“I wouldn’t be in the least surprised, for example, if it turned out that some arithmetic thinking is carried out by executing previously memorised algorithms that are defined over public language symbols for numbers (“now carry the ‘2’ and so forth”).” (Fodor 1998, p. 72)This looks bad for A&A, but the context matters. So, here is more of Fodor's book review:
I want to end by returning to a point I've already made in passing. I don't think that there are decisive arguments for the theory that all thought is in Mentalese. In fact, I don't think it's even true, in any detail, that all thought is in Mentalese. I wouldn't be in the least surprised, for example, if it turned out that some arithmetic thinking is carried out by executing previously memorized algorithms that are defined over public language symbols for numbers ("Now carry the '2,'" and so forth). It's quite likely that Mentalese co-opts bits of natural language in all sorts of ways; quite likely the story about how it does so will be very complicated indeed by the time that the psychologists get finished telling it.Now, this is a kind of puzzling concession on Fodor's part, but he seems to be willing to make it only because he thinks nothing philosophically interesting turns on it (and because the evidence is less than decisive). And, if I thought that I might agree. But, something philosophically interesting does seem to me to turn on this, so I don't agree.
But here's a bet that I'm prepared to make: For all our philosophical purposes (e.g., for purposes of understanding what thought content is, and what concept possession is, and so forth), nothing essential is lost if you assume that all thought is in Mentalese. Hilary Putnam once remarked that if you reject the analytic/synthetic distinction, you'll be right about everything except whether there is an analytic/synthetic distinction. Likewise, I imagine, in the present case: If you suppose that all thought is in Mentalese, you'll be right about everything except whether all thought is in Mentalese. More than that is maybe more than it's reasonable to ask for. (Fodor, 1998, p. 72).
So, I want some empirical evidence that we do arithmetic in English or in pictures. Fodor notes the inadequacy of the taking literally the familiar claim that we think in English. This seems to me to be all that Menary has.
As for Dehaene, I'm not holding my breath for decisive evidence. The issue has been around for a while without resolution to the satisfaction of all.
Fodor, J. (1998). In Critical Condition: Polemical Essays on Cognitive Science and the Philosophy of Mind. Cambridge, MA: MIT Press.