Multigrade Predicates

Oliver, Alex

doi:10.1093/mind/113.452.609

Cited by 37 publications

(13 citation statements)

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“…taken together. For this reason, it seems that we need to adopt multigrade predicates in the style of [23], which take arbitrary sequents of terms as arguments. If we let be such a multigrade predicate for the relation of strict full ground, we can formalize the first example as: Multigrade predicates, however, mean a significant deviation from standard logic to infinitary logic.…”

Section: Resultsmentioning

confidence: 99%

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Axiomatic Theories of Partial Ground I

Korbmacher

2017

J Philos Logic

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This is part one of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of arithmetic and show that the theory is a proof-theoretically conservative extension of the theory P T of positive truth. We construct models for the theory and draw some conclusions for the semantics of conceptualist ground.

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Section: Resultsmentioning

confidence: 99%

“…24 23 Note that the translation of s t is in the same spirit as the translation of ϕ ≺ ψ in the proof of Proposition 1: while there we had τ (…”

Section: Corollarymentioning

confidence: 99%

Axiomatic Theories of Partial Ground I

Korbmacher

2017

J Philos Logic

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“…In “Berta believes that Anna believes that Plato is wise” the second “that” takes two arguments, “Plato” and “is wise”, while the first “that” takes three arguments: “Anna”, “believes” and the complex singular term “that Plato is wise”. Dummett's (, p. 45) claim that Frege's conception of incomplete expressions does not allow for multigrade expressions has been refuted in Oliver and Smiley (, section 3.2).…”

Section: Potential Objectionsmentioning

confidence: 99%

On Indirect Sense and Reference

Skiba

2014

Theoria

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According to Frege, expressions shift their reference when they occur in indirect contexts: in “Anna believes that Plato is wise” the expression “Plato” no longer refers to Plato but to what is ordinarily its sense. Many philosophers, including Carnap, Davidson, Burge, Parsons, Kripke and Künne, believe that on Frege's view the iteration of indirect context creating operators gives rise to an infinite hierarchy of senses. While the former two take this to be problematic, the latter four welcome the hierarchy with open arms. In this paper I argue (against the quartet) that the hierarchy should be avoided and (against all of them) that it can be avoided.

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“…Finally, one might object to the use of variable degree predicates in characterizing the fundamental structure of the world. See Oliver and Smiley () and MacBride () for an overview of the objections against multigrade predicates and some responses.…”

Section: Nominalism: Variable Degree Predicatesmentioning

confidence: 99%