On Dualities and Equivalences Between Physical Theories

The main aim of this paper is to make a remark about the relation between (i) dualities between theories, as `duality' is understood in physics and (ii) equivalence of theories, as `equivalence' is understood in logic and philosophy. The remark is that in physics, two theories can be dual, and accordingly get called `the same theory', though we interpret them as disagreeing---so that they are certainly not equivalent, as `equivalent' is normally understood. So the remark is simple: but, I shall argue, worth stressing---since often neglected. My argument for this is based on the account of duality developed by De Haro: which is illustrated here with several examples, from both elementary physics and string theory. Thus I argue that in some examples, including in string theory, two dual theories disagree in their claims about the world. I also spell out how this remark implies a limitation of proposals (both traditional and recent) to understand theoretical equivalence as either logical equivalence or a weakening of it.
Comment: 54 pages, 1 figure. Forthcoming in `Philosophy Beyond Spacetime' (Oxford University Press), edited by N. Huggett, B. Le Bihan and C. Wuethrich. Dedicated to Graeme Segal