Karyat (literally meaning "from effect"): An effect is produced by a cause, and likewise, the universe must also have a cause. Causes (according to Naiyayikas) are of three kinds: Samavayi (in case of the universe, the atoms), Asamavayi (the association of atoms) and Nimitta (which is Ishvara). The active cause of the world must have an absolute knowledge of all the material of creation, and hence it must be God. Hence the existence of the Creator is established from the creation.
Ayojant (literally meaning, "from combination"): Atoms are inactive and properties are unphysical. So it must be God who creates the world with his will by inducing the atoms to join. Self-combination of inanimate and lifeless things is impossible, or else atoms would only combine randomly, creating chaos. The hand of a wise organiser can be seen behind the systematic grouping of the ultimate atoms into dyads and molecules. That final organiser is God.
Dhrite (literally meaning, "from support"): Just as a material thing falls off without a support, similarly, God is the supporter and bearer of this world, without which the world would not have remained unified. This universe is thus superintended within God, which proves his existence.
Padat (literally meaning, "from word"): Every word has the capability to exemplify a certain object. It is the will of God that a thing should be exemplified by a certain word. Similarly, knowledge of the different things here cannot come to oneself, unless there is a source of this knowledge. The origin of all knowledge should be omniscient and, consequently, omnipotent. Such a being, however, cannot be seen in this universe, and so it must be outside it. This being is God.
Pratyatah (literally meaning, "from faith"): the Hindu holy scriptures, the Vedas, are regarded as the source of eternal knowledge. Their knowledge is free from fallacies and are widely believed as a source of proof. Their authors cannot be human beings because human knowledge is limited. They cannot obtain knowledge of past, present, and future, and indepth knowledge of mind. Hence, only God can be the creator of the Vedas. Thus, his existence is proved from his being the author of the Vedas, which he revealed to various sages over a period of time.
Shrutéh (literally meaning, "from scriptures"): The Shrutis, e.g., the Vedas glorify God and talk about his existence. "He is the lord of all subjects, omniscient, and knower of one's internal feelings; He is the creator, cause and destroyer of the world", state the Shrutis. The Shrutis are regarded as a source of proofs by Naiyaikas. Therefore, the eistence of God is proved.
Vakyat (literally meaning, "from precepts"): Again, the Veda must have been produced by a person, because it has the nature of "sentences," i.e., the sentences of the Veda were produced by a person because they have the nature of sentences, just as the sentences of beings, like humans. That person must have been God.
Samkhyvihesht (literally meaning, "from the speciality of numbers"): The size of a dyad or a molecule depends on the number of the atoms that constitute it. This required number of the atoms that form a particular compound could not have been originally the object of the perception of any human being; thus its contemplator must be God.
Adrishtat (literally meaning, "from the unforeseen"): It is observed that some people in this world are happy, some are in misery. Some are rich, and some are poor. The Naiyaikas explain this by the concept of Karma and reincarnation. The fruit of an individual's actions does not always lie within the reach of the individual who is the agent. There ought to be, hence, a dispenser of the fruits of actions, and this supreme dispenser is God.