Monique Whitaker

Although many fields of study have been radically reshaped by feminist critiques, formal a priori disciplines like mathematics and computer science have proven more intransigent; feminist critiques have largely emphasized goals like increasing enrollment or participation in these fields, stopping short of proposing radical critiques of their theoretical foundations. In this paper, we discuss how Valerie Plumwood’s work on reading classical logic as a logic of domination can be extended to provide grounds for authentic feminist theories of mathematics. We argue that the relevant arithmetic $$\mathsf{R}^{\sharp}$$ described by Plumwood’s collaborator Robert K. Meyer satisfies the criteria characteristic of a Plumwoodian critique of arithmetic. The setting of $$\mathsf{R}^{\sharp}$$ is finally used to investigate several consequences of such an approach, including the degree to which such an arithmetic parts ways with classical mathematics as regards arithmetical truths.

The algorithms and processes of modern technologies affect almost all aspects of our lives. No human being is making individual subjective choices in each, or any, instance of these processes—all cases are treated with perfect technological indifference. Hence, a commonsense assumption about the technologies we interact with, and the algorithms many of them implement, is that they are neutral and impartial. Of course, this is simply not the case. As has been extensively documented and discussed, bias exists in all facets of technology, from how and why it was first conceived and then developed to its inputs, processes and outputs. I examine instances of technological bias in visual representation and criminal justice technologies, and argue that they produce, among other epistemic concerns, a form of hermeneutical injustice by means of obstructing the deployment of the necessary and otherwise available hermeneutical resources needed to accurately understand these technologies and their effects. Such epistemic harm is inevitable, unless the relationship between our human biases and the technological processes produced by us is made explicit and significantly rethought.

John Searle roundly rejects what he calls the Bad Argument: a long-standing equivocation in philosophy over the contents and the objects of perception. But, as Josh Armstrong points out, this insight is not unique to Searle. By the late 19th Century the equivocation had been observed by Franz Brentano and students of his, such as Alexius Meinong and Kazimierz Twardowski, and was highlighted too in the 20th century by G. E. M. Anscombe. What Armstrong does take to be a novel to Searle is his use of this observation to undermine some of the primary objections to a realist theory of perception. In fact, though, it had already been put to much the same use by Mary Shepherd in her 1827 book Essays on the Perception of an External Universe and Other Subjects Connected with the Doctrine of Causation. Shepherd not only argues that the equivocal use of the term “things we perceive” is a crucial flaw in Berkeley’s case for Idealism, but also goes on to use this in service of her own, largely realist, theory of perception.

In this dissertation I provide a novel logic of the ordinary-language conditional. First, however, I endeavor to make clearer and more precise just what the objects of the study of the conditional are, as a lack of clarity as to what counts as an instance of a given category of conditional has resulted in deep and significant confusions in subsequent analysis. I motivate for a factual/counterfactual distinction, though not at the level of particular instances of the conditional. Instead, I argue that each individual instance of the conditional may be interpreted either factually or counterfactually, rather than these instances dividing into distinct types. I examine the classic Oswald–Kennedy pair of sentences, typically taken to be the quintessential example of how conditionals must be split into two different categories, to show that they in fact do not demonstrate this. I then present my account of the logic underlying the ordinary-language conditional, the system C3, and a justification of the form it takes. This logic provides distinct interpretations of the conditional as it concerns what is factual or what is counterfactual, respectively. The factual interpretation is true when both antecedent and consequent are true at the actual world, false when the antecedent is true and consequent false, and not truth-apt otherwise. The counterfactual interpretation incorporates a ceteris paribus clause, ensuring that it is not falsified by extraordinary, unforeseeable occurrences, and is true when, at all worlds at which the antecedent is ceteris paribus true, the consequent too is true. It is false when, at any of these worlds the consequent is false; and not truth-apt otherwise. I go on to examine alternative theories of the conditional—from the suppositionalist approach to evaluating the putative indicative conditional, to Stalnaker’s combined indicative and counterfactual account, and Lewis’s analysis of the counterfactual; among a number of others—and offer comparison to my own theory. Finally, I look at various challenges to my account of the conditional. Being a strict conditional (albeit variably so), that of C3 is open to the objection that it fails to match ordinary speakers’ intuitions as regards its truth-value assignments to, for instance, conditionals with necessarily true consequents. I address these so- called paradoxes of the strict conditional, and also discussion the question of truth-preservation in the C3 system in the case of such inferences as those relying on transitivity and that of modus ponens. I maintain that these inferences are indeed truth-preserving under certain, specifiable, conditions, and I close by offering possible avenues for further research.

Ordinary speakers intuitively assign truth-values to conditional utterances in everyday conversation, but, despite the general ease with which this occurs, it is notoriously difficult to give an account of the implicit logic that is followed in making these truth-value assignments. I propose a twofold logic of the conditional – a relatively simple “factual” logic for conditionals interpreted with regard to what is actually the case, largely following the logic of the material conditional; combined with a variably strict possible-worlds counterfactual logic for conditionals interpreted with regard to with what may be (or may have been) the case, incorporating a ceteris paribus clause. This theory is able to deal with a number of challenges for other prominent views of the conditional, such as counter-intuitive truth-value ascriptions provided by notions of similarity or closeness, and difficulties adequately accounting for phenomena such as reverse Sobel sequences.

One of the significant problems for philosophy’s development into a more diverse discipline is the familiar sharp reduction in the proportion of women and students of color after initial, introductory-level courses. This contributes to a lack in the breadth of perspective and experience that both upper-level students and faculty bring to philosophy, which in turn undermines the strength of the discipline as a whole. Much of the transformation of philosophy must necessarily happen at the departmental, and even university, level; but there are, nonetheless, a number of strategies available to individual teachers of philosophy to help to retain marginalized students—from the composition of course syllabi and assignment choices, to increased awareness of challenges within the discipline to students’ success and embracing error as a learning tool. This variety of pedagogical tools provides a means to help to make philosophy more broadly inclusive.