ABSTRACT
You now have ten rules of inference. (I shall give you fifteen altogether.) Before we go on, here are some general remarks on how to use them.
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RULES 1- 10 |
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1 |
ELIMINATION (ELIM) |
GIVEN P or Q and Not P, we may conclude Q. |
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2 |
AFFIRMING THE ANTECEDENT (MPP) |
GIVEN If P then Q and P, we may conclude Q. |
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3 |
DENYING THE CONSEQUENT (MTT) |
GIVEN If P then Q and Not Q, we may conclude Not P. |
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4 |
DOUBLE NEGATION (DN) |
GIVEN Not not P, we may conclude P, and vice versa. |
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5 |
'AND' INTRODUCTION (&I) |
GIVEN P and Q, we may conclude P and Q. |
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6 |
'AND' ELIMINATION (&E) |
GIVEN P and Q, we may conclude P. |
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7 |
CHAIN RULE (CH) |
GIVEN If P then Q and If Q then R, we may conclude If P then R. |
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8 |
DILEMMA (DIL) |
GIVEN If P then R and If Q then R, we may conclude If (P or Q) then R. |
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9 |
CONTRAPOSITION (CONTRA) |
GIVEN If P then Q, we may conclude If not Q then not P, and vice versa. |
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10 |
NEITHER/NOR RULE (NNOR) |
GIVEN Not P and not Q, we may conclude Not (P or Q), and vice versa. |
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('P or Q' is short for 'a statement of form P or Q' (etc.)> and any statement whose form is a substitution instance of P or Q is a statement of form P or Q.) |
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