Transcript Process of Inference

Process of Inference
Dr.Shrinivasa Varakhedi
[email protected]
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.
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.
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.
Instrument of Inference
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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)
Smoke
Fire
“VyApti” or Invariable concomitance
VyApti relation is defined as “hetu-vyApaka-sAdhyasAmAnAdhikaraNyam” 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
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Generation Process
Instrument
Mediator
Result
vyApti-nAnam
parAmarsha
anumiti
Concomitance
Cognition
Application
Inferential
Judgement
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
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
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.

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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.
Technical Terms (Beware of them!)
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Paksha – Subject of Inference
sAdhya – predicated property to be proved
– Probandum
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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
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

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No deductive mechanism as in FOPL
Deduction Method and P-Logic
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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
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.
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Propositional logic is the simplest..
Predicate logic is an extension of Pro.Logic
Boolean Logic is new version of P-logics.
Proof Theory (Logic Vs Nyaya)
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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.
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)
Truth and Validity
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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!)
Is NN system deemed to be Logic ?
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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.
Beyond Mechanism
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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!
Summary
I conclude my presentation with the following
remarks..
1.
NN system should be restudied in this different
context. It should open for new borrowings
(Like power of deductive mechanism of Blogic).
2.
The inferential techniques developed by NN
systems may be useful for Relational Logic
(The logic based on relations of concepts)
3.
NN system is Not a LOGIC that has limited
scope.
THANKS