 However, even after Leibniz and up to the present, many logicians seem to have avoided a commitment to a strong notion of necessity as truth in all (actual and) counterfactual circumstances. Thus Bolzano, in line with his interpretation of Aristotle mentioned above, characterizes necessary propositions as those whose negation is incompatible with purely general truths (see Bolzano 1837, §119). Frege says that “the apodictic judgment [i.e., roughly, the judgment whose content begins with a ‘necessarily’ governing the rest of the content] is distinguished from the assertory in that it suggests the existence of universal judgments from which the proposition can be inferred, while in the case of the assertory one such a suggestion is lacking” (Frege 1879, §4). Tarski is even closer to the view traditionally attributed to Aristotle, for it is pretty clear that for him to say that e.g. (2c) “must” be true if (2a) and (2b) are true is to say that (2) is a particular case of the “formal” generalization “For all suitable \(P\), \(Q\) and \(R\), if no \(Q\) is \(R\) and some \(P\)s are \(Q\)s, then some \(P\)s are not \(R\)” (see Tarski 1936a, pp. 411, 415, 417, or the corresponding passages in Tarski 1936b; see also Ray 1996). Quine is known for his explicit rejection of any modality that cannot be understood in terms of universal generalizations about the actual world (see especially Quine 1963). In some of these cases, this attitude is explained by a distrust of notions that are thought not to have reached a fully respectable scientific status, like the strong modal notions; it is frequently accompanied in such authors, who are often practicing logicians, by the proposal to characterize logical truth as a species of validity (in the sense of 2.3 below). (See Williamson 2013, ch. 3, and 2017, for a recent endorsement of the idea that logical truths are to be seen as instances of true universal generalizations over their logical forms, based on the scientific or “abductive” fruitfulness of the idea, though not on a disdain of modal notions.)