1. 世界悉檀 Worldly accomplishment. Preaching which accords to the conventional understanding of the world. Phenomena (dharmas) exist because of the combination of causes and conditions and have no particular natures of their own. It is the standpoint of communication in which people can speak of the existence of composite things (such as carts and people) as though they were real. The Āryas, however, understand that this is not the true situation.
2. 各各爲人悉檀 Accomplishment for each individual. Preaching according to the abilities and levels of understanding of the people listening. This is a teaching given to a particular person based on that personʼs particular circumstances and personality. Therefore, such teachings are not suitable for other people. Examples cited are the Buddhaʼs method of argument that seems nihilistic when dealing with someone holding substantialist views or that seems substantialist when dealing with someone holding nihilistic views. The teachings are tailored to correct the views held by the person and not meant as a general assertion.
3. 對治悉檀 Corrective/diagnostic accomplishment. Preaching aimed at destroying strong defilement or evil karma of certain beings. These are teachings which are used to counteract and nullify particular afflictions that hinder the student, just as certain medicines are good for fevers but not other illnesses. In the same way, a method to suppress lust is not appropriate to suppress hate, and vice versa. A method for suppressing delusion will be useless for suppressing lust or hate.
4. 第一義悉檀 Accomplishment of supreme truth. Preaching of reality as understood by the Buddha himself. Siddhânta of Supreme Truth: All teachings, dharmas, axioms, and so forth that can be asserted can also be countered and rejected. What remains when all positions are relinquished is the ineffable reality. Hence, this siddhânta is the rejection of all conventional and speculative views. The lengthy story of the Brahmin Dīrghanakha explains that it is the siddhânta used to eliminate the delusions found among very intelligent philosophers who attempt to assert one view or another over other views using sophisticated logic and argumentation. These four also generally map to the four approaches to teaching 四假 taught in the Sanlun xuanyi. 〔三論玄義 T 1852.45.0013a19〕

1. sarvatantra-siddhânta: a tenet which is accepted by all schools. For example, all schools accepted the existence of five objects of the senses.
2. pratitantra-siddhânta: a tenet which is accepted by only one school or one group of related schools, but rejected by all others. For example, the assertion that something cannot arise from nothing was an assertion peculiar to the Sāṃkhya 數論.
3. adhikaraṇa-siddhânta: a hypothetical tenet - that is, a tenet that if it were accepted would lead to the acceptance of another tenet. For example, asserting that there is a soul apart from the senses which can experience their objects requires the acceptance of many other supporting assertions.
4. abhyupagama-siddhânta: an implied tenet that is not explicitly declared, but which is implied by another position being asserted. For example, an argument for the eternal or non-eternal nature of sound presupposes the position that it is a substance. In debating texts, abhyupagama is also used in the sense of the tactic of accepting an assertion made by an opponent in order to refute it by examining its underlying assumptions. cf. A History of Indian Logic, pp. 59–60

Vidyabhusana, Satis Chandra. 1971. A History of Indian Logic: Ancient, Mediaeval, and Modern Schools.. Delhi:  Motilal Banarsidass.