Argument ad vertiginem; Lat. vertigo “movement of rotation, vertigo”.

The argument of vertigo is defined by Leibniz in his New Essays Concerning Human Understanding [1795], as a follow-up to his discussion of Locke’s four kinds of argument, S. Collections (3: Modernity and tradition.

We might bring yet other arguments which are used, for example the one we might call ad vertiginem, when we reason thus: if this proof is not received we have no means of attaining certainty on the point in question, which we take as an absurdity.

This argument is valid in certain cases, as if any one wished to deny primitive and immediate truths, for example, that nothing can be and not be at the same time, or that we ourselves exist, for if he were right there would be no means of knowing anything whatever. But when certain principles are produced and we wish to maintain them because otherwise the entire system of some received doctrine would fall, the argument is not decisive; for we must distinguish between what is necessary to maintain our knowledge and what serves as a foundation for our received doctrines or practices.

Use was sometimes made among jurisconsults of probable reasoning in order to justify the condemnation or torture of pretended sorcerers upon the deposition of others accused of the same crime, for it was said: if this argument falls, how shall we convict them? And sometimes in a criminal case certain authors maintain that in the facts where conviction is more difficult, more slender proofs may pass as sufficient. But this is not a reason. It proves only that we must employ more care, and not that we must believe more thoughtlessly, except in the case of extremely dangerous crimes, as, for example, in the matter of high treason, where this consideration has weight, not to condemn a man, but to prevent him from doing harm; so that there may be a mean, not between guilty and not guilty, but between condemnation and banishment in judgment, where law and custom allow it.
Leibniz, New Essays Concerning Human Understanding [1765]. P. 437.

In substance, the argument from vertigo urges us to accept certain kinds of proof for if we don’t, we are left powerless. This is a subspecies of arguments by unacceptable consequences, S. Pragmatic argument; Absurd; Pathetic; Ignorance.

These consequences are “absurd” and dramatic, when dealing with the first principles of knowledge, such as the principle of non-contradiction, which every person must admit on pain of being unable to say anything scientific. Unlike the argument from ignorance, the argument ad vertiginem would therefore be valid insofar as the impossibility on which it is based is not a subjective impossibility, related with such and such a person or group, but an objective, rational impossibility concerning humanity as such.

However, Leibniz operates a distinguo between epistemic situations where our power to know is at stake, “what is necessary to maintain our knowledge”, and social situations dealing with human affairs and ideology, that “[serve] as a foundation for our received doctrines or practices”.
Since demonstrative reasoning cannot apply in the latter case, “probable reasoning” must be rehabilitated in this domain, for lack of a better proof. But having to make do with weaker proof in the criminal domain implies that a person can be condemned on the basis of insufficient proofs, which Leibniz finds undesirable. So, in an interesting maneuver, he proposes to re-equilibrate the weakness of the proofs motivating the condemnation by softening the condemnation itself.