Schedule
Logic of Metaphysics - Potsdam
University of Potsdam | 25.09.26. - 26.09.26.
Am Neuen Palais 10, 14469 Potsdam, House 8 Room 1.08.0.58.
Dinner: L'Osteria Potsdam | 19:00 | Otto-Braun-Platz 1, Potsdam, DE 14467
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Day 1
Day 1
09:30 - 9:45 Welcome
09:45 - 10:10 Opening
Opening remarks by the Logic and Metaphysics team, with a brief welcome from our Potsdam hosts, Leon Isenmann, Marvin Thinschmidt and Madara Vaserberga, introducing the weekend's theme: the logic of metaphysics.
10:00 - 11:00 Keynote: Naomi Thompson
Logic and the epistemology of metaphysical structure
In recent years we’ve seen the introduction of several new primitives’ notions of metaphysical structure to our 'metaphysical toolbox'. The most influential of these is grounding, where much of the discussion about the nature of grounding has centred on the logical properties of the relation. Grounding is generally thought to be transitive, irreflexive, asymmetric, and hyperintensional. Each of these properties however has been challenged in some part of the recent literature.
In this talk I briefly introduce some of these challenges, and suggest that competition in the form of alternative formally defined structural relations apparently better suited than grounding for some kinds of explanatory work ought to serve, in the absence of a better epistemology for grounding, to weaken the dominance of the notion in contemporary metaphysics.
Matters of Meaning
Chair: Alexandros Duskos
11:10 - 12:00
Pietro Lampronti & Daniel Wimmer: Necessary Truth Preservation Simpliciter
Logical consequence is taken to be necessary truth preservation in virtue of form. Necessary truth preservation without form can be called metaphysical consequence—it is a matter only of metaphysical necessity: A conclusion is a metaphysical consequence of a set of premises just in case it is metaphysically impossible that the premises be true while the conclusion is false.
We give an account of the metaphysical necessity that underwrites metaphysical consequence. We do so in a hyperintensional framework, consulting a state space familiar from truthmaker semantics. The relation of metaphysical consequence between a set of sentences and a sentence is explained via a relation between states of the state space: the relation of metaphysical necessitation. Drawing from the apparatus of truthmaker semantics, we discuss two candidate ways to explicate metaphysical necessitation: as a relation between (a) loose truthmakers or between (b) exact truthmakers. Both candidates are evaluated conceptually and formally.
We argue that such a hyperintensional framework, and especially candidate (b), is apt for accounting for metaphysical consequence mainly for conceptual reasons: Both (a) and (b) allow us to distinguish necessarily equivalent propositions, but (b) is more informative as to the nature of the metaphysical necessity underlying metaphysical consequence.
Formally: While in (a), metaphysical necessitation can be captured via the familiar notion of truthmaker-preservation (of loose truthmakers), in (b) it is not immediate what formal relation needs to hold between the states that are the relata of metaphysical necessitation. We discuss the possibility of making metaphysical necessity precise via an order relation of the relevant states: the exact truthmaker of a conclusion being below or equal to the fusion of the exact truthmakers of the premises. The state spaces of truthmaker semantics are generally held to be partial orders, the order relation being interpreted as parthood. However, if metaphysical necessitation is formalised in the proposed way, the resulting state space has to be modified: Since two distinct states can metaphysically necessitate each other, we need to relax anti-symmetry, so the resulting state space is not a partial order but merely a pre-order. From this, we can conclude that metaphysical necessitation can not be fully accounted for in terms of mereological parthood. Whether it can be fully accounted for by a unique relation, or it is the result of the workings of several relations holding simultaneously, we hope to investigate in future work.
12:10 - 13:00
Theodoros Giannopoulos: The Meaning Edge: What it’s Like Without Metaphysics
People tend to trust their experience. Logical Empiricists have taken that to a dogmatic extreme; only empirically verifiable statements have meaning. Yet, everyday life is rife with behavior born from unverifable (and unfalsifiable) premises; for example, we treat other people, animals, and maybe other objects not as mere phenomena, but as entities for whom there is something it is like to exist (famously worded by Nagel [1974]). That gap is hard to bridge by experience alone (Chalmers [1995]). 'Does my partner experience things like I do?' is a grammatically sound, logically formed, meaningful question, and yet not empirically verifiable in principle. In this paper it is going to be argued that metaphysical suppositions are necessary for meaning.
