Argument Diagramming Part I

PHIL 121: Methods of Reasoning

January 30, 2013

Instructor:Karin Howe

Binghamton University

Some important definitions

• statement (or proposition)

• argument

• conclusion

• premises

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.

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)

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

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.

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."

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– Rewritten as: If P, then Q

• "unless"– P unless Q– Rewritten as: If not Q, then P

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.”

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.

Types of Argument Structures: Convergent Argument

Types of Argument Structures: Linked Argument

Types of Argument Structures: Chain Argument

Putting it all together … complex arguments

Comparing Linked Arguments and Chain Arguments

1. If I study hard for the first exam then I'll get an A on the exam.

2. If I get an A on the first exam, then I'll get an A on all of the rest of the exams.

3. 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.

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.

Diagramming Arguments

A Quick How-to Guide

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)

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

conclusionConventions:

• 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

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)

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."

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