8th of June
9:00-9:30: Opening of the Conference
9:30-11:00: Keynote Speaker: Gillian Russell (Australian National University), Social Spheres
11:00-11:15: Coffee Break
11:15-11:55: David Grčki (University of Rijeka), Logical Evaluation Beyond Consequence: Rethinking the Monism–Pluralism–Nihilism Debate
12:00-12:40: [Online] Fabien Schang (Lycée Rosa-Parks), The Logic of the Left-Right Cleavage (as a Bivalent Structure of Political Thought)
12:40-14:00: Lunch Break
14:00-15:30: Keynote Speaker: Elia Zardini (Complutense University of Madrid), Becoming Something Else
15:30-15:45: Coffee Break
15:45-16:25: Anthony Stoner (University of California, Riverside), Philosophy of Logical Practice
16:30-17:10: [Online] Rashed Ahmad (Kuwait University and CUNY), From Vagueness to Liberation
Conference dinner at the Alterez-vous restaurant https://www.alterezvous.be/
9th of June
9:00-9:30: Opening of the Conference
9:30-11:00: Keynote speaker: Franci Mangraviti (ETH Zurich), Can a theorem be harmful?
11:00-11:15: Coffee Break
11:15-11:55: Becca Kosten (University of Minnesota), Mutual, Non-Dominant Strategies for Dialogue Across Difference
12:00-12:40: Noah Greenstein (unaffiliated), Inference & Punchline
12:40-14:00: Lunch Break
14:00-15:30: Keynote speaker: Ellie Ripley (Monash University), Mayonnaise and genderqueer logic
15:30-15:45: Coffee Break
15:45-16:25: [Online] Mehmet Mirioğlu (Bilkent University), Infinite Regress and Tarskian Hierarchy: Dissolving Yablo's Paradox
Gillian Russell (Australian National University), Social Spheres
This paper adapts Lewis’ “Ptolemaic Astronomy” from Counterfactuals for use in thinking about social hierarchy and subordination.
David Grčki (University of Rijeka), Logical Evaluation Beyond Consequence: Rethinking the Monism–Pluralism–Nihilism Debate
The debate between logical monism, pluralism, and nihilism is typically framed in terms of logical consequence: whether there is exactly one, more than one, or no correct consequence relation. This framing presupposes that logical evaluation, i.e. assessment of inferences as valid or invalid, is fundamentally a matter of determining what follows from what. In this paper, I argue that this presupposition is too narrow. Logical evaluation cannot be adequately understood in terms of consequence relations alone. Once we adopt a broader conception of logic, inspired by recent work by Williamson (2013, 2022), the traditional opposition between monism, pluralism, and nihilism is significantly reshaped, and some of the central pressures motivating pluralism and nihilism are defused.
I begin by examining the standard conception of logical consequence as characterized by truth-preservation, formality, necessity, and normativity. While these features capture an important core, they do not by themselves settle how logical evaluation should proceed. In particular, the normativity of logic, i.e. its role in guiding reasoning, remains contested. If logical consequence is essentially normative, then evaluating an inference involves more than checking a relation between sentences; it involves assessing reasoning against standards that are themselves subject to philosophical dispute. This already suggests that logical evaluation may not be exhausted by any single formally defined consequence relation.
The limitations of consequence-based approaches become apparent when we consider the main positions in the debate. Logical monism holds that there is a single correct consequence relation, often identified with classical logic. However, familiar challenges—such as the paradoxes of material implication and the principle of explosion—put pressure on the claim that classical consequence captures all legitimate inference. Logical pluralism responds by allowing multiple admissible consequence relations, as in the case-based pluralism of Beall & Restall(2006), where different specifications of “cases” yield different validities. Yet pluralism faces serious difficulties. It struggles to explain the unity of logic, since if multiple consequence relations are equally correct, it becomes unclear what makes them all instances of the same subject. It also threatens to undermine the notion of genuine logical disagreement: if different logics are equally correct, disputes between them risk collapsing into merely verbal or framework-relative differences. Moreover, pluralism faces a metalogical challenge: it must explain which logic governs the reasoning used to formulate and defend pluralism itself.
Logical nihilism pushes these concerns further by denying that any formal consequence relation adequately captures natural-language inference. Arguments from diversity and expressive limitation suggest that no formal system can fully represent the richness of informal reasoning (Cotnoir 2018), while Russell (2018) doubts the existence of exceptionless logical laws. However, nihilism faces its own instability. If no consequence relation is correct, it becomes difficult to account for logical error, disagreement, and criticism, and the arguments for nihilism themselves appear to lose their normative force.
