1. Argument Diagramming Part I
PHIL 121: Methods of Reasoning
January 30, 2013
Instructor:Karin Howe
Binghamton University

2. Some important definitions
statement (or proposition)
argument
conclusion
premises

3. Statement (or proposition)
A statement is a sentence that is either true or false.
Examples:
I like cats.
Papa John's makes better pizza.
If today is Wednesday, then tomorrow is Thursday.
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. (we will cover validity and soundness in the next lecture)

5. Types of Statements Conditionals Form: if A then B
Example: If you like apples then you also like bananas.
A part = antecedent; B part = consequent
Conjunctions
Form: A and B
Example: I like apples and bananas.
A part = left conjunct; B part = right conjunct
Disjunctions
Form: A or B
Example: I like either apples or bananas for breakfast.
A part = left disjunct; B part = right disjunct

6. Types of Statements, con't.
Biconditionals
Form: A if and only if B
Example: I like apples if and only if I like bananas.
Negations
Form: not A
Example: I don't like apples.
Universal statements
Form: All A are B
Example: All apes like bananas.
Existential statements
Form: Some A are B
Some apes like bananas.

7. Rewriting conditional statements in standard form
If Marvin stays, then Nancy leaves.
Nancy leaves if Marvin stays.
The statement following the word 'if' is the antecedent; accordingly, the statement that follows the word 'if' is placed before the statement following the word 'then' (which is the consequent). The statement is then said to be in "standard form."

8. 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

9. 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.”

10. 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.

11. Types of Argument Structures: Convergent Argument

12. Types of Argument Structures: Linked Argument

13. Types of Argument Structures: Chain Argument

14. Putting it all together … complex arguments

15. Comparing Linked Arguments and Chain Arguments
If I study hard for the first exam then I'll get an A on the exam.
If I get an A on the first exam, then I'll get an A on all of the rest of the exams.
If I get an A on all of the exams then I'll get an A in the course.
Therefore, If I study hard for the first exam then I'll get an A in the course.

16. Syntax vs. Semantics
What do we mean by the syntax of an argument diagram?
The rules for the formation of grammatical sentences in a language.
What do we mean by the semantics of an argument diagram?
The meaning, or an interpretation of the meaning, of a word, sign, sentence, etc.

17. Diagramming Arguments
A Quick How-to Guide

18. 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)

19. Identifying premises and conclusions
Step 3: Identify the conclusion and subconclusion(s), if there are any
Step 4: Identify the explicit premises
Step 5: Identify any implicit premises, subconclusions or conclusion
Conventions:
Label your explicit premises as follows: P1, P2, P3, etc.
Label subconclusions as SC1, SC2, etc.
Label your conclusion as C
Label any implied premises as IP1, IP2, etc. and any implied subconclusions or conclusions as ISC or IC, respectively

20. Step 6: 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
Example: Therefore, you should study hard, since you want an A in this class.
Example: Since you want an A in this class, you should study hard.
"And" statements (conjunctions)
Statements you should never break:
"Or" statements (disjunctions)
"If then" statements (conditionals)
"If and only if" statements (biconditionals)
"Not" statements (negations)

21. Step 7: Rewrite the statements as complete independent statements
Remove (or incorporate) parentheticals
Remove any premise or conclusion indicators
Standardize concepts
Replace pronouns with their referents wherever possible.
Rewrite conditionals in "standard form."

22. Step 8: Diagram the Argument
Finally!!
Let's practice! 
Lab exercises p. 13
Lab exercises p. 14
Lab exercises p. 15
Lab exercises p. 16
Lab exercises p. 17
Lab exercises p. 20
Lab exercises p. 21