere auxiliary notion that is really inappropriate to the constant, 'eternal' essence of the propositions of logic. | |
From: Moses Schönfinkel (Building Blocks of Mathematical Logic [1924], §1) | |
A reaction: He presumably thinks that what the variables stand for (and he mentions 'argument places' and 'operators') will be included in the essence. My attention was caught by the thought that he takes logic to have an essence. |
10805 | A sentence should be recarved to reveal its content or implication relations [Yablo] |
Full Idea: A sentence invites recarving iff it will then do better justice to the internal structure of its content and/or its implication relations. | |
From: Stephen Yablo (Carving Content at the Joints [2002], §11) | |
A reaction: This invites human intervention in a logical process (by choosing which recarvings to do, instead of allowing all equivalences to generate them). He seems to think we should abstract in order to reveal logical form. |
19216 | Propositions (such as 'that dog is barking') only exist if their items exist [Williamson] |
Full Idea: A proposition about an item exists only if that item exists... how could something be the proposition that that dog is barking in circumstances in which that dog does not exist? | |
From: Timothy Williamson (Necessary Existents [2002], p.240), quoted by Trenton Merricks - Propositions | |
A reaction: This is a view of propositions I can't make sense of. If I'm under an illusion that there is a dog barking nearby, when there isn't one, can I not say 'that dog is barking'? If I haven't expressed a proposition, what have I done? |