The book I quoted from is the exact chapter where
You then linked his argument to the ridiculous medieval Church doctrines about hell-fire and purgatory - Aquinas did not do that - he based his argument on scripture...and if you were around in 13th century you would almost certainly have been convinced by it because you buy almost the same argument to justify the "shunning" of erstwhile members of your Congregations who are guilty of "heresy" - except you call it "apostasy". Both the Watchtower and Aquinas based their arguments principally around the principle in 1 Corinthians 5:6 and the example of capital punishment in the Mosaic Law and both you and he made the "negative influence" of wilful wrongdoers on the rest of the congregation the main concern. That is really the only principle that Aquinas was concerned with - the overall good of society - that moved him to support capital punishment (which was, in any case, the norm in those days).
Aquinas writes:
Furthermore, just as a physician looks to health as the end in his work, and health consists in the orderly concord of humors, so, too, the ruler of a state intends peace in his work, and peace consists in “the ordered concord of citizens.” Now, the physician quite properly and beneficially cuts off a diseased organ if the corruption of the body is threatened because of it. Therefore, the ruler of a state executes pestiferous men justly and sinlessly in order that the peace of the state may not be disrupted.
Hence, the Apostle says, in 1 Corinthians (5:6): “Know you not that a little leaven corrupts the whole lump?” And a little later he adds: “Put away the evil one from among yourselves” (1 Cor. 5:13)...
...Indeed, in the law which says “You shall not kill” there is the later statement: “You shall not allow wrongdoers to live” (Exod. 22: 18).
The Watchtower publication Keep Yourselves in God's Love has an appendix that uses the same argument - but the other way round - i.e. it goes Mosaic Law to Corinthians - to justify disfellowshipping and shunning.
...reflect on the severe cutting off mandated in God’s Law to Israel. In various serious matters, willful violators were executed. (Leviticus 20:10; Numbers 15:30, 31) When that happened, others, even relatives, could no longer speak with the dead lawbreaker. (Leviticus 19:1-4; Deuteronomy 13:1-5; 17:1-7) Though loyal Israelites back then were normal humans with emotions like ours, they knew that God is just and loving and that his Law protected their moral and spiritual cleanness. So they could accept that his arrangement to cut off wrongdoers was fundamentally a good and right thing.—Job 34:10-12. 10 We can be just as sure that God’s arrangement that Christians refuse to fellowship with someone who has been expelled for unrepentant sin is a wise protection for us. “Clear away the old leaven, that you may be a new lump, according as you are free from ferment.” (1 Corinthians 5:7)
And by the way, it wasn't Jesus who made the comment about leaven and lumps - it was Paul.
So - OK - I know you did not intend to open a debate on the similarities between Aquinas' medieval Church reasoning and 21st century Watchtower teachings - remarkable though that is - but if you take away the mischaracterization of Aquinas' argument from your OP, all you have really said is "people have different ideas about God - how do we know which is right?" - isn't it?
I'm guessing that your intention was to lead people to the conclusion that the "answers" are to be found in the Bible...and therefore to the more specific conclusion that we need to find someone (or more specifically some - perhaps God-appointed - organization) that knows how to interpret the Bible correctly...yes?
But should we really be trusting an interpreter that essentially uses the same kind of logical thought patterns that the medieval Church used to justify capital punishment for heresy?
Should we even be putting our trust in a collection of writings that are - it would seem - so open to ghastly misinterpretation that Aquinas was able to make a perfectly logical case for capital punishment for heresy based on the same scriptures?
I'm sorry if I seem to be reframing your debate - but I think these are very pertinent questions. Don't you?