From a historical point of view, Peter F. Strawson’s philosophical studies are an important element within contemporary interdisciplinary investigations of the mind-body problem. The aim of this article is to present and analyze Strawson’s program of descriptive metaphysics, along with the associated conception of persons, that he has proposed. In the second part, I also present his non-reductive naturalism, focusing on two of his analyses that belong to the field of mind-body relations: these concern the problem of other minds, and the question of the nomological reduction of mental states of persons to physical ones (i.e. mind-body identity theory). I then point to several possibilities of using Strawson’s conception of persons in the context of issues raised by other questions linked to the mind-body problem (namely, personal identity as it relates to split-brain persons, and the different phases of a person’s development).

For Peter F. Strawson, transcendental arguments were an important part of his philosophical method, referred to as a connective analysis. Both Strawson and his critical commentators have devoted a lot of effort to determining the nature, scope and purpose of those arguments. In this text, I intend, first of all, to reconstruct and characterize the basic elements of transcendental argumentation, specifying its general form, features and purpose. Secondly, I reconstruct some of the most representative examples of this argumentation. Thirdly, I refer to the basic objections against transcendental arguments formulated in the literature. Finally, I point to a few peculiarities in those arguments, commonly omitted by commentators and interpreters. The overall message of the paper is moderately positive: transcendental arguments are a legitimate way of reasoning in philosophy, and in particular, they constitute a comprehensible and well-founded part of Strawson’s connective analysis.