檢視 Logic 的原始碼

'''Logic''' (Skt. ''nyāya'' or ''yukti''; [[Wyl.]] ''rigs pa'' or ''blo rig'') employed in Tibetan Buddhist commentaries and debates most commonly takes the form of the Indic syllogism (Skt. ''prayoga''; Wyl. ''sbyor ba''). 

What's important for the Western Dharma student to understand is that, although the form is different, the underlying logic is not—it is the same logic as finds expression in the Aristotelian syllogisms of Western philosophy. This means that any Indic syllogism may be recast as an Aristotelian syllogism, and vice vera.

In order to introduce the formal characteristic of the Indic syllogism, a brief overview of the representations of logic most familiar to people of Western education are presented. It is intended that, by identifying the common elements of Indic and Aristotelian syllogisms, this might aid the reader in gaining insight into the interpretation and application of this powerful system.

We begin by considering the two main branches of logic within Western philosophy, namely: '''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 used in Western philosophy is the Aristotelian syllogism.

For example:
* All human beings have a liver.
* Socrates is a human being.
* Therefore, Socrates has a liver.

Arguments 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 irresistible.


{| border="1" style="background:#ffdead;" cellpadding="4"
| width="100pt" |                                     '''General''' 
| width="120pt" |                                     &nbsp; 
| width="105pt" style="background:red; color:white" | All human beings 
| width="90pt" |                                      have a liver
|- 
|                                                     '''Specific''' 
| align="right" |                                     Socrates is  
| style="background:red; color:white" |               a human being 
|                                                     &nbsp;  
|- 
|                                                     '''Conclusion''' 
| align="right" |                                     Therefore, Socrates 
|                                                     &nbsp; 
|                                                     has a liver. 
|}


===Indic Syllogisms===
The form of the syllogism used in Tibetan Buddhism is derived from the works of [[Dignāga]] and [[Dharmakīrti]]. [[Dignāga]]'s work was a reformation of 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''<br>
:''Do not inherently exist, like a reflection,''<br>
:''Because these things lack, in reality, a nature of neither one nor many.''<br>


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

{| border="1" style="background:#ffdead;" cellpadding="4"
| width="100pt" | '''Subject''' || width="300pt" | These things propounded by ourselves and others
|- style="background:#ffffb1;" 
| '''Predicate'''  || Do not inherently exist, like a reflection,
|- style="background:#bfffef;" 
| '''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====
# 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".
# 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"
# The third mode is '''The Counter Pervasion'''—the negative of the predicate is completely pervaded by the negative of the sign. This means that whatever inherently exists must possesses, in reality, a nature of either one or many.

====Comparison 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.


{| border="1" style="background:#ffdead;" cellpadding="4"
| width="100pt" |                                     '''General''' 
| width="250pt" |                                     &nbsp; 
| width="200pt" style="background:red; color:white" align="center" | All things that lack, in reality, a nature of neither one nor many 
| width="150pt" |                                     do not inherently exist, like a reflection
|- 
|                                                     '''Specific''' 
| align="right" |                                     These things propounded by ourselves and others are
| style="background:red; color:white" align="center"| things that lack, in reality, a nature of neither one nor many
|                                                     &nbsp;
|- 
|                                                     '''Conclusion''' 
| align="right" |                                     Therefore, these things propounded by ourselves and others
|                                                     &nbsp; 
|                                                     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 forward 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.


[[Category:Pramana]]