# Philosophy:Jaina seven-valued logic

## The seven predicates

The Saptabhangivada, the seven predicate theory may be summarized as follows:[4]

The seven predicate theory consists in the use of seven claims about sentences, each preceded by "arguably" or "conditionally" (syat), concerning a single object and its particular properties, composed of assertions and denials, either simultaneously or successively, and without contradiction. These seven claims are the following.

1. Arguably, it (that is, some object) exists (syad asty eva).
2. Arguably, it does not exist (syan nasty eva).
3. Arguably, it exists; arguably, it doesn't exist (syad asty eva syan nasty eva).
4. Arguably, it is non-assertible (syad avaktavyam eva).
5. Arguably, it exists; arguably, it is non-assertible (syad asty eva syad avaktavyam eva).
6. Arguably, it doesn't exist; arguably, it is non-assertible (syan nasty eva syad avaktavyam eva).
7. Arguably, it exists; arguably, it doesn't exist; arguably it is non-assertible (syad asty eva syan nasty eva syad avaktavyam eva).

There are three basic truth values, namely, true (t), false (f) and unassertible (u). These are combined to produce four more truth values, namely, tf, tu, fu, and tfu (Three-valued logic). Though, superficially, it appears that there are only three distinct truth values a deeper analysis of the Jaina system reveals that the seven truth values are indeed distinct. This is a consequence of the conditionalising operator "arguably" denoted in Sanskrit by the word syat. This Sanskrit word has the literal meaning of "perhaps it is", and it is used to mean "from a certain standpoint" or "within a particular philosophical perspective".

In this discussion the term "standpoint" has been used in a technical sense. Consider a situation in which a globally inconsistent set of propositions, the totality of philosophical discourse, is divided into sub-sets, each of which is internally consistent. Any proposition might be supported by others from within the same sub-set. At the same time, the negation of that proposition might occur in a distinct, though possibly overlapping subset, and be supported by other propositions within it. Each such consistent sub-set of a globally inconsistent discourse, is what the Jainas call a "standpoint" (naya). A standpoint corresponds to a particular philosophical perspective.[4]

In this terminology, it can be seen that the seven predicates get translated to the following seven possibilities. Each proposition p has the following seven states:[4]

1. p is a member of every standpoint in S.
2. Not-p is a member of every standpoint in S.
3. p is a member of some standpoints, and Not-p is a member of the rest.
4. p is a member of some standpoints, the rest being neutral.
5. Not-p is a member of some standpoints, the rest being neutral.
6. p is neutral with respect to every standpoint.
7. p is a member of some standpoints and Not-p is a member of some other standpoints, and the rest are neutral.

## Comparison with Catuskoti and Aristotelian Logic

Saptabhangi Logic Catuṣkoṭi Logic Aristotelian logic
It is : (P) It is : (P) It is : (P)
It is not : (P') It is not : (P') It is not : (P')
It is and it is not : (P^P') It is and it is not : (P^P')
It is unassertible : (U(P)) It is neither : (P^P')'
It is and it is unassertible : (P^U(P))
It is not and it is unassertible : (P'^U(P))
It is and it is not and it is unassertible  : (P^P'^U(P))
Negation Table
Logical Truth value

P

Negation

~P

True False
Unassertible Unassertible
False True