1.2 Recognizing Arguments

Concepts:

• factual claim
• inferential claim (14): explicit & implicit
• two uses of the word "since" temporal versus logical sense (15)
• the role of interpretation in evaluating information/arguments (16)
• Non-arguments lacking inferential claims (16-17)
• Be careful to note that reports, explanations, expository passages and illustrations as well as arguments may look quite similar and the author is often inconsistent when he applies these labels in the exercises that follow.

Breakdown:

Passages lacking an inferential claim:

1. Warnings & Pieces of Advice (16)
2. Statements of Opinion: these must always be supported by evidence to be considered arguments in the strict logical sense.(16)
3. Loosely Associated Statements(17)
4. Report: absent here is the claim that the statements support or imply anything.(17)
5. Expository passage: just as it sounds, this is merely an explanation.(18-19)

• NOTE: some passages can be interpreted both as expository passages and as arguments.(18)

6. Illustration: statement and examples that further clarify the category being discussed.

Explanations: (20-21)

Two Parts:

1. Explanans: "statement or group of statements that purports to do the explaining" reasons).(20)
2. Explanandum: "statement that describes the event of phenomenon to be explained"(20)

Please reread the statement about the difference between explanations and arguments at the bottom of page 21.

Note: the method for distinguishing arguments from explanations on p.21.

• Context is everything and the intended audience plays a large role in determining what the context actually is.(21)
• There is a wealth of ambiguity here. Note the paragraph on mid-21 about explanations that resemble arguments.

Conditional Statements: (22-23)

• These are "if … then" statements.
• Review the definition of antecedent & consequent.(22)
• One conditional statement does not an argument make.(19)
• Note the rules for recognizing conditional statements as arguments.(24)
• Necessary & Sufficient conditions: based on the conditional statement: If A, then B.(24)

1. Necessary: A cannot occur without the occurrence of B.
2. Sufficient: the occurrence of A is all that is needed for the occurrence of B.

• This is an idea that you will encounter again and again in academic writing and argumentative literature. For those planning a trip to law school, this is a critical concept.

Summary:(24)

1. Look for indicator words (Section 1.1, p. 3 ),
2. an inferential relationship between statements, and
3. typical kinds of non-arguments discussed in this section.

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1.3 Deduction and Induction

Numbers in parenthesis refer to page numbers in the text.

Deductive Argument: conclusion follows necessarily from the premises (100%) certainty(33)

Indicator words: certainly, absolutely, definitely(34)

See examples p. 34.

Types of Deductive Arguments:

1. arguments based on mathematics(35)
2. arguments from definition (35)
3. categorical syllogisms (35)
4. hypothetical syllogisms (35-36)
5. disjunctive syllogisms (36)

Inductive Argument: conclusion follows probably from the premises (51% or better)(36)

Indicator words: improbable, plausible, implausible, likely, unlikely, reasonable(34)

Types of Inductive Arguments:

1. predictions(36)
2. arguments from analogy(36)
3. inductive generalizations(37)
4. arguments from authority(37)
5. arguments based on signs(37)
6. causal inferences(37)

Factors that help us decide between deductive and inductive arguments:

1. The presence of indicator words.(34)
2. The "actual strength of the inferential ink between premises and conclusions."(34)
3. Instances in which the conclusion does not follow from the premises either necessarily or probably.(35)

Some cautions/notes from reading:

• Geometric arguments are always deductive (35)
• Scientific arguments can be either inductive or deductive.(38)
• The common definition for distinguishing between deductive and inductive arguments (general/particular) does not hold. See the note at the bottom of page 38.

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1.4 Validity, Truth, Soundness & Cogency

Valid Deductive Arguments

• There is no middle ground; an argument is either valid or invalid.(44)
• Validity is not determined by the truth or falsity of the premises.(45)
• Validity is determined by the relationship between premises and conclusion.(45)(i.e., Ask yourself: do the premises support the conclusion?)
• View chart on page 46. Note that all invalid arguments are unsound.
• Sound argument = true premises, true conclusion (46) Both conditions must be met for an argument to be sound. There is only one kind of sound argument.

Inductive Arguments

• Strong Inductive Argument = "improbable that premises are true and conclusion is false"(47)
  • Strong arguments have a probability of 51% or greater.(49) See examples on p. 48. The conclusion, however, is not guaranteed, it is only likely.(49)
  • "A cogent argument is strong and has all true premises; if either condition is missing, the argument is uncogent."(50) In a cogent argument the premises must not ignore relevant information that would make them untrue.(50)
• Weak Inductive Argument = "conclusion does not follow probably from the premises"(48-49)
  • See examples on p.49.
  • Read section on probabilistic support (p.48); support is at issue here, not the truth or falsity of the premises.(48)
  • Review chart p.49. Notice that there is only one type of sound, cogent argument: true premises, true conclusion.(49)

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1.5 Argument Forms: Proving Invalidity

Numbers in parenthesis refer to page numbers in the text.

This week we are looking at the validity/invalidity of deductive arguments. "The validity of an argument has nothing to do with its specific subject matter. ...Its validity rests purely upon the arrangement of the letters within the statements and it has nothing to do with what the letters might stand for."(56)

The process of "uniformly substituting terms or statements in place of the letters in an argument form is called a substitution instance of that form."(56)

 

Valid Form: Categorical Syllogism	Invalid Form: Categorical Syllogism
mm All A are B. All B are C. All A are C.	mm All A are B. All C are B. All A are C.

 

Counterexample Method:

We use the counterexample method to prove invalidity; it cannot be used to prove validity.(58) This method proves an argument invalid by generating an example of a given argument form with true premises and a false conclusion. Please note that the technique of using a counterexample to prove arguments invalid only works for deductive arguments.(60-61)

There are a few easy steps we can follow to produce an counterexample:

1. Symbolize the given argument using statement letters in place of phrases. This reveals the argument's form.
2. Consistently substitute the generic terms: cats, dogs, mammals, fish and animals to generate an argument with true premises and a false conclusion.
3. It is helpful to begin your term substitutions with the conclusion by choosing two terms that make it false. Next, work through the premises selecting a third term that makes the premises true.
4. If you are presented with a hypothetical syllogism, try using the suggested substitutions from page 59: e.g., Abraham Lincoln, suicide and dead. The goal is to use terms that have a necessary connection (e.g., rain-wet, snow-cold, suicide-dead).
5. If the conclusion is a conditional statement, join a true antecedent with a false consequent.(60)

Things to remember when working on substitution:

• Be sure to separate form words from content words. Form words for categorical and hypothetical syllogisms are: "all", "no", "some", "are", "not", "if", and "then." In addition, other types of deductive arguments include the form words: "either", "or", "both", and "and."(60)
• Remember the word "some" means "at least one" in logic.(59)
• This technique is difficult at first, but like other challenging endeavors, will get easier with practice. Thus, you should try to do as many problems as you can to gain skill and confidence.
• If you are struggling with a particular problem and cannot generate a counterexample, move on to other problems and return to the difficult one later.

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