As we know from Žižek, the subject ($) gets represented by the Master-Signifier (S1) for the chain of signifiers (S2) and objet petit a is the remainder of this signifying operation. Lacan’s four discourses turn around these four terms. Let us now explain these terms via a simple example: the teaness of a tea.
It is not at all obvious that a tea is a tea. Tea is a plant that’s boiled for drinking. But “tea” is also a bundle of expectations from a beverage. If the same plant is boiled too much, it may no longer taste like tea and the resulting beverage ceases to be a “tea”. On the other hand, the cold version of it can legitimately pass as “tea”. How is this possible?
The teaness of a tea is in the eye of the beholder, in other words: The teaness of the tea is a Master-Signifier that represents the subject. In the “teaness of a tea”, we must distinguish (1) the mention of a supposed “tea” and (2) the recognition of its “tea”ness. The initial mention of a tea is not immediately a tea, it is something else. Say, the so-called “tea” is just a glass of something put on a table. It’s approved as a “tea” in the second step when the subject says “This is a tea”. In this way, the subject declares the teaness of a tea and gets himself/herself represented in this teaness.
This signifying operation leaves out a remainder by raising the question: Why did the subject declare the teaness of the tea? In other words, what is the exact je ne sais quoi that makes it a tea? This remainder of the signifying operation is the objet petit a.
Be careful: There is nothing between the mention of a tea and the recognition of its teaness other than the subject’s declaration. The question “Why?” and the answers “because (of its taste, its color) …” only emerge from this subjective declaration. This is crucial: The question and the answers come after the declaration, not before it. The question “Why?” aims to abolish the subjective declaration and emphasize the gap between the mention and the recognition of a tea. The answers “because…” aim to replace the declaration with an objective explanation that bridges the gap.
Now we can distinguish the four discourses in this example situation. The Master’s discourse is the subject getting represented by declaring the teaness of a tea. The hysteric’s discourse is the question “Why?” that emerges after this initial declaration to emphasize the gap between the mention of a tea and the recognition of its teaness. The University discourse consists of the answers “because…” that come to explain this gap by objective reasons. And the analyst’s discourse points out that the hysterical question emerges from the objet petit a that has remained from the Master’s initial declaration.