Augumenta e silentio, or arguments from silence, have been used by some Orientalist scholars to prove that certain aḥādīth were later fabrications, since earlier sources are silent about those traditions and have not mentioned them. They thus seek to estimate the date when a ḥadīth came into being by searching for the earliest [written] source that mentions it, arguing that if the ḥadīth had indeed been from the Prophet or Companion, it would have been known and hence in circulation from their own time, or at least in the immediate decades that followed. Therefore, if a ḥadīth compiler does not mention a tradition in his collection, it indicates that he was either unaware of that tradition or that it never existed during his time. Now if the ḥadīth in question was one of great importance, it is highly unlikely that a ḥadīth expert would be ignorant about it; so the only remaining explanation is that it never existed and was fabricated at a later date.
Interestingly, the basic idea being propounded here is not new to Muslim scholarship. It is quite similar to the principle: law kāna la bāna (had it existed, it would have been known) and is even subject to the same conditions. Essentially, three basic requirements have to be met before the principle can take effect: (1) The matter addressed is so important that there is no way any expert scholar would be unaware about it; (2) Despite its importance, the expert scholar (or any person who ought to know it) does not evince it as proof when discussing something directly pertaining to it; (3) There is no reasonable explanation for his lack of reference to it, such as dissimulation (taqiyya), etc. If all these conditions are met, according to the principle of law kāna la bāna, the matter or tradition did not exist at the time of that particular scholar and was a later fabrication.
The principle of law kāna la bāna, also referred to variously as: law kāna la ẓahara (had it existed, it would have been manifest), law kāna lashtahara (had it existed, it would have been popularly known), and law kāna la waṣala (had it existed, it would have reached us) by different scholars, has generally been accepted as long as it meets the required conditions. However, in practice it is very difficult to ascertain the fulfillment of all the requirements in order to employ this principle as evidence. This is due to a number of factors, such as the many lost works of ḥadīth that have not reached us, which makes it impossible to know whether or not the compiler mentioned a given tradition in his other, now lost, compilations. Hence, though theoretically the principle is sound, in practical terms it does not hold much value today.
This is not to say that there are no traditions that can be questioned using this principle. For example, ʿAllāmah Amīnī mentions in his seminal work al-Ghadīr (5:354) that the purported statement attributed to the Noble Prophet (ṣ) in which he reportedly addressed Abū Bakr and ʿUmar saying “No one will take precedence over you two after me” is an obvious later fabrication because if the Prophet had indeed said this, it would have been known to the people and even the first two caliphs would have used this statement as evidence of their right to caliphate, which they never did, and neither did any of the companions. Hence, it becomes clear that using the principle of law kāna la bāna, this was a later fabrication. That being said, however, such examples are very few and cannot be compared to the application of e silentio arguments by Orientalists for a large number of traditions, which is obviously motivated by their biases against ḥadīth.