Logic: The
Language of
Philosophy
What is Logic?
• Logic is the study of argumentation
o In Philosophy, there are no right or wrong opinions, but
there are arguments that are better than others.
What is an “Argument”?
• Argument: a set of statements
consisting of at least two premises
and at least one conclusion.
o Premises: reasons supporting the conclusion
o Conclusion: the statement you are trying to
prove
Philosophers write arguments like
this:
1. Socrates is a man.
2. All men are mortal
--------------------------3. Socrates is mortal
(premises)
(conclusion)
Arguments must be valid and sound
• An argument is valid when the
premises guarantee the conclusion
o This is not subjective
• An argument is sound if
(1) it is valid; and
(2) the premises are true
Argument Forms
I. Modus Ponens (“Affirming Mode”)
P→Q
P
------Q
1. If the ground is wet, then it was
raining.
2. The ground is wet.
-----------------------------------------------------3. Therefore, it was raining.
Modus Tollens
• Latin for “Denying Mode”
P→Q
~Q
------~P
1. If the ground is wet, then it was raining.
2. It was not raining
----------------------------------------------------3. Therefore, the ground is not wet.
Common Errors
Denying the Antecedent
P→Q
~P
-------~Q
Affirming the Consequent
P→Q
Q
--------P
Denying the Antecedent
P→Q
~P
-------~Q
1. If Socrates is French, then Socrates is mortal
2. Socrates is not French
-----------------------------------------------------------------3. Socrates is not mortal
NOT VALID!
Affirming the Consequent
P→Q
Q
-------P
1. If Socrates is French, then Socrates is mortal.
2. Socrates is mortal.
-------------------------------------------------------------------3. Socrates is French
NOT VALID!
Chain Reasoning
PQ
QR
-------PR
1. Nellie is a dog.
2. A dog is a mammal.
----------------------------3. Nellie is a mammal.
Disjunctive Syllogism
PQ
~P
-------Q
1. Either the maid did it or the butler did
it.
2. The maid did not do it.
-----------------------------------------------------3. Therefore, the butler did it.
Hypothetical Syllogism
P→Q
Q→R
------P→R
1. If Jim comes to the party, then Chris will
come too.
2. If Chris comes to the party, then Pat will
come too.
------------------------------------------------------------3. Therefore, if Jim comes to the party,
Pat will come too.