This chapter may have confused you;

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Chapter 1.1

• This chapter may have confused you
• Rather, it was intended to
• set forth the concepts of argument, validity
  and soundness, etc.
• give you an intuitive understanding of those
  concepts
• persuade you that there must be more systematic
  ways of testing an argument, especially for
  validity and
• encourage you, therefore, to anticipate and
  appreciate the systematic skills yet to be
  learned.

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Central concepts

• Central concepts
• Argument v. non-argument
• Deduction v. Induction
• Validity Soundness v. Strength Cogency

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Argument

• Notion of argument basic to logic
• Arguments defined
• A group of statements (declarative statements)
  such that one, a claim (conclusion), is supported
  by others, reasons (premises).
• Conclusion can come anywhere what is the
  authors point?
• Declarative statements rhetorical questions
  (which can masquerade as declarative statements)
• Implicit statements (as opposed to explicit)

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Analyzing an Argument

• Illatives (L. ppl. inferre illatus to infer,
  inference)
• Conclusion thus, then, so, therefore, as a
  result, such that, means that, it can be seen,
  consequently, hence, we see that, it follows,
  ergo, etc.
• Premise because, since, when, whenever, if,
  assume, for, as, for the reason that, etc.
• Intellectual charity--helping author to construct
  argument as intended

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Non-arguments

• Confusion
• Explanations--when truth of conclusion is not in
  doubt
• Conditions--if/then type may be part of an
  argument, but are not arguments per se
• Analogies--again, may be part of an argument, but
  are not arguments themselves.
• Once an argument has been identified, is it
  deductive or inductive?
• Squishiness (multi-logical) requires context,
  judgment

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Distinguishing is a squishy (multi-logical)
business Given truth of premises

• Induction
• Possible, but unlikely that conclusion is false
  (contingent)
• If so, called strong
• Usually moves logically from specific cases to
  generalization re those cases
• May include weasel words
• All appeals to authority, uses of surveys,
  studies, analogies types of chicken logic
• Never valid or invalid
• All intended to be strong

• Deduction
• Impossible that conclusion is false (certain)
• If so, called valid
• Usually moves logically from a general case to
  more specific case (hence deduction)
• May include language of certainty
• Virtually all arguments of form All x are y
• Never strong or weak
• All intended to be valid

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Deductive arguments are intended to be sound to
succeed but they may not be successful.
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Deductive arguments may fail be unsound for one
or both of two reasons

• The arguments themselves are invalid.
• I.e., the truth of the premises does not
  necessarily yield the truth of the conclusion
  or, alternatively, even if the premises were
  true, the conclusion would not follow from
  them.
• The premises themselves are false.

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An argument is

• Valid if the truth of the premises guarantees
  the truth of the conclusion (I.e., if the
  conclusion necessarily follows from the
  premises--theres no avoiding it!)

• Invalid if the premises, whether true or false,
  cannot guarantee the truth of the conclusion
  (I.e., the conclusion doesnt necessarily
  follow--there are other ways to explain the
  outcome).

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Caveats

• To say an argument is valid, however, doesnt
  mean that it is sound or that its conclusion
  actually is true
• Example All dogs are blue animals. All blue
  animals fly. So, all dogs fly.
• The argument above is valid (if the premises were
  actually true, its conclusion must necessarily
  follow), but the conclusion is false and the
  argument is unsound because one or more of the
  premises is false.

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Caveats, contd.

• An argument can have true premises and a true
  conclusion and still be unsound if it reasons
  invalidly
• Example All dogs are mammals. All terriers are
  mammals. So, all terriers are dogs.
• All the propositions in the argument above are
  true, but the truth of the conclusion is only
  coincidental, and does not necessarily follow
  from the premises, because the reasoning is
  invalid (the form of the argument commits a
  reasoning error called undistributed
  middle--which well learn about later--but can
  be demonstrated intuitively by substituting
  cats for terriers and yielding the
  conclusion, All cats are dogs, clearly a false
  conclusion).

