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The Reality of Logic

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Title: The Reality of Logic


1
The Reality of Logic
  • David Davenport
  • Computer Eng. Dept., Bilkent University, Ankara
    06533 - Turkey.email david_at_bilkent.edu.tr

2
Outline
  • Background
  • Logic its Problems
  • Fuzzy other deviant logics
  • Truth
  • A Cognitive solution
  • The new Reality

Don't Trust Me
(non) standard disclaimer
3
Logic
  • Deductive vs. Inductive
  • Classical Logic The study of valid
    arguments or The study of consistent beliefs
    is a paragon of clarity, elegance, and
    efficiency. - Quine
  • Founded on three laws,
  • Identity AA
  • Excluded Middle A or A only two possible truth
    values
  • Contradiction (A and A) nothing can be true
    false

4
Logic
  • Declarative sentences Is it true that x
  • Contrast with questions, commands, etc.
  • Grammatical substitution! feels right to native
    speaker!
  • Arguments
  • Statement supporting reasons
  • Conclusion given premises deduce or infer
  • Valid Argument
  • no possible situation where premises are all true
    but the conclusion is not. entailment
  • Dependent on meaning truth!

5
Logic - problems?
  • Reference The King of France is bald
  • Borderline cases Ted Bartlett is fat
  • Others...
  • Monotonicity, semantics,
  • temporal, modal, etc.

6
Fuzzy Logic
  • Roots in
  • Russells Vague Logic
  • Jan Lukasiewiczs multivalued logic
  • Denies Law of Excluded Middle (A or A)
  • t(s) 0 or t(S) 1
  • vs.
  • 0 lt t(S) lt 1
  • Snow is White Grass is green
  • grass is 85 green

7
Fuzzy Logic - examples
8
Fuzzy Logic - examples
9
Fuzzy Logic - examples
10
Truth
  • The common notion
  • reality, historical, mathematical, logical
  • Existing Theories of truth
  • Correspondence Theory
  • Coherence Theory
  • Pragmatic Theory
  • Others (Deflationary, Semantic, Appraisal, etc.)

p iff p
11
Computational Systems
  • Modeling the world
  • Purpose is prediction
  • States of model map to states of the world
  • Rely on causality
  • Multiple models
  • But no mind, no model!

12
Computation and Cognition
  • Cognitive agents
  • satisfy needs in complex world
  • are computational systems
  • Mental Models, connect to the world
  • (causal links, accurate reflection,
    corresponding states, etc.)
  • Linguistic utterances

13
Representation
  • Mind/representation must be logical!
  • Traditionally, if a b c then z
  • but, not very realistic.
  • Alternative, Inscriptors if z then a
    b c
  • naturally fuzzy, predictive, but require not
  • models scientific invalid reasoning

14
Language
  • Learn words
  • ostensibly
  • by verbal defn.
  • Sentences
  • abstract grammar
  • utter word at time.
  • Purpose
  • communication
  • manipulation!

15
Meaningful Utterances
  • Making sense of utterances
  • Selecting therelevant model
  • True, False Unknown

16
Some Other Possible Relations between
Utterance, Mind World
17
And Truth
  • Matching is coherence
  • Correspondence
  • but of utterance mental model
  • Mind-dependent notion of truth
  • shared language, environment senses

18
Utterances about truth
Snow is white
It is true that snow is white
Snow is white is false
19
The Liar Paradox
  • This sentence is false
  • Paradox found

20
Paradox Lost
  • Philosophical whirlpool - stay clear!

21
Summary
  • Mind as computational system
  • making predictions to guide actions to satisfy
    needs.
  • must (of necessity) be inherently logical
  • Need to store/represent info.
  • inscriptor formulation, defused borderlines!
  • Utterances
  • meaning
  • truth utterances about truth
  • defused liar paradox!

22
Some Conclusions
  • Reality does not come pre-cut and labeled.
  • Truth is a relation btw utterance mind.
  • Representation is predictability.

23
There's more to life than logic
Thank you.
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