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.
Suppose that Adam is a risk-taker—in general a highly successful one—and Bill prefers to play it safe. You believe that the organization is highly likely to thrive under Adam’s leadership, though there is still a small chance his investment could fail. On the other hand, Bill’s risk-averse strategy will allow the organization to profit to some degree, but it won’t be nearly as successful as in Adam’s best-case—and most likely—scenario. Yet the organization will fare better than Adam’s worst-case—and fairly unlikely—scenario. The following example sounds true in this context:
(1) If Adam takes the lead, the organization will be more successful than (it will be) if Bill takes the lead.
In this talk, I point out that the truth conditions of (1) do not align with the prediction of the standard quantificational view of conditionals (Kratzer 2012), coupled with extant theories on the interaction between comparatives and quantifiers (Schwarzschild & Wilkinson 2002, Heim 2006, Schwarzschild 2008, Beck 2010, among many others). I suggest that a working solution can be developed by dropping the assumption that conditionals are quantifiers over possible worlds.
This is an attempt to explain the exceptional scope behavior of specific indefinites in terms of ‘dynamic presuppositions’—presuppositions with anaphoric content in addition to propositional content. It is also claimed that puzzling interpretive properties of ‘certain’ indefinites are straightforwardly explained as dynamic presuppositions with functional anaphora.
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.
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.
People draw on event co-occurrences as a foundation for causal and scientific inference, but in which ways can events co-occur? Statistically, one can express a dependency between events A and C as P(C|A) != P(C), but this relation can be further specified in a variety of ways, particularly when A and/or C are themselves conditional events. In the psychology of reasoning, the conditional P(C|A) is often thought to become biconditional when people add the converse, P(A|C), or inverse, P(not-C|not-A), or both, with the effects of these additions largely treated as equivalent. In contrast, from a coherence based logical perspective it makes a difference whether the converse or the inverse is added, and in what way. In particular, the addition can occur by forming the conjunction of two conditionals, or by merely constraining their probabilities to be equal. Here we outline four distinct ways of defining biconditional relationships, illustrating their differences by how they constrain the conclusion probabilities of a set of inference forms. We present a Bayesian latent-mixture model with which the biconditionals can be dissociated from one another, and discuss implications for the interpretation of empirical findings in the field.
I identify and develop a solution to the puzzle of anankastic conditionals that is novel in the sense that it has gone largely unnoticed, but also well-worn in that the materials for it have long been available. The solution involves an integration of the classical Kratzerian premise semantics and a default theory of reasons (such as the one presented in Horty, 2012, leveraging several decades of research on default logic). To stress-test the proposal I also investigate how it might be applied to the variety of anankastic-adjacent data discussed by Condoravdi and Lauer (2016). The resulting approach is not just an exceptional fit for the problem of anankastic conditionals, but also an independently promising upgrade on the classical account of modals.
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.
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.