Are there forms of thought which are alien to us, but home to others? Is our form of thought just one among many? Or is it (in essentials) the form of thought per se? Are such questions even sensible? Descartes, Kant, Frege, Wittgenstein, among many, were exercised by such questions. Frege, and then Wittgenstein, discussed the possibility of a logical alien, a thinker whose thought is guided by a different logic yet still counts as a thinker. In 1991 Chicago philosopher James Conant published a paper which brought this issue into clear form and placed its illuminatingly into historical context. A 2011 Conference at the University of Porto - Portugal marked the twenty years of its publication. The present volume gathers the original article and the reflections on it by a number of distinguished philosophers (Jocelyn Benoist, Matthew Boyle, Arata Hamawaki, Martin Gustafsson, Adrian Moore, Barry Stroud, Peter Sullivan. and Charles Travis), followed by answers by Conant. The issues range from the nature of logical truths (the initial focus of Conference) to the nature of thinkers, and the nature of philosophy.--