The line of reasoning "parted from being either singular or plural" (gcig-du bral-gyi gtan-tshigs, the syllogism of neither one nor many), used to analyze the essential nature (ngo-bo) of all phenomena. Of the three gateways to liberation (rnam-par thar-pa'i sgo gsum), this line of reasoning opens the way to the voidness of true existence (stong-pa-nyid) itself. The classic example is, "The subject, all phenomena, such as a sprout, lacks true existence, because it is neither a truly existent singular entity nor truly existent plural entities."
The line of reasoning "vajra droplets" (rdo-rje gzegs-ma'i gtan-tshigs, the syllogism of vajra fragments), used to analyze causes. This line of reasoning is called "vajra droplets" because it destroys incorrect views about the nature of causality, like droplets of water wearing down a rock mountain. Of the three gateways to liberation, this line of reasoning opens the way to the lack of a sign (of a truly existent cause) (mtshan-ma med-pa). The classic example is, "The subject, functional phenomena, such as a sprout, lacks a truly existent arising, because it does not arise from its (truly existent) self, from something (truly existent) that is other, from both, or from neither, equivalent to from no cause."
The line of reasoning "refuting the arising of something already existent or nonexistent" (yod-med skye-'gog-gi gtan-tshigs), used to analyze results. Of the three gateways to liberation, this line of reasoning opens the way to the lack of a hope (for a truly existent result) (smon-pa med-pa). The classic example is, "The subject, functional phenomena, such as a sprout, lacks true existence, because it does not arise as something that, at the time of its cause, was truly existent, truly nonexistent, both, or neither."
The line of reasoning "refuting the four possibilities of arising" (mu-bzhi skye-'gog-gi gtan-tshigs), used to analyze both causes and results. The classic example is: "The subject, functional phenomena, lacks true existence, because from the deepest point of view (don-dam-par), one (truly existent) cause cannot give rise to either one or many (truly existent) results, and many (truly existent) causes cannot give rise to either one or many (truly existent) results."
The line of reasoning "dependent arising" (rten-'brel-gyi gtan-tshigs), is the king of reasons (rigs-pa'i rgyal-po), used to establish the lack of true existence of all phenomena. The classic example is, "The subject, functional phenomena, cannot be established as having true existence, because it dependently arises."
According to the Svatantrika division of Madhyamaka, the five great Madhyamaka lines of reasoning employ components of lines of reasoning, such as sprouts and voidness, that opponents in a debate cognize validly in the same way as do the proponents. According to the Gelug interpretation of Svatantrika, this means that both the proponent and opponent validly cognize defining characteristics (mtshan-nyid) findable on the sides of these items that establish the conventional existence of these items. For example, although Chittamatra and Svatantrika assert different objects nullified (dgag-bya) by the voidness of all phenomena, nevertheless both tenet systems assert as objects of valid cognition findable defining characteristics on the side of voidness.
The Gelug Prasangika position is that these five lines of reasoning can be used to prove the voidness of true existence to an opponent only through an inferential cognition employing what is well known to others (gzhan-la grags-pa'i rjes-dpag). This means through an inferential cognition that employs items, such as findable defining characteristics on the side of objects, that merely the opponent in a debate asserts are objects of valid cognition. Only those who assert true existence accept that truly findable defining characteristics on the side of phenomena are objects of valid cognition. Since Prasangika does not accept even the conventional existence of such defining characteristics, inferential cognition employing them is valid cognition merely for such opponents.
In addition to the five great Madhyamaka lines of reasoning, Prasangika also employs argumentation through absurd conclusions (thal-'gyur, Skt. prasanga) in order to help someone who asserts true existence to reject true existence as something impossible. This method uses assertions that the opponent accepts, such as that a rice sprout arises from something other than itself, namely from a rice seed, and then draws out the absurd conclusions that would follow if the assertion were the case on the basis of true existence. If a truly existent rice sprout could arise from something that existed truly as something other than itself, then it would absurdly follow that a truly existent rice sprout could arise from anything, such as from a truly existent barley seed, because such a seed was truly different from it. Having been shown the absurd conclusions that follow from his or her assertions, the opponent in the debate will give up these assertions, rather than have to accept a different assertion that has been proven though a formal line of reasoning as in the Svatantrika method.