Process of Inference

1. Process of Inference Dr.Shrinivasa Varakhedi shrivara@gmail.com

2. Role of Inference in Life • Contribution: • Much information we get through Inference • Little we perceive / listen to and infer a lot more. • Inferential power : Faculty of brain • Every living being uses inference. • Human mind is considered to be supreme for its inferring ability. • Every action in mind involves inference. • All tasks require reasoning on knowledge.

3. Inference – Judgment on evidences • Standard Examples • If you see “flood in the river” at the bottom of a hill, you will infer that “a big rainfall occurred on the hill’s top”. • After seeing smoke on hill’s top, you just think that “Hill has Fire” because “it has smoke” • These judgments are drawn from the known facts – Flood and Smoke. • The flood is sign/mark of rainfall ; smoke is of the fire.

4. How to arrive at Inference? • Causal connection between two cognitive events: Cognition of Smoke  Cognition of Fire Cognition of Flood  Cognition of Rainfall • What made this possible ? • Not just the perception of smoke on hills and flood in river. • On seeing them, the relation between their counterparts triggers in the mind ; that relation leads to inference.

5. Instrument of Inference • Sense organs and Sentences are NOT causes. • The awareness of relation that smoke and fire have is major factor. • This relation is called “Vyapti” – invariable concomitance. • “wherever smoke resides, there resides fire” • x [ smoke (x)  Fire (x) ] • This is NOT causal relation ; but “pervasion” / coverage. (Of course cause always pervades effect)

6. “VyApti” or Invariable concomitance • VyApti relation is defined as “hetu-vyApaka-sAdhya-sAmAnAdhikaraNyam” by NN school of thought. • This means that If A is reason (hetu) for B, then B is pervasive of A and A & B are co-located. • It can be represented in Predicate Logic as : ~ {x [~Sx ۸ Hx]} ۸ {x [Hx ۸ Sx] where S = sAdhya, H = hetu. In FOPL vyApti is expressed as (I should NOT say it is vyApti !!!) x [Hx  Sx] = x [~Hx ۷ Sx] = Hx set Є Sx set

7. Generation Process Instrument Concomitance Cognition Mediator Application Result Inferential Judgement vyApti-nAnam parAmarsha anumiti

8. Paramarsha OR Application • Paramarsha is immediate cause for Anumiti • “vahni-vyApya-dhUmavAn parvataH” • “Hill has smoke that is pervaded by Fire” • Paramarsha cognises vyApti relation as well as relation with the locus i.e., subject of inference. • VyApti relates smoke with Fire, but it doesn’t lead to conclude that Fire is located in hills. • If Smoke is found to be located in hills, then fire could be placed on hills. • Thus vyApti relation and paksha-dharmata (residing in subject) are two important concepts in inferential process

9. Argument = Syllogism = Nyaya • NN school of though proposes Five limbed Nyaya or syllogism • “hill has fire” – The thesis / PratijnA • “Because it has smoke” – Reason / hetu • “Wherever is smoke, there is fire as in kitchen” – udAharaNa (with vyApti) / Eg. • “hills has smoke that is pervaded by Fire” – Application / upanaya • The hills has fire” – Conclusion / nigamanam

10. Syllogism and Nyaya • Aristotelian system of logic admits three limbed argument • Major premise: All men are mortal. • Minor premise: Socrates is a man. • Conclusion: Socrates is mortal. • On the contrast, five limbed syllogism is admitted in NN school of thought • It is necessary to invoke “akAnkshA” expectancy in hearer’s mind • This is called “parArtha” meant for others. “svArtha” is inference for self.

11. Technical Terms (Beware of them!) • Paksha – Subject of Inference • sAdhya – predicated property to be proved • Probandum • Hetu – Reason / evidence (prover property) • vyApti – pervasion - Invariable concomitance • Paksha-dharmatA – Being related with Paksha • Sapaksha – Loci where probandum is determined • Vipaskha – Loci where probandum is known to be absent

12. Major points in NN theory of Inference • NN system deals with mental / psychological process • This process involves mental events / states. • Inference and its causal factors are cognitive episodes • Never NN system talked of form & content separation • Propositions returns truth value and cognitions return content • No deductive mechanism as in FOPL

13. Deduction Method and P-Logic • A complete deductive mechanism based on “form” or “syntax” • The semantics of AND, OR, NOT, IF-THEN is captured by truth-table • With the flavour of Boolean Algebra (+, *, ~) you may find logic more mathematical and easier • This mechanism is thru the power of “Form” • Form and Content are separated • Form is nothing but shape that helps to manipulate • Content is information required

14. P- logic  B - logic • In general a logic is defined by • syntax: what expressions are allowed in the language. • Semantics: what they mean, in terms of a mapping to real world • proof theory: how we can draw new conclusions from existing statements in the logic. • Propositional logic is the simplest.. • Predicate logic is an extension of Pro.Logic • Boolean Logic is new version of P-logics.

15. Proof Theory (Logic Vs Nyaya) • NN Theory has developed a complete system of proof checking the validity of an inference thru `hetvAbhAsa’ = fallacies that are based on content. • P-Logic gives proof for valid conclusion thru its axiom-based testing methods, which is purely mechanical. • NOTE : Validity = properness or Being according to rules ; Truth = Correspondent to the reality.

16. Truth and Validity • Truth = correspondance to the reality • Test is based on Content ; Not on the form • Logic excludes this test from its scope • Validity = coherence among the Ps • Test is based on Form ; Not on the content • Logic explains such formal tests (Yo can say inference is valid if it passes thru the formal tests)

17. Truth and Validity • According to P-Logic, any conclusion of a valid argument must be true if all the premises are true • This shows that Validity of an argument guarantees you about the truth of the conclusion • Whereas NN system decides the truth of a conclusion basing on it’s content (Even true inference may deduce from untrue cognition!)

18. Is NN system deemed to be Logic ? • According to me NN is Not LOGIC in the sense that P-Logic is called so. • However it can anytime take inputs from different systems and can be improved to do logic • More over, it must be noted that Never Indian systems tried to separate the “Form and Content” or “Syntax and Semantics” • They knew that there is a small line between them. Panini has used this and achieved mechanism in his system.

19. Beyond Mechanism • The hardcore logicians believe that everything could be reduced to the level of Formal structure and be processed mechanically • It is NOT so. Ultimately you must stop somewhere in basic level of semantics, for semantics is the supreme • NN system holds that vyApti relation is a basic relation of the whole reality, which you must have somewhere at the end. Accept it now……Yet to be established!

20. Summary I conclude my presentation with the following remarks.. • NN system should be restudied in this different context. It should open for new borrowings (Like power of deductive mechanism of B-logic). • The inferential techniques developed by NN systems may be useful for Relational Logic (The logic based on relations of concepts) • NN system is Not a LOGIC that has limited scope.

21. THANKS