I mean, it seems like pretty elementary words that can occur in different type of situations. Why wouldn't they exist ?
English once did not have words for "yes" and "no" as they are precisely used today.
Yes, for example, comes from ge (whence "yea") + sie, a subjunctive form of to be (beon). It literally meant "It is so."
No in fact meant "not ever". From Etymonline:
"negative reply," early 13c., from Old English na (adv.) "no, never, not at all," from ne "not, no" + a "ever." First element from Proto-Germanic *ne (source also of Old Norse, Old Frisian, Old High German ne, Gothic ni "not"), from PIE root *ne "no, not" (see un- (1)). Second element from PIE *aiw- "vital force, life, long life, eternity" (see aye (adv.)).
It was only over time that the two words became the simple answer words meaning "yes" and "no."
In that sense, Latin certainly does have words for "yes" and "no," they're just not so simple. In Late Latin, for example, two ways emerged in Gaul to mean yes: simple hoc and hoc ille. The former became oc in Occitan and the latter became oui in French, thus dividing Medieval French languages. (Obviously there were more and greater distinctions, but it's the one that the people picked up on, for some reason.)
In Classical Latin, we have a plethora of words that are used to affirm or negate questions depending on exact usage. Note though that the simplest way is by repeating the verb: "Amasne?" "Amo!" "Visne?" "Nolo."
For affirmative words, you typically see ita, sic (whence Spanish sí), vero, or some combination. In more unusual cases, you'll also see immo.
Sic typically means "so" and wasn't the most common way, but because of its influence on the Romance languages, I see it very often online today. See the Lewis and Short entry:
- In answers, yes = the French, Italian, and Spanish si (ante - class. and rare): Ph. Phaniam relictam ais? Ge. Sic, Ter. Phorm. 2, 2, 2: De. Illa maneat? Ch. Sic, id. ib. 5, 3, 30: Ch. Sicine est sententia? Me. Sic, id. Heaut. 1, 1, 114.
Ita was a more common way. Like sic, it also means "thus" or "so." It quite often is strengthened by additional adverbs, like vero "truly" (which could be "yes" on its own), profecto "indeed", prorsus "straightaway, truly", or plane "plainly."
For negations, while I noted the most common way above, the verb doesn't always have to appear. You can have a simple non, cf. Cicero's Pro Roscio:
"exhereditavitne (pater filium)? Non." Cic. Rosc. Am. 19.54
Lewis and Short list further examples:
Cic. Verr. 1, 7, 20; id. Ac. 2, 30, 97; id. N. D. 1, 25, 70.—（τ) In questions, non expresses surprise, and doubt of the possibility of denial (v. Madv. Gram. § “451): non sum ego servus Amphitruonis Sosia?” Plaut. Am. 1, 1, 247: “non tu scis, etc.?” id. ib. 2, 2, 71: “haec non turpe est dubitare philosophos, quae ne rustici quidem dubitant,” Cic. Off. 3, 19, 77; id. Leg. 3, 20, 47: “Quid? aviam tuam pater tuus non manifesto necavit,” id. Clu. 14, 40.
Interestingly, you can also combine it with ita: ita non est: "It is not so."
For a very strong negation, you could use minime! "the least!" or "not at all," or numquam "never." However, that's not so different from English:
"Do you want to be with me?" "Ha! Never!"
In mea sententia, this sounds like a case where a speaker of one language cannot comprehend the thought process behind the speaker of another language. Everyone has experienced it if they have come across an idiom that, when translated literally, simply doesn't make sense. However, to the people that used that idiom, it made perfect sense, as it was accompanied by the cultural context needed to understand it. As C. M. Weimer points out, every language has its own version of the affirmative and negative. In English, we use "yes" and "no" and take them to mean the same thing respectively. In Latin, however, the Romans would have used sic, minime, et cetera as "yes" and "no". But when we, English speakers, translate these words, we get definitions such as "thus" or "in the least." It's at this point where idioms become important. Although the word itself doesn't literally mean "yes" or "no," it was used in the same context as those words and are thus synonyms.
Context has always been incredibly important to our understanding of language. It is, in fact, the reason we can translate anything. Words of one language used in similar situations as words of another language can yield a translation between the two, even if the words don't mean exactly the same thing. Babies also learn language through context, by associating objects and ideas with the words used to describe them. And this, in turn, is why it is often difficult to understand foreign idioms and new languages, because our more developed brains must learn to associate new words to a new context. This becomes more difficult as we get older and the neurons associated with language become less malleable.
So I apologize for going on a psychological tangent there, but this idea has always been quite interesting to me. Although I do not reach a different conclusion to C. M. Weimer, I do provide some science background to this topic which may be useful to know. To summarize both of our answers: There are words that, in context, meant "yes" and "no" in Latin, even if they don't translate literally to those definitions.