I argue that these difficulties arise in part because the debate assumes that logical evaluation is fundamentally a matter of consequence. This assumption forces all positions to compete over the same narrow target: the correct specification of a consequence relation. As a result, pluralism and nihilism gain traction when no single relation seems able to capture all aspects of inference, while monism appears overly restrictive. However, this framing overlooks a broader role of logic.
Drawing on Williamson’s work, I propose that logic is better understood not primarily as a theory of a metalinguistic relation of validity, but as the study of highly general structural truths about reality. On this view, logical laws are not merely statements about which arguments preserve truth, but expressions of general features of how things can and cannot be. Logical evaluation, correspondingly, is not exhausted by checking whether a conclusion follows from premises under a given consequence relation. Rather, it involves assessing whether an inference respects these general structural constraints.
This shift in perspective has several consequences. First, it explains why consequence-based accounts face persistent difficulties: they attempt to capture logical evaluation at the wrong level of abstraction. Second, it provides a new way of understanding logical disagreement. Disputes between proponents of different logics need not be disagreements about a single consequence relation; they may instead reflect disagreements about which structural features of reality are relevant to evaluating inference. This allows for a form of disagreement that is neither merely verbal nor straightforwardly contradictory, but nevertheless substantive.
Finally, the broader conception of logic supports a modest form of monism. If logic is unified by its subject matter—highly general structural truths—rather than by a single formally defined consequence relation, then the unity of logic does not depend on identifying one privileged calculus. At the same time, this view avoids the permissiveness of pluralism and the instability of nihilism. It preserves the idea that there is a single subject matter of logic, while allowing that different formal systems may capture different aspects of that subject matter.
The conclusion is not that the debate between monism, pluralism, and nihilism is misguided, but that it is incomplete when framed solely in terms of logical consequence. By shifting the focus from consequence relations to logical evaluation and its underlying structural basis, we can better understand both the appeal and the limitations of the competing positions, and reopen a more promising path for a unified account of logic.
Fabien Schang (Lycée Rosa-Parks), The Logic of the Left-Right Cleavage (as a Bivalent Structure of Political Thought)
Logic is applied to political discourse, following the results of a book devoted to the political right-left cleavage and forthcoming by April 30.
The entire line of reasoning consists of fifteen deductive steps. It runs as follows:
(1) The language of politics is a speech theory based on value judgments with respect to some model of social harmony; such a speech includes general relations such as the opposition between the concepts of left and right.
(2) Any attempted definition of the concepts of left and right results from a conceptual construction inside a political lexical field; thus, it relies on a set of theoretical choices in the definition of both concepts, among which the middle term of center.
(3) The meaning of the concepts of left and right cannot be afforded in terms of truth-conditions, due to their normative import.
(4) A speech act theory is in position to throw some light on their intended meaning, on the basis of a theory of statements in terms of illocutionary force and propositional content.
(5) Political speech can be accounted both in terms of expressive speech acts and inference relations between such acts; but it faces theoretical difficulties like the Frege-Geach Problem.
(6) A solution to this difficulty lies in the hybrid nature of political speech, by virtue of which any statement of this form includes both an assertive and expressive import that characterizes the “thick” concepts of left and right.
(7) The thickness of political concepts requires a “light weight” reading of the concept of truth, by virtue of which any political statement may be told true (or false) without corresponding to any state of affairs.
(8) The connection made between truth values and moral values helps to introduce moral inference rules, isomorphic to the logical inference rules of Modus Ponens and Modus Tollens.
(9) The concepts of left and right may be parsed off formally by means of a combination of speech act theory and moral inference rules, irrespective of the historical context that makes sense of political parties and their various ideologies.
(10) Political speech results from such a formal combination, and three distinctive models may be set forth in accordance to the established relation between the metapolitical concepts of left and right and ideological concepts.
(11) The first model is predicative. According to the latter, political speech proceeds from a number of issues whose combination yields some peculiar political position; the left-right distinction results from, or is one the ensuing items of, such a combination.
(12) The second model is relational, according to which the meaning of the concepts of left and right is not absolute but, rather, relative to the judgment made by a given political agent about another agent and on the basis of the assessment criteria assigned to the latter.
(13) The third model is inferential : the meaning of the concepts of left and right turns on both a kind of agent, a corresponding ideological commitment, and the attitude such an agent is deemed to have in accordance with some moral inference rules.
