I put in this line just before the post goes

The writer is very likely from the UK--an American would say "I put in this line just before the mail is picked up" or ". . . just before mailing." Americans do not commonly use "post" to refer to correspondence, which they do commonly refer to as "the mail." In the sentence "I put in this line just before the post goes" the writer is referring either to the sentence before that sentence, or the sentence which comes after--it is not clear which is referred to. I suspect, however, that it refers to the sentence about Plato, and any succeeding sentences.

Line often means simply a sentence, but if can have a variety of meanings. An American might say "drop me a line" to mean send me a letter. (Keep in mind that electronic mail is replacing hand-written or typed letters, so such expressions are going out of use.) Someone writing a brief letter might say: "Just a line to say hello and to thank you for your last letter." One would write this even though the letter contained more than one sentence. So, the text about Plato and succeeding sentences could easily be referred to as a line, even though it refers to more than one sentence.

Set nailed it. Only thing one also may refer to a line of reasoning such as a syllogism

Hard to do this on a phone

Bye