Combining Philosophers

Ideas for B Hale / C Wright, Fred Sommers and David Hume

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6 ideas

5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic

18897	Predicate logic has to spell out that its identity relation '=' is an equivalent relation [Sommers]
	Full Idea: Because predicate logic contrues identities dyadically, its account of inferences involving identity propositions needs laws or axioms of identity, explicitly asserting that the dyadic realtion in 'x=y' possesses symmetry, reflexivity and transitivity.
	From: Fred Sommers (Intellectual Autobiography [2005], 'Syllogistic')

5. Theory of Logic / E. Structures of Logic / 1. Logical Form

18893	Translating into quantificational idiom offers no clues as to how ordinary thinkers reason [Sommers]
	Full Idea: Modern predicate logic's methods of justification, which involve translation into an artificial quantificational idiom, offer no clues to how the average person, knowing no logic and adhering to the vernacular, is so logically adept.
	From: Fred Sommers (Intellectual Autobiography [2005], Intro)
	A reaction: Of course, people are very logically adept when the argument is simple (because, I guess, they can test it against the world), but not at all good when the reasoning becomes more complex. We do, though, reason in ordinary natural language.

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not

18903	Sommers promotes the old idea that negation basically refers to terms [Sommers, by Engelbretsen]
	Full Idea: If there is one idea that is the keystone of the edifice that constitutes Sommers's united philosophy it is that terms are the linguistic entities subject to negation in the most basic sense. It is a very old idea, tending to be rejected in modern times.
	From: report of Fred Sommers (Intellectual Autobiography [2005]) by George Engelbretsen - Trees, Terms and Truth 2
	A reaction: Negation in modern logic is an operator applied to sentences, typically writing '¬Fa', which denies that F is predicated of a, with Fa being an atomic sentence. Do we say 'not(Stan is happy)', or 'not-Stan is happy', or 'Stan is not-happy'? Third one?

5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic

18894	Predicates form a hierarchy, from the most general, down to names at the bottom [Sommers]
	Full Idea: We organise our concepts of predicability on a hierarchical tree. At the top are terms like 'interesting', 'exists', 'talked about', which are predicable of anything. At the bottom are names, and in between are predicables of some things and not others.
	From: Fred Sommers (Intellectual Autobiography [2005], 'Category')
	A reaction: The heirarchy seem be arranged simply by the scope of the predicate. 'Tallest' is predicable of anything in principle, but only of a few things in practice. Is 'John Doe' a name? What is 'cosmic' predicable of? Challenging!

5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms

12230	Singular terms refer if they make certain atomic statements true [Hale/Wright]
	Full Idea: Anyone should agree that a justification for regarding a singular term as having objectual reference is provided just as soon as one has justification for regarding as true certain atomic statements in which it functions as a singular term.
	From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9)
	A reaction: The meat of this idea is hidden in the word 'certain'. See Idea 10314 for Hale's explanation. Without that, the proposal strikes me as absurd.

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox

10631	If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright]
	Full Idea: If we stipulate that 'x is heterological' iff it does not apply to itself, we speedily arrive at the contradiction that 'heterological' is itself heterological just in case it is not.
	From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2)