Thursday, October 15, 2009

Conventionalim and Realism - are they incompatible?

Conventionalism and Realism are often presented as alternatives (for example, I recently heard a talk about whether Frege should be understood as a realist or a conventionalist about number). But (at least on my own best understanding of what `conventionalism' might be) it's not at all clear that this is the case.

I'm tempted to understand realism and conventionalism as follows, in which case (I am going to argue) the two are perfectly compatible.

You are a realist about Xs iff you think there really are some Xs.
You are a conventionalist about Xs iff you think that we can reasonably address boundary disputes about just what is to count as an X, or what properties Xs are supposed to have by imposing arbitrary conventions.

Here's an example. I think there really are living things. But I don't think the distinction between living and non-living things is such an incredibly natural kind that much would be lost by stipulating some slight re-definition of "alive" that clearly entails viruses are/aren't "alive". Hence, (by the above definition) I'm both a realist and a conventionalist about living things.

Maybe compatibility between realism about Xs and conventionalism about certain facts about Xs only applies conventionalism with regard to tiny boundary disputes about the extension of the concept X? But here's another example where the extension of X will be completely different depending on what stipulation we make.

I'm a realist about human bodies, in that I think that there are indeed human bodies. But should human bodies be identified with *open* or *closed* sets of space time points? This issue, is (just like the viruses question above) one that it seems perfectly natural to settle by stipulation.

Thus, I don't buy the argument that Frege's willingness to allow some questions about what the numbers are to be determined by convention (assuming, as the speaker suggested, he was indeed so willing) shows that he's an anti-realist about about number in anything like the ordinary sense of the term.

[edit: To put the point another way - you can be a realist about the all items that potentially count as numbers but think it's vague which things exactly do count as numbers.

Taking the extension of a concept to be somewhat arbitrary/conventional doesn't require thinking that the objects which are candidates to fall under that concept are somehow unreal]


  1. As I keep trying to tell you being a realist doesn't simply mean you are willing to assert "there are some x's." If that was the all it took to be a realist than *every* philosopher would be a realist about numbers since they are all willing to assert "there exists a prime number." I know that's a bit of an exageration but you see my point.

    The mistake you keep making is to assume there is a coherent notion of realism/coventionalism etc... Yet, whatever is true in phil of math is necessarily true so there can't be a coherent notion of more than one (conflicting) attitude to mathematics.

    You need to give up trying to charachterize realism/conventionalism/etc. These views can't be captured as a list of propositions. I mean there aren't any fixed propositions that a realist (as normally understood) would endorse but every hardcore antirealist/ficitonalist/etc would reject. There is always going to be someone who applies the same kind of anti-realist interpratation to these very propositions, e.g., accept them as true because they 'really' understand them in such and such a way.

    Rather words like realism, conventionalism and the like need to be understood as being, as a matter of 'definition', a way of dividing up the philosophical approaches to language. In other words part of what it means to be a realist is that you reject prototypical anti-realist views, e.g., conventionalism. Similarly to be an anti-realist your theory must be in conflict with prototypical realist views. So you can't possibly coherently have the view as you partially express above (you don't think this is some special exception for conventionalism you feel similarly about ficitonalism etc..).

    I mean if you think about it for a bit it has to work this way. We don't grasp realism/conventionalism/fictionalism etc.. via explicit definition. They are terms that were introduced to divide up the space of philosophical ideas and we understand them in terms of prototypical examples and non-examples. In other words we understand realism as the thing which Godel's et. al views endorse but conventionalists, fictionalists etc.. reject.

    You might think there is no principled distinction in the neighborhood. I know I do. But that's not saying that realism is actually compatible with all these prototypically anti-realist views. It's saying that realism is an incoherent concept and we should stop using the word.

  2. 1. Fictionalism isn't compatible with realism because realism says there are sets, and fictionalism says there aren't.

    2, I do sympathize with the feeling that realism vs. antirealism isn't a helpful way of dividing up views on philosophy of math...if i'm right that a paradigmatic instance of antirealism (conventionalism) turns out to be compatible with realism this shows one way in which this division is unhelpful/potentially confused.