 Different authors have extracted opposed lessons from incompleteness. A common reaction is to think that model-theoretic validity must be unsound with respect to logical truth. This is especially frequent in philosophers on whose conception logical truths must be a priori or analytic. One idea is that the results of a priori reasoning or of analytic thinking ought to be codifiable in a calculus. (See e.g. Wagner 1987, p. 8.) But even if we grant this idea, it's doubtful that the desired conclusion follows. Suppose that (i) every a priori or analytic reasoning must be reproducible in a calculus. We accept also, of course, that (ii) for every calculus \(C\) sound with respect to model-theoretic validity there is a model-theoretically valid formula that is not derivable in \(C\). From all this it doesn't follow that (iii) there is a model-theoretically valid formula \(F\) such that for every calculus \(C\) sound for model-theoretic validity \(F\) is not derivable in C. From (iii) and (i) it follows of course that there are model-theoretically valid formulae that are not obtainable by a priori or analytic reasoning. But the step from (ii) to (iii) is a typical quantificational fallacy. From (i) and (ii) it doesn't follow that there is any model-theoretically valid formula which is not obtainable by a priori or analytic reasoning. The only thing that follows (from (ii) alone under the assumptions that model-theoretic validity is sound with respect to logical truth and that logical truths are a priori and analytic) is that no calculus sound with respect to model-theoretic validity can by itself model all the a priori or analytic reasonings that people are able to make. But it's not sufficiently clear that this should be intrinsically problematic. After all, a priori and analytic reasonings must start from basic axioms and rules, and for all we know a reflective mind may have an inexhaustible ability to find new truths and truth-preserving rules by a priori or analytic consideration of even a meager stock of concepts. The claim that all analytic truths ought to be derivable in one single calculus is perhaps plausible on the view that analyticity is to be explained by conventions or “tacit agreements”, for these agreements are presumably finite in number, and their implications are presumably at most effectively enumerable. But this view is just one problematic idea about how apriority and analyticity should be explicated. (See also Etchemendy 1990, chs. 8, 9, for an argument for the unsoundness of higher-order model-theoretic validity based on the conception of logical truth as analyticity simpliciter, and Gómez-Torrente 1998/9, Soames 1999, ch. 4, Paseau 2014, Florio and Incurvati 2019, 2021, and Griffiths and Paseau 2022, ch. 9, for critical reactions.)