*Principle: what constitutes "correct" language is what the majority of informed speakers says it is. However, in any language, there is always movement towards new vocabulary and grammar, especially in a language as widely spoken as English. A case in point: before things became so overwhelmingly expressed in economic terms, we did not "grow" much of anything but hair or crops --- we caused things to grow or made them grow. Now, we grow the economy, grow the deficit, grow businesses, etc.
In the case of syllabus, or rather, more than one syllabus, both "syllabuses" or "syllabi" are correct. In Latin, "syllabi" is in fact the correct plural form of "syllabus." However, if we ignore the Latin root and just follow the basic rules for the English language, "syllabuses" is correct for the linguistic norm imposed by the language in which most of this this site is written. We might note the same sort of situation with the Greek "criteria" versus the English-adapted "criterions," .
So as speakers and writers, we have to decide the following: which rules are we playing by? Do we want to display our knowledge of the correct locution in another language or do we want to go for uniformity of grammar and usage? We can say, "spaghetti is my favorite food" although in Italian (or for that matter, in French), this is technically incorrect. Why? Since "spaghetto" means "string" and "spaghetti" means "strings," Italians would say "2 spaghetti," but "1 spaghetto." In French, it's "1 spaghetti" and "2 spaghettis," and, although I'm less certain about this, in Spanish it's "1 espagueti" and "2 espaguetis." Therefore, under the rules of the language from which we borrowed the word, we English speakers should actually be saying "Spaghetti ARE my favorite food." Especially if we are always pridefully saying things like "syllabi" and "criteria."
In locutions like "the data shows" vs. "the data show" or "if I was rich" vs. "if I were rich;" our choice of words ultimately depends on how valuable we think erudition (in the first case) and correct usage (in the second) are to the context of our situation. Obviously, if the context is a test in Latin or English grammar, we had better use our Latin or our English as correctly as we can. On the other hand, if we're way out in the country somewhere, we're probably better off sticking to local linguistic registers: "ya gots ta dance with them what brung ya." And don't forget, "two plus two is four" is incorrect; we should say "two plus two ARE four."
A final consideration is the lexicon itself. In our everyday conversations in English, we confidently use the word "entrepreneur" to mean a small business owner/commercial innovator neither knowing nor caring that in the original French, the word means either a building contractor or an undertaker. We call the main dish of a meal an entrée, but it's really just the first of several courses in that meal. On the other hand, such words as "boutique," "hors-d'oeuvre," and "pâté" have no English equivalents, so we just use the French words. Unfortunately, from our pronunciation or misuse of these words, the French might never know it. My favorite is the horrendous "boocooze" (beaucoup) to mean "a lot."
This all adds up to our always trying to be aware of what we're really doing when we're using a language. The more so we are, the more powerful we become. "Savoir, c'est pouvoir."