Combining Philosophers

Ideas for Lynch,MP/Glasgow,JM, Ian Hacking and Brian Ellis

unexpand these ideas     |    start again     |     choose another area for these philosophers

display all the ideas for this combination of philosophers

---

5 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

12666	We can base logic on acceptability, and abandon the Fregean account by truth-preservation [Ellis]
	Full Idea: In logic, acceptability conditions can replace truth conditions, ..and the only price one has to pay for this is that one has to abandon the implausible Fregean idea that logic is the theory of truth preservation.
	From: Brian Ellis (The Metaphysics of Scientific Realism [2009], 1)
	A reaction: This has always struck me as correct, given that if you assign T and F in a semantics, they don't have to mean 'true' and 'false', and that you can do very good logic with propositions which you think are entirely false.

5. Theory of Logic / A. Overview of Logic / 4. Pure Logic

13845	The various logics are abstractions made from terms like 'if...then' in English [Hacking]
	Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication.
	From: Ian Hacking (What is Logic? [1979], §15)
	A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation?

5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic

13840	First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
	Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem.
	From: Ian Hacking (What is Logic? [1979], §13)

13844	A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
	Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification.
	From: Ian Hacking (What is Logic? [1979], §13)
	A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours.

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic

13842	Second-order completeness seems to need intensional entities and possible worlds [Hacking]
	Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds.
	From: Ian Hacking (What is Logic? [1979], §13)