What Is A Sentence?
This sounds like a daft question because in the process of asking what a sentence is, you have to use a sentence to do so (yes, a question is a sentence). The ontological question of what a sentence is not only an exercise in semantics but is also a meta-exercise in semantics; with it being concerned with itself. Formal Semantics which is the the branch of linguistics and logic which is concerned with meaning, is distinct from Lexical Semantics which is more concerned with how a word is used in context and how it fits into the contextual relations around it.
Put simply a sentence is a textual unit consisting of one or more words that are grammatically linked. That's it. That might sound strange that you can have a sentence consisting of only one word but if that word by itself conveys enough meaning to imply a clause, even if it is not explicit, then it is a sentence. Very simple phrases can also be sentences, provided they also convey enough meaning to imply a clause.
What is a Clause? A clause is that part of a sentence that constitutes a predicate. What is a Predicate? A predicate is that unit of speech which says that a thing is doing something. Note that a predicate is functionally different to a verb which is a "doing something" word and a verb may in fact act as the predicate but a predicate in a sentence may include adjectives, prepositions and even adverb.
Of course you can not have a predicate which says that a thing is doing something unless there is a subject, that there is indeed a thing that is doing something. Subjects are usually nouns (either common, proper) though they can also be adverbs.
Therein lies all the information you need to answer the question of what a sentence is. Since a sentence is a textual unit which implies a clause and a clause consists of subject and a predicate, then a sentence is a textual unit which implies a subject and a predicate.
Let me give you an example of a complete sentence which contains neither a verb or a noun but which implies both and also conveys enough meaning to imply a clause. Since I like the sport of cricket, this is one of my favourite examples:
How many balls are left in the over?
That one word "two" in this case is a cardinal adjective. While "two" is a noun which is a number, it is being used in this case as a description (that is an adjective) of a subject. The subject "How many balls" contains a noun (balls) and an adjective. The verb clause "are left" contains the second-person singular and plural form of the verb "to be" as well as the verb "left" which means to let remain or have remaining behind after going.
That one word "two" by itself is implying the entirety of "there are two balls are left in the over"; which is a standard subject-verb clause which is declarative (that is, it is making a declaration and a claim about a thing), and as such it is a sentence.
It must be said that our magnificent bastard tongue of English is either a gloriously stupidly easy language to learn because the only rule which holds hard and fast is that "every sentence contains a verb" (which is almost a tautology because a sentence must imply a clause) or it is a notoriously difficult language to learn because there is only one rule and that means that you get no help at all. It seems counter-intuitive to me that Germanic languages which have almost no rules would produce so many cultures of people who are sticklers for rules.
If all of that fails, then you can just remember the chorus to The Tale of Mr. Morton.
Mister Morton is the subject of the
Sentence and what the predicate says,
Because English is such a louche language when it comes to rules (I'll even start this sentence with "because" because I jolly well can; so there), it means that we can understand people who we think are butchering the language with relative ease, like Yoda.
Fear is the path to the dark side. Fear leads to Anger. Anger leads to Hate. Hate leads to Suffering.
Why does anyone assume, given all that we know about Yoda who is very obviously speaking in a second language, that his most famous statements are grammatically correct? This is the same person whose regular subject order clauses generally messed up are. Occult health and safety officer should he be not.
What would happen if you pass Yoda's statements through some kind of algorithm which could generate the order in which they would become more Yoda-y? If you ran Yoda's statements through the algorithm multiple times, would you end up in a weird kind of nonsense gobbledegook which is then unparseable? Moreover, is it possible to run Yoda's statements through the algorithm backwards and arrive at the proper original meaning of what he meant to say?
If the statement is exactly backwards then you get:
Suffering leads to Hate. Hate leads to Anger. Anger leads to Fear.
All of this seems equally valid and as an aphorism, equally vapid.
I note that the end point of Yoda's arc, ends up with him talking to Luke Skywalker on a planet with weird mountain outcrops and he decides to burn all of the Jedis' writings to the ground. It isn't actually said but maybe Yoda realises that the Jedi religion is rubbish.
If only he'd stopped at the beginning and decided that if suffering leads to hate, then maybe they should have eliminated suffering in the galaxy. I don't know, maybe the Galactic Senate could have done something about enacting Universal Universal Healthcare, finding a cure for cancer, doing something about pollution and recycling instead of razing planets and moving on; instead of flying about the place and waving colourful laser swords like a bunch of ten year old children.