Could someone tell me when the current terminological distinction between "sound" and "valid" was first made in the development of logic?

If the distinction was first drawn in writings in non-English and then translated to English as "sound" and "valid", that would suffice. Also useful would be information on what work(s) drew that distinction.

  • 1
    This question asks about a definition, but not for the definition itself. It belongs to the history of philosophy and is not off topic per the help center. (+1, interesting question)
    – user2953
    Commented Apr 25, 2015 at 12:53

1 Answer 1


You can see this post for some historical references.

The English translation (1950) of

A formula of the predicate calculus is called logically true or, as we also say, universally valid only if [...].

The modern concept of validity [Allgemeingultigkeit] regarding propositional logic has been introduced by Bernays in his Habilitationsschrift (1918) :

Every provable formula is a valid formula and conversely

where a "valid" formula is

one that yields a true proposition according to the interpretation given for any arbitrary choice of propositions to substitute for the variables [...].

For first-order logic,

this notion [Allgemeingultigkeit] seems to be have been defined for the first time by Behmann (1922).

Of course, the notion of "valid argument" is as old as "formal logic" itself; see Aristotle's logic :

A deduction is speech (logos) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so [emphasis added]. (Prior Analytics I.2, 24b18-20)

The core of this definition is the notion of “resulting of necessity” . This corresponds to a modern notion of logical consequence: X results of necessity from Y and Z if it would be impossible for X to be false when Y and Z are true. We could therefore take this to be a general definition of “valid argument”.

Aristotle proves invalidity by constructing counterexamples. This is very much in the spirit of modern logical theory: all that it takes to show that a certain form is invalid is a single instance of that form with true premises and a false conclusion. However, Aristotle states his results not by saying that certain premise-conclusion combinations are invalid but by saying that certain premise pairs do not “syllogize”: that is, that, given the pair in question, examples can be constructed in which premises of that form are true and a conclusion of any of the four possible forms is false.

If we "jump to" a pre-modern text :

a "traditional" treatise full of new (and hidden) hinsights, we can find the same basic notion :

Caput VI : De artificio consequentie [How consequence works]

Consequence is the transmittal, or inference, from one truth to another. [...] We say that the inference from one truth to another is valid [Dicitur valere illatio ab una veritate ad aliam] whenever one cannot holds without the other.

And again in Caput VIII : Quid sit argumentatio, regarding syllogism :

An argument is a speech in which something is inferred from something other [Argumentatio est oratio, in qua unum ex alio infertur].

The discussion of syllogistic figures end with the remark that :

the nineteen modes seen above concludes by virtue of form alone [dictos novemdecim modos concludere ratione formae].

In the first modern English math log textbook :

A non-empty domain of individuals having been selected, a wff is said to be valid in that domain if it has the value t tor all possible values of its free variables [...].

We can see also [page 55] :

Since it is intended that proof of a theorem shall justify its assertion, we call an interpretation of a logistic system sound if, under it, all the axioms either denote truth or have always the value truth, and if further the same thing holds of the conclusion of any immediate inference if it holds of the premisses. In the contrary case we call the interpretation unsound.

The same modern definition of validity we can find in :

We can find the definitions of valid and sound arguments in :

  • Stephen Cole Kleene, Mathematical logic (1967 - Dover ed 2002), page 59 and 68, respectively.

A scketchy conclusion we can drawn from the historical development is the following :

  • the fundamental notion of "valid argument" has to be "disentangled" from the intuitive notion of inferring a truth from another.

A valid argument, i.e. an argument that is "correct" by virtue of form alone, must not pressupose the truth of its premises.

Having "rediscovered" in moder time this basic notion (already known to Aristotle), the need arises for a term denoting a valid argument with true premises : a sound argument.

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    This looks like good work, Mauro, but is that book introducing/coining those terms, or just explaining them? It's unclear from the quote. Commented Apr 24, 2015 at 18:38

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