(14) The latter model is preferred over the preceding two ones, in the sense that it brings a
univocal definition of the metapolitical concepts of left and right in addition to their subdivisions that are extremes and centers.
(15) The concept of extreme center is introduced into the traditional representation of the political landscape; it is presented as a kind of political attitude that is morally inconsistent.
Assuming that logic proceeds as an abstract theory of three main structures: ordering, algebraic, and topological, the left-right cleavage may be accounted for and organized in terms of these complementary structures. The talk will focus on three specific parts of the book that correspond to each of these three abstract structures.
1. The dimensions of politics (Topological structure)
The usual representation of the political landscape as a one-dimensional line implies some a priori conclusions on political thought: extreme left and extreme right are maximally opposed to each other; center is none of these and lies between right and left. A number of alternative representations is proposed, including non-linear or many-dimensional structures, and a corresponding debate is proposed around many-valued logics to show that the political landscape is bivalent without reducing to any black-and-white content. This will lead to the ultimate model of a question-answer semantics, where the usual true-false dichotomy of single bivalence is replaced by a more comprehensive view of expressive bivalence in terms of ordered yes-no answers. Values are thus thought of as structured ordered objects, rather than single elements.
Furthermore, the relational model of the left-right cleavage helps to make sense of the reason why extreme agents tend to reject most of their fellows in the opposed side of the cleavage, in light of Julien Freund’s view that one chooses one’s own friends whilst one is chosen by one’s declared enemies. Such an asymmetric relationship between friendship and enmity will be explained by means of a relational model of the left-right cleavage.
2. Naming and Order (Ordering structure)
Borrowing to Kripke’s discussion of the Kantian classification of truth judgments, an analogous case is presented inside political discourse. Such an alternative classification is based on a two-tiered distinction between metaphysical and epistemological concepts in the Kantian tradition: analytic and synthetic, on the one hand; a priori and a posteriori, on the other hand. Correspondingly, Kripke’s view that necessary judgements may be a posteriori (and contingent judgments may be a priori) is made on a par with the view that right-wing agents may be progressivists (and left-wing agents may be conservatives). A corresponding structure of opposition is derived from these isomorphic considerations, with the help of a corresponding question-answer semantics that makes sense of these political attitudes in terms of ordered Boolean values.
3. Left nazism? Right expressivism! (Algebraic structure)
Starting from Jair Bolsonaro’s statement, “Nazism was a left-wing political party”, the point is to deconstruct Bolsonaro’s rationale as a set of complementary Aristotelian and hypothetical syllogisms.The Frege-Geach Problem is tackled with respect to the hybrid import of political speech, and a comparison is made between assertive and expressive statements to show that both rely on analogous inference rules. The final result is a reconstruction of Leo Strauss’ reductio ad hitlerum as a modal inferential rule that proceeds like Modus Tollens into a bivalent imperative logic. The modal import of such rules makes sense of the extremes in the political
landscapes, and a corresponding classification of political attitudes is proposed in terms of partition semantics.
If any part of the aforementioned steps are taken to be essential toward a formal theory of political speech, then political and moral philosophy may make some fruitful use of these. Philosophy of language includes these both areas of philosophy to yield the intended essay on metapolitics, by analogy with the akin area of metaethics: just as the latter doesn’t afford any precise content fo the concept of good, metapolitics doesn’t purport to afford the tenets of an alleged “good” political thought; rather, it merely aims to account for the basic workings of political speech.
Finally, the basically polemical nature of political activity accounts for the relevance of the concepts of friendship and enmity, on the one hand, but also the explanatory role played by the left-right opposition with respect to any political behavior. Whilst the meaning assigned to both concepts largely depends on various periods of time and places, it is one and the same process of agreement and disagreement that always occurs between any political agents in order to make sense of their activity whose central purpose is the achievement of common good. For all the reasons, the concept of opposition is taken to be essential to politics and, accordingly, the theory of logical opposition appears as an appropriate tool of analysis for the corresponding political speech. Such a speech relies first and foremost on some criteria of ideological commitment and the moral attitude taking any ideology as good or bad. The resulting project of formal politics may be viewed as an extension of formal ethics, finally: the former is a particular case of the latter, both dealing with the concepts of good and evil whilst the first theory restricts these to the particular area of common good.
