Criticism
Quine has criticized higher-order logic (with standard semantics) as "set theory in sheep's clothing". Quine's criticism focuses on the lack of an effective, sound, complete proof theory; he argues that this makes HOL not a "logic". Shapiro has responded to this criticism, arguing that the additional semantic expressiveness can offset the lack of a proof theory, and arguing that a "logic" need only have a deductive system or a semantical system, but perhaps may not have both.
Read more about this topic: Higher-order Logic
Famous quotes containing the word criticism:
“I consider criticism merely a preliminary excitement, a statement of things a writer has to clear up in his own head sometime or other, probably antecedent to writing; of no value unless it come to fruit in the created work later.”
—Ezra Pound (1885–1972)
“A friend of mine spoke of books that are dedicated like this: “To my wife, by whose helpful criticism ...” and so on. He said the dedication should really read: “To my wife. If it had not been for her continual criticism and persistent nagging doubt as to my ability, this book would have appeared in Harper’s instead of The Hardware Age.””
—Brenda Ueland (1891–1985)
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—Laurence Sterne (1713–1768)