LOGIC & ARGUMENTS

AN ARGUMENT CONTAINS A NUMBER OF PREMISES AND A CONCLUSION.

P1

P2

...

Pn
____

Therefore: C

INDUCTIVE vs DEDUCTIVE

        INDUCTIVE EXAMPLE:

    Premise: ALL EMERALDS THAT HAVE BEEN OBSERVED HAVE BEEN GREEN.

    Conclusion: SO, ALL EMERALDS ARE GREEN.

                    OR

    Conclusion: SO, PROBABLY ALL EMERALDS ARE GREEN.

    IN GENERAL: IN A GOOD INDUCTIVE ARGUMENT THE PREMISES, IF TRUE, PROVIDE GOOD EVIDENCE FOR THE CONCLUSION, BUT NOT CONCLUSIVE EVIDENCE.

    IN A GOOD DEDUCTIVE ARGUMENT, THE PREMISES IF TRUE PROVIDE CONCLUSIVE EVIDENCE FOR THE CONCLUSION.

IN THAT CASE WE CALL THE ARGUMENT VALID.

IF THE PREMISES ARE TRUE AND THE ARGUMENT IS VALID, THEN WE SAY THAT THE ARGUMENT IS SOUND.

TWO CONCEPTS OF VALIDITY

(1) (Syntactic) AN ARGUMENT IS VALID IF ONE CAN DERIVE THE CONCLUSION FROM THE PREMISES; (ALTERNATIVELY) IF THE CONCLUSION FOLLOWS FROM THE PREMISES.

(2) (Semantic) AN ARGUMENT IS VALID IF WHENEVER ALL THE PREMISES ARE TRUE, THE CONCLUSION IS TRUE; (ALTERNATIVELY) IF THERE IS NO WAY FOR THE PREMISES TO BE TRUE AND THE CONCLUSION FALSE.