How do we know that the correspondence of Seneca and St. Paul was a forgery?

Question

There is ancient but discredited tradition that St. Paul and Seneca the Younger corresponded. Here is the Latin text along with an English translation. (Or this better side-by-side edition.)

St. Jerome mentions the correspondence in his De Viris Illustribus, XII:

Lucius Annaeus Seneca Cordubensis, Sotionis Stoici discipulus, et patruus Lucani poetae, continentissimae vitae fuit, quem non ponerem in catalogo Sanctorum, nisi me illae Epistolae provocarent, quae leguntur a plurimis, Pauli ad Senecam, et Senecae ad Paulum. In quibus cum esset Neronis magister, et illius temporis potentissimus, optare se dicit, ejus esse loci apud suos, cujus sit Paulus apud Christianos. Hic ante biennium quam Petrus et Paulus coronarentur martyrio, a Nerone interfectus est.

The above Wikipedia article cites Lightfoot, Dissertations on the Apostolic Age, who categorically denies their authenticity:

The poverty of thought and style, the errors in chronology and history, and the whole conception of the relative positions of the Stoic philosopher and the Christian Apostle, betray clearly the hand of a forger.

It may be a tall order, but an ideal answer could list some concrete points that establish Lightfoot's thesis. To make it even more clear, I'll bullet-list the three general categories mentioned above as questions:

• What style choices make it clear that Paul/Seneca did not write the respective epistles?
• What chronological/historical errors are there?
• What ideas are present that do not make sense for a Stoic philosopher or an early apostle to voice?

Partial answers (as long as they have concrete points) are encouraged!

Answer 1

In the first letter, Seneca seems to refer to Paul's letters as having been bound together as a collection. That seems extremely unlikely at such an early date. Letters 13 and 14 are dated in the consulship of Leo and Sabinus - there appears to be no record of two men with these names being consuls, and they do not appear in the comprehensive Wikipedia list of Roman consuls. I think I am right that Leo is an unlikely name for a consul of this period. The name Sabinus may have been chosen by the author of the letters because Sabina was one of Poppaea's names.

These letters are mentioned in a work by St Jerome dating from the end of the 4th century, by St Augustine and in a 4th century account of the martyrdom of Paul known as Pseudo-Linus. Others may be able to confirm whether, as I suspect, these are the first surviving mentions of them, but, if the letters were genuine, one would have expected earlier Christian writers to have referred to them. Tertullian, who died around the year 240, described Seneca as "saepe noster" - "often one of us" - but this was in a work (De Anima) where Tertullian said that some other non-Christian philosophers and writers shared some Christian views, and anyway the wording suggests that Tertullian probably did not regard Seneca as having really adopted the Christian faith.

In the standard English translation, in letter 2 Paul refers to Seneca as a sophist. I do not have access to the original text, but, if the translation is accurate, I think Seneca might not have reacted well to being so described.

In Letter 7 Seneca refers fairly insultingly to Paul's supposed lack of education, as if he is some rustic who has never studied. The evidence is that Paul was highly educated - his Epistles demonstrate this.

The substance of the letters has all the hallmarks of a pious Christian imagination at work.