The Workshop will take place from April 13th to 14th in Lecture Room 3A on the third floor of the Department of Philosophy of the University of Vienna (Universitätsstraße 7, 1010 Vienna).
Virtual Venue: https://univienna.zoom.us/j/68366932623?pwd=YMMs9KbxerhR8oFaNQMiKHdmc3vP0e.1
Pablo Dopico (University of Konstanz)
Leon Horsten (University of Konstanz)
Andrea Iacona (University of Turin)
Hannes Leitgeb (LMU Munich)
Friederike Moltmann (CNRS)
Matteo Plebani (University of Turin)
Fabian Pregel (University of Vienna)
Lorenzo Rossi (University of Turin)
Pedro Teixeira Yago (SNS Pisa)
Elia Zardini (Complutense University of Madrid)
Pablo Dopico Half-full, half-empty? On the duality of super- and sub-valuationist solutions to truth and vagueness
A handful of theorists in the literature have argued that subvaluationism should be seen as entirely dual to supervaluationism and as faring, at least, no worse than the latter, at both the philosophical and the logical levels (Hyde 1997; Varzi 2000; Colyvan and Hyde 2008). In fact, some have gone further and argued that subvaluationism holds the higher ground (Beall and Colyvan 2001; Cobreros 2010). These considerations, however, are mostly limited to the applications of super- and subvaluationist semantics to vagueness phenomena and overlook a relevant application of supervaluationist semantics: theories of truth and the Liar paradox. The present work aims to remedy this by exploring the supposed duality of the s-valuationist solutions in the context of Kripke’s theory of truth (Kripke 1975): we provide a series of results that analyse which aspects of the duality are upheld and which ones fail when we consider the s-valuationist logics of truth, and compare them to the dualism of s-valuationist solutions to vagueness phenomena.
Leon Horsten Flexible objects and rigid objects
A property is modally non-rigid if it does not have the same extension in each possible world. (Being two meter tall is a property of that kind.) In this paper, I explore, in the spirit of formal philosophy, the idea that just are there modally flexible and modally rigid properties, there are also rigid and modally flexible objects. In the theory that I will develop to some extent, there will be, intuitively speaking, no fixed class in the sense that which objects are rigid is determined by more fundamental facts about the world. Rather, rigidity will function somewhat like imposing a coordinate system on the class of objects.
Andrea Iacona Vagueness and Relative Truth
According to a view called ‘nihilism’, sentences containing vague expressions cannot strictly speaking be true or false, because they lack definite truth conditions. While most theorists of vagueness tend to regard nihilism as a hopeless view, a few isolated attempts have been made to defend it. This talk aims to develop such attempts in a new direction by showing how nihilism, once properly spelled out, can meet three crucial explanatory challenges that, respectively, concern truth, assertibility, and communication.
Hannes Leitgeb Ramsification and Semantic Indeterminacy Reconsidered
In Leitgeb (2023)*, I proposed that we should deal with semantic indeterminacy—including vagueness—by Ramsifying Tarskian semantics. Amongst others, I argued that this would save classical logic in a better way than supervaluationism does. My talk will reconsider that idea, present its main outlines, and add some new considerations on "factually defective“ discourse in general.
*: Leitgeb, H.,"Ramsification and Semantic Indeterminacy", Review of Symbolic Logic 16/3 (2023), 900-950.
Friederike Moltmann Positionalist Alternative to the Notion of a Variable Embodiment
Fine (1999) introduced the influential notion of a variable embodiment in order to account for (i) the possibility of the replacement of parts or matter in certain types of objects (structured objects or ‘the water in the container’) and (ii) the ontology of roles such as ‘the president of the US’, which can be manifested by different individuals at different times.
Th notion has been subject to critique, tough, as being much too unconstrained. In a different paper, Fine (2000) argues for relations being neutral, not involving an order among their arguments. In this talk I will argue that a positionalist view of relations (and properties) renders the notion of a variable embodiment redundant and avoids its shortcomings when combined with a view on which the structure of objects is built from neutral relations and partial specifications of their positions with entities or types of entities. I show that there is significant support for an ontology of positions from natural language.
