This paper investigates how Peirce manages to establish a transdisciplinary fallibilist view of the sciences that is not hostile to religious spirituality viewed as a complementary fallibilist knowledge type. I focus on Peirce’s attempt to construct an alternative to classical mechanical ontology with its reversible time concept and the ontological view of absolute transcendental laws of nature. His triadic semiotic pragmaticism has empiricism in common with the logical positivists, but it shares the fallibilist critical stance with Popper, with whose critical rationalism Peirce also shares a thorough-going evolutionary approach. With Hegel and Schelling, Peirce shares a kind of evolutionary objective idealism and with Whitehead a thoroughgoing process view, and finally with Wittgenstein, he shares a pragmatic view of the meaning of words and concepts. What knits together all these apparently incompatible views is his dynamic Tychism and his Synechist field view. Together these produce a transdisciplinary irreversible view of habits as “laws” of nature, mind, and society that emerge in the development of the cosmos. Though Peirce is somehow close to Hegel’s phenomenological and dialectical view on cosmogony, a number of aspects are quite unique about his approach: the most important of these are his dynamic triadic categorically-based semiotics that makes him understand human beings as well as the universe as symbolic self-organizing developing processes. This is an interesting alternative to modern mechanical info-computationalism.