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Ideas for 'Frege on Extensions from Concepts', 'Truthmakers' and 'Number Determiners, Numbers, Arithmetic'

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4 ideas

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
18489 Connectives link sentences without linking their meanings [MacBride]
     Full Idea: The 'connectives' are expressions that link sentences but without expressing a relation that holds between the states of affairs, facts or tropes that these sentences denote.
     From: Fraser MacBride (Truthmakers [2013], 3.7)
     A reaction: MacBride notes that these contrast with ordinary verbs, which do express meaningful relations.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
18476 'A is F' may not be positive ('is dead'), and 'A is not-F' may not be negative ('is not blind') [MacBride]
     Full Idea: Statements of the form 'a is F' aren't invariably positive ('a is dead'), and nor are statements of the form 'a isn't F' ('a isn't blind') always negative.
     From: Fraser MacBride (Truthmakers [2013], 2.1.4)
     A reaction: The point is that the negation may be implicit in the predicate. There are many ways to affirm or deny something, other than by use of the standard syntax.
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
10001 An adjective contributes semantically to a noun phrase [Hofweber]
     Full Idea: The semantic value of a determiner (an adjective) is a function from semantic values to nouns to semantic values of full noun phrases.
     From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §3.1)
     A reaction: This kind of states the obvious (assuming one has a compositional view of sentences), but his point is that you can't just eliminate adjectival uses of numbers by analysing them away, as if they didn't do anything.
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10007 Quantifiers for domains and for inference come apart if there are no entities [Hofweber]
     Full Idea: Quantifiers have two functions in communication - to range over a domain of entities, and to have an inferential role (e.g. F(t)→'something is F'). In ordinary language these two come apart for singular terms not standing for any entities.
     From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3)
     A reaction: This simple observations seems to me to be wonderfully illuminating of a whole raft of problems, the sort which logicians get steamed up about, and ordinary speakers don't. Context is the key to 90% of philosophical difficulties (?). See Idea 10008.