Matteo Pleabani Semantic paradoxes: a global approach
Semantic paradoxes like Curry’s paradox or the liar confront us a with a piece of reasoning such that each step of the reasoning seems impeccable, and yet the conclusion of the reasoning is clearly false. An assumption that is made virtually everywhere in the literature on semantic paradoxes is that any satisfactory treatment of these paradoxes should isolate the faulty step in the paradoxical derivation. I want to question this assumption. I will explore a view according to which it is indeterminate where the paradoxical reasoning breaks down in much the same sense in which it is indeterminate where the boundary between the bald and non-bald people lies. I will also explore the analogies between the approach to the semantic paradoxes explored here and Kit Fine's "global" approach to vagueness.
Fabian Pregel Three Faces of Open Texture
The philosophical literature groups at least three phenomena under 'open texture'. Adapting Kit Fine's specification space framework, I formalise each as a different kind of gap in the space of admissible precisifications. I then explore the conditions under which they coincide or come apart. Finally, I use this taxonomy and the supervaluationist framework to clarify whether open texture and Sorites-type vagueness differ not only in motivating examples but also in their logical profiles.
Lorenzo Rossi Supervaluational truth and quantifiers
Quantification has long been both a stumbling block and a testing ground in semantics. Building on Frege, Tarski developed the modern model-theoretic semantics for first-order logic (FOL), but many quantifiers (because of the Compactness and Löwenheim–Skolem Theorems) cannot be expressed within FOL. Mostowski and Lindström extended Tarski’s framework to capture quantifiers such as "finitely many" and "most", giving rise to Generalized Quantifier Theory (GQT), now a standard tool in formal and natural language semantics. Still, challenges remain, especially where semantic indeterminacy arises. We focus on three sources of indeterminacy: (P) presupposition failure, (V) vagueness, and (L) semantic paradoxes. To address them, we propose a general framework for quantifier semantics in the presence of indeterminacy, and we develop two formal systems that (a) meet key desiderata for handling P, V, and L, and (b) recover a substantial fragment of GQT.
Pedro Texeira Yago Arbitrary Numbers, Hyperreals And Hypernaturals
A hyperreal field is a real closed field which extends R with numbers which are smaller than any real number, that is, arbitrarily close to 0. They offer a natural framework for the formalization of analysis in terms of infinitesimals – that is, by defining limits, derivatives and integrals on the base of infinitesimal numbers –, and thus allow the formulation of a framework whose concepts are much closer to Leibniz’s initial intuition.
But what does it mean for a number to be arbitrarily close to 0? In the context of the theory of arbitrary objects – whose main proponents are [2] and [4] –, a natural way of making sense of that is by taking the number arbitrarily close to 0 to be an arbitrary real number a which may assume values arbitrarily close to 0 – that is, such that, for any n ̸= 0, it may assume a value an such that |an| < |n|. In this sense, being arbitrarily close to 0 is not understood as always assuming values which are closer to 0 than any n ∈ R, but as assuming a value lesser than n for each such n.
The most common construction of a hyperreal field is by an ultrapower of R by a free ultrafilter (for a quick exposition, one might check [3] or [1]). In those constructions, an infinitesimal is the equivalence class of a function whose values are ultrafilter-smaller than any real number – that is, a function whose values are ultrafilter-always smaller than each real number. However, as shown in [6], AI /U is a hyperreal field iff there is a total order on I according to which U is a tails ultrafilter. Furthermore, U is a tails ultrafilter for some order over I iff for any f in the equivalence class of a given infinitesimal of AI /U , there is a set X of indexes j such that for each n ∈ R there is j ∈ X such that f (j) < n. In other words, AI /U is a hyperreal iff its infinitesimals are equivalence classes of functions which assume values arbitrarily close to 0.
Following a vein similar to [5]’s application of the theory of arbitrary objects to boolean valued sets, in this talk we shall argue hyperreal (and hypernatural) numbers are, in general, classes of equivalence of arbitrary numbers of a real closed field (respectively, of the naturals). We shall then investigate the implicated interpretations of derivatives and integrals, the notion of arbitrariness which arises from the identification, show how a fragment of the arbitrary natural numbers precisely model the hypernaturals, and the philosophical ramifications of these outcomes.
