In this paper, we study basic properties of symmetric stable random vectors for which the spectral measure is a copula, i.e., a distribution having uniformly distributed marginals.

The necessary and sufficient condition for a function $f:(0,1)\to [0,1]$ to be Borel measurable (given by Theorem stated below) provides a technique to prove (in Corollary 2) the existence of a Borel measurable map $H:{\{0,1\}}^{\mathbb{N}}\to {\{0,1\}}^{\mathbb{N}}$ such that $ℒ\left(H\left({\mathbf{\text{X}}}^p\right)\right)=ℒ\left({\mathbf{\text{X}}}^{1/2}\right)$ holds for each $p\in (0,1)$, where ${\mathbf{\text{X}}}^p=(X_1^p,X_2^p,...)$ denotes Bernoulli sequence of random variables with $P[X_i^p=1]=p$.

Logic and Probability, as theories, have been developed quite independently and, with a few exceptions (like Boole's), have largely ignored each other. And nevertheless they share a lot of similarities, as well a considerable common ground. The exploration of the shared concepts and their mathematical treatment and unification is here attempted following the lead of illustrious researchers (Reichenbach, Carnap, Popper, Gaifman, Scott & Krauss, Fenstad, Miller, David Lewis, Stalnaker, Hintikka...