The title of this note might perhaps be better in the plural: argumenta e silentio. It is not only that Dr Brandon draws attention to a number of instances of a surprising silence in the ancient sources, both Jewish and Christian. It must also be noticed that silence can be interpreted in more ways than one, and that different lines of interpretation rely for their force upon a different logic. It is with a brief glance at the different logical principles that we will begin.
First, there is the direct argument, which uses the silence of a witness to cast doubt upon an alleged, or otherwise attested, fact. It may be schematised like this:
(a) X makes no mention of y;
(b) X would surely have known y, if it were true;
(c) he would surely have mentioned y;
y is not true.
This is the argumentum e silentio proper, and it is to this class that the chief arguments to be examined belong.
But secondly, there is also the reverse argument, which uses an alleged or agreed fact to cast doubt upon the integrity of a witness who is silent about it. In schematic form it runs like this:
(a) X makes no mention of y;
(b) and X must surely have known y;
(c) and he ought surely to have mentioned it; therefore,
(d) since y is a well-attested fact, or well-established inference, his silence is due to deliberate concealment.
Both the direct and the reverse argument are in principle sound. Whether in practice they will carry conviction will depend on the soundness of the individual links, (a), (b), (c) and (d).