Latin is probably a more orderly language than English in many ways. But it’s not a model of efficiency, where only one rule applies in any given situation, and for any object or action there’s only one word. Take the act (or lack of act, I suppose), “not talking” or “being quiet.” In Latin there’s “tarcere,” which means to be silent. But there’s also “silere,” which means the same thing.
The interesting thing here, of course, is not Latin, but what happened to those Latin words once they arrived (as all good Latin words hope to) in English. “Silere,” fairly obviously, is the root of “silent,” which has been in common, everyday usage since the 1500s. The nearest comparison for the root “tarcere” is probably “tacent;” a word that appeared sometime in the 1600s, but was never widely used and by now has virtually disappeared. One of the only citations comes from The loves and adventures of Clerio & Lozia: a romance by Antoine du Perier, whose French was translated by Friar Kirkman in 1652: “There was a fair Tragedy, whose subject I will be tacent of.”
But the adventures of “tacere,” once it made the difficult passage to the New Language, were different. Instead of one main derivation entering English usage, “tacere” ended up being the source of several subtly different words. There’s “tacit,” which refers to something unspoken (for example, “there was a tacit understanding between the two Latin transplants not to interfere with each other in their new language”), and “taciturn,” which refers to a characteristically silent person. “Taciturn” was used by the interestingly-named Tobias George Smollett in The Expedition of Humphry Clinker in 1771: “Grieve..was very submissive, respectful, and remarkably taciturn.”
And then, of course, there’s “tact”…except there isn’t. “Tact” has two main meanings. The first is a “delicate sense of what is fitting and proper,” as in “…the word Tact, to denote that delicate sense of propriety which enables a man to feel his way in the difficult intercourse of polished society,” (Dugald Stewart, Outline Moral Philosophy, 1801). The second meaning of “tact” is the sense of touch. “Tact” doesn’t come from “tarcere;” it comes from “tactus” instead, and “tactus” also means “touch”.
Now, you’d think that “tactic” would come from “tact” — and in fact one sense of “tactic” does; the sense that means “related to touch.” Thomas Jackson explained it well in his Treatise Containing the Originall of Vnbeliefe in 1625: “Touch is but an apprehension or feeling of its own tactick qualities being actually moved by other of the same kind.” But another sense of “tactic” is more common nowadays, and is often paired with “strategy.” It relates to the deployment of military forces, and it comes from a Greek word, “tactica” (“τακτικά”).
“Intact” might have to do with anything that hasn’t been demolished by a tactical military operation — but no, it comes from the version of “tact” that means touch. “Intact” means “untouched.” Aha, you say, but if “tact” means touch and “intact” means untouched, then surely “inflammable” means fireproof, right? In this case please direct your attention to the comment, above, about Latin being more orderl. That tacitly implies that English is less orderly. Possibly “inorderly.” Because “inflammable” doesn’t mean fireproof; it means flammable. “Inflammable” comes from “inflame,” which has several senses, but all of them have to do with setting things on fire, either literally or figuratively.
It’s seldom considered tactful to set things on fire, and fire itself is not tactic (although it’s sometimes a tactic). And as for the inconsistent (which means not consistent) use of “in-” in English, maybe the best approach is to be silent. Taciturn. Tacent. Mute — and this may or may not be relevant, but back in the 15th century “mute” meant “bird poop.”