Shapiro's full semantics treats second-order quantifiers as ranging over the actual power set of the domain, so metatheoretic AC-independence reflects set-theoretic indeterminacy, not semantic ambiguity in the logic itself.
?Rate how convincing each reason is below to see the overall strength.
No one has weighed in yet. Be the first to share reasons for or against this statement.
Sign in or register to share your perspective on this statement.
A genuine lack of determinedness or definiteness in the basic mathematical objects (sets) themselves, not just in how we talk about them.
Shapiro(The statement refers to her specific theoretical requirements)
A philosopher (Laurie Shapiro) who studies the philosophy of mind and cognitive science; she has argued specific criteria for when we should consider something a real scientific category.
domain(Both f1 and f2 have the reals as their domain)
The set of input values over which a function is defined.
metatheoretic(Used to characterize the role of logical semantics)
Providing a framework for theorizing about the relationship between symbols (used externally in language and internally in thought) and the world, rather than positing cognitive entities for computational manipulation
power set(Used in Cantor's theorem: every set has cardinality strictly less than its power set.)
The set of all subsets of a given set.
semantics(Distinguished from metasemantics and pragmatics in Kaplan 1989)
The domain that concerns the facts about what meanings words or phrases have.