Regarding
"logic extremists," I would tend to think that's more a general characterization of those who espouse taking logic to the most extreme of conclusions and accordingly radical of actions—which seems apt for an admiral running an operation like Section 31—than a moniker specific to a particular terrorist sect, or supremacist/secessionist political party, or other organized group. It's probably roughly equivalent to "religious fundamentalist"—logic being very much akin to a religion among Vulcans.
Every faith has its zealots, often including examples to be found among holders of high rank and office. Yet, despite sharing a certain fanaticism in common, they
won't all share the same specific beliefs (nor even overall vision) with one another, they won't always align in their goals and methods and associations, and the same goes for their supporters and sympathizers.
There's no reason why Patar's agenda and machinations need have coincided with those of the
"small faction" of
"renegades" who bombed the learning center, nor the misguided youth who tried to assassinate Sarek as
"a rallying cry to those who value logic above all" for Vulcan to
"withdraw from the failed experiment known as the Federation" just because they each followed extreme interpretations of logic. On the other hand,
"humans are inferior" might well be a credo she whole-
heart-where-her-liver-should-be-edly accepted as an axiom, and she merely turned the other way in her thinking from there, taking it upon her superior self to make what she saw as the ruthlessly logical calls needed to prevent the experiment from failing. (Again, sounds appropriately Section 31-esque to me...)
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MMoM
