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Mastering Logical Truths: A Guide to Understanding Validity in Arguments

Delve into the essence of logic by exploring logical truths, tautologies, and the validity of statements. Learn how to identify logic truths and prove arguments with truth tables and proofs. Click to uncover more!

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Mastering Logical Truths: A Guide to Understanding Validity in Arguments

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  1. Statements The most important idea in logic: Validity of an argument.

  2. Statements The most important idea in logic: Validity of an argument. However, there are other important concepts that concern statements.

  3. Statements Logical Truths (Tautologies) Contradictions Contingent Statements

  4. Logical Truth A statement is a logic truth (tautology) iff it cannot be F.

  5. Logical Truth A statement is a logic truth (tautology) iff it cannot be F. So its truth table has all Ts on the output column.

  6. Logical Truth A statement is a logic truth (tautology) iff it cannot be F. So its truth table has all Ts on the output column. Samples: P>P Pv-P

  7. Logical Truth A statement is a logic truth (tautology) iff it cannot be F. Samples: P>P Pv-P Good news: Logical Truths are always true.

  8. Logical Truth A statement is a logic truth (tautology) iff it cannot be F. Samples: P>P Pv-P Good news: Logical Truths are always true. Bad news: Logical Truths do not carry information.

  9. Logical Truth A statement is a logic truth (tautology) iff it cannot be F. Samples: P>P Pv-P Good news: Logical Truths are always true. Bad news: Logical Truths do not carry information. Desperate Weather Report: If it is raining then it is raining.

  10. Logical Truth P P>P TT FT * P P v -P TT F FT T * To show a statement A is a logic truth ... with a table: The output row for A has all Ts.

  11. Logical Truth P P>P TT FT * P P v -P TT F FT T * To show a statement A is a logic truth ... with a table: The output row for A has all Ts. with a proof: Prove A.

  12. Logical Truth P P>P TT FT * P P v -P TT F FT T * To show a statement A is a logic truth ... with a table: The output row for A has all Ts. with a proof: Prove A. P>P GOAL

  13. Logical Truth P P>P TT FT * P P v -P TT F FT T * To show a statement A is a logic truth ... with a table: The output row for A has all Ts. with a proof: Prove A. 1) P PA 2) P>P 1-1 >I

  14. Logical Truth P P>P TT FT * P P v -P TT F FT T * To show a statement A is a logic truth ... with a table: The output row for A has all Ts. with a proof: Prove A. 1) P PA 2) P>P 1-1 >I Pv-P GOAL

  15. Logical Truth P P>P TT FT * P P v -P TT F FT T * To show a statement A is a logic truth ... with a table: The output row for A has all Ts. with a proof: Prove A. 1) P PA 2) P>P 1-1 >I 1) -(Pv-P) PA ?&-? Pv-P 1-? -O

  16. Logical Truth P P>P TT FT * P P v -P TT F FT T * To show a statement A is a logic truth ... with a table: The output row for A has all Ts. with a proof: Prove A. 1) P PA 2) P>P 1-1 >I 1) -(Pv-P) PA 2) -P&--P 1 DM 3) Pv-P 1-2 -O

  17. Logical Truth 1) P PA 2) P>P 1-1 >I 1) -(Pv-P) PA 2) -P&--P 1 DM 3) Pv-P 1-2 -O P P>P TT FT * P P v -P TT F FT T * To show a statement A is a logic truth ... with a table: The output row for A has all Ts. with a proof: Prove A. with a tree: The tree for -A closes.

  18. Logical Truth 1) P PA 2) P>P 1-1 >I 1) -(Pv-P) PA 2) -P&--P 1 DM 3) Pv-P 1-2 -O P P>P TT FT * P P v -P TT F FT T * To show a statement A is a logic truth ... with a table: The output row for A has all Ts. with a proof: Prove A. with a tree: The tree for -A closes. -(P>P)

  19. Logical Truth 1) P PA 2) P>P 1-1 >I 1) -(Pv-P) PA 2) -P&--P 1 DM 3) Pv-P 1-2 -O P P>P TT FT * P P v -P TT F FT T * To show a statement A is a logic truth ... with a table: The output row for A has all Ts. with a proof: Prove A. with a tree: The tree for -A closes. -(P>P) P -P *

  20. Logical Truth 1) P PA 2) P>P 1-1 >I 1) -(Pv-P) PA 2) -P&--P 1 DM 3) Pv-P 1-2 -O P P>P TT FT * P P v -P TT F FT T * To show a statement A is a logic truth ... with a table: The output row for A has all Ts. with a proof: Prove A. with a tree: The tree for -A closes. -(P>P) P -P * -(Pv-P)

  21. Logical Truth 1) P PA 2) P>P 1-1 >I 1) -(Pv-P) PA 2) -P&--P 1 DM 3) Pv-P 1-2 -O P P>P TT FT * P P v -P TT F FT T * To show a statement A is a logic truth ... with a table: The output row for A has all Ts. with a proof: Prove A. with a tree: The tree for -A closes. -(P>P) P -P * -(Pv-P) -P --P *

  22. Logical Truth To show a statement A is a logic truth (tautology) ... with a table: The output row for A has all Ts. with a proof: Prove A. with a tree: The tree for -A closes. For more click here

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