Susanne Bobzien

In my talk I offer a mildly revisionist logic of identity that makes room for the possibility of vague objects at the level of logic without undermining the use of the identity relation in mathematics. The paper challenges Evans’s infamous and still widely accepted 1978 argument that indeterminate identity is incoherent and that any coherent notion of identity must be governed by the modal system S5, with a determinateness operator in lieu of the necessity operator. Building on a suggestion by Ken Akiba (2014) and my own view on vagueness (Bobzien 2025), the talk replaces Evans’s S5 with something a little more flexible.

Rashed Ahmad

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 (manuscript) 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 Issues of Overinternalization: ω-inconsistency (manuscript), I show that first-order CLP can accommodate a theory of (standard) arithmetical truth, and that theory is ω-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.

Teresa Kouri Kissel

Ferrari and Orlandelli (2019) propose that an admissibility condition on a proof-theoretic logical pluralism be that the logics in question must be harmonious. For them, this means that they must have connectives which are (a certain brand of) unique and conservative. This allows them to develop an innovative pluralism where the admissible logics are both useful and balanced, which shows variance on two levels: the level of validity and the level of connective meanings.

Here, I will show that we can extend the system one step further, and induce a three-level logical pluralism, which better fits the criteria of usefulness and balance. The first and second levels remain as suggested by Ferrari and Orlandelli (2019), but we can allow for multiple notions of uniqueness in the definition of harmony, or multiple notions of harmony. Either of these options generates a pluralism at the level of our admissbility conditions. This generates a pluralism at three levels: validity, connective meanings, and admissibility conditions. But it still preserves the spirit of Ferrari and Orlandelli (2019): balance and usefulness remain the admissibility constraints across the board.

Filippi Ferrari

In this talk, I address the question of whether logic is intrinsically or extrinsically normative. I begin with some taxonomical remarks and introduce distinctions relevant to assessing the normativity of logic. I then examine a prominent extrinsicist strategy that grounds the normativity of logic in truth and raise a few objections to it. In the final part, I sketch an intrinsicist account of the normative role that logic plays in reasoning.

Matthew Chrisman

Robust realists and quasirealist expressivists have both been accused, in different ways, of being committed to an alienated stance towards fundamental oughts, reasons, and values. Either normative facts obtain completely independently of our cares and concerns, in which case, why do we care about them as much as we do? Or their reality is something more like a projection from or construction out of our ways of normative thinking, in which case why should we care about them as much as we do? Sometimes this looks like philosophical bedrock in metaethics. But in this paper I want to explore the possibility that inferentialism offers a way past the impasse. In the first instance, this is by suggesting that normative terms can be viewed analogously to logical terms in getting their meaning neither from what they refer to nor from what attitudes they primarily serve to convey. But I also want to propose a way of thinking of normative/logical facts and normative/logical thinking as reciprocally related to each other in a way that rejects both the realist’s commitment to the explanatory independence of normative/logical facts from normative/logical thinking and the expressivist’s commitment to starting our explanation of normative/logical facts with an account of normative/logical thinking.

Zeynep Soysal

In this talk I will defend the metalinguistic solution to the problem of mathematical omniscience for the possible-worlds account of propositions. The metalinguistic solution says that mathematical propositions are possible-worlds propositions about the relation between mathematical sentences and what these sentences express. This solution faces two types of problems. First, it is thought to yield a highly counterintuitive account of mathematical propositions. Second, it still ascribes too much mathematical knowledge if we assume the standard possible-worlds account of belief and knowledge on which these are closed under entailment. I will defend the metalinguistic construal of mathematical propositions against these two types of objections by drawing upon a conventionalist metasemantics for mathematics and an algorithmic model of belief, knowledge, and communication.

Yale Weiss

In her recent book, Russell (2023) examines various so-called “barriers to entailment”, including Hume’s law, roughly the thesis that an ‘ought’ cannot be derived from an ‘is’. Hume’s law bears an obvious resemblance to the proscription on fallacies of modality in relevance logic, which has traditionally formally been captured by the so-called Ackermann property. In the context of relevant modal logic, this property might be articulated thus: no conditional whose antecedent is box-free and whose consequent is box-prefixed is valid (for the connection, interpret box deontically). While the deontic significance of Ackermann-like properties has been observed before, Russell’s new book suggests a more broad-scoped formal investigation of the relationship between barrier theses of various kinds and corresponding Ackermann-like properties. In this talk, I undertake such an investigation by elaborating a general relevant bimodal logical framework in which several of the barriers Russell examines can be given formal expression. I then consider various Ackermann-like properties corresponding to these barriers and prove that certain systems satisfy them. Finally, I respond to some objections Russell makes against the use of relevance logic to formulate Hume’s law and related barriers.

Xinhe Wu

There are numerous apparent examples of vague identity, i.e., examples where two objects appear to be neither determinately identical nor determinately distinct. Philosophers disagree on whether the source of vagueness in identity is semantic or ontic/metaphysical. In this talk, I explore the use of Boolean-valued models as a many-valued semantic framework for identity. I argue that this semantics works well with both a semantic and ontic conception of vague identity. I also discuss, in the context of Boolean-valued logic, responses to the Evans’ argument under the two conceptions.