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In this paper I will argue that (principled) attempts to ground a priori knowledge in default reasonable beliefs cannot capture certain common intuitions about what is required for a priori knowledge. I will describe hypothetical creatures who derive complex mathematical truths like Fermat’s last theorem via short and intuitively unconvincing arguments. Many philosophers with foundationalist inclinations will feel that these creatures must lack knowledge because they are unable to justify their mathematical assumptions in terms of the kind of basic facts (...) 

Aron Gurwitsch made two main contributions to phenomenology. He showed how to import Gestalt theoretical ideas into Husserl’s framework of constitutive phenomenology. And he explored the light this move sheds on both the overall structure of experience and on particular kinds of experience, especially perceptual experiences and conscious shifts in attention. The primary focus of this paper is the overall structure of experience. I show how Gurwitsch’s Gestalt theoretically informed phenomenological investigations provide a basis for defending what I will call (...) 

ABSTRACT The aim of this paper is to establish a phenomenological mathematical intuitionism that is based on fundamental phenomenologicalepistemological principles. According to this intuitionism, mathematical intuitions are sui generis mental states, namely experiences that exhibit a distinctive phenomenal character. The focus is on two questions: what does it mean to undergo a mathematical intuition and what role do mathematical intuitions play in mathematical reasoning? While I crucially draw on Husserlian principles and adopt ideas we find in phenomenologically minded mathematicians such (...) 

According to the most popular nonskeptical views about intuition, intuitions justify beliefs because they are based on understanding. More precisely: if intuiting that p justifies you in believing that p it does so because your intuition is based on your understanding of the proposition that p. The aim of this paper is to raise some challenges for accounts of intuitive justification along these lines. I pursue this project from a nonskeptical perspective. I argue that there are cases in which intuiting (...) 

One of the important discussions in the philosophy of mathematics, is that centered on Benacerraf’s Dilemma. Benacerraf’s dilemma challenges theorists to provide an epistemology and semantics for mathematics, based on their favourite ontology. This challenge is the point on which all philosophies of mathematics are judged, and clarifying how we might acquire mathematical knowledge is one of the main occupations of philosophers of mathematics. In this thesis I argue that this discussion has overlooked an important part of mathematics, namely mathematics (...) 

One sometimes believes a proposition without grasping it. For example, a complete achromat might believe that ripe tomatoes are red without grasping this proposition. My aim in this paper is to shed light on the difference between merely believing a proposition and grasping it. I focus on two possible theories of grasping: the inferential theory, which explains grasping in terms of inferential role, and the phenomenal theory, which explains grasping in terms of phenomenal consciousness. I argue that the phenomenal theory (...) 

In a series of works, Jody Azzouni has defended deflationary nominalism, the view that certain sentences quantifying over mathematical objects are literally true, although such objects do not exist. One alleged attraction of this view is that it avoids various philosophical puzzles about mathematical objects. I argue that this thought is misguided. I first develop an ontologically neutral counterpart of Field’s reliability challenge and argue that deflationary nominalism offers no distinctive answer to it. I then show how this reasoning generalizes (...) 

It is plausible to think that, in order to actively employ models in their inquiries, scientists should be aware of their existence. The question is especially puzzling for realists in the case of abstract models, since it is not obvious how this is possible. Interestingly, though, this question has drawn little attention in the relevant literature. Perhaps the most obvious choice for a realist is appealing to intuition. In this paper, I argue that if scientific models were abstract entities, one (...) 

Orthodox epistemology tells us that knowledge requires belief. While there has been resistance to orthodoxy on this point, the orthodox position has been ably defended and continues to be widely endorsed. In what follows I aim to undermine the belief requirement on knowledge. I first show that awareness does not require belief. Next I turn my attention to the relation between knowledge and awareness, showing that awareness entails knowledge and thus that the cases of awareness without belief that I discuss (...) 

This paper explores the relationship between phenomenal properties and intentional properties. In recent years a number of philosophers have argued that intentional properties are sometimes necessitated by phenomenal properties, but have not explained why or how. Exceptions can be found in the work of Katalin Farkas and Farid Masrour, who develop versions of reductionism regarding phenomenallynecessitated intentionality (or "phenomenal intentionality"). I raise two objections to reductive theories of the sort they develop. Then I propose a version of primitivism regarding phenomenal (...) 

Traditionally, conceptual thinking is explored via philosophical analysis or psychological experimentation. We seek to complement these mainstream approaches with the perspective of a first person exploration into pure thinking. To begin with, pure thinking is defined as a process and differentiated from its content, the concepts itself. Pure thinking is an active process and not a series of associative thoughtevents; we participate in it, we immerse ourselves within its active performance. On the other hand, concepts are also of an experiential (...) 

There are three interconnected goals of this paper. The first is to articulate and motivate a view of the methodology for doing metaphysics that is broadly phenomenological in the sense of Husserl circa the Logical Investigations. The second is to articulate an argument for the importance of studying the history of philosophy when doing metaphysics that is in accordance with this methodology. The third is to confront this methodology with a series of objections and determine how well it fares in (...) 