Month: October 2024

The Metalinguistic Construal of Mathematical Propositions

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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.

Disentangling conditional dependencies

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Nicole Cruz (with Michael Lee)

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.