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The Reality of Logic

The Reality of Logic. David Davenport Computer Eng. Dept., Bilkent University, Ankara 06533 - Turkey. email: david@bilkent.edu.tr. Outline. Background Logic & its Problems Fuzzy & other deviant logics Truth A Cognitive “solution” The new Reality. Don't Trust Me.

jessamine-blanchard
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The Reality of Logic

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  1. The Reality of Logic David Davenport Computer Eng. Dept., Bilkent University, Ankara 06533 - Turkey.email: david@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 LogicThe study of valid arguments or The study of consistent beliefs “… is a paragon of clarity, elegance, and efficiency.” - Quine • Founded on three “laws,” • Identity A=A • 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. Mind I ndependent 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 Russell’s Vague Logic & Jan Lukasiewicz’s multivalued logic • Denies Law of Excluded Middle (A or ~A) t(s) = 0 or t(S) = 1 vs. 0 <= t(S) <= 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. model world mind world model 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. mind world utterances 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. z a c b Representation • Mind/representation must be logical! • Traditionally,“ifa & b & cthenz” • but, not very realistic. • Alternative, Inscriptors“ifzthena & b & c” • naturally fuzzy, predictive, but require “not” • models scientific & invalid reasoning

  14. Situation in which word “CAT” is heard & cat is seen audio senses visual senses “CAT” Language • Learn words • ostensibly • by verbal defn. • Sentences • abstract grammar • utter word at time. • Purpose • communication • manipulation!

  15. mind W U mind W U mind ? U Meaningful Utterances • Making sense of utterances • Selecting therelevant model • True, False & Unknown

  16. mind mind (b) (a) U1 W1 W U U2 W2 U3 W3 mind1 mind1 (d) (c) W1 U W U mind2 mind2 W2 mind1 U1 (e) W mind2 U2 Some Other Possible Relations between Utterance, Mind & World

  17. Truth Mental Model World Utterance Map or Model Truth Truth And Truth… • Matching is coherence • Correspondence • but of utterance & mental model • Mind-dependent notion of truth • shared language, environment & senses

  18. mind W U (a) mind (b) W U Utterances about truth “Snow is white” “It is true that snow is white” “Snow is white is false”

  19. mind Uliar mind U1 U2 The Liar Paradox • “This sentence is false” • Paradox found

  20. mind U mind mind U1 U1 U2 U2 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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