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Decoding Logical Statements: The Mystery of Modus Ponens

Explore the intricacies of logical statements and the Modus Ponens rule through an engaging narrative involving the Kennedy assassination scenario. Understand the logic behind hypothetical messages and how they shape arguments. Dive into the concept of time and tense in logical statements. Unravel the complexities of logical statements and their deductive validity.

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Decoding Logical Statements: The Mystery of Modus Ponens

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  1. Previously on THG…

  2. April, 1985 A train from Paddington to Bodmin…

  3. The Mystery of…. Modus Ponens

  4. Lewis Carroll

  5. Achilles and the Tortoise

  6. [A] Someone shot Kennedy • [B] Oswald didn’t • [C] If A and B, then Z • [D] If A and B and C, then Z • [E] If A and B and C and D, then Z • [F] If A and ……oh, forget it!

  7. mc : md *,mi

  8. Compound Messages cannot be True (or False)

  9. The Independent message is affirmed outright, unless there is rational reason to think otherwise

  10. Selection of ‘if’ accords the dependent message the status of an hypothesis

  11. Which means: It is being treated as true… …whether or not it really is.

  12. Logic

  13. IfOswald didn’t shoot Kennedy, somebody else did

  14. Hypothetical ‘if’-message

  15. Logical ‘if’-message

  16. Stand Alone If P, then Q There is an Antecedent And a Consequent

  17. If Oswald didn’t shoot Kennedy, somebody else did whines, we beat him Oswald didn’t shoot Kennedy (YES)

  18. Contraposition If P, then Q If not Q, then not P

  19. If Oswald didn’t shoot Kennedy, somebody else did whines, we beat him If nobody else shot Kennedy, then Oswald did (YES)

  20. Time and Tense Tense: time registered by form Time: time the message is about

  21. If Oswald didn’t shoot Kennedy, somebody else did whines, we beat him Tense: Past Time: Past (Tense = Time)

  22. Logical ‘if’-messages • Pass Stand-Alone • Contrapose • Tense = Time

  23. Logical ‘if’-messages … … are condensed arguments

  24. If P, then Q P. So Q

  25. IfOswald didn’t shoot Kennedy …then somebody else did

  26. Oswald didn’t shoot Kennedy So: Somebody else did

  27. Logical ‘if’-messages • Cannot have Truth-values • Are condensed Arguments • Their standard is Deductive validity

  28. Non-logical hypothetical messages • The dog – ifit was a dog – ran off • Ifit rained, it didn’t rain hard • Ifthe Mayor is married, his wife did not accompany him

  29. Non-logical hypothetical messages • If it didn’t run off, it wasn’t a dog • If it rained hard, it didn’t rain • If his wife did accompany him, the Mayor is not married

  30. Non-logical hypothetical messages • The dog – ifit was a dog – ran off • Ifit rained, it didn’t rain hard • Ifthe Mayor is married, his wife did not accompany him

  31. Non-logical hypothetical messages • Affirm the Consequent • Are not condensed Arguments • Pass Stand-Alone • Don’t Contrapose • Tense = Time

  32. The Mystery of…. Modus Ponens

  33. Modus Ponens • P • If P, then Q • So: Q

  34. Oswald didn’t shoot Kennedy… • And if Oswald didn’t shoot Kennedy… • …then somebody else did. • So: Somebody else did.

  35. If, as we now know, Oswald didn’t shoot Kennedy… …then somebody else did.

  36. [A] Someone shot Kennedy • [B] Oswald didn’t • [C] If A and B, then Z • [D] If A and B and C, then Z • [E] If A and B and C and D, then Z • [F] If A and ……oh, forget it!

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