UNIVERSITY OF MASSACHUSETTS
PHILOSOPHY 321: HISTORY OF MODERN PHILOSOPHY


ARGUMENTS

A. An argument is a sequence of statements,
    1. each of which has a truth-value (i.e., is either true or false); and
    2. one of which is the argument's conclusion, the others being its premises.

B. In an argument, the conclusion is supposed to be logically related to its premises.
    1. It is supposed to follow logically from them, or be a logical consequence of them.
    2. An argument whose conclusion is actually so related to its premises is a valid argument.

C. The property of validity (the relation of logical consequence) is such that,
    1. if an argument is valid and all of its premises are true, then its conclusion must also be true, so that
    2. in a valid argument, the truth of the premises guarantees the truth of the conclusion.

D. An argument that is valid and all of whose premises are true is a sound argument.

E. An argument containing one or more conditional statements is a conditional argument.

F. A conditional statement (or, more simply, a conditional) is a statement of the form 'If P then Q', where
    1. 'P' and 'Q' are themselves statements, and
    2. 'P' is the antecedent and 'Q' is the consequent of the conditional.

G. A conditional having the form 'If P then Q'
    1. also has the form 'P only if Q' (i.e., these two forms are equivalent), and
    2. can also be expressed by the formula 'P -> Q'.

H. When two conditionals of the forms 'If P then Q' and 'If Q then P' are conjoined, the result is a
   biconditional of the form 'P if and only if Q'. This can also be expressed as 'P iff Q' and as 'P <-> Q'.

I. Conditional arguments of the following forms are valid:

    1. (P1) P -> Q        2. (P1) P -> Q        3. (P1) P -> Q
        (P2) P                     (P2) Not-Q            (P2) Q -> R 
        -------------              -------------           -----------------
         (C) Q                      (C) Not-P               (C) P -> R

       (Modus Ponens)   (Modus Tollens)   (Hypothetical Syllogism)


J. Conditional arguments of the following forms are invalid or fallacious:

    1. (P1) P -> Q        2. (P1) P -> Q        3. (P1) P -> Q
        (P2) Q                    (P2) Not-P
        -------------              -------------           ----------------
          (C) P                      (C) Not-Q              (C) Q -> P

       (Affirming the       (Denying the       (Illicit Conversion) [Click here for example] 
         Consequent)           Antecedent)