This is typically how Analogies work. I want to explain some concept to someone, say A->B (A implies B). After a while, I find that the logical relationship between A and B is quite difficult to get across. I then resort to an analogy, say X->Y (X implies Y). I pick this analogy from everyday life so that the logical relationship between X and Y are evident, if not obvious. Then, with some conviction, I claim that as X->Y is so obviously true, A->B must also be true. The unsuspecting listener vaguely gets A->B, but looking at how strongly X->Y holds, she is convinced that A->B must hold as well.
The catch is that whether A==X and B==Y is never touched upon, let alone proved.
Let me give an analogy to explain this – (grimace)
Say my aunt wants to prove it to me that a guru is required to navigate the path to enlightenment, she first tries to convince me by using just their merits and interactions. I am hardly convinced, and thats when she resorts to an everyday analogy. We all know how a little curd is necessary and sufficient to ferment a whole vessel of milk into curd. Similarly, a guru is necessary and sufficient to get you across the sea of ignorance into nirvana. I am now thinking – Oh! Where do I find my own guru?
See the catch? Who is to ever suspect that my aunt never touched upon the similarity between the situations? Did she prove that a guru equals a tea spoon of curd? Or that I am a vessel of milk? Or that enlightenment is a vessel of curd that I am interested in, etc.
Informal reasoning of this sort has had me always suspecting every analogy that anyone throws at me to make me see their points. I grimace every time I do it myself. This had led me to believe that there are some severe restrictions when it comes to proving something to someone.
As I lamented about this with the vaakpatu (vaachaLi?) Nisrani Ramchandra, he told me that Nyaya says that there are four odd sources of knowledge.
– Pratyaksha (Perception)
– Anumana (Inference and Contrapositive)
– Upamana (Analogy)
– Aptavakya (Testimony)
If A->B was obvious by perception, there would be no need for a proof. If whenever A were present, B were seen (inference); if whenever B were not present, A would not be present (contrapositive) – QED. We have already covered Analogy. And of course, if some one whom I consider wise, someone whom I trust, were to tell me that A indeed implies B, I would just believe it. That would be Aptavakya.
I also want to add two more such concepts.
Proof by Contradiction: When you see that everything else is eliminated, whatever is left, however counter-intuitive, must be true. (Sherlock Holmes would’ve smiled)
Proof by Enlightenment: When you know that ‘it’ is true. You just know it. No proof is ever required.
I wonder what formal logic theory says about these techniques. I have seen various mathematical proofs which use these notions formally, but when it comes to social sciences, or philosophical reasoning, I feel the void. Many a time, I have felt this desperate craving to have things formal, so that the wheel of thought need not be reinvented during each dialogue. Sigh.
Finally, in spite of so much thought about logic, conviction, proofs, etc., there is this feeling that everything comes down to faith/belief/trust; Or so I believe.