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Argument soundness

• Sound arguments
• reason validly from
• actually true premises to an
• actually true conclusion.

• Unsound arguments
• reason invalidly from premises
• whether true or false, or
• validly from
• untrue premises to conclusion.

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In either case, soundness--or the lack
thereof--depends on

• The validity (structure) of the reasoning,
• Which is relatively easy to test, but may be
  tricky to grasp master, and/or
• The truth (reliability) of the premises
• Which may be difficult to test and master in an
  infinite universe of propositions.

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Arguments v. propositions

• Arguments are
• Valid or invalid and
• Sound or unsound but
• Never true or false.

• Propositions are
• True or false but
• Never valid/invalid or sound/unsound

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The study of logic, furthermore

• is concerned with validity
• the form of arguments
• as opposed to soundness
• which involves the truth of propositions as
  well as validity

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Language of Logic

• To help us grasp more easily the concept of
  validity (the structure of an argument), as
  opposed to soundness (the truth of the individual
  propositions), and to be able to study validity
  better in isolation, logicians frequently cast
  arguments using
• Nonsense words
• All mimsies are borogroves . . .
• Or symbols
• All m are b . . . .
• As you can see, in the cases above we arent
  inclined to think about the truth of the
  propositions, but rather only the structure of
  the argument.

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Chapter 1.2 Argument forms

• Commercial break
• Some deductive arguments take very familiar
  forms.
• Modus Ponens, aka Affirming the Antecedent
• Modus Tollens, aka Denying the Antecedent
• Hypothetical Syllogism
• Disjunctive Syllogism
• Constructive Dilemma

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Forms method

• If we can reduce an argument to one of the forms,
  its validity is very easy to establish.
• Simplify
• Substitute
• Compare

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Demonstrations

• Modus Ponens
• aka Affirming Antecedent
• Modus Tollens
• aka Denying Consequent
• Fallacy of Denying Antecedent
• Fallacy of Affirming Consequent

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Chapters 1.3 1.4 Preview

• Chapter 1.3
• Informal refutation v. proof
• Two common fallacious forms
• Counterexample method
• Categorical statements
• Section 1.4
• Induction (v. deduction)
• Strength cogency

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Chapter 1.3 Testing Deductive Arguments

• What are two informal ways of testing deductive
  arguments?
• Informal refutation
• Informal proof

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Chapter 1.3 Refutation Proof

• What is refutation?
• A demonstration that, even if premises are true,
  conclusion is false
• Under what conditions will this be successful?
• Only if argument is invalid

• What is proof?
• A demonstration of a sequence of individual,
  logically valid maneuvers from given premises to
  conclusion
• Under what conditions will this be successful?
• Only if argument is valid

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Chapter 1.3 Proof

• If an argument cannot be refuted, it may be valid
  and require proof.
• If an argument can be proved, then it is valid
  and cannot be refuted (although it may still be
  unsound).
• Proof requires a demonstration that, beginning
  with true premises, a true conclusion necessarily
  follows through a valid sequence of individual
  maneuvers.

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Chapter 1.3 Two Common Fallacious Forms

• What five common valid argument forms did we
  acquire in Chapter 1.2?
• What two common fallacious forms did we learn
  about in Chapter 1.3?
• How do we know that they are invalid?

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Chapter 1.3 The Method of Refutation by
Counterexample (Analogous Reasoning)

• What is a counterexample?
• Why is it called a counterexample?
• Literally, an analogous example of the argument
  that runs counter to the claim/conclusion
• What is the counterexample method? How is
  refutation by counterexample done?
• Fabricate an analogous scenario in which the
  premises are true but conclusion is false (the
  definition of invalidity).
• Substitute variables for statements or terms.
• Substitute new, logically sensitive statements or
  terms for variables, beginning with a clearly
  false conclusion.
• Substitute new logically sensitive statements or
  terms for corresponding variables to yield
  clearly true premises.

