Quantum mechanics tells us that states involving indistinguishable fermions must be antisymmetrized. This is often taken to mean that indistinguishable fermions are always entangled. We consider several notions of entanglement and argue that on the best of them, indistinguishable fermions are not always entangled. We also present a simple but unconventional way of representing fermionic states that allows us to maintain a link between entanglement and non-factorizability.

In the context of discussions about the nature of ‘identical particles’ and the status of Leibniz’s Principle of the Identity of Indiscernibles in Quantum Mechanics, a novel kind of physical discernibility has recently been proposed, which we call witness-discernibility. We inquire into how witness-discernibility relates to known kinds of discernibility. Our conclusion will be that for a wide variety of cases, including the intended quantum-mechanical ones, witness-discernibility collapses extensionally to absolute discernibility, that is, to discernibility by properties.

When people deny that there are objects of a certain kind, they normally take this to be a reason to stop speaking as if such objects existed. For instance, when atheists deny the existence of God, they take this to be a reason to stop speaking about God’s will or His mercy. Or, to take a more mundane example, when people deny that there are round squares or that there are unicorns, they take this to be a reason to stop (...) speaking as if rounds squares or unicorns existed. (shrink)

My thesis discusses the unique challenge that platonistic mathematics poses to philosophical naturalism. It has two main parts. ;The first part discusses the three most important approaches to my problem found in the literature: First, W. V. Quine's holistic empiricist defense of mathematical platonism; then, the nominalists' argument that mathematical platonism is naturalistically unacceptable; and finally, a radical form of naturalism, due to John Burgess and Penelope Maddy, which dismisses any philosophical criticism of a successful science such as mathematics. I (...) find faults with all of these approaches. ;The second part attempts to do better. First, I develop an improved epistemological challenge to mathematical platonism. Roughly, this challenge asks for an account of what mathematicians' justification for believing in platonistic mathematics consists in. I argue this challenge is immune to the criticism I leveled against the traditional challenges. To show that it has bite, I apply this challenge to Quine's philosophy of mathematics. I argue this shows that Quine must invoke, in addition to his confirmational holism, a semantic indeterminacy thesis that is so radical as to be implausible. Finally, I attempt to develop a better response to the improved challenge. I defend an unorthodox view of the concept of an object and argue this makes room for a neo-Dedekindian view of mathematical objects which identifies mathematical existence with the logical coherence of the theory describing the structure in question. This view transforms metaphysical and epistemological questions about mathematical objects into corresponding, but more tractable questions about the logical notion of coherence. (shrink)

Is the natural number 3 identical with the Roman emperor Julius Caesar? In Grundlagen Frege raised some peculiar questions of this sort.1 There are two kinds of intuitions regarding such questions. On the one hand, these questions seem not only to be pointless but to be downright meaningless. Regardless of how much arithmetic one studies, no answer to the opening question will be forthcoming. Arithmetic tells us that 3 is the successor of 2 and that it is prime, but not (...) whether it is identical with Caesar. So questions concerning the identity of numbers and people seem not to be provided for. On the other hand, it seems that the opening question must be answered negatively. For numbers are not the sorts of things that can be identical with people. In fact, since the number 3 is an abstract object and Caesar is not, it follows by Leibniz’s law that they are not identical. (shrink)