Bell V: Mill vs Ayer
A week or so ago I was talking to a friend of mine about Bell’s book and some of its arguments. At some point I suggested that some of the claims made, or the way in which the arguments were put, reminded me of a disagreement that John Stuart Mill and A.J. Ayer had over the status of mathematics. Surprisingly, when I got to pg. 128 in the book, Mill’s epistemology is given a positive mention. No surprise there!
The difference between Mill and Ayer can be put simply. How far the disagreement between them can be applied to Bell’s discussion is a different question. The difference for Ayer and Mill concern the nature of mathematical propostions such as “5 + 7 = 12” and how to understand them.
For Mill, the origin of our belief in the truth of such propositions is empirical (a posteriori). We see five oranges next to seven oranges and see this as twelve oranges. So, for Mill, such propositions are not about the relationship between concepts, but rather about the relationship between — or behavior of — oranges (objects). But Mill goes further: he also thinks that the justification of such propositions is also empirical. So, if I want to know whether the proposition is true, I see if it keeps holding up in experience. When five oranges sit next to seven oranges, there are twelve oranges.
Given that Mill thinks that justification is also empirical, he thinks that the truth of the mathematical proposition is always open to falsification. One day, he thinks, seven oranges and five oranges might total eleven oranges. As a result, Mill denies that mathematics is an a priori field.
Ayer agrees that the origin of such propositions is a posteriori (he is an empiricist, after all). But he denies that the justification of mathematics is also empirical, and so here he differs from the more radical empiricism of Mill. For Ayer, learning the mathematical proposition starts with seven and five oranges equalling twelve oranges. But after this, I can glean from the empirical propsition the propostion that “7 + 5 = 12”. This proposition is not empirical, and so its justification can be carried out a priori.
So Mill is a radical empiricist, whereas Ayer is a moderate one.
On pg. 128, “Demo” argues:
In a way you’re more of a liberal than I am. Liberals from JS Mill onward believe that he validity of beliefs can’t be assured a priori, and that it’s important to keep open the possibility of changing decisions already made should better arguments come to light.
Now we know from EMW that Bell thinks that the origin of normative claims is empirical, because these claims are generated in local empirical circumstances. But now we see (Demo’s claim is approved by Lo) that he also thinks that the justification of such claims is also empirical.
So Bell is a radical empiricist of sorts, in the tradition of Mill.
But there are different reasons for being a “Millian.”
Option 1: Mill doesn’t beleive that the objects of mathematical propositions exist. To claim that “All triangles equal 180 internal degrees” isn’t true as a statement about metaphysics because there are no such perfect triangles in the world and he doesn’t believe that imagistic concepts related to triangles can exist either. This doesn’t mean that mathematical propositions are bogus – they are useful generalizations about the real world. It’s just that perfect triangles don’t exist. So by this option, the validity of beliefs cannot be justified a priori because the objects of such propositions don’t exist.
Option 2: the objects corresponding to such propositions do exist, but we simply have no epistemic access to them. Argument and discussion might bring us closer, but we never actually access them.
What about Bell on human rights and norms?
My question is which, of option 1 or 2, does Bell embrace when it comes to normative claims? Does he think that norms are empirically justified because there are no “objects” or “moral facts” that correspond to a priori statements about norms? Or does he think that such things do exist, but the best we can hope for epistemically are the kinds of propositions that mutual argument and dialogue allow us to access?
Of course, there are a lot of interesting themes running in this thread, so feel free to comment on any of them. One large question: should we adopt an “Ayer” like approach to norms and rights? Or a “Millian” one?