Sam Dickson

The aim of this paper is two-fold. We argue against the received conception of epistemic malevolence and give a broader characterisation that, we argue, captures its real scope. We tackle the current notion of epistemic malevolence (EM) on three fronts. We claim that this notion fails to capture cases of EM that are (i) not knowledge directed (but that affect the agent's epistemic character), (ii) not robustly volitional (that do not involve an active opposition to the epistemic good by the malevolent agent) and that (iii) are not merely transactional (as opposed to structural). As a result, we claim that the received notion of EM fails to recognise (arguably) clear instances of EM because it is too narrow. Ultimately, we argue that such narrowness gives the false impression that, unlike its moral counterpart, EM is uncommon. After arguing for this, we offer a wider characterisation of EM and show the role this can play in generating solutions to the problem the phenomena poses.

Fictionalism is a popular approach to handling possible worlds discourse. It gives one the power of possible world semantics without being committed to undesirable consequences. The standard approach of reparsing possible world statements by attaching a fictional operator suffers from a problem that we argue is structural for all kinds of narrow fictionalism. To show this, we develop a toy theory of temporal fictionalism, showing that it is vulnerable to the same problem. We develop a solution in the form of a broad account of modal fictionalism. Broad modal fictionalism is a contentious view and its usefulness needs to be clarified. Given this, towards the end of the paper we offer some motivations for why broad modal fictionalism is useful and gesture towards how modal talk arises in everyday discourse.

Some argue that intuitive judgments about mathematical statements lead us to believe in Mathematical Platonism. But the mathematical objects of platonistic theories are supposed to be non-spatiotemporal and detached from the world; more precisely, they are acausal. This is problematic because if mathematical objects are detached from the world, then it would seem that they make no difference to the world. The world would be the way it is even if there were no mathematical objects. Moreover, people like Benacerraf (1973) argue that given a causal theory of knowledge, and given its acausal nature, we could never know about mathematical objects and therefore should not postulate them. Elsewhere in the literature, indispensability arguments are made for mathematical objects (e.g., Baker, 2009). Our best scientific theories seem to rely on explanations that quantify about mathematical objects, so we should believe in them just as we believe in the unobservable objects of science. We can then say that we know mathematical objects exist by inference to the best explanation based on our best scientific theories. But that doesn’t tell us what mathematical objects are like, and most importantly, it still doesn’t answer the »makes no difference« argument. We may be forced to believe in them, but that doesn't tell us whether or not they actually do anything. I'd like to discuss one way that mathematical objects might do something. I think there is a useful and informative way we can talk about mathematical objects as causal. I do this by discussing a case of mathematical constraint as proposed by Marc Lange (2017). I will elaborate on the notion of mathematical constraint and talk about the constraint relation in general. I then discuss structural equation models and how they can be used to represent causal relationships. This fits particularly well with the interventionist view of causality that I will describe, and how it can be used as a test to determine which relationships are causal. I think that mathematical constraint passes this test. Using this framework, I will discuss a specific structural equation model that represents a constraint relationship. This specific constraint relationship is also clearly causal. I think that the structure of this relation naturally maps on to the structure of an archetypal example of a mathematical constraint. Not only do they share a common structure, but both relations behave in the same way in interventionist treatments. This should give us reason to say that mathematical constraint is causal. For those interested in the epistemology of mathematics, this may provide a workaround to Benacerraf-type objections; it would be puzzling how we know about acausal mathematical objects, but since mathematical objects are causal, we can explain our knowledge. For those who sympathize with or are concerned about the »makes no difference« argument, we again have an answer: mathematical objects are causal, so it would make a difference to the world if they did not exist.

Fictionalism is a popular approach to handling possible worlds discourse. It gives one the power of possible world semantics without being committed to undesirable consequences. The standard approach of reparsing possible world statements by attaching a fictional operator suffers from a problem that we argue is structural for all kinds of narrow fictionalism. To show this, we develop a toy theory of temporal fictionalism, showing that it is vulnerable to the same problem. We develop a solution in the form of a broad account of modal fictionalism. Broad modal fictionalism is a contentious view and its usefulness needs to be clarified. Given this, towards the end of the paper we offer some motivations for why broad modal fictionalism is useful and gesture towards how modal talk arises in everyday discourse.

This paper discusses the question of whether all counterfactuals with necessarily false antecedents (counterpossibles) are vacuously true. The orthodox view of counterpossibles (vacuism) answers that question in the affirmative. This paper explains vacuism before turning to examples from science which seem to require us to reason non-trivially using counterpossibles; and it seems that the counterpossibles used in such cases can be true or false. This is a threat to vacuism. It is then argued that the same kind of reasoning which produces non-trivial counterpossibles in scientific cases can be extended to the case of counterpossibles in mathematics. Ordinary counterfactual reasoning relies on rejecting background assumptions in order to assume the truth of the antecedent. A failure to perform this process in the counterpossible case is what leads one to vacuism and it is explained how this process produces non-vacuous; counterfactuals, scientific counterpossibles and mathematical counterpossibles.