An important Talmudic rule says, "'We didn't see it' is no proof [that it doesn't exist or that it didn't happen]".
In Hebrew, "sight" (רְאִיָה) and "proof" (רְאָיָה) – both from the root "to see" (ראה) – are spelled the same but vocalized differently.
When two qualified (kosher) witnesses see an event and testify to it in court it serves as sufficient proof that the event did in deed occur. But as a rule, if they testify "we didn't see it" – e.g., that the girl next door, whom we see daily, got married – it serves as no proof that it didn't occur.
The reason behind this rule is that not all that exists and takes place (even on the macroscopic level) is readably and necessarily visible to the human eye. Maybe the girl did get married, but in private, in secret.
Extending this rule teaches us that there exists a hidden world (עלמא דאתכסיא) behind the revealed world (עלמא דאתגליא) in which we live and that we see.
So we might conclude that sight and proof are the same only in one direction: Seeing something is proof of its existence, but not seeing it is no proof of its non-existence.
But one may argue that this is not satisfactory. If the two words are the same in Hebrew, the language of creation, then on a certain plane sight must be a necessary condition (i.e., an antecedent whose denial entails the denial of the consequent) for proof of existence. In other words, on that plane, if you don't see something it is proof it doesn't exist!
This indeed is the ideal of the future, the level of sight (of everything) that we will reach in the third, eternal Temple, where we will come to see and be seen by God (who is one and everything). Coming closer to this ideal – rebuilding in our consciousness the Holy Temple – is the spiritual service of the month of Tamuz, the month associated in Kabbalah with the sense of sight.