Sam is a fireman.
Dorothy is the mother of a fireman.
Only one of your syllogisms quoted above. All of them lack one thing...Dorothy, Sam, Evelyn, Gordon, and Mary were all created beings. And who created them? Yes indeed...
John 1
In the beginning was the Word, and the Word was with God, and the Word was God. 2 He was in the beginning with God. 3 All things were made through Him, and without Him nothing was made that was made.
It does not matter whether a syllogism deals with humans, angels, God, or anything else.
The terms in a syllogism are ABSOLUTELY IRRELEVANT to the issue of validity.
If you don’t understand that, then you have absolutely NO CLUE what logic is about. You have not understood PAGE ONE of any logic textbook.
The following three syllogisms are identical in form, and all three are valid:
Dorothy is the mother of Sam.
Sam is a fireman.
Dorothy is the mother of a fireman.
Mary is the mother of Jesus.
Jesus is the incarnate Word of God, the Second Person of the Trinity.
Mary is the mother of the incarnate Word of God, the Second Person of the Trinity.
Mary is the mother of Jesus.
Jesus is God.
Mary is the mother of God.
Anyone who says that any one of these syllogisms is invalid because one of the terms is “God,” does not have any idea what the science of Logic is about.
In the third syllogism, the word “God” is used twice—both times in EXACTLY the same sense.
Arthur, still using that false syllogism? That was discredited some time ago. It suffers from an inappropriate distribution of the middle term. As redleghunter points out, a fireman is a different kind of thing than the triune God. To distribute the middle term correctly, you would need to treat the term “god” the same way you treat fireman, like this:
Martha is the mother of Sam
Sam is a god
Therefore Martha is the mother of a god
Which of course would also be false, but not because of structure, only because one of the premises is false.
But the structural falsity is a more powerful and therefore a more dangerous error, because it is harder to detect than a blatantly false premise. For example, tell me what’s wrong with the following logic:
“I’m the most responsible person around here, because it seems I’m responsible for everything that’s going wrong.”
We recognize this as a joke, but only because we spot that the word “responsible” shifted meaning between its first use and its second. That is what an undistributed middle term is, a term that shifts meaning from one premise to the next. It invalidates the syllogism.
Remember that theotokus was never designed to be primarily about Mary. It was the burden of Chalcedon to affirm against heresy that Jesus did not acquire the divine nature at some later time, but had it from the womb. And in this we agree. It is unfortunate that Marian factionalism has hijacked the term, and even more unfortunate that it was so vulnerable to being hijacked, because the truth it was originally meant to express is sound enough. But the words of man tend to froth and error, whereas the word of God is the best and most helpful expression of God’s truth.
Peace,
SR