Argument Diagramming Part I

PHIL 121: Methods of ReasoningJanuary 30, 2013

Instructor:Karin HoweBinghamton University

Some important definitions

• statement (or proposition)• argument• conclusion• premises

Statement (or proposition)

• A statement is a sentence that is either true orfalse.

• 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 orfalse. It makes no sense to say "The statement(premise) is valid," or "The statement (premise) issound." The terms valid and sound refer ONLY toarguments. (we will cover validity and soundnessin 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 statementsin standard form

• If Marvin stays, then Nancy leaves.• Nancy leaves if Marvin stays.

• The statement following the word 'if' is theantecedent; accordingly, the statement that followsthe word 'if' is placed before the statementfollowing the word 'then' (which is theconsequent). 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 Examples1. 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 theexistence 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 theothers (the premises).

• Arguments are attempts to prove the truth of aclaim (the conclusion) on the basis of other claims(the premises).

• Arguments are attempts to convince you ofsomething; namely to convince you to accept aconclusion based on your acceptance of thepremises.

Types of Argument Structures:Convergent Argument

Types of Argument Structures:Linked Argument

Types of Argument Structures:Chain Argument

Putting it all together … complexarguments

Comparing Linked Argumentsand Chain Arguments

1. If I study hard for the firstexam then I'll get an A on theexam.

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

3. If I get an A on all of theexams then I'll get an A in thecourse.Therefore, If I study hard forthe first exam then I'll get anA in the course.

Syntax vs. Semantics• What do we mean by the

syntax of an argumentdiagram?– The rules for the formation

of grammatical sentences ina language.

• What do we mean by thesemantics of an argumentdiagram?– The meaning, or an

interpretation of themeaning, of a word, sign,sentence, etc.

Diagramming Arguments

A Quick How-to Guide

Steps 1 and 2: Finding Premiseand 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 intoseparate 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 inthis 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 ascomplete 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 ArgumentFinally!!

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