This talk presents numerous results from the area of quantitative investigations in logic and type theory. For the given logical calculus (or type theory) we investigate the proportion of the number of distinguished set of formulas (or types) $A$ of a certain length $n$ to the number of all formulas of such length. We are especially interested in asymptotic behavior of this fraction when $n$ tends to infinity. The limit $\mu(A)$ if exists, is an asymptotic probability of finding formula from the class $A$ among all formulas or the asymptotic density of the set $A$. Often the set $A$ stands for all tautologies of the given logical calculus (or all inhabited types in type theory). In this case we call the asymptotic of $\mu(A)$ the \emph{density of truth}. Most of this research is concern with classical logic and sometimes with its intuitionistic fragments but there are also some attempts to examine modal logics. To do that we use methods based on combinatorics, generating functions and analytic functions of complex variable with the special attention given to singularities regarded as a key determinant to asymptotic behavior.