Empirical scientific statements, such as 'The surface temperature of the sun is 5500° C', aren't as innocent as they might seem, either. What does that proposition actually convey, and what happens when we remove its metaphysical grounding? Intersubjectivity, constancy of time and physical behavior, rigidity of our designations of nature, inference of the reliability of measuring instruments are not what we would call empirically verifiable in isolation (Quine [1951]), they span the fields of metaphysics and logic rather than answering individually to empirical testing.
Let us imagine an individual that genuinely doesn't believe in the necessity of other minds and constancy of time (a peculiar mix of epistemic solipsism and presentism), call them a spatiotemporal solipsist. The spatiotemporal solipsist has the same experience that an identical individual with common beliefs about reality would have. They talk with a friend, or measure the temperature of the sun. Their experience isn't minimal, but it is all they have. What meaningful statement can this individual produce, without abandoning their agnostic position? Can they say 'I am talking with a friend' without constancy in time, a conception of intersubjectivity or friendship beyond their experience alone? Can they say anything about the surface of a star they can't ascribe a metaphysical reality to? Even saying 'It seems like I am talking with a friend/measuring temperature' would merely be to borrow metaphysical suppositions for the purposes of conveying meaning.
Carnap [1931] lambasted metaphysical statements as meaningless, but he made his point using seemingly logically contradictory or arbitrary examples. The inverse is the case. Consistent metaphysics are necessary for meaning, and the edge of spatiotemporal solipsism is used to draw a line from meaninglessness towards meaning.
13:00 - 14:30 Lunch break
Matters of Concept
Chair: Marvin Thinschmidt
14:30 - 15:20
Robert Finan: Conceptual idealism is not Metaphysical: Hofweber on Facts and Effability
Can linguistic analysis yield genuine and surprising metaphysical conclusions? Thomas Hofweber claims that Conceptual Idealism (CI)—the thesis that reality, understood as the totality of facts, is range-dependent on human minds—follows from Internalism about fact-talk as a substantial metaphysical result. This paper argues that CI, as Hofweber defends it, is metaphysically inert, exposing a recurrent problem with reasoning from language to metaphysics.
This paper’s argument proceeds in two stages. First, given Hofweber’s own account of quantification, the Structural Effability Thesis (SET)—that every fact is structurally effable—must be understood on its inferential reading: a conjunction of internal, language-relative claims of the form ‘that-p is structurally effable’. Since each conjunct of SET is purely linguistic and metaphysically inert, so too is their conjunction. Thus, SET cannot bear the metaphysical load assigned to it. Even if the alternative domain-conditions reading is permitted, it yields only a vacuously true universal claim over an empty domain, which equally fails to support CI.
Second, by tracking Hofweber’s commitments across languages of varying expressive power through a revised impoverished-language objection, it is revealed that ‘facts’ within his system just means ‘effable facts expressible in my language’. CI thus collapses to the claim that what we can truly state is limited by what we can state, which is a linguistic truism, not a metaphysical discovery.
Hofweber’s framework is therefore committed to a de facto quietism. It cannot coherently pose the question of structural effability as a genuine metaphysical question, let alone resolve it in favour of idealism. Internalism does not entail metaphysical idealism, and the label ‘idealism’ actively distorts by importing connotations of mind-dependence that the internalist framework cannot sustain. This failure is instructive beyond Hofweber’s system.
15:30 - 16:20
Chad Hall: Higher-Order Vagueness and Ideal Language Philosophy
Ideal language philosophy, as embodied in the work of Gottlob Frege and (later) Rudolf Carnap, is a neglected approach to the problem of vagueness. According to this approach, natural language is defective in myriad ways, and these defects often manifest themselves as philosophical problems. Therefore, an ideal language, a formal language that is logically perfect and precise, ought to be used to solve—or, rather, dissolve—philosophical problems.
The ideal language philosopher’s diagnosis of vagueness has it that the problem—which is classically motivated by the Sorites paradox—is a byproduct of defective natural language predicates that admit of borderline cases. Hence, once we develop new predicates with well-defined extensions that do not admit of borderline cases, the problem is thereby dissolved. While this ostensibly solves the problem of first-order vagueness, it fails to address higher-order vagueness, such as when metalinguistic predicates are themselves vague or when it is not clear that something is a clear case of some arbitrary (and vague) object language predicate. Of course, the ideal language philosopher would say that they owe us no explanation for higher-order vagueness, since just as vague first-order predicates like “bald” are not terms in the ideal language, neither are vague metalinguistic predicates like “vague” and epistemic predicates like “clear.” Thus, the problem of higher-order vagueness does not exist for ideal language philosophy. The higher-order problem, with the first-order one, is thereby dissolved.
