\textit{R. Dedekind} introduced the modular law, a lattice equation true in most of the lattices associated with classical algebraic systems [Ueber Zerlegungen von Zahlen durch ihre grössten gemeinsamen Teiler'', Braunschw. Festschr. 1-40 (1897), reprinted in ``Gesammelte mathematische Werke, Vol. 2'', pp. 103-148, Chelsea, New York (1968)]. Although this law is one of the most important tools for working with these lattices, it does not fully describe the equational properties of these lattices. This was made clear by \textit{R. Freese} and \textit{B. Jónsson} [Algebra Univers. 6, 225-228 (1976; Zbl 0354.08008)], who showed that any modular congruence variety actually satisfies the (stronger) Arguesian law. (A congruence variety is a variety generated by all the congruence lattices of the members of a variety of algebras.) In this note the author shows that no finite set of lattice equations is strong enough to describe the equational properties of the lattices associated with classical algebraic systems in the following strong sense: there is no modular, nondistributive congruence variety which has a finite basis for its equational theory. This question was posed by George McNulty in the problem session on lattice theory at the Jónsson symposium. Jónsson has asked a similar question [\textit{B. Jónsson}, Universal algebra, Colloq. Math. Soc. János Bolyai 29, 421-436 (1982; Zbl 0489.06008)]. He asked, in Problem 9.12, whether there is a nontrivial variety whose congruence variety is neither the variety of all lattices nor the variety of all distributive lattices, but which is finitely based.