I propose a formal framework for intuitive probabilistic reasoning (IPR), which aims to capture the informal, yet logical, process by which individuals justify beliefs about uncertain claims, as in legal arguments, mathematical conjecture, scientific hypothesizing, and common sense reasoning. The proposed model of IPR is independent of, but can be viewed as complementary to, Bayesian and related personalist decision theories. In this talk, I highlight the key ideas of this new system including its philosophical grounding in mathematical intuitionism (Brouwer, 1981; Heyting, 1971; Dummett, 2000) and its formalization in intuitionistic Martin- Löf type theory (Martin-Löf, 1984, 1987, 1996) and homotopy type theory (Univalent Foundations Program, 2013). In addition to describing the formal system (syntax and semantics) and its immediate consequences, I compare and contrast with more conventional theories of decision under uncertainty, in particular Bayesian decision theory, Dempster–Shafer theory, and imprecise probability.