Logic

Western philosophy generally identifies two forms of logic: inductive and deductive.

Inductive Logic

Inductive logic is reasoning from the specific to the general.

For example:

• All known swans are white (specific),
• Therefore all swans are white (general).

The arguments built from inductive reasoning are never very strong, but often very persuasive. If we examine our confidence that today we will not die, we will find that it is supported by a species of inductive logic.

• All known days have passed without my death (specific),
• Therefore [on any given day] I will not die (general).

Of course, we understand that one day we will die, but it's the rigour that inductive logic lacks that allows us to not be very compelled by this fact.

The conclusions of inductive logic reach beyond the support of their arguments, and this is their weakness. But these conclusions are not necessarily mistaken, and they are not unrelated to their arguments, and this is their strength. Most thinking proceeds inductively, as the process of induction allows the thinker to make educated guesses that leap beyond the confines of their arguments. However, once a line of reasoning has been discovered via induction, it must be established using deductive analysis for its conclusions to be considered reliable.

Deductive Logic

Deductive logic is reasoning from the general to the specific.

Aristotelian Syllogisms

The form of deductive logic that would be most familiar to people of Western eduction is that of the Aristotelian syllogism.

For example:

• All human beings have a liver.
• Socrates is a human being.
• Therefore, Socrates has a liver.

Arguements built from deductive logic are very strong. This is because the conclusion is entirely contained within the premises - produced by analytically deducting their common factors. In the above example, 'human being' is the factor common to both of the premises. When it is deducted, and the remainder of the premises combined, you have the conclusion. Thus, if the truth of the premises is accepted, then the truth of the conclusion is irresistable.

General		All human beings	have a liver
Specific	Socrates is	a human being
Conclusion	Therefore, Socrates		has a liver.

Indic Syllogisms

The form of the syllogism widely used in Tibetan Buddhist literature and debate, is derived from the works of Dignāga and Dharmakīrti. Dignāga's work was a logical reform based on the system propounded by the Naiyāyikas, which was then later refined by Dharmakīrti.

As an example of this form of syllogism, we will take the third of the four great logical arguments of the Middle Way - taught extensively by the Great Abbot Shantarakshita in his treatise, the Madhyamakalankara - the argument of 'neither one nor many'.

• These things propounded by ourselves and others
• Do not inherently exist, like a reflection,
• Because these things lack, in reality, a nature of neither one nor many.

The process of deductive analysis used here is explained as follows:

Subject	These things propounded by ourselves and others
Predicate	Do not inherently exist, like a reflection,
Sign	Because these things lack, in reality, a nature of neither one nor many.

• The subject is that which is under investigation, about which a claim is being made.
• The predicate is the claim that is being made about the subject.
• The sign is what is used to establish the probandum (what is to be proven), which is the valid connection between the subject and the predicate.
• The probandum is the relationship between the subject and the predicate – that which is to be proven through the syllogism

In assessing the validity of a syllogism, you start with the subject and work your way through the three modes of logic until you get to the predicate.

The first mode establishes the relationship of the subject with the sign.

Then the second and third modes establish the relationship of the sign to the predicate. Establishing these three modes establishes the probandum.

The Three Modes of Logic

1. The first mode is The Property of the Subject - the sign must be a property of the subject. Here, "lacking, in reality, a nature of neither one nor many" must be a property of "these things propounded by ourselves and others".
2. The second mode is The Forward Pervasion - the sign is completely pervaded by the predicate. This means that all things that are "lacking, in reality, a nature of neither one nor many" "do not inherently exist, like a reflection"
3. The third mode is The Counter Pervasion - the negative of the sign is completely pervaded by the negative of the predicate. This means that whatever possesses, in reality, a nature of either one or many must inherently exist.

Comparision with the Aristotelian Syllogism

The argument of 'neither one nor many' may be expressed in the Aristotelian form:

• All things that lack, in reality, a nature of neither one nor many do not inherently exist.
• These things propounded by ourselves and others are things that lack, in reality, a nature of neither one nor many.
• Therefore, these things propounded by ourselves and others do not inherently exist.

General		All things that lack, in reality, a nature of neither one nor many	do not inherently exist, like a reflection
Specific	These things propounded by ourselves and others are	things that lack, in reality, a nature of neither one nor many
Conclusion	Therefore, these things propounded by ourselves and others		do not inherently exist, like a reflection.

The statement of the general premise of an Aristotelian syllogism corresponds to both the second and third logical modes. The term "all" (which makes it a general statement) covers both the foward and counter pervasions, establishing the relationship between the predicate and the sign.

The specific instance premise covers the first logical mode, establishing that the sign is a property of the subject.

What is analytically deducted from the Aristotelian syllogism corresponds to the sign.

The Aristotelian conclusion corresponds to the Indic probandum - that which is to be proven.