Daniel Kuby

Various philosophers authors have argued—on the basis of powerful examples—that we can have compelling moral or practical reasons to believe, even when the evidence suggests otherwise. This paper explores an alternative story, which still aims to respect widely shared intuitions about the motivating examples. Specifically, the paper proposes that what is at stake in these cases is not belief, but rather acceptance—an attitude classically characterized as taking a proposition as a premise in practical deliberation and action. I suggest that acceptance’s theoretical usefulness in the ethics of belief has been hidden by its psychological obscurity. I thus aim to develop an empirically adequate and mechanistically specific psychological profile of acceptance. I characterize acceptance as centrally involving a cognitive gating function, in which we prevent a target belief state from having its characteristic downstream effects on reasoning, cognition, and action, and restructure those downstream processes. I then argue that there is substantial empirical support for the existence of the cognitive mechanisms needed to instantiate this view, coming from the science of emotion regulation. I argue that acceptance involves deploying the same mechanisms used in emotional response modulation to belief states: acceptance is doxastic response modulation. I then propose that having a better understanding of the psychological profile of acceptance leaves us better positioned to appreciate its potential usefulness for making progress on various puzzles within the ethics of belief.

This article addresses the question of fundamental entities in set theory. It takes up J. Hamkins’ claim that models of set theory are such fundamental entities and investigates it using the methodology of P. Maddy’s naturalism, Second Philosophy. In accordance with this methodology, I investigate the historical case study of the use of models in the introduction of forcing, compare this case to contemporary practice and give a systematic account of how set-theoretic practice can be said to introduce models as new entities. In conclusion, I argue for a view that takes both sets and models to be fundamental entities in set theory.

There are different narratives on mathematics as part of our world, some of which are more appropriate than others. Such narratives might be of the form ‘Mathematics is useful’, ‘Mathematics is beautiful’, or ‘Mathematicians aim at theorem-credit’. These narratives play a crucial role in mathematics education and in society as they are influencing people’s willingness to engage with the subject or the way they interpret mathematical results in relation to real-world questions; the latter yielding important normative considerations. Our strategy is to frame current narratives of mathematics from a virtue-theoretic perspective. We identify the practice of mathematizing, put forward by Freudenthal’s ‘Realistic mathematics education’, as virtuous and use it to evaluate different narratives. We show that this can help to render the narratives more adequately, and to provide implications for societal organization.

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often model-theoretic constructions that add sets to models are cited as evidence in favour of the latter. This paper informs this debate by developing a way for a Universist to interpret talk that seems to necessitate the addition of sets to V. We argue that, despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We present a method of interpreting extension-talk (V-logic), and show how it captures satisfaction in `ideal' outer models and relates to impredicative class theories. We provide some reasons to regard the technique as philosophically virtuous, and argue that it opens new doors to philosophical and mathematical discussions for the Universist.

In the genealogy of logical empiricism, the so-called “First Vienna Circle” (Neurath, Frank, Hahn) has been considered an essential episode, connecting the philosophy of Mach and the French conventionalists with the later logical empiricism of the Vienna Circle around Schlick. The present paper makes three claims: (1) We make the historical claim that the lack of archival sources on the “First Vienna Circle” does not allow a reliable reconstruction of such a discussion group, and even allows some doubts about its existence, at least as a regular discussion group. (2) We emphasize the interaction of the young Neurath, Hahn and Frank, in Vienna around 1910, with a group of philosophers strongly influenced by Meinong and claim that this interaction was very advantageous for a reception of the new symbolic logic and especially of Russell´s philosophy of logic and mathematics. New archival sources permit us to reconstruct such an interaction. (3) We claim that this Meinongian context in Vienna shaped some philosophical positionss of Neurath and Hahn, especially their view of the nature of logic and mathematics. We claim that at least Neurath, but probably also Hahn, endorsed a logical realism similar to that of Russell and Meinong. It was only after the reception of the Tractatus in the Vienna Circle that such a logical realism was unanimously rejected by the logical empiricists. Besides the obvious influence of Mach and the French conventionalists on the young Neurath, Hahn and Frank, this heritage from the Meinong school should be taken into account in an evaluation of the early philosophies of our mentioned trio.