Elia Zardini (Complutense University of Madrid), Becoming Something Else
This paper discusses a specific puzzle of change concerning what is the case in the result of change, as when e.g. a lump of clay becomes a statue of a boy. In the result of that change, it would seem that the lump has become the statue, and so that the lump is the statue. However, in what sense can a lump be a statue? After critically reviewing some natural and traditional views on the issue that weaken the sense in which, in the result of the change, the lump is the statue, I develop my own proposal, which vindicates that idea in its strongest sense, while respecting the platitude that nothing can be both a lump and a statue. The proposal starts with the idea that, in the result of the change, the state of affairs that x is the lump is unstable in that it determines the state of affairs that x is the statue. This metaphysical circumstance is then observed to give rise to the logical circumstance that contraction fails. By representing natural-language predications in terms of formal-language restricted universal quantifications, it is subsequently shown that the resulting system provides a theory on which indeed the lump is the statue while nothing can be both a lump and a statue. I close by drawing out some consequences that the proposal has for the notions of predication, existence and identity, and by indicating how it can be extended to deal with several other puzzles in the vicinity.
Anthony Stoner (University of California, Riverside), Philosophy of Logical Practice
I argue for a philosophical elaboration of logical practice, analogous to the turn taken in contemporary “philosophy of mathematical practice.” I argue that a practice-focused philosophy of logic is an integral part of naturalism about logic—a resolute denial of the positing of Platonist or otherwise supernatural entities to explain logic, and an attempt to view logic as arising from and embedded in human material activity. Any such logical naturalism, I argue in my dissertation, must involve a reorientation of philosophy of logic from foundational epistemological and metaphysical issues to historical ones about the development of logic and sociological ones about the practices involved in doing logic.
What exactly does it mean to “do” logic, however? As students of logic, we engage in learning different logical systems and different logical theories; as reasoners, we attempt to bracket various beliefs about the real world to focus only on inferential connections of validity, and grasp compatible and incompatible assertions; as logicians in our own right, we experiment with and develop different logical systems, e.g., in formalizing proofs of various conjectures, or in tracking the implications of some axiomatic system. The notion of “doing” logic doesn’t do very much for philosophy of logic beyond point us back to a notion of logic as something more than a merely static body of content, but as an activity, which we can learn and in which we can engage. But to understand the notion of logic as an activity, we need further to analyze the fuzzy notion of “logical practice(s)” we’ve been working with.
A first-pass analysis of the notion of “logical practice” might result from a view from above: We could perhaps decompose the activity people doing logic engage in into its constituent parts. Just as we might analyze the activity of religion in terms of practices of sacrifice, spiritual meditation, social union, etc., or we might analyze the activity of philosophy in terms of practices of interrogation, argumentation, conjecture, proof, and abduction, we ought to be able to analyze the activity of logic into constituent practices. Even if doing so won’t give us a definite content of logic any more than a similar sociological analysis of philosophy or of religion as an activity would give us a definite content of either, it ought at least to give us a general understanding of how the activity works, of how different practices might contribute to the unity of some human activity.
At the very least, from above then, perhaps we could analyze the constituent practices of the activity “logic” as including (a) cognitive practices of bracketing information deemed irrelevant to “purely” or “strictly” logical matters, (b) cognitive or notational practices of regimenting information, (c) practices of constructing conjectures, proofs, and models, (d) practices of disputation about the best practices for (a-c). By no means should this list be considered exhaustive or complete. We might think of (b) as the ways we come up with the syntax of a language, or the form of our diagrams, and so on; orof (c) as the ways we determine the semantics of our logical vocabulary or language, and explore the inferential relations in which parts of our given language or system stand to one another. (Note that thisway of putting the matter says nothing about what sort of inferential relations those must be—formal ormaterial, etc.). I would suggest these are what we could call internal practices of the activity.
But any sufficiently naturalistic account of a branch of human activity should consider not only the practices internal to the activity but practices external to the activity or at least the activity “as such,” the activity “proper,” but which are necessary for its continuation or at least its institutionalization, its survival among other human activities and its ability to fulfill human needs in some social setup. In other words, a full naturalistic account of a branch of human activity must address the social reproduction of that activity.
This first-pass analysis of “logical practice” ought to clear up a few issues: First, “logical practice” should not be taken as a technical term but as a generic name for the things that people doing logic do. Therefore, my argument for a “philosophy of logical practice” should be taken as a call for a reorientation to the things logicians, students, and ordinary reasoners do, and an assertion of the explanatory importance of these things to what is normally deemed “logic proper.”
