Notes on Colyvan, "The Indispensabilityof Mathematics" Chapter 2

Chapter 2: The Quinean backdrop

"I will argue that the two essential theses for our purposes--confirmational holism and naturalism--can be disentangled from the rest of the Quinean web."

Naturalism:

"Naturalism involves a certain respect for the scientific enterprise--that much is common ground--but exactly how this is cashed out is a matter of considerable debate. For instance, for David Armstrong naturalism is the doctrine that 'nothing but Nature, the single all-embracing spatio-temporal system exists', whereas for Quine naturalism is 'the abandonment of the goal of a first philosophy'." Quine rejects the view that philosophy precedes science or oversees science. This thesis has implications for the way we should answer metaphysical questions: we should determine our ontological commitments by looking to see which entities our best scientific theories are committed to.

So this means that we're defining science as the scientific practice? That doesn't seem very useful. Enter Cornell realism? "In the disccusion so far I've glossed over the question of what constitutes our best scientific theories. There is also the question of what constitutes a scientific theory as opposed to a non-scientific theory. I won't enter into that debate here: I'll assume that we have at least an intuitive idea of what a scientific theory is."

"It is worth bearing in mind that the primary targets of the indispensability argument are scientific realists disinclined to believe in mathematical entities. These scientific realists typically subscribe to some form of naturalism, so my accpetance of a broadly naturalistic perspective is not as serious an assumption as it may seem at first."

"Now, defences of such fundamental doctrines as naturalism are hard to come by. Typically such doctrines are justified by their fruits." Meaning, doctrines which eliminate in principle the possibility of philosophical justification only could have some kind of justification from the fruits of the theory. "So in order to defend Quinean naturalism over other versions of naturalism I'll examine some of the consequences of the Quinean position."

Good quote of Quine's: "From the point of view of Quine's naturalised epistemology there is no more secure vantage point than the vantage point of our best scientific theories. Thus, the naturalized epistemologist "no longer dreams of a first philosophy, firmer than science, on which science can be based; he is out to defend science from within, against its self doubts.""

Two Dogmas: "Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system. Even a statement very close to the periphery can be held true in the face of recalcitrant experience by pleading hallucination or by amending certain statements of the kind called logical laws. Conversely, by the same token, no statement is immune to revision. Revision even of the logical law of excluded middle has been proposed as a means of simplifying quantum mechanics; and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy or Einstein Newton or Darwin Aristotle?" The main point is that the history of science has taught us that what were once considered analytic truths, such as that Pythagoras's theorem holds in our wolrd or that any massive body can be accelerated without bound have been given up in order to cohere with new and better scientific theories. Thus by an inductive argument from such examples, we conclude that there are no analysitc truths.

First reaction: I'm not crazy about this book. It doesn't seem so careful as I would like.