Indicative conditionals, restricted quantification, and naive truth

This paper extends Kripke’s theory of truth to a language with a variably strict conditional operator, of the kind that Stalnaker and others have used to represent ordinary indicative conditionals of English. It then shows how to combine this with a different and independently motivated conditional operator, to get a substantial logic of restricted quantification within naive truth theory

If P, Then P!

The Identity principle says that conditionals with the form 'If p, then p' are logical truths. Identity is overwhelmingly plausible, and has rarely been explicitly challenged. But a wide range of conditionals nonetheless invalidate it. I explain the problem, and argue that the culprit is the principle known as Import-Export, which we must thus reject. I then explore how we can reject Import-Export in a way that still makes sense of the intuitions that support it, arguing that the differences between indicative and subjunctive conditionals play a key role in solving this puzzle

Conditional Heresies

Philosophy and Phenomenological Research, EarlyView

What If? The Exploration of an Idea

A crucial question here is what, exactly, the conditional in the naive truth/set comprehension principles is. In 'Logic of Paradox', I outlined two options. One is to take it to be the material conditional of the extensional paraconsistent logic LP. Call this "Strategy 1". LP is a relatively weak logic, however. In particular, the material conditional does not detach. The other strategy is to take it to be some detachable conditional. Call this "Strategy 2". The aim of the present essay is to investigate Stragey 1. It is not to advocate it. The work is simply an extended exploration of the strategy, its strengths, its weaknesses, and the various dierent ways in which it may be implemented. In the first part of the paper I will set up the appropriate background details. In the second, I will look at the strategy as it applies to the semantic paradoxes. In the third I will look at how it applies to the set-theoretic paradoxes

The Conditional in Three-Valued Logic

By and large, the conditional connective in three-valued logic has two different functions. First, by means of a deduction theorem, it can express a specific relation of logical consequence in the logical language itself. Second, it can represent natural language structures such as "if/then'' or "implies''. This chapter surveys both approaches, shows why none of them will typically end up with a three-valued material conditional, and elaborates on connections to probabilistic reasoning

Metaphysical Dependence and Set Theory

In this dissertation, I articulate and defend a counterfactual analysis of metaphysical dependence. It is natural to think that one thing x depends on another thing y if had y not existed, then x wouldn\u27t have existed either. But counterfactual analyses of metaphysical dependence are often rejected in the current literature. They are rejected because straightforward counterfactual analyses fail to accurately capture dependence relations between objects that exist necessarily, like mathematical objects. For example, it is taken as given that sets metaphysically depend on their members, while members do not metaphysically depend on the sets they belong to. The set {0} metaphysically depends on 0, while 0 does not metaphysically depend on {0}. The dependence is asymmetric. But if counterfactuals are given a possible worlds analysis, as is standard, then the counterfactual approach to dependence will yield a symmetric dependence relation between these two sets. Because the counterfactual analysis fails to accurately capture dependence relations between sets and their members, most reject this approach to metaphysical dependence. To generate the desired asymmetry, I argue that we should introduce impossible worlds into the framework for evaluating counterfactuals. I review independent reasons for admitting impossible worlds alongside possible worlds. Once we have impossible worlds at our disposal, we can consider worlds where, e.g., the empty set does not exist. I argue that in the worlds that are ceteris paribus like the actual world, where 0 does not exist, {0} does not exist either. And so, according to the counterfactual analysis of dependence, {0} metaphysically depends on 0, as desired. Conversely, however, there is no reason to think that every world that is ceteris paribus like the actual world, where {0} does not exist, is such that 0 does not exist either. And so 0 does not metaphysically depend on {0}. After applying this extended counterfactual analysis to several set-theoretic cases, I show that it can be applied to account for dependence relations between other mathematical objects as well. I conclude by defending the counterfactual analysis, extended with impossible worlds, against several objections

The Metaphysics of Moral Explanations

It’s commonly held that particular moral facts are explained by ‘natural’ or ‘descriptive’ facts, though there’s disagreement over how such explanations work. We defend the view that general moral principles also play a role in explaining particular moral facts. More specifically, we argue that this view best makes sense of some intuitive data points, including the supervenience of the moral upon the natural. We consider two alternative accounts of the nature and structure of moral principles—’the nomic view’ and ‘moral platonism’—before considering in what sense such principles obtain of necessity

Justification for a Probabilistic Account of Conditionals

In this dissertation I argue that a probabilistic account of conditionals similar to the one proposed by Robert Stalnaker in 1968 is the logical account of conditionals that most aptly models conditional use in natural language. I argue that a probabilistic account of conditionals is best able to account for the most systematic and widespread uses of conditionals in natural language as is evidenced by both its compatibility with the descriptively accurate psychological account, as well as its ability to take into account expert intuitions that diverge from the material conditional interpretation. I provide expert support for Stalnakers account by describing the ways that a probabilistic conditional can avoid the paradoxes of the material conditional. I argue that the predictive accuracy of the alternative mental models account provides support for the claim that Stalnakers logical account of conditionals is descriptively accurate. I conclude that both expert and naive reasoners uses of conditional statements are most accurately modelled by a probabilistic account of conditionals similar to that proposed by Stalnaker