Analogous turns in philosophy of science or philosophy of mathematics have been solicited and to some degree undertaken. Significant literature has been devoted in philosophy of science and Science and Technology Studies (STS) on the relevance of laboratory practices, pedagogical practices, and broader social connections to issues proper to some science or another. Similarly, in the past thirty years, philosophers and mathematician have begun explicitly to address the relevance of “mathematical practice” to mathematics proper.
Secondly, my call for a “philosophy of logical practice” is a call for a philosophical reorientation to the plural practices involved in logic. In other words, “logical practice” should not be taken as a homogeneous and neatly definable, separate sphere. What we need to do in explicating a philosophy focused on logical practice is to give an account of the relation between different practices involved in logic to one another, and to the more abstract and canonical content of logic proper—logical vocabulary and connectives, norms of reasoning, etc. In tracing this relationship between practices and “logical content,” we need to maintain both a forward- and backward-looking perspective: A fully developed philosophy of logical practice needs to explain both how the activity of the embodied, material animal beings we are becomes structured so as to produce “logical content,” and the relation between “logical content” and the subsequent activities of human beings themselves.
Much philosophy of logic—largely taking its cue from Russell—has denied that these practices have an explanatory role with respect to the content of logic. At most, these are taken to be necessary conditions of the disciplinary practice of logic, but extrinsic to logic proper. However, there also exist significant figures within the history of logic and philosophy of logic who have focused on these practices as related in some way to, if not wholly determinative of, the content of logic. In other words, certain philosophers of logic and their followers have focused on the pragmatics of logic as a way systematically to philosophize both about the role of logic in philosophy and life, and the semantics of logical vocabulary and, with it, the relationship of logic and natural language. Among these more practice-focused philosophers, we could include Charles Sanders Peirce, Imre Lakatos, Robert Brandom, and Catarina Dutilh Novaes.
Each of these practice-focused philosophers, however, has approached the topic of the practices involved in logic in different ways. Peirce, as one of the progenitors of modern formal logic, actively considered the relationship between the formal and symbolic, and the human practices which give themsignificance, in connecting his semiotics, as a general theory of human significance, to logic. Brandom, as someone heavily influenced by Peirce’s pragmaticism, has largely focused on the relation of the pragmatics of inferences as the basis for the semantics of logical vocabulary in the development of his inferentialism. From a different tradition, Lakatos’ work in the philosophy of mathematics helped lay the foundations for interpreting proofs in terms of a social process of proving. In other words, although most of Lakatos’ work is focused in philosophy of mathematics rather than philosophical logic directly, by interpreting the notion of proof, central to modern formal logic, in terms of “moves” made by different participants in a dialogue, he opens the door for a dialectical perspective of a central logical notion. This perspective is one taken up by Dutilh Novaes’ genealogical method which attempts to apply this Lakatos-inspired dialectical perspective to deduction and to historicize it by attempting to show how the social, dialogical roots of deduction could have been obscured in the history of a progressively more formal discipline.
Rashed Ahmad (Kuwait University and CUNY), From Vagueness to Liberation
In assessing different logics, we appeal to the theoretical virtues the logics may enjoy. These theoretical virtues include (but are not necessarily limited to) expressive power, generality, topic-neutrality, simplicity, elegance, and adequacy to the data. In terms of expressive power and generality, Jonathan Erenfryd and I argued in Classical Logic of Paradox (forthcoming) that CLP can accommodate naive theories of truth, validity, and paradoxicality without the threat of revenge and metainferential paradoxes nor of overinternalization of semantic concepts. Additionally, in Overinternalization Issues: -inconsistency (Manuscript), I show that first-order CLP can accommodate a theory of (standard) arithmetical truth, and that theory is -consistent. These results stand witness to CLP's expressive power and generality. However, for a logic to be general, it must also be able to accommodate other theories, such as queer feminist and liberation theories. In this paper, we nominate CLP as a good candidate for serving as the basis of a theory of liberation. Before doing so, however, we argue that, given the analysis of Val Plumwood's argument that classical logic creates a natural hotspot for dualisms that promote oppression, there is a tight relation between theories of liberation and theories of vagueness. So, for a logic to even qualify as a basis for a theory of liberation, it must first be able to be a basis for a theory of vagueness. Thus, we first show how CLP handles vagueness, then present and defend Val Plumwood's argument against classical logic, and show that classical logic is neither topic-neutral, simple, nor elegant. Finally, we show how a theory of liberation built on CLP fares compared to other proposals in the literature.
Franci Mangraviti (ETH Zurich), Can a theorem be harmful?
