1 / 22

Statements

Statements. The most important idea in logic: Validity of an argument. Statements. The most important idea in logic: Validity of an argument. However, there are other important concepts that concern statements. Statements. Logical Truths (Tautologies) Contradictions

lmeeker
Download Presentation

Statements

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related