In this paper, I argue that ideal language philosophy’s dissolution of higher-order vagueness fails. Higher-order vagueness can be deflated through modal nesting, wherein we analyze higher-order vagueness in terms of iterated epistemic modality. However, in order to do that, we need to define the apparent higher-order predicates in terms of vague first-order predicates. Thus, ideal language philosophy faces a dilemma: either refuse to acknowledge higher-order vagueness or admit the vague predicates it was designed to exclude. If vagueness also vitiates our attempts at constructing ideal languages, this suggests that the problem of vagueness does not stem merely from linguistic sloppiness. Thus, if ideal languages must admit of some vagueness, then any attempt to fully eliminate vagueness through linguistic reform necessarily fails.
16:30 - 17:30 Keynote: Alice v’ant Hoff
Choosing (higher-order) metalanguages
Debates in philosophy often turn on what we take the background metalanguage to be. In this talk, I investigate which considerations should guide our choice of metalanguage, focusing on an issue that arises in higher-order metaphysics. In recent years, a number of philosophers, most prominently Agustin Rayo, have argued that if quantification in an n-th order language is absolutely unrestricted, then an adequate model-theory requires an (n+1)-th order language. This result might seem to create a pressure towards an ever-ascending hierarchy of metalanguages, metametalanguages, and so on.
Drawing in part on abductive approaches, I will argue against this kind of ascent. In doing so, I hope to shed some light on three related methodological issues: first, the role and limitations of appeals to theoretical virtues; second, the weight that should be accorded to rigour and intuition, where these desiderata pull in opposing directions; and third, and most pertinently, the role of logic in metaphysical enquiry.
19:00 Conference Dinner
L'Osteria Potsdam
DAY 2
DAY 2
09:30 - 10:00 Welcome
10:15 - 11:15 Keynote: Frédérique Janssen-Lauret
Logic and Metaphysics in Dorothy Wrinch's Theory of Judgment
In 1919, Dorothy Wrinch extended Bertrand Russell’s multiple-relation theory of judgment, first with logical forms and then with operators expressing quantification and sentence connectives, introducing her own novel formalism which prefigures the Polish notation. Despite answering the two major objections to the multiple-relation theory—nonsense and quantification—Wrinch’s paper has been sadly neglected. A minor Wrinch revival has recently begun, her proposal being the subject of a book chapter (Lebens 2017) and two papers (Felappi 2021, 2022), while also receiving brief favourable mentions in discussions of the multiple-relation theory. But all these authors assume that Wrinch posits logical forms, and none examine her formalism in much detail. Yet Wrinch makes explicit that ‘the form may be deleted’ (1919: 323). Her form-deleting system is of great historical interest, yielding a multiple-relation theory extended only with operators in prefix position and variable-free quantifiers, years before the earliest known use of these devices by Lukasiewicz and Schönfinkel. Historians have overlooked this until now because Wrinch’s formalism is incomplete and riddled with misprints.
I systematise Wrinch’s formalism and show how it frees her from ontological commitment to forms.
Matters of Modality
Chair: Leon Isenmann
11:20 - 12:20
Arkadiusz Synowczyk: Towards a Neo-Aristotelian Hybrid Metaphysics of Modality
Most work in neo-Aristotelian metaphysics of modality divides into two broad approaches: essence-first and powers-first. The former defines necessity as truth in virtue of essences, and possibility as what is not false in virtue of essences. The latter begins with possibility, understood in terms of potentialities, and defines necessity as the absence of potentialities for the contrary. A hybrid essence-and-powers approach, by contrast, has been considered by Vetter, but only to be rejected. This paper argues that such a view remains a viable option.
Vetter’s core objection is that a hybrid account cannot preserve the familiar dualities between necessity and possibility. This argument, however, relies on a particular formalisation of the relation between essences and potentialities. Specifically, Vetter requires the attribution of a potentiality for p, or of the absence of a potentiality for ¬p, to be evaluated with respect to the very same plurality X whose essences are invoked. I propose instead that the relevant biconditionals be formulated over the total configuration of essences and potentialities involved. On this basis, I argue that Vetter’s counterexamples do not establish the failure of duality. Moreover, given assumptions common to neo-Aristotelian approaches to modality, I show that the duality between essences and potentialities is bound to hold.
Beyond the problem of duality, Vetter argues that any account restoring the modal dualities threatens overdetermination. In response, I place the hybrid account within a more general account of objective modality. On this proposal, it is necessary that p iff ¬p is incompatible with the overall nature of the things involved, and possible that p iff p is compatible with that nature. This, however, does not introduce a separate ground of modality. Rather, in considering the nature of things to assess possibility and necessity, one is examining precisely essences and powers.