When it comes to acknowledging potential for harm, there is a growing body of literature reducing the distance between logic and other disciplines. However, how this can or should affect the status of particular logical laws (whether basic or derived) remains undertheorized. In this talk I distinguish several ways in which logical laws are interacted with, and for each I examine - through examples - whether it can lead to harm. If time permits, I will also discuss what kind of responses any such harms might warrant.
Becca Kosten (University of Minnesota), Mutual, Non-Dominant Strategies for Dialogue Across Difference
Early models of social identity in a feminist logic context have focused on how individual agents conceptualize their own identities. However, in order to meet the needs of intersectional feminist movements, models must account for how agents negotiate social positions in shared contexts. This paper seeks to expand existing models to represent such negotiations in dialogue between agents across difference.
The initial focus on individual agents in the literature is sensible, in light of Plumwood's argument that classical negation is the underlying culprit behind several feminist critiques of logic. In direct response to this argument, Eckert and Kosten have each explored alternative, non-classical negations for modeling individual agents' approaches to social identity.
Nevertheless, while these models do demonstrate better alternatives to classical negation, particularly with regard to the relationships between specific dominant groups and their corresponding subordinated others, they are not sufficient to meet the needs of intersectional feminist movements today.
To remedy this limitation, I return to the initial development of intersectionality as both living practice and social theory in Black feminist traditions in the United States in order to bring existing models into better alignment with these approaches. As emphasized by Collins, Isoke, and Stewart in their individual analyses of intersectionality, nothing is truly intersectional if it is isolated to a single individual. Rather, intersectionality emerges as a dynamic response to social structures and a fundamental aspect of interactions across difference.
These requirements suggest that models can be improved by focusing not just on individual conceptions of social identity, but also on how shared understandings of social position are negotiated. Consequently, based on Dembroff and Saint-Croix's analysis of agential identity as the mediating factor between social identity and social position, I map out several common starting points for dialogue across difference.
Then, grounded in and inspired by Audre Lorde's understanding of mutual, non-dominant difference, I create a series of models in Heyting-Brouwer logic to examine three sorts of moves agents might make to alter these starting points when in dialogue with one another.
First, agents sometimes adjust the shared model through shifting relevancy constraints as certain types of social position become more or less salient. Such shifts can occur through calling attention to a shared position in an effort to create foundations for joint advocacy or through calling attention to previously unacknowledged differences which demand more nuanced treatment.
Second, agents often engage in conceptual revision when prompted by an interlocutor. Typically, such prompting occurs because an agent's understanding of available social positions does not include their counterpart's full position in some way. Lorde herself spent much of her career challenging people to engage in such revisions, be it white women who centered their own concepts of womanhood in feminist organizing, activists in the gay rights movement who focused exclusively on the rights of same-sex couples, or civil rights leaders who focused on the rights of Black men at the expense of the broader Black community.
Third, agents frequently impact models through changing their attitudes toward specific identity categories. This can happen when an agent shifts their own desired social position or when they recognize the social position of their counterpart in a new way. In addition to reflecting each agent's understanding of themselves, these attitudes reflect how deeply interlocutors understand one another's positions.
Once these moves are presented, I use this framework to demonstrate why demands for shared identity and fellow feeling are often counterproductive, despite their commonality in surface-level organizing. This commonality is present in several problematic approaches to feminism, such as those recently identified by Khader in her analysis of the myths supporting white feminism, Schuller in her counter-history of who ought to be lauded as heroes of the feminist movement, and Lewis in her searing account of reactionary feminist stances which cause more harm than good.
In contrast to such approaches, I argue that conceptual compatibility and mutual recognition provide much more effective grounds for intersectional feminist advocacy today. Furthermore, since these models of dialogue across difference provide such grounds, they serve as a helpful guide for anyone looking to build truly intersectional approaches to feminist logic.
Noah Greenstein (unaffiliated), Inference & Punchline
What is the logic of a joke? There seems to be an almost too simple parallel between a joke set-up and punchline, and the premises and conclusion of a proof. The difficulty is that if the punchline of a joke followed just like the conclusion of a proof, there wouldn’t be anything funny about it: logical conclusions are trivial consequences of the premises. On the other hand, following the Incongruity Theory of humor, the logic of jokes should rely upon contradictory, incongruous conclusions to generate the humor. However, this yields the exact same problem: contradictions aren’t inherently funny either. So there is a problem with both the punchline following from the set-up or the punchline contradicting the set-up in that neither captures what is funny about a joke. Irrespective of the structural similarity between jokes and proofs, is then logic simply just not the right tool for studying humor?
