Puns abound in the following lines. The gravedigger claims that “if I drown myself wittingly . . . an act hath three branches,” therefore, “she drowned herself wittingly.” The words “three branches” conjure up the cause of Ophelia's death, the snapping of a tree branch that led to her drowning, and in this case can be used as a literal consequent in the gravedigger's argument: the gravedigger is taking it as a given that an act containing “three branches” or “tree branches” is a necessary condition for her to have drowned herself intentionally; therefore, he surmises that she drowned herself intentionally. Recall that in logic there are statements known as conditionals. These take the form of if-then statements. To name a pertinent example: if she drowned herself intentionally, then the act has tree branches. In this example, “she drowned herself intentionally” is the antecedent and “an act has tree branches” is the consequent. Without getting too entrenched in logic, intuitively, it makes sense that if a conditional statement is given and if it is known without a doubt that the antecedent is true, then redundantly, without any further information one can conclude that the antecedent is in fact true. As sound as this particular argument may be in the gravedigger's mind, in the world of logic it falls through because his conclusion is established on a grossly unsubstantiated premise—nowhere in the premises of the gravedigger's argument does he state that it is known if Ophelia drowned herself wittingly or that the act had three branches. In fact, the most that can be surmised is that a phonetic misinterpretation of the consequent is true, the act certainly contained “tree branches”, but that does not logically mean that the antecedent is true—that is, by the gravedigger's argument, it is unknown whether or not she drowned herself intentionally. Therein lies the humor. Arthur Schopenhauer claims that, “all laughter . . . is occasioned by a paradox.” The gravedigger's argument is simultaneously sound in his own mind and illogical in reality, leading to an incongruity that incites amusement, perhaps even laughter. Now, it may not be the case that all laughter is generated by a paradoxical action or expression, but Roger Fouts, a researcher at Central Washington University, found that non-human primates subscribe to a form of “simian humor” that makes use of incongruities for comedic effect. This suggests that there may be an evolutionary mental underpinning that causes people to find comedy in paradoxes and incongruities, which is perhaps why this joke continues to register as humorous centuries after it was first produced.
However, returning to the original pun, the word “branches” can also signify a division between concepts: “to act, to do, to perform,” revealing the duplicity of meanings inherent in the gravedigger's words. Arguably, one could claim this dual meaning is too far-fetched to be regarded as a proper pun, but according to Catherine Bates, a pun, in the broadest sense, is “one signifier . . . attached to two or more signifieds”, that is, when a “word can mean two or more things.” Clearly, then, the word “branches” is a pun by this definition, but whether or not it is a “good” pun stands entirely up to the reader's own interpretation. Given this, it isn't too far of a stretch to perceive yet more wordplay in the gravedigger's next line: “Give me leave.”  The word “leave”, phonetically similar to the word “leaf”, can be seen as another instance of arboreal punning. Neither is this characteristic pun unprecedented in Hamlet. Bates makes mention of a similar pun spoken earlier in the play: “when Horatio warns Hamlet not to approach the Ghost . . . lest he be lured 'to the dreadful summit of the cliff / That beetles o'er his base into the sea.' Hamlet remains determined to obey its summons: 'It waves me still.'” In both cases, the focus of the pun is honed down from a larger whole, from "branches" to “leave” or “leaf” and from “sea” to “wave”. As well, this play on words appears flippant given the overarching sobriety of Ophelia's demise, and serves as a veiled mockery of death that is easily dwarfed by the greater totality of the ensuing lines—in this instance, the gravedigger's explanation of Christian doctrine in regards to what constitutes suicide:
