- Greeks are citizens of Greece.
- Greece rejected Socrates.
- Socrates was not a Greek.
Does that syllogism work?
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Does that syllogism work?
First of all this is not a syllogism. Syllogisms have terms with logical connections. 'Rejected' and 'citizen' are not terms with logical connections. The U.S. has in its history rejected traitors, imprisoning them and depriving them of the vote, and then tried them for execution exactly because they are citizens. We clearly do not consider foreign nationals traitors to our country, just enemies -- and once we have taken them prisoner as POWs we cannot execute them.
Other nations (Chile?) near us have rejected their governments and exiled them, depriving them of citizenship. So there is no clear, logical connection between these two statements.
So we need a context to interpret the connections that is not logical and outside the realm of syllogism. We can't find one.
There were no citizens of Greece at the time. So no, it makes no sense. Greece, like Germany, and post-Roman Italy, was not a single nation until after the culture already had a long shared history. (This has led German philosophers like Hegel and Nietzsche to link and contrast the psychological foundations of the Greek, German, and renaissance Italian cultures.)
Socrates was a citizen of Athens, one of the few Greek states that had citizens at all. The rest were run by Tyrants, and therefore had subjects.
Also, Socrates was not exiled or ostracized, he was sentenced to death and followed through on the sentence instead of taking on a different nationality. He insisted on not requesting exile, despite that he could have counter-plead for that punishment, and would probably have gotten it. And he insisted on not escaping, even though some of his students seem to have arranged a way for him to do exactly that, and offered him the option. So he was Athenian to the end.
Greeks are citizens of Greece.
It's possible to be both Greek and not yet a citizen of Greece. A first generation Greek immigrant into Ireland, say, could still justifiably call himself Greek without being a Greek national. He's merely recognising his birth-right. You could, alternatively say
Greek citizens are citizens of Greece
This, of course, is a tautology - so how can it be wrong? Well, you go on to write:
Greece rejected Socrates
Except of course, Greece was not constituted as Greece, then. Greece, is a modern nation-state; whereas then, there were city-states and alliances of such - compare with now, alliances of states such as the EU, or a federation of states, such as the USA. Thus, Greece could not have rejected Socrates, as there was no such place as Greece then (in the sense of having established political rights, and thus, making it possible to be a citizen there-of).
Moreover, the history is wrong - whereas Socrates was sentenced to death; Athens repented of its deed after he was executed. So, one could hardly call that 'rejection' per se. If anything, Socrates is now, more synonymous and emblematic of Greece than any other Greek figure one could care to name.
Socrates was not a Greek
This is true. But not by the chain of so-called deductive logic that you have outlined.