Philosophy 244/244W/444
Philosophy of Mind
Fall 2006
Arguments
An argument is a sequence of declarative sentences. The last sentence in the sequence is the conclusion of the argument. The sentences preceding the conclusion are the premises of the argument.
Some Sample Arguments
A. 1. Reincarnation sometimes occurs.
2. If reincarnation sometimes occurs, then some humans have souls.
3. Therefore, some humans have souls.
B. 1. If reincarnation sometimes occurs, then some humans have souls.
2. Reincarnation sometimes occurs.
3. Therefore, some humans have souls.
C. 1. Snow is green.
2. Grass is red.
3. Therefore, snow is green and grass is red.
D. 1. If Hillary Clinton is President of the USA, then she is a federal employee.
2. Hillary Clinton is a federal employee.
3. Therefore, Hillary Clinton is President of the USA.
E. 1. If it is raining, then the streets are wet.
2. The streets are not wet.
3. Therefore, it is not raining.
F. 1. If it is raining, then the streets are wet.
2. It is not raining.
3. Therefore, the streets are not wet.
Some Definitions of Technical Terms
D1. Argument A is valid if and only if (iff) it is impossible for all of A’s premises to be true while A’s conclusion is false. (Equivalently: if A’s premises were true, then A’s conclusion would also be true.) Argument A is invalid iff it is not valid.
D2. Argument A is sound iff: (1) A is valid and (2) all of A’s premises are true. Argument A is unsound iff it is not sound.
Some Common Valid Argument Forms
Modus Ponens (MP)
1. If P, then Q
2. P
3. Therefore, Q
Multiple Modus Ponens (MMP)
1. P
2. If P, then Q
3. If Q, then R
4. Therefore, R
Modus Tollens (MT)
1. If P, then Q
2. not-Q
3. Therefore, not-P
Conjunction (Conj)
1. P 1. P
2. Q 2. Q
3. Therefore, P and Q 3. Therefore, Q and P
Hypothetical Syllogism (HS)
1. If P, then Q
2. If Q, then R
3. Therefore, if P, then R
Disjunctive Syllogism (DS)
1. P or Q 1. P or Q
2. not-P 2. not-Q
3. Therefore, Q 3. Therefore, P
Two Common Invalid Argument Forms
Affirming the Consequent
1. If P, then Q
2. Q
3. Therefore, P
Denying the Antecedent
1. If P, then Q.
2. not-P
3. Therefore, not-Q
A Complicated Instance of Modus Ponens
1. If snow is white and grass is green, then roses are red and violets are blue.
2. Snow is white and grass is green.
3. Therefore, roses are red and violets are blue.
Complex Arguments
A complex argument is a sequence of arguments. The conclusion of the last argument in the sequence is the main conclusion of the complex argument. The conclusions of the other arguments in the sequence are the subconclusions of the complex argument. The other sentences appearing in a complex argument are its premises.
G. 1. Reincarnation sometimes occurs.
2. If reincarnation sometimes occurs, then some humans have souls.
3. Therefore, some humans have souls.
4. If some humans have souls, then materialism is false.
5. Therefore, materialism is false.
D3. A complex argument A is valid iff every (simple) argument in A is valid.
D4. A complex argument A is sound iff: every (simple) argument in A is sound.