Logic's Point of Departure
It was stated above that in Tibet, the final division of Svatantrika and Prasangika was dictated by the way each produces an understanding of emptiness in the mind of an opponent. The very names of the schools reflect their insistence on certain argumentative procedures: Svatantra means Autonomous Reason, while Prasanga means Consequence. In practice, this means that a Prasangika will be satisfied that any intelligent being, upon hearing the absurd consequence of some position, will perceive the correct understanding of the matter. A Svatantrika will insist that the implied result of the consequence must be explicitly stated in a syllogism of its own.
It seems that the Svatantrikas' and Prasangikas' logical modes of attack are based on preliminary preference for their respective beliefs regarding the mode of existence of conventional phenomena. According to Tsongkapa's Great Exposition of the Stages of the Path to Enlightenment, "The reason why they assert autonomous signs [proofs] in their Svatantrika system is this conventional existence of own-character, that is, establishment by way of the object's own entity conventionally" (7). So it can be said that a Svatantrika's choice of reasoning methods derives from his view that conventional phenomena exist by way of their own character. Conversely, a Prasangika's use of the consequentialist method derives from her (7) view that phenomena don't exist by way of their own character. The difference of opinion may ultimately be traced back to the beliefs regarding scriptural interpretation rules as stated above.
Some might claim that by using scripture as a reference point, Buddhists employ a pre-rational methodology that can only lead to irrational results. However, the scriptural reference points described are just one aspect of the schools' theories of existence. A proponent of either view might easily maintain that due to the correctness of his logical methodology one can see that the rules chosen for scriptural interpretation were the correct ones. The axioms as well as the methodology are part of a system that is held up, as a whole, to the light of experience.
A considered analysis of western science shows that it too has axiomatic truths founded on beliefs rooted in the cultures that gave it life. In a more concrete sense, just as a researcher working at a particle accelerator will refer to the works of Niels Bohr and Werner Heisenberg when elaborating on his own ideas, so a Prasangika will refer to a well-known argument by Kaydrup or Tsongkapa to make a point that is generally accepted by the community in which he works. In both cases, it is the present experience and reasoning of the experimenter that supports or denies the theory, not the voice of authority. The Buddha himself insisted that followers test his ideas rather than accept them just out of respect for him. Thus armed with the axioms of their tradition, Buddhists rationally explore the implications of their theories as they can be applied to experience. Leaving the paradigm comparisons for later, we can proceed to analyze the tools used to dissect existence in Madhyamika tradition.