Reasoning by analogy: 'Is' considered harmful

Just back from sitting by a canal with Belvina, discussing her dislike of the verb 'to be' in philosophy.

I tried to make the point that it's in part a historical accident that we have logic based on the Greek syllogism, and that we treat this as the one true way to understand the world.

The classic example of a greek syllogism runs:

1. Socrates is a man
   
2. All men are mortal
   
3. therefore Socrates is mortal
   

This is clear, but useless. How do we know all men are mortal? In the real world, we can't. The Greek syllogism is great as a tool within mathematics (where we can define our terms as we like), but useless in talking about the real world.

In India, a different kind of syllogism developed in the Nyaya (logic) school:

1. There is fire on the hill (called Pratijñā, required to be proved)


2. Because there is smoke there (called Hetu, reason)



3. Wherever there is smoke, there is fire, e.g. in a kitchen (called Udāhārana, example of vyāpti)


4. The hill has smoke that is pervaded by fire (called Upanaya, reaffirmation or application)


5. Therefore there is fire on the hill (called Nigamana, conclusion)

This also seems to make a general claim. But it (and many of the traditions using it), shift the emphasis in two important ways, compared to the Greek version:

1. With the fire example, we're already in the realm of evidence rather than absolutes. In fact, Nyaya developed to discuss counter-examples and degrees of certainty.
   
2. With the fire example, we are concerned with similarity rather than identity. The stove in the kitchen burns, the forest on the hill burns, but we don't claim the hill is therefore a kitchen.