12:20 - 13:50 Lunch break
Matters of Frame
Chair: Leon Isenmann
13:50 - 14:40
Nike Frings: The relevance of feminist logic to Feminist Metaphysics
“Analytic feminist philosophers, by contrast, aim both to critique patriarchal social structures by utilizing mainstream philosophical tools and to shape mainstream philosophy with the help of feminist political insights” (own emphasis, Mikkola 2021, 213). Feminist metaphysicians for example address questions such as what kind gender is and engage in metatheoretical critique on metaphysical concepts and their values (famously by Sally Haslanger). Like other analytic metaphysicians, feminist metaphysicians can utilize logical tools to prove or support their theses. However, in recent years, feminists have encountered difficulties in this regard because the classical logical system operates binary. Think of “¬(p & ¬p)” which genuinely leads us to dualistic interpretations: p either holds or not.
As Plumwood, the first feminist logician, points out: “Dualism is a relation of separation and domination inscribed and naturalised in culture and characterised by radical exclusion” (Plumwood 1993, 447). To put it bluntly: through dualisms we create a hierarchical superior starting point and its opposite, the inferior derivative thereof. If we can only say that p is or is not the case, we make our statement and insights completely dependent on p; in other words, in many cases we define not positively but merely by negation. Imagine we ask ourselves whether S is a man and our logical analysis shows us that this is not the case. That doesn’t tell us much about S but merely defines S in contrast to something else, which doesn’t do S justice. These ex negativo statements make important aspects of S ́s being invincible. Another problem with dualisms Plumwood highlights is that of radical exclusion (cf. Plumwood 1993, 448-450). Dualisms lead us to polarized interpretations. Even if it is only one of many characteristics that led us to conclude that S is not a man, the conclusion “S is not a man” suggests that S has nothing to do with being a man. This is unsuitable for feminist ideas based on non-rigid and divers conceptions of gender. In conclusion, classical logical deduction is not exhaustive, especially not for feminist needs. Nevertheless, classical logic is often treated as exhaustive.
Finally, my presentation addresses the question of how this problem of feminist metaphysics and logic can be resolved. I will examen Plumwood, who advocates for a more differentiated treatment of classical logic. But I will also consider more modern accounts, such as the claim that it needs contradictory logic to face these problems (Ayhan 2025).
14:50 - 15:40
Siebren Telkamp: Noeist Logic and Meinongian Nihilism
In this paper I aim to show how a change in logical framework can redirect an established metaphysical debate. By adopting noneist logic, the ongoing debate between mereological nihilism and common sense will no longer be centered on semantics, but instead of ontological cost.
Mereological nihilism asserts that only mereological simples properly exist and that composite objects do not. It is vulnerable to a familiar objection based upon common sense: nihilism renders most familiar ways of speaking and propositions literally false. Such speech freely quantifies over composite objects. The standard remedy is van Inwagen’s (1990) paraphrasing strategy. This deviates the debate into one about semantics in which the costs of nihilism are conceptualized as the burden of a revisionary way of speaking. Such semantic strategies amount to damage control: they manage the symptom of common-sense conflict without engaging the underlying friction between the two views: the question of what there is.
I propose that an alternative logic, specifically the noneist logic tradition developed by Routley (1980) and subsequently Priest (2005), provides an unfamiliar way of bridging the gap between common sense and nihilism. This tradition treats the standard quantifier (∃) as ontologically neutral, ranging over any object in the Meinongian sense, whether it exists or not, and introduces an existence predicate (E!) to indicate strict existence. Using these logical resources, I argue that the nihilist can neutrally quantify over any composite object using the ontologically neutral ∃, while E! is solely used to indicate strict existence among simples. Hence, common propositions can be formalized in a straightforward sense with an alternative logic. Crucially, common-sense propositions do not have to be paraphrased: "the table has four legs" remains literally true, but the table has an unusual ontological status. The result is a two-tiered logical language representing a two-tiered ontology which incorporates strictly existing mereological simples and Meinongian composite objects into one coherent whole.
This method shows the force of logic in redirecting metaphysical debates. The nihilist is no longer participating in damage control, but is instead directly engaging the common-sense view on an ontological level. This is not without cost. The debate between the nihilist and common sense will be centered around which different types of being we desire in an ontology and whether composite objects are Meinongian non-existent objects with sosein. Thus, the costs are now less semantic in nature and instead ontological/metaphysical.
15:40 - 16:00 Final discussion
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