Quantification Without a Domain

Much recent work in the philosophy of mathematics has been concerned with indefinite extensibility and the problem of absolute generality. It is not uncommon to take the set-theoretic paradoxes to illustrate a phenomenon of indefinite extensibility whereby certain concepts, for example, set and ordinal , are indefinitely extensible. What is less clear is how to articulate this response to paradox or what it means for the prospects of absolute generality. While some philosophers take the indefinite extensibility of certain concepts to imply the unavailability of unrestricted quantification over their instances, others seem inclined to conclude that there is no comprehensive domain. 1 These conclusions are importantly different: One seems to place a serious limitation on thought and language while the other might seem a subtle ontological discovery. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.