Secrecy, Content, and Quantification

Abstract

While participating in a symposium on Dave Ripley’s forthcoming book Uncut, I had proposed that employing a strict-tolerant interpretation of the weak Kleene matrices provided a content-theoretical conception of the bounds of conversational norms that enjoyed advantages over Ripley’s use of the strong Kleene matrices. During discussion, I used the case of sentences that are taken to be out-of-bounds for being secrets as an example of a case in which the setting of conversational bounds in practice diverged from the account championed by Ripley. In this paper, I consider an objection that my treatment of quantifiers was mistaken insofar as the confidentiality of a sentence ϕ(t) may not lift to the sentence ∃xϕ(x) and draw from this objection that neither the strong nor the weak Kleene interpretation of quantifiers suffices, but that a novel interpretation may do so.

Monstrous Content and the Bounds of Discourse

“…will rest on an account of the interaction between them. 9 Consider the complex λ ∨ (λ ∧ @#$%&!). From the perspective of either ST and wST, the positions [λ ∨ (λ ∧ @#$%&!)…”

“…The character of the interaction between the two types of defect will determine the resulting logic. To illustrate, let us use 1 2 to represent the strong Kleene truth-value 9 There exist traditions according to which λ should be regarded as meaningless. In these cases, as Kripke remarks, "[i]f we had regarded a Liar sentence as meaningless, presumably we would have had to regard any compound containing it as meaningless" [15, p. 700], i.e., weak Kleene would be the correct tool for both veridical and content-theoretic bounds.…”

“…The "monstrous" content that we have considered is just an exceptionally obvious sort of defect 5. A detailed discussion of this in the case of privacy is carried out in[9].…”

“…The discussion in[9] considers the "immune" quantifiers introduced in[13]-so called due to their analogy to the immune matrices of[14]-to be potentially fruitful. However, evaluations on Kripke's models of[15] with the immune quantifiers will not be monotonic, which is a critical ingredient of proving completeness.…”

Tableaux and Restricted Quantification for Systems Related to Weak Kleene Logic

“…2 There are potential alternatives to consider. In the context of strict-tolerant interpretations of weak Kleene, [12] considers Carnielli et al's quantifiers from [13], calling them "immune Kleene quantifiers" due to their being infinitary analogues of the immune connectives of [14]. The discussion in [12] suggests that it is plausible that the restricted quantifiers here respect the immune quantifiers.…”