Articles #logic

'I am a dialetheist, or glut theorist, and on that basis I also think some paraconsistent logic is correct. An example of a true contradiction is that for any set, there is always a bigger set than that (Cantor’s theorem), but also there is a set of all sets (the universe of sets) which is as big as it can be—so the universe is bigger than itself, and not. Obviously. ... Or for a more mundane example, if you quit smoking six weeks ago, then you might be both a smoker and not a smoker. Do you want a cigarette? Yes and no. Continuing the End Times series, Richard Marshall interviews Zach Weber

When you start looking closely at the conditions which made possible the emergence of early analytic philosophy in Cambridge in the late 1890s, you find great variety and a host of influences at work—from engagement with the great dead philosophers, other philosophical schools in England, Scotland and further afield from the continent, and other disciplines as well, including mathematics, the natural sciences and classics. Early analytic philosophy was an interdisciplinary and Pan-European achievement. I think that Russell and Moore’s intellectual stature didn’t consist solely in their intrinsic brilliance, although they had that too, but in their capacity to channel these forces even for a while. And we can say something similar about the Polish School and the Vienna Circle which succeeded Moore and Russell at the forefront of developments in analytic philosophy. Continuing the End Times series, Richard Marshall interviews Fraser MacBride

The only way I know of getting at mathematical metaphysics and epistemology is to start with mathematical method. Mathematics is designed to enable us to reason efficiently and effectively, and that has a strong influence on the kinds of objects we talk about and the way we talk about them. I can't see how to make sense of the nature of mathematical objects without understanding their role in mathematical thought. Continuing the End Times series, Richard Marshall interviews Jeremy Avigad