Emergence, reduction and supervenience: A varied landscape

For a special issue of Foundations of Physics This is one of two papers about emergence, reduction and supervenience. It expounds these notions and analyses the general relations between them. The com-panion paper analyses the situation in physics, especially limiting relations between physical theories. I shall take emergence as behaviour that is novel and robust relative to some comparison class. I shall take reduction as deduction using appropriate auxiliary definitions. And I shall take supervenience as a weakening of reduction, viz. to allow infinitely long definitions. The overall claim of this paper will be that emergence is logically independent both of reduction and of supervenience. In particular, one can have emergence with reduction, as well as without it; and emergence without supervenience, as well as with it. Of the subsidiary claims, the four main ones (each shared with some other au-thors) are: (i): I defend the traditional Nagelian conception of reduction (Section 3); (ii): I deny that the multiple realizability argument causes trouble for reduc-tions, or “reductionism ” (Section 4); (iii): I stress the collapse of supervenience into deduction via Beth’s theorem (Section 5.1); (iv): I adapt some examples already in the literature to show supervenience without emergence and vice versa (Section 5.2)