In one of his very useful writings, Robert Harper writes the following thoughtful sentence:

But the upshot of Gödel’s Theorem is that as soon as we fix the concept of formal proof, it is immediate that it is not an adequate conception of proof *simpliciter*, because there are propositions that are true, which is to say have a proof, but have no *formal proof* according to the given rules.

With *simpliciter* Harper presumably (?) alludes to, and warns readers against, the logical fallacy *a dicto secundum quid ad dictum simpliciter *which was already known to, and warned against by, Kant.

*A **dicto secundum quid ad dictum simpliciter* is Latin, whose literal translation is roughly *from what-is-the-secondary-saying to the absolute saying,* and can be rendered into more usual English as something like *from a qualified claim to conclude an absolute claim. *It means, it seems to me, the error of, from a statement-given-under-certain-qualifying-conditions, to conclude a statement-purported-to-be-true-absolutely.

A physical example of *a **dicto secundum quid ad dictum simpliciter* often given is the seemingly unqualified statement *Water boils at 100 degrees Celsius. *This is a seeming *dictum simpliciter* which really is a *dictum secundum *that has forgotten (or hidden) a qualification: atmospheric pressure.

The connection to *a **dicto secundum quid ad dictum simpliciter* not being explicitly made in loc. cit., to make a precise connection of *a **dicto secundum quid ad dictum simpliciter* with Gödel’s first incompleteness theorem one of course now has to *speculate:* one attempt, in words, would be the following. One views Gödel’s first incompleteness theorem to show that a naive absolute conception of provability is itself a fallacy. For example, one could write, if only words are allowed, and abbreviating w.t.s.f. ‘within the same formalization’:

- Gödel’s first incompleteness theorem shows that to conclude from the fact that in special instances formal statements
*can* be proved w.t.s.f., the absolute statement that *every *true formal statement can be proved w.t.s.f., is to commit *a **dicto secundum quid ad dictum simpliciter.*

Readers who would like some in-depth-reading on *simpliciter *may like to read D.G.Walton, Logique & Analyse 129-130 (1990), 113-154.

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