References
[1] Chen C. Chang and Howard J. Keisler. Model Theory. Studies in Logic and the Foundations of Mathematics (3rd ed.). Elsevier, 1990.
[2] Kit Fine. Reasoning with Arbitrary Objects. Blackwell, New York, NY, USA, 1985.
[3] Robert Goldblatt. Lectures on the Hyperreals: An Introduction to Nonstandard Analysis. Springer New York, 1998.
[4] Leon Horsten. The Metaphysics and Mathematics of Arbitrary Objects. Cambridge University Press, Cambridge, 2019.
[5] Leon Horsten. Boolean-valued sets as arbitrary objects. Mind, 133(529):143–166, 2024.
[6] Pedro T. Yago. Hierarchies of direct powers, ultrapowers and cumulative powers. manuscript.
Elia Zardini Borderline Cases
The nontransitive approach to vagueness developed in Zardini [2008]; [2019] provides a tolerance-based account of the Sorites paradox but no account yet of borderline cases. In this paper, I introduce a notion of determinacy such that determinate Fness consists in sufficient distance from the ~Fs. I argue that the continuity of a soritical series from the Fs to the ~Fs requires that not every object be sufficiently distant from the Fs or from the ~Fs, and so that there be borderline cases of Fness. I show that borderline cases so introduced exhibit a very different behaviour from the one postulated by mainstream theories of determinacy, including a different sense in which their being positive or negative can arbitrarily be decided.
References
Zardini, E. [2008], ‘A Model of Tolerance’, Studia Logica 90, pp. 337–368.
Zardini, E. [2019], ‘Non-Transitivism and the Sorites Paradox’ in Oms, S. & Zardini, E. (eds), The Sorites Paradox, Cambridge University Press, Cambridge, pp. 168–186.
Day 1 – Monday, April 13, 2026
09:30 – 10:00 Gathering
10:00 – 10:15 Opening
10:15 – 11:15
Hannes Leitgeb (LMU Munich) “Ramsification and Semantic Indeterminacy Reconsidered”
11:15 – 11:30 Break
11:30 – 12:30
Lorenzo Rossi (University of Turin) “Supervaluational truth and quantifiers”
12:30 – 15:00 Lunch: Bierheuriger Gangl, Alserstraße 4 / Hof 1, 1090 Wien
15:00 – 16:00
Pablo Dopico (University of Konstanz) “Half-full, half-empty? On the duality of super- and sub-valuationist solutions to truth and vagueness”
16:00 – 16:15 Break
16:15 – 17:15
Elia Zardini (Complutense University of Madrid) “Borderline Cases”
17:15 – 17:30 Break
17:30 – 18:30
Andrea Iacona (University of Turin) “Vagueness and Relative Truth”
19:00 Conference Dinner: Restaurant Roth, Währinger Straße 1, 1090 Vienna
Day 2 –T uesday, April 14, 2026
9:00 – 10:00
Friederike Moltmann (CNRS) “A Positionalist Alternative to the Notion of a Variable Embodiment”
10:00 –10:15 Break
10:15 – 11:15
Matteo Plebani (Univesity of Turin) “Semantic Paradoxes: a Global Approach”
11:15 –11:30 Break
11:30 – 12:30
Fabian Pregel (University of Vienna) “Three Faces of Open Texture”
12:30 – 15:00 Lunch: Fromme Helene, Josefstädter Str. 15, 1080 Wien
15:00 – 16:00
Pedro Teixeira Yago (SNS Pisa) “Arbitrary Numbers, Hyperreals and Hypernaturals”
16:00 –16:15 Break
16:15 – 17:15
Leon Horsten (University of Konstanz) “Flexible objects and rigid objects”
This workshop is organised by
Leon Horsten (University of Konstanz) and the AG Horsten research group
Ludovica Conti (University of Vienna), ESPRIT Program, "The logic of Abstraction", Austrian Science Fund (FWF) DOI:10.55776/ESP210
For further information, please write to ludovica.conti[@]univie.ac.at or to ag-horsten[@]uni-konstanz.de