Summary: Uses Maxwell’s model of the ether as a case study in accounting for the role of fictions in science. Argues that we should understand idealisation and abstraction as being different from fiction. Fictional models for Morrison are those that are deliberately intended to be such that the relationship between their structure and the structure of the concrete systems they model is not (immediately) apparent. This is different from mere idealisation, where certain structural features are omitted to make calculations more tractable.
What’s there to know?
Summary: Defends an account of mathematical knowledge in which mathematical knowledge is a kind of modal knowledge. Leng argues that nominalists should take mathematical knowledge to consist in knowledge of the consistency of mathematical axiomatic systems, and knowledge of what necessarily follows from those axioms. She defends this view against objections that modal knowledge requires knowledge of abstract objects, and argues that we should understand possibility and necessity in a primative way.
Three Forms of Naturalism
Summary: A clear introduction to mathematical naturalism and its Quinean roots; developing and defending Maddy’s own naturalist philosophy of mathematics. Maddy claims that the Quinian ignores some nuances of scientific practice that have a bearing on what the naturalist should take to be the real scientific standards of evidence. Historical studies show that scientists sometimes do not take themselves to be committed to entities that are indispensably quantified over in their best scientific theories, hence the Quinian position that naturalism dictates that we are committed to entities that are indispensably quantified over in our best scientific theories is incorrect.
Nominalism
Summary: Introduction to mathematical nominalism, with special attention to Chihara’s own development of the position and the objections of John Burgess and Gideon Rosen. Chihara provides an outline of his constructibility theory, which avoids quantification over abstract objects by making use of contructibility quantifiers which instead of making assertions about what exists, make assertions about what sentences can be constructed.
Pragmatism and Deflationism
Summary: A contemporary defense of a pragmatist account of truth, which contrasts the view with various versions of deflationism. Misak defends the claim that to grasp the concept of truth by exploring its connections with practices we engage in – including assertion, believing, reason-giving, and inquiry. The pragmatist conception of truth, it is argued, helps to elucidate realism/anti-realism: inquiry is truth-apt when it aims at establishing propositions that are indefeasible.
“Algebraic” Approaches to Mathematics
Summary: Surveys the opposition between views of mathematics which take mathematics to represent a independent mathematical reality and views which take mathematical axioms to define or circumscribe their subject matter; and defends the latter view against influential objections.
Representationalism
Abstract: Representationalism, in its most widely accepted form, is the view that the human mind is an information-using system, and that human cognitive capacities are to be understood as representational capacities. This chapter distinguishes several distinct theses that go by the name “representationalism,” focusing on the view that is most prevalent in cogntive science. It also discusses some objections to the view and attempts to clarify the role that representational content plays in cognitive models that make use of the notion of representation.
Varieties of Externalism
Abstract: Externalism comes in varieties. While the landscape isn’t tidy, I offer an organizing framework within which many of the forms it has taken (though perhaps not all) can be located. This taxonomy should be useful in itself. I’ll also use it to survey and compare arguments for different kinds of externalism, while probing related intuitions.
Persistence Through Time
Introduction: Things change: objects come into existence, last for a while, go out of existence, move through space, change their parts, change their qualities, change in their relations to things. All this would seem to be uncontroversial. But philosophical attention to any of these phenomena can generate perplexity and has resulted in a number of long-standing puzzles. One of the most famous puzzles about change threatens to demonstrate that nothing can persist through time, that all existence is momentary at best. Let’s use the term ‘alteration’ for the sort of change that occurs when a persisting object changes its properties.
What is it Like to Be Boring and Myopic?
Summary: A response to Thomas Nagel’s famous paper “What is it Like to be a Bat?”. Akins uses neuroscientific data to argue that we can find out that bats may not actually have a point of view, and that, contrary to Nagel, this kind of objective study can bring us closer to understanding individuals’ subjective experiences, not further away.