According to the Crash Course Philosophy video today, George Berkeley summarized his empirical philosophy with the phrase "esse est percipi", to be is to be perceived. However, it feels somewhat incorrect to use infinitives this way. "Cogito ergo sum", I think, therefore I am, uses present singular. If "seeing is believing" were to be translated, it feels like it should use gerunds, although it could be converted to "to see is to believe", which sounds more awkward. So then, why infinitives in this case?
The expression esse est percipi is grammatical. Notice that the gerund does not have a nominative form at all. If you want the corresponding nominative (or accusative when there is no preposition), you need to use infinitive.
The grammatical structure is the same as in giraffa est alta ("the giraffe is tall"). You are simply saying that something is something, and it does not really matter grammatically what these things are. The predicate is est and the subject can be esse just as well as giraffa.
If you want to say "seeing is believing", infinitives are a good choice again. You can say the same thing in English as "to see is to believe" — there might be a slight difference in nuance but the meaning is the same. I would suggest videre est credere. You can't really phrase this as concisely with any other structure.
On the other hand, cogito ergo sum is a very different kind of sentence. It has two clauses and the subject in both of them is the implicit ego.
Cogito ergo sum does not mean "seeing is believing". It in fact means "I think therefore I am." Decartes used it as a statement of epistemology: If he can think, if he can conjure up rational process, it follows that he must exist. It establishes the I.
In Latin, there is no nominative of the gerund. What that means is that you'll never see a gerund as the subject of the sentence. Instead, the infinitive is used. A case can actually be made that the infinitive functions as the nominative of the gerund. (It can't actually be the nominative, but essentially they're equivalent.)
Therefore, indeed esse est percipi is fully grammatical.
Verbi infinitivi nomina sunt
I started to "get" infinitives when I understood that they're nouns. It's called an infinitive because it's not "bound", i.e. tied to, a time—hence it doesn't make a claim, which is what verbs do. Instead, the infinitive carries the meaning of a verb abstractly. It's a name for that meaning—in other words, a nomen, a noun.
Aliud est velle, aliud posse.
(It's one thing to wish, another to be able.)
Genus et numerus
Just like any other noun, an infinitive even has gender and number. It's neuter and singular, which an adjective must agree with:
Errare humanum est.
(To err is human.)
Objectum est subjectum
Infinitives are different from ordinary nouns in that they can take objects and adverbs just like verbs, and they can take an accusative noun as their subject, like this:
Hodie necesse est te solum ambulare.
(Today it is necessary that you walk alone.)
Since an infinitive doesn't make a claim about its subject, it doesn't agree in number with its subject. When an infinitive has a subject, it's just abstractly denoting "the subject doing that action" without claiming anything about it. The claiming is done by the real verb of the sentence, in this case est.
Taking an accusative noun as a subject enables the infinitive to operate on the object of another verb, like this:
Iulia Marcum discedere vidit.
(Julia saw Marcus leave.)
The object of vidit is Marcum, but the infinitive extends it so the sentence claims that Julia saw the act of Marcus leaving. The act of Marcus leaving is named rather than asserted directly as it would be in Marcus discedit, which has a tense.
Thus the infinitive enables verbs to chain together to form compound verbs without subordinating conjunctions or relative pronouns, like this:
Desine fata deum flecti sperare precando.
(Stop hoping to bend the will of the gods by praying.)
Discrimina a gerundiis
Gerunds provide the function of the infinitive in oblique cases, but they lack the infinitive's ability to take another verb's object as their subject. In the previous example, precando isn't part of the chain of verbs: it functions as an adverbial phrase modifying the compound action.
English gerunds work differently: they somewhat blurrily overlap with infinitives and participles, participating in ad hoc rules about how each specific verb can chain with others. For example, stop can only chain to a gerund, but hope can only chain to a to-infinitive, as in the last example.
There's nothing comparable to those rules in Latin. In many cases, the gerund and infinitive are equivalent in English, as in "Seeing is believing" and "To see is to believe." But the phrasal nature of English grammar creates strange complexities, which is why "Being is being perceived" and "Being is to be perceived" don't work.
A role of English gerunds comparable to their role in Latin is to serve as nouns in prepositional or adverbial phrases, e.g. by praying = precando. Also in both languages, if you want to give a gerund a subject, you need to put the subject in the genitive case.