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Project Statement

In his book, The Indispensability of Mathematics, Mark Colyvan (<> gives a clear and apparently persuasive argument for Platonism on the basis of the Quine-Putnam indispensability argument. Unfortunately, I believe that he fails in his attempt for X main reasons. These reasons can largely be grouped into two categories: those arising from concerns regarding the ontological commitments of Quinean naturalism; and those arising from concerns regarding the applicability of IBE in a mathematical context.


Chris Wilcox - Thesis Outline

A little rough at the moment.


Management Type Stuff

To Do (broad directions)
- 1. Develop outline and first draft of thesis
- 2. Return to Colyvan and Lipton.
- 3. Fill in any gaps.

Due 27 October.


Building Blocks

Colyvan Indispensability
The core argument I am reacting to.

Inference to the Best Explanation
A basic outline of IBE.

Mathematical Antirealism
Attempting to deal with variations on Dummett.

Yablo Ontology
Pointing out some problems with Quine's ontology.

Price Naturalism
Pointing out some more problems with Quine's ontology.

Non Deductive Mathematics
Paseau on the role of induction and the uncertainty of deduction in mathematics.

Bandu on I B E in Mathematics
An attempt to refute the use of IBE in platonist arguments.

Price Naturalism Without Representationalism
A new-fangled kind of naturalism without the ontological worries.

Lipton I B E
A more detailed look at IBE.
I'm working my way through this book but I think it'll be more useful to discuss things as I go along rather than try to recall everything I wanted to deal with along the way at the end.

Carnap Empiricism Semantics Ontology
Carnap's reaction to the realism debate.

Quine On What There Is
What ontology is for Quine.

Stanford Concepts
Coming to terms with the range of issues concerning concepts.

Sober Mathematics and Indispensability
Sober's attempt to argue against Quine's confirmational holism.

Maddy Indispensability and Practice
Maddy criticising the decriptive accuracy of confirmational holism in a couple of ways.

Resnik Scientific vs Mathematical Realism
Resnik responds to Maddy and Sober, formulating a pragmatic indispensability argument.

On Field Scientific Theory And Practice
Me trying to work out whether distinguishing between practical and theoretical indispensability has any implications for Field's argument.

On The Involvement of I B E
Me trying to sort out the different ways in which I need to approach the use of IBE in the indispensability argument.

Colyvan Redux
A return to Colyvan's book with a view to seeing exactly how my arguments and his connect.

Stanford Abstract Objects
Gathering material for one of my major criticisms re: what it means for an object to be abstract.


Other Projects
Other stuff I have to work on during the honours year.

Williamson Reading Group
Notes for my 5,000 word paper (and the associated reading group) on Williamson's The Philosophy of Philosophy.

Seminar Paper 2
Continental ethics using Critchley's "Infinitely Demanding" as a starting point.

Seminar Paper
Dealing with McDowell's Mind and World, in particular the metaphilosophy.

Metaphysics Paper
Assessing Dummett's anti-realism.

Metaphysics Tutorials
In desperate need of updating, sometime, somehow…


Other Other Projects

More pie-in-the-sky type stuff.


Important Similarities and the Problem of Grue


The Limiting Mechanism in Subject Naturalism

Using Conceptual Receptivity in Argument


Induction Universals Particulars

Post Honours Reading

Skepticism about mathematics

Philosophical discourse as continuous not discrete

Role of philosophy in science and maths


Construction Zone

A building space for various position-statement pages. I'll move them to the "Building Blocks" section when I think they have been developed enough to be worth looking at by anyone apart from me.

High Priority


Van Fraassen on I B E
On hold until I work through Lipton's book.

Low Priority (not directly related to topic)

Mathematical Constructivism

Social Constructivism About Mathematics