What is, what could, and what should be a speculative phenomenology? If, according to Fink, Husserl’s phenomenology was characterized by an “anti-speculative attitude”, we have to decide what “speculative” means here and if phenomenology can really take such an attitude. Rather than trying to lead phenomenology toward a speculative thinking that is “extrinsic” to it, we will try to find out in what sense phenomenology can find a speculative thinking that is, and remains, intrinsic to it, in a dimension characterized by a radical metaphysical neutrality. After showing that the phenomenological approach is per se “speculative”, namely in the more original and non-metaphysical (or metaphysically neutral) meaning of the ancient “The/ria”, I will outline four forms of such speculative phenomenology as forms of Mathesis. In the second part, I will present the basic concepts and theses towards a Mathesis of subjectivity as part of a phenomenological-speculative approach to forms of self-reference and to an existential dimension. In the third part, this approach will be integrated in a renewed form of meta-theoretical Mathesis as a new issue for the old phenomenological project of a theory of possible forms of theories. In the fourth part, I will focus on the deep relationship between a speculative nonmetaphysical approach to knowledge (theories) and the need to sketch a phenomenological meta-ontology (meta-ontological Mathesis). In the fifth and last part of the paper, I will present a general perspective inwhich the previous forms of Mathesis converge in a non- or metametaphysical questioning about reality
