Preserving suspension of judgment

PAILOS, FEDERICO MATÍAS; BORZI, AGUSTINA; TORANZO CALDERÓN, JOAQUÍN

Amsterdam

Otro; DIP Colloquium; 2024

Universiteit van Amsterdam

It is common -and reasonable- to think that, in a valid inference, or at least insound ones, premises provide support for the conclusions. Or, put otherwise, thataccepting the premises provides reasons for accepting the conclusions. Nevertheless,this way of understanding validity does not represent all the different kinds of epistemic support that certain propositions can receive in various normative situationsfaced in everyday and philosophical life. In particular, sometimes suspending judgement about a set of sentences provides reasons for suspending judgement about someconclusion. Here, we seek to provide three different accounts for representing theformal epistemic norms that regulate the preservation of suspension of judgement.The first way to achieve our goal will be through a Strong-Kleene mixed logic[1]. We will use n for {12}. The logic we will introduce can be represented with apair of labels representing standards, i.e., a set of (premise-relative or conclusionrelative) designated values. While the first sign of the pair stands for the “premisestandard”, the second sign represents the “conclusion standard”. Our first logic,nn (introduced by [4] and developed in [3]), is a paraconsistent and a paracomplete contraclassical logic, because neither Explosion—in the more standard formA,¬A ⊧ B—nor Excluded Middle—i.e., ⊧ A ∨ ¬A—are nn-valid. The interpretation of this logic as preservation of suspension of judgement—the intermediate valuerepresenting this epistemic attitude—is straightforward. As an example, the validity of A ⊧ ¬A and ¬A ⊧ A is justified by understanding that suspending judgmenteabout A forces suspending judgemente about its negation, while the invalidity ofExcluded Middle is justified in the possibility of accepting instances of it.This last fact seems to avail for the following criticism: even though it is possible to suspend judgement about a sentence p, the agent is committed to acceptingp ∨ ¬p. But in nn, A ⊧ A ∨ ¬A is valid. This can be understood as meaning thatif the judgement about A is suspended, the judgment about A ∨ ¬A should alsobe suspended. And this (or so the critic goes) seems unaceptable. It is possibleto bypass this objection through supervaluationism. Nevertheless, the validity relation that we are interested in is not giving by the preservation of super-truth(which stands for the truth-preservation in [2]), but the one that sanctions as validinferences from neither supertrue nor superfalse premises to neither supertrue norsuperfalse conclusions, which can also be understood as preservation of suspensionof judgement. Supervaluationism, presented in terms of a set of classical valuations, is such that every instance of Excluded Middle is supertrue. Therefore, theinference turns out not valid.Nevertheless, supporters of paracomplete or paraconsistent solutions to the soritesparadox might take this solution as simply wrong. For them, suspending judgementabout a sentence means suspending judgement for every sentence built with saidsentence, about which judgment has been suspended. Or, more precisely, if judgement is suspended about an atomic sentence p, then it should also be suspendedabout every sentence with p as its only atomic subformula. At this point, one caneither turn to the weak Kleene truth-tables, or opt for a non-deterministic framework, all while keeping the validity notion of nn. In the latter, it so happens thatfor every valuation v, if v(ϕ) =12, then v(ϕ ∨ ¬ϕ) ∈ {1,12} and v(ϕ ∧ ¬ϕ) ∈ {0,12}.Restricting the valuation space might suitably accommodate the intuitions of thesupporter of Strong-Kleene deterministic nn and also the preferences of the onesthat benefit the supervaluationist approach to this problem.References[1] E. Chemla, P. Egr´e, and B. Spector. Characterizing logical consequence in many-valued logic.Journal of Logic and Computation, 2017. DOI: https://doi.org/10.1093/logcom/exx001.[2] P. Cobreros, P. Egr´e, D. Ripley, and R. van Rooij. Tolerant reasoning: nontransitive or nonmonotonic? Synthese, (DOI: https://doi.org/10.1007/s11229-017-1584-):1–25, 2017.[3] F. Pailos. Pure three-valued logics. Manuscript.[4] Y. Sharvit. A note on (strawson) entailment. Semantics and Pragmatics, 10(1):1–38, 6 2017