The meaning of this sentence 2

This sentence is pregnant with meaning. Could somebody construe it for me?
I understand most of it however I do not understand its last part.

On the other hand, a proposition that cannot be denied without contradiction must contain something in the predicate that is already in the subject, so that the item does turn up posited in the subject but negated in the predicate of the denial.

I think that I understand the sentence now.
I do not understand why but sometimes I do not understand some sentences. Yet, if I read them a couple of days later I understand them. Why is that? Why do I understand a sentence better a few days later and not the day when I read it. In college time is very important and not understanding a sentence when you need to can make a difference.

What do u want to do with that sentence???

Maybe its because u arenr focused on the context?

This is not really about the sentence it is rather a question about why a person can understand a sentence at one time and not understand it at another.
I guess the need expressed behind my question is how I can teach my mind to understand sentences better.