Beyond the Fregean Myth: The Value of Logical Values

Abstract

One of the most prominent myths in analytic philosophy is the socalled "Fregean Axiom", according to which the reference of a sentence is a truth value. In contrast to this referential semantics, a use-based formal semantics will be constructed in which the logical value of a sentence is not its putative referent but the information it conveys. Let us call by "Question Answer Semantics" (thereafter: QAS) the corresponding formal semantics: a non-Fregean many-valued logic, where the meaning of any sentence is an ordered n-tupled of yes-no answers to corresponding questions. A sample of philosophical problems will be approached in order to justify the relevance of QAS. These include:(1) illocutionary forces, and the logical analysis of speech-acts;(2) the variety of logical negations, and their characterization in terms of restricted ranges of logical values;(3) change in meaning, and the use of dynamic oppositions for belief sets.

Is ‘No’ a Force-Indicator? Yes, Sooner or Later!

“…Perhaps, instead, it invokes a "rationally" condition, though this is notoriously difficult to pin-down. 13 Even so, we see at least three different criteria for the correctness for assertion (truth-claims) and rejection (falsity-claims), following those given in [26]. Thus, the so-called Bivalentists, Paracompletists and Paraconsistentists subscribe to distinct conditions of truth-ascription with variable grades of involvement: strong (truth as a conclusive evidence), mild (truth as a state of affairs), and weak (truth as an evidence).…”

“…Recall Grice's Maxim of Quantity, discussed above, which provides explanation for why most, but not all, "no"-answers function as strong rejections 26. This also clarifies our underlying inferentialist approach to logic, in the sense that we require evidence for truth.…”

“…Our point is that the latter attitude is not a single one and can be split into a strong reading (as a commitment of negative assertion, or falsity-claim) and a weak reading (as a mere denial 7 We take it that the motivations for QAS accords both with Smiley's [30] and Textor's [32, p.447] philosophical construal of rejection. See [26] for further details. 8 Nonetheless, the distinction between sense and reference explains how judgments can be embedded, where, in section 2.3, it will be argued that such embedding reproduce the Fregean account of opaque contexts or referential opacity, according to which a reference turns into a sense once it is in a specific context of discourse.…”

“…We think that this view of conditionals holds more widely, and requires a distinction between proto-and pro-statements. 26 As such, our explanation is analogous to a conditional bet of the form "I bet that if p, then q", where the condition on which the bet rests is not a truth but a potential speech act, i.e. a proto-statement.…”

The Football of Logic

“…Thus, the two polar answers "yes" and "no" are the basic units of meaning conveyed by affording some information with a sentential content. There is no eternal Proposition descending from the Fregean "Third Realm" of thoughts [7], in such a perspective; that is, truth and falsity are nothing but commitments made by a speaker about what is accepted or strongly rejected in the speaker's belief set. There is no sufficient space to discuss at length about the epistemological stakes of rejectivism, in the following paper [10].…”