The Reality of Logic

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The Reality of Logic

• David Davenport
• Computer Eng. Dept., Bilkent University, Ankara
  06533 - Turkey.email david_at_bilkent.edu.tr

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Outline

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

Don't Trust Me
(non) standard disclaimer
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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

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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!

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Logic - problems?

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

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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

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Fuzzy Logic - examples
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Fuzzy Logic - examples
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Fuzzy Logic - examples
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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
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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!

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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

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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

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Language

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

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Meaningful Utterances

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

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Some Other Possible Relations between
Utterance, Mind World
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And Truth

• Matching is coherence
• Correspondence
• but of utterance mental model
• Mind-dependent notion of truth
• shared language, environment senses

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Utterances about truth
Snow is white
It is true that snow is white
Snow is white is false
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The Liar Paradox

• This sentence is false
• Paradox found

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Paradox Lost

• Philosophical whirlpool - stay clear!

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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!

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Some Conclusions

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

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There's more to life than logic
Thank you.