Abstract: The goal of the research programme I describe in this article is a realist epistemology for arithmetic which respects arithmetic's special epistemic status (the status usually described as a prioricity) yet accommodates naturalistic concerns by remaining funda- mentally empiricist. I argue that the central claims which would allow us to develop such an epistemology are (i) that arithmetical truths are known through an examination of our arithmetical concepts; (ii) that (at least our basic) arithmetical concepts are accurate mental representations of elements of the arithmetical structure of the inde- pendent world; (iii) that (ii) obtains in virtue of the normal functioning of our sensory apparatus. The first of these claims protects arithmetic's special epistemic status relative, for example, to the laws of physics, the second preserves the independence of arithmetical truth, and the third ensures that we remain empiricists.

Summary: Morrison and Morgan argue for a view of models as 'mediating instruments' whose role in scientific theorising goes beyond applying theory. Models are partially independent of both theories and the world. This autonomy allows for a unified account of their role as instruments that allow for exploration of both theories and the world.

Summary: This entry provides an overview of attempts to analyse knowledge, including the topics: knowledge as justified true belief; lightweight knowledge; the Gettier problem; no false lemmas; modal conditions; doing without justification?; is knowledge analyzable?; epistemic luck; virtue-theoretic approaches; knowledge first; pragmatic encroachment; contextualism; and an introduction that briefly discusses what it is to analyse knowledge.

Abstract: Natural theology is the branch of theology and philosophy that attempts to gain knowledge of God through non-revealed sources. In a narrower sense, natural theology is the discipline that presents rational arguments for the existence of God. Given that these arguments rarely directly persuade those who are not convinced by their conclusions, why do they enjoy an enduring appeal? This article examines two reasons for the continuing popularity of natural theological arguments: (i) they appeal to intuitions that humans robustly hold and that emerge early in cognitive development; (ii) they serve an argumen- tative function by presenting particular religious views as live options. I conclude with observations on the role of natural theology in contemporary analytic philosophy of religion.

Summary: Wetzel raises an important but underdiscussed argument for Platonism. We quantify over types (contrast with tokens) in sentences that we take to be true. This means we are, prima facie, committed to the existence of types. Wetzel considers various 'nominalization' strategies to get rid of type discourse and finds them all wanting. As a result, argues Wetzel, nominalism is untenable.

Summary: Thomasson argues that merely verbal disputes arise in metaphysics when ontologists misuse the words 'thing' and 'object'. Application conditions fix the conditions under which a claim can be applied or refused, but some ontological disputes involve using the terms 'thing' and 'object' in such a way that they lack application conditions. When this happens there is no way to determine the truth values of the claims being made.

Summary: Grover argues that one should be unconcerned about the liar paradox. In formal languages there are uniform ties between syntax and semantics: a term, in all its occurrences, carries a fixed meaning; and sequences of sentences that are (syntactically) proofs are always (semantically) inferences. These two features do not hold of natural languages. Grover makes use of this claim to argue that there are no arguments to contradictions from liar sentences in natural languages, as the relevant syntactic 'moves' do not come with relevant semantic 'moves'.

Publisher's Note: Mainstream and Formal Epistemology provides the first easily accessible yet erudite and original analysis of the meeting point between mainstream and formal theories of knowledge. These two strands of thinking have traditionally proceeded in isolation from one another but in this book Vincent F. Hendricks brings them together for a systematic comparative treatment. He demonstrates how mainstream and formal epistemology may significantly benefit from one another, paving the way for a new unifying program of 'plethoric' epistemology. His book will both define and further the debate between philosophers from two very different sides of the epistemological spectrum.

Abstract: Epistemic logic is the logic of knowledge and belief. It provides insight into the properties of individual knowers, has provided a means to model complicated scenarios involving groups of knowers and has improved our understanding of the dynamics of inquiry.

Abstract: This essay presents a moral argument for the rationality of theistic belief. If all I have to go on morally are my own moral intuitions and reasoning and those of others, I am rationally led to skepticism, both about the possibility of moral knowledge and about my moral effectiveness. This skepticism is extensive, amounting to moral despair. But such despair cannot be rational. It follows that the assumption of the argument must be false and I must be able to rely on more than my own human powers and those of others in attempting to live a moral life. The Christian God has such a function. Hence, if it is rational to attempt a moral life, it is rational to believe in the Christian God.