Date:
Friday June 20th
Venue: Seminari Ramon Llull, Facultat de Filosofia, 4th floor
Schedule:
10-11:30 – Camila Gallovich (IIF-SADAF-CONICET/UBA), “Trees for ungrounded truth”.
12-13:30 – Camillo Fiore (IIF-SADAF-CONICET/UBA), “Truth, give me strength”.
15:30-17 – Pilar Terrés (U. València), “Truth as an inconsistent concept”.
17:15-18:45 – Aylén Bavosa (IIF-SADAF-CONICET/UBA), “Outside the purview of truth and falsity”.
Organizers: José Martínez, Sergi Oms
Camila Gallovich Trees for Ungrounded Truth
The process of grounding the statements of a first order language with truth and the characterization of the semantic notions associated with that process can be made precise in different ways. In his Outline of a theory of truth, Kripke provides a bottom-up explanation of the process that makes use of a fixed-point semantics. The fixed-point construction allows for a rigorous characterization of the notions of groundedness, paradoxicality, hypodoxicality, s-truth, and s-falsity. Alternatively, in Truth, Dependence, and Paradox, Yablo provides a top-down explanation of the process of grounding that makes use of the elements of graph theory. The dependence account yields characterizations of the notions of groundedness and paradoxicality that are coextensive with those provided by the fixed-point conception of truth. One limitation affecting Yablo’s proposal is that it remains silent on the semantic status of statements that are neither grounded nor paradoxical. To the extent that both theories are intended to serve as formal explanations of different aspects of the concepts of groundedness and ungroundedness, they can be naturally seen as motivating a form of theoretical pluralism. However, one may contend that the two approaches are not equally good since Yablo’s treatment of ungroundedness is not as fine-grained as one might expect. The aim of this talk is to build on the dependence account and argue that, at least to the extent that fine-grainedness is concerned, there is no principled reason to prefer one explanation over the other. The talk will run as follows. In the first part, I make Kripke’s fixed-point construction and Yablo’s dependence-based construction precise. In the second part, I provide dependence-style characterizations of the relevant semantic notions and show that the resulting characterizations extensionally coincide with those provided by the fixed-point conception.
Camillo Fiore Truth, Give me Strength
Arguably, the most echoed argument against non-classical theories is that they are deductively weaker than the corresponding classical theories. A typical example that illustrates this point is given by the axiomatic theories of truth KF and PKF, both formulated using Peano arithmetic. KF and PKF yield axiomatizations of Kripke’s fixed-point conception of truth in classical and non-classical logic, respectively. However, these theories are not on a par. One reason for this disparity is their difference in proof-theoretic strength: KF is much stronger than PKF. In this work, we provide two different answers to the argument from strength, focusing on KF and PKF as our test case. Our first answer is that, despite appearances, the difference in deductive power between KF and PKF is not detrimental to the non-classical theory. In particular, we contend that evaluating whether KF is superior to PKF (or vice versa) requires adopting not only a specific conception of truth but also a specific conception of arithmetic. We review some alternatives offered in the literature and conclude that PKF fares as well as (if not better than) KF according to most of these conceptions. The second response is based on an argumentative strategy usually known as classical recapture. There is a natural way to improve the proof-theoretical power of PKF using additional axioms. In particular, we shall extend PKF with a subset of the grounded instances of the principle of excluded middle, and we will show that the resulting theory has the same proof-theoretical power as KF. (This is joint work with Camila Gallovich and Lucas Rosenblatt.)
Pilar Terrés Truth as an inconsistent concept
In this talk I explore the claim that truth is an inconsistent concept, a thesis defended, among others, by Scharp (2013) and, recently, Liggins (forthcoming). What makes a concept inconsistent, according to the view, is that its constituent principles entail something that is not the case, (such as the Liar paradox) which makes the concept somehow defective. The different authors draw different consequences from the inconsistency claim: Scharp claims that truth needs to be substituted by two different concepts (ascending and descending truth), while Liggins argues for a nihilist view, according to which there are no truths at all. After exploring a contextual response to the inconsistency claim, I will explore how to understand the nihilist claim “nothing is true” where true is inconsistent, and suggesting that a metalinguistic negation is involved in its interpretation.
Aylén Bavosa Castro Outside the purview of truth and falsity
There have been many debates about what it means for logic to be normative and what can count as epistemic goals for choosing a logical system. In those debates, some positions have argued that logical theories are not only descriptive features of a consequence relation between sentences, but that they have in mind certain epistemic aims and (truth-)norms (Field, 2009; Blake-Turner & Russell, 2018). Epistemic truth-norms such as “believe true propositions”, or its reverse side of the coin “avoid believing false propositions”, are the common practice that the pluralists tend to have in mind for that task. This is also standard practice in many epistemological fields, even when the norms tend to get more and more complex in order to avoid their own set of problems (McHugh, 2012; Olinder, 2012; Wedgewood, 2002; Sorensen, 1988; Steglich-Petersen, 2013). However, for this telic pluralism to be a (truly) tenable position, each logical system must be accompanied by their own truth-norms. For this presentation I will analyze what can be said about truth-norms with regards to metainferential systems (Pailos & Da Ré, 2023), this is, logics that differ not only in the set of inferences they take as valid but also on inferences between inferences and so on, and how this affects the pluralist position on the face of a different type of collapse argument. The type of questions I intend to answer are the following: can two different logical systems have the same type of truth-norms? In what sense is that not a collapse? What happens with systems that differ in their metainferences, but not in their set of truth-norms? And finally, is it possible to have a truth-norm pluralism, and thus a full-blooded pluralism in terms of epistemic norms? Might this be necessary?
References:
Barrio, E. A.; Pailos, F. & Szmuc, D. (2018). Substructural logics, pluralism and collapse. Synthese 198 (Suppl 20):4991-5007.
Blake-Turner, C. & Russell, G. (2018). Logical pluralism without the normativity. Synthese 1-19.
Carnielli, W. & Rodrigues, A. (2019). An epistemic approach to paraconsistency: a logic of evidence and truth. Synthese 196 (9):3789-3813.
Chan, T. H. W. (ed.) (2013). The Aim of Belief. Oxford, GB: Oxford University Press.
Field, H. (2009). Pluralism in logic. Review of Symbolic Logic 2 (2):342-359.
McHugh, C. (2012). The truth Norm of belief. Pacific Philosophical Quarterly 93 (1):8-30.
Olinder, R. F. (2012). Rescuing Doxastic Normativism. Theoria 78 (4):293-308.
Pailos, F. & Da Ré, B. (2023). Metainferential Logics. Springer Verlag.
Sorensen, R. A. (1988). Blindspots. New York: Oxford University Press.
Steglich-Petersen, A. (2013). Doxastic Norms and the Aim of Belief. Teorema 32 (3):59-74.
Stei, E. (2020a). Non-Normative Logical Pluralism and the Revenge of the Normativity Objection. Philosophical Quarterly 70 (278):162–177.
Stei, E. (2020b). Rivalry, normativity, and the collapse of logical pluralism. Inquiry: An Interdisciplinary Journal of Philosophy 63 (3-4):411-432.
Wedgwood, R. (2002). The aim of belief. Philosophical Perspectives 16: 267-97.
Whiting, D. (2010). Should I Believe the Truth? Dialectica 64 (2):213-224.
