Summary: Suppose elements \(a_1,\dots,a_{k-1}\) of a Boolean algebra \(A\) are assigned fixed truth values \(\rho_1,\dots,\) \(\rho_{k-1}\in\{0, 1\}\), and an element \(a_k\) is tentatively assigned a probability value \(\rho\in[0, 1]\). Let \(a_{k-1}\in A\). De Finetti showed that there is a closed interval \(\mathcal{I}(\rho)\subseteq[0, 1]\) such that the set of probabilities of \(a_{k+1}\) which are coherent with the probability assignment \(\rho\) coincides with \(\mathcal{I}(\rho)\). Now suppose \(\rho\) undergoes a small perturbation \(\rho\to\rho+d\rho\). Using the preservation properties of coherent sets of betting odds, we study the resulting modification \(\mathcal{I}(\rho)\to\mathcal{I}(\rho + d\rho)\).