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All the ideas for 'Necessary Existents', 'Building Blocks of Mathematical Logic' and 'Quantification and Descriptions'

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4 ideas

2. Reason / D. Definition / 7. Contextual Definition
Contextual definitions eliminate descriptions from contexts [Linsky,B]
     Full Idea: A 'contextual' definition shows how to eliminate a description from a context.
     From: Bernard Linsky (Quantification and Descriptions [2014], 2)
     A reaction: I'm trying to think of an example, but what I come up with are better described as 'paraphrases' than as 'definitions'.
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
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.
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Definite descriptions, unlike proper names, have a logical structure [Linsky,B]
     Full Idea: Definite descriptions seem to have a logical structure in a way that proper names do not.
     From: Bernard Linsky (Quantification and Descriptions [2014], 1.1.1)
     A reaction: Thus descriptions have implications which plain names do not.
19. Language / D. Propositions / 3. Concrete Propositions
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?