Contingent A statement is contingent iff it is neither a logical truth nor a contradiction.

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Presentation transcript:

Contingent A statement is contingent iff it is neither a logical truth nor a contradiction.

Contingent A statement is contingent iff it is neither a logical truth nor a contradiction. So the output row for a contingent statement must contain at least one F and at least one T.

Contingent A statement is contingent iff it is neither a logical truth nor a contradiction. So the output row for a contingent statement must contain at least one F and at least one T. Sample contingent statement: P>Q

Contingent To show a statement A is contingent... with a table: The output row for A has a F and a T.

Contingent To show a statement A is contingent... with a table: The output row for A has a F and a T. with a proof:No proof test is possible.

Contingent To show a statement A is contingent... with a table: The output row for A has a F and a T. with a proof:No proof test is possible. There is also no proof test for invalidity.

Contingent To show a statement A is contingent... with a table: The output row for A has a F and a T. with a proof:No proof test is possible. with a tree:The tree for -A is open and the tree for A is open.

Contingent To show a statement A is contingent... with a table: The output row for A has a F and a T. with a proof:No proof test is possible. with a tree:The tree for -A is open and the tree for A is open. Common Mistake: The tree has one open and one closed branch.

Contingent To show a statement A is contingent... with a table: The output row for A has a F and a T. with a proof:No proof test is possible. with a tree:The tree for -A is open and the tree for A is open. Common Mistake: The tree has one open and one closed branch. WRONG! You need to do TWO trees.

Contingent To show a statement A is contingent... with a table: The output row for A has a F and a T. with a proof:No proof test is possible. with a tree:The tree for -A is open and the tree for A is open. A is not a logical truth and A is not a contradiction.

Contingent To show a statement A is contingent... with a table: The output row for A has a F and a T. with a proof:No proof test is possible. with a tree:The tree for -A is open and the tree for A is open. A is not a logical truth and A is not a contradiction.

Contingent To show a statement A is contingent... with a table: The output row for A has a F and a T. with a proof:No proof test is possible. with a tree:The tree for -A is open and the tree for A is open. A is not a logical truth and A is not a contradiction.

Contingent To show a statement A is contingent... with a table: The output row for A has a F and a T. with a proof:No proof test is possible. with a tree:The tree for -A is open and the tree for A is open. Sample: Here are trees that show that P>Q is contingent. -(P>Q) P -Q P>Q -P Q open

Contingent To show a statement A is contingent... with a table: The output row for A has a F and a T. with a proof:No proof test is possible. with a tree:The tree for -A is open and the tree for A is open. For more click here