1. A Crash Course in Logic 80-100: Introduction to Philosophy
May 19, 2009
Instructor:Karin Howe
Carnegie Mellon University

2. Some important definitions
statement or proposition
argument
conclusion
premises
valid
invalid
sound
unsound

3. Statement or proposition
Working definition: a statement is a sentence that is either true or false.
Examples:
I like cats.
Papa John's makes better pizza.
If today is Tuesday, then tomorrow is Wednesday
You may have either an apple or an orange for a snack.

4. Sentences that are not statements
Shut the door!
Is the door open?
Ouch!
Important Final Note! - Statements are true or false. It makes no sense to say “The statement (premise) is valid,” or “The statement (premise) is sound.” The terms valid and sound refer ONLY to arguments.

5. Arguments
An argument is a set of statements, one of which (the conclusion) supposedly follows from the others (the premises).
Arguments are attempts to prove the truth of a claim (the conclusion) on the basis of other claims (the premises).
Arguments are attempts to convince you of something; namely to convince you to accept a conclusion based on your acceptance of the premises.

6. The Kangaroo Argument All kangaroos can fly. Jim is a kangaroo.
_____________________
Therefore, Jim can fly.

7. Evaluating arguments
All arguments have two different features that must be separately evaluated: form and content:
The evaluation of the form of an
FORM argument asks whether the
conclusion follows from the
premises.
The evaluation of the content of
CONTENT an argument asks whether all of
the premises are true.

8. FORM: validity vs. invalidity
A valid argument is one having the form such that it is impossible that all of its premises are true and its conclusion false.
An invalid argument is one having the form such that it is possible that all of its premises are true, and yet the conclusion is false.

9. Recall the Kangaroo Argument
All kangaroos can fly.
Jim is a kangaroo.
_____________________
Therefore, Jim can fly.

10. True Fact:
97% of all questions about validity can be answered by thinking about kangaroos. :-D

11. Content: soundness vs. unsoundness
An argument is sound if and only if (iff): it is valid and has all true premises.
An argument is unsound if and only if (iff): it is either invalid, or has one or more false premises.
Quick Quiz: Kangaroo Argument -- sound or unsound?

12. Mapping Arguments
A Quick How-to Guide

13. Steps 1 and 2: Finding Premise and Conclusion Indicators
Premise Indicators:
since
however
but (at the beginning of a sentence)
and (at the beginning of a sentence)
for
Conclusion Indicators
therefore
thus
hence so
consequently
it follows (that)
which goes to show (that)

14. Identifying premises and conclusions
Step 3: Identify the conclusion and subconclusion(s), if there are any
Step 4: Identify the explicit premises

15. Step 5: Break the argument down into separate statements
A word of caution:
There are some statements you can, and should break, and others which you should not break!
Statements you should break:
Sentences that contain both a premise and a subconclusion or conclusion, joined by either a premise indicator or a conclusion indicator
"And" statements (conjunctions)
Statements you should never break:
"Or" statements (disjunctions)
"If then" statements (conditionals)

16. Step 6: Rewrite the statements
Remove (or incorporate) parentheticals
Remove any premise or conclusion indicators
Standardize concepts
Write statements in "standard form."

17. Rewriting statements in standard form
If Marvin stays, then Nancy leaves
The statement following the word 'if' (or its synonym 'provided that') is the antecedent; accordingly, the statement that follows the word 'if' is placed before the statement following the word 'then' (which is the consequent).

18. Conditionals are tricksy fellas…
Necessary Conditions
– P is a necessary condition for Q
– Rewritten as: If Q, then P
– Mnemonic: neceSSary conditions come second
Sufficient Conditions
P is a sufficient condition for Q
Rewritten as: If P, then Q
Mnemonic: suFFicient conditions come first
"only if"
P only if Q
"unless"
P unless Q
Rewritten as: If not Q, then P

19. Some Examples
1. The Heat makes it to the playoffs only if the Hawks lose to the Cavs.
2. Your having a quiz average over 90 is a sufficient condition for being excused from the final.
3. The settlement of the west could only take place if the Indian barrier were removed.
4. Hannah could save her company if only the president would promote her.
5. Aquinas thought that the fact that the intellect is under the control of the will is a necessary condition for the existence of intellectual virtues.
6. “Now we shall have duck eggs, unless it is a drake.”

20. Step 7: Map the Argument
Finally!!
Let's practice! :-)

21. My Three Sons Man 1: Yes, I’m married and have three fine sons.
Man 2: That’s wonderful! How old are they?
Man 1: Well, the product of their ages is equal to 36.
Man 2: Hmm. That doesn’t tell me enough. Give me another clue.
Man 1: O.K. The sum of their ages is the number on that building across the street.
Man 2: Ah ha! I’ve almost got the answer, but I still need another clue.
Man 1: Very well. The oldest one has red hair.
Man 2: I’ve got it!