In this paper I seek to give a logic of jokes. Achieving this will require sophistication beyond what might initially appear to be a straightforward logical formalization. First we’ll need to find a way to represent the incongruity of jokes that maintains the significance of the premises and punchline so that they do not become logically trivial. This will require us to formalize the social or linguistic norms that are usually involved in the set-up of a joke. I’ll use Deontic Modal logic to represent these norms as obligations, that is, the set-up of a joke will have background assumptions formalizable in the form, "It is normatively obligated that ...". We then can see jokes as deploying multiple incompatible obligations. Having competing obligations, that is, obligations with incompatible commitments, is a classic philosophical dilemma, going back, at least, to Plato’s Republic (331c). Not only does this sort of dilemma respect the non-trivial incongruity of jokes, it is also formally schematizable: Op ∧ O¬p. Since IS does not follow from OUGHT, as many things that ought to be the case do not exist, formulas of this form (Op ∧ O¬p) do not reduce to contradiction (p ∧ ¬p). And yet they are recognizable as deontically problematic.
Even generating such normative dilemmas will not be logically straightforward. Most jokes aren’t laying out all their background assumptions, and even if we try to list all assumptions, it is not clear we will get a dilemma of the right sort (Op ∧ O¬p) as a matter of deduction. In place of deduction, abductive inferences will be used to select the right sort of norm. I’ll argue that in the context of a joke set-up, the relevant norm that follows from the abductive inference will be obvious: that the norm is obvious is what makes a good set up and punchline.
Finally, merely having a conflict of normative obligations is not sufficient for humor, though: not being able to satisfy your obligations is an unhappy state of affairs. The difference between a joke and a moral dilemma, I will claim, is that the joke will always rank one normative obligation as more fundamental than the other. This move is historically justified in that the classic Superiority Theory of humor, going back to Plato, Hobbes and up through the modern day, necessarily involved putting the joke teller socially higher and someone else socially lower. However, in terms of logic, having one norm effectively "cancelled" in favor of another is structurally like dismissing a premise in a proof by contradiction. Just as we take on a hypothetical premise in order to show it yields a triviality and must be false, the initial norm taken on by the joke set-up is then treated as if it yielded a triviality via the dilemma of obligations. It is thus dismissed and we are left with the competing normative obligation as the fundamental norm. Getting this easy answer to what appeared to be a normative dilemma, this return to a fundamental background norm, I contend, is part of what we find enjoyable in humor.
While these sophisticated logical operations are used to explain the logic of jokes, taken together they don’t require more than a few lines in a proof, and nothing that we couldn’t expect an audience to be able to follow. The logic also covers a wide variety of jokes and humor. Moreover, this account provides an answer to one of the outstanding questions in the Incongruity Theory of humor: how to make sense of an incongruity or contradiction when they are usually just sources of confusion and trouble. By casting them as normative dilemmas with (perhaps overly) easy solutions, it shows how jokes have non-trivial value.
Ellie Ripley (Monash University), Mayonnaise and genderqueer logic
In "Purity, impurity, and separation" (1994), Lugones distinguishes two types of separation: split-separation and curdled-separation. Split-separation, like separating the yolk from the white of an egg, aims at a clean unmixture: to the extent that any yolk remains in the white or vice versa, the project has not totally succeeded. Curdled-separation, like when mayonnaise de-emulsifies, is a messier business: sure, the oil and water come apart more than intended, but not in any clean way, not any way that would allow them to be split back into different bowls. Lugones uses this distinction between kinds of separation to discuss a range of oppressed and resisting identities, drawing particularly (but not exclusively) on interplay between cultural identities at the US/Mexico border.
I've been thinking about this Lugones paper recently, as I read Eckert's forthcoming "De-centering and genderqueering Val Plumwood's feminist logic", which offers an application of FDE (done on the American plan) as capturing the way genderqueerness destabilises binary gender categories, by adding two options to each categorisation: for example, someone can be a man, or not a man, or both, or neither.
In this talk, I'll argue that Eckert's discussion does not achieve its stated goals, basically for reasons articulated by Lugones. The four-valued approach, like its close relative the more classical two-valued approach, is an application of split-separation only. That's going to massively distort genderqueerness, which often involves heavy doses of curdled-separation as well. I will instead defend Eckert's application of FDE on other grounds: as itself destabilising the split-separated worldview that it, and much other philosophical logic besides, takes as background.
Mehmet Mirioğlu (Bilkent University), Infinite Regress and Tarskian Hierarchy: Dissolving Yablo's Paradox
Although Yablo claims to have constructed a paradox that escapes Tarski's hierarchical framework by eliminating self-reference, a principled extension of Tarski's own commitments is sufficient to dissolve it.
Yablo's paradox is standardly presented as a decisive challenge to hierarchical solutions to the liar paradox. Tarski's strategy restricts the application of the truth predicate across language levels: a sentence at level Ln can be evaluated for truth only from a strictly higher level Ln+1. This restriction is typically understood as targeting sentences that apply the truth predicate to themselves, whether through direct selfreference or via a finite referential loop. Yablo's construction appears to exploit this narrow reading. He introduces an infinite sequence of sentences S0, S1, S2, ... such that each Sn asserts the falsity of all sentences Sk with k > n. Since no sentence refers to itself, and all reference moves strictly forward along the sequence, the construction seems to fall outside the scope of Tarski's hierarchy. The standard derivation then yields a contradiction: assuming any Sn is true forces the truth and falsity of Sn+1 simultaneously, and assuming no sentence is true vindicates S0, reinstating the contradiction. On this basis, Yablo concludes that self-reference is not the source of semantic paradox, and that hierarchical approaches fail to diagnose the problem correctly.
This paper argues that the conclusion does not follow. Yablo's argument presupposes that the sentences in the sequence are already available for truth evaluation: that each Sn is a meaningful truth-bearer to which the predicate T can be coherently applied. This presupposition is never defended. It is simply taken for granted. The present paper challenges it by making explicit a condition already implicit in Tarski's framework, which I call the Level-Determinacy Condition on Truth (LDC).
The LDC states that a truth attribution T(φ) is semantically meaningful only if φ occupies a determinate level in the semantic hierarchy that is, only if there exists some Lk such that φ ∈ Lk. This is not an external constraint added to Tarski's theory. It is a condition that falls directly out of the structure of that theory: Tarski's truth predicate is defined relative to a language level, and its meaningful application presupposes that the target sentence has been assigned to one. The LDC simply makes this applicability condition explicit.
When the LDC is applied to Yablo's sequence, the construction fails at a prior stage. The truth of any Sn is semantically dependent on the truth values of all sentences Sk with k > n. Each such sentence is in turn dependent on all sentences further along the sequence. Because the sequence is infinite, this chain of semantic dependencies never bottoms out. No sentence can be assigned a determinate level compatible with the structural constraints imposed by truth attribution: since Sn makes truth claims about all later sentences, it must occupy a level strictly higher than each of them; but since Sn's truth depends on those sentences, they must occupy a level at least as high as Sn. These requirements jointly produce a conflict that no level assignment can resolve. For every n, the conditions ∀k > n [Level(Sn) > Level(Sk)] and ∀k > n [Level(Sk) > Level(Sn)] cannot be simultaneously satisfied. The sentences therefore fail to meet the preconditions for truth evaluation. The truth predicate cannot be meaningfully applied to any element of the sequence.
A natural objection is that an arbitrary initial level assignment could be stipulated to get evaluation started. The paper argues that this objection misunderstands the role of levels in Tarski's framework. Levels are not external labels that can be freely attached to sentences; they are determined by the semantic relations that sentences bear to one another. A truth claim about a sentence fixes a structural constraint on the relative positions of the two sentences in the hierarchy. Stipulating a level for Sn does not dissolve the conflicting constraints, it relocates the problem without addressing it. Moreover, allowing arbitrary level assignment would reopen the liar paradox itself, since the same strategy could be applied there. Tarski's solution depends on levels being structurally determined, not conventionally fixed.
The conclusion is that Yablo's sequence does not produce a genuine semantic paradox. What it produces is a case of semantic indeterminacy: the conditions required for meaningful truth evaluation are never satisfied, and so the contradiction Yablo derives never arises. Yablo's construction does not escape the Tarskian hierarchy: it fails precisely where that hierarchy sets the preconditions for the application of the truth predicate. The broader implication is that the boundaries of formal semantic theory are wider than Yablo's challenge suggests: a hierarchy understood not merely as a device against self-reference, but as a framework for governing the applicability conditions of the truth predicate, remains fully adequate to the case.
More generally, the LDC points to a question that any application of formal logic must face: whether the preconditions for meaningful evaluation are satisfied before the apparatus is set in motion. Attending to these preconditions is prior to any question about the scope or limits.