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Chapter 1.3 Refutation by counterexample
(analogous reasoning)

• How does refutation by counterexample (analogous
  reasoning) work?
• Because validity/invalidity is strictly a matter
  of argument form, if one can demonstrate that an
  identical form is invalid (I.e., true premises
  yielding false conclusion), then the original
  argument is invalid.
• In what way is refutation by counterexample not
  always reliable? Why do you need to be careful
  when refuting by analogous reasoning?
• You must craft an argument that is exactly
  identical (logically sensitive) in form--any
  deviation yields a false analogy that will not
  necessarily disprove the original argument.

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Chapter 1.3 Categorical Statements

• What is a statement?
• What is a category?
• What, then, is a categorical statement?
• Can you cite an example of a categorical
  statement?
• What makes it categorical?
• What is the form of a categorical statement?
• Can you enumerate the exhaustive list of
  categorical statement forms?
• What is a term?
• How does it differ from a statement?
• We will devote chapters 5 6 to categorical
  logic.
• Commercial break
• Exercises

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Chapter 1.4Induction (Strength Cogency)

• To this point we have limited discussion to
  issues in deductive logic and only introduced the
  terms inductive logic (in Chapter 1.1).
• How does induction differ from deduction?
• What are the standards for deductive logic?
• What are the standards for inductive logic?
• What three examples of inductive argument types
  does our text adduce?
• How does the idea of more or less apply to
  these types?
• Exercises

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Chapters 2.1 2.2 (2.3 EC) Preview

• WARNING This chapter may seem squishy.
• Chapter 2.1Arguments Non-arguments
• Distinguishes arguments from other kinds of
  passages, including unsupported assertions, like
  reports, illustrations, explanations, and
  conditionals.
• Chapter 2.2Well-Crafted Arguments
• Explains how to simplify usually complicated
  everyday arguments into more assessable
  well-crafted arguments using six principles to
  charitably ferret out conclusions,
  sub-conclusions, explicit and implicit premises,
  standard form, unnecessary verbiage, and
  uniformity.
• Chapter 2.3Argument Diagrams (EC)
• For extra-credit, demonstrates the helpfully
  clarifying, but not absolutely essential, step of
  diagramming arguments schematically in order to
  grasp the relationship of assertions to their
  support.

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Strategic observations

• Unlike examples encountered so far in our text,
  arguments may be extensive and complicated.
• There may be arguments supporting premises and
  premises for those arguments.
• There may be more than one line of reasoning for
  a conclusion.
• There may be more than one kind of reasoning.

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Major tactical maneuvers

1. Begin by asking yourself, What is the author
   trying to say? What is his/her point? This
   should yield the conclusion.
2. Next, ask yourself, What are the main reasons
   she/he adduces for believing that? This should
   yield the explicit premises (evidences) of the
   argument.
3. Finally, ask, What would one have to believe to
   accept what this author has said? This should
   yield the implicit premises (assumptions) of the
   argument.

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Minor tactical considerations

• In texts written in English, by writers in
  Western the tradition, most conclusions appear at
  the beginning (deductive approach) or at the end
  (inductive approach) or at the end of the
  beginning.
• Explanations, examples, definitions, and attempts
  to preempt objections are almost never
  conclusions of an argument or even premises, in
  the strict sense.
• Ancillary information, as in supporting
  documentation, notes, parenthetical asides are
  never conclusions and almost never premises, in
  the strict sense.
• A conclusion will never appear in a subordinate
  clause.
• Look for illatives.

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Preview of 3.1 - 3.3

• Problem areas
• 3.1
• Proposition
• 3.2
• Subtlety of definitional terms
• 3.3
• Largely unproblematic

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Why care about definitions?

• Define literally means to put limits around
  (fr. L. de about finis limit).
• So, definition limits meanings.
• Minimizes
• vagueness (meanings shading off into other areas)
• ambiguity (more than one meaning)
• Minimizes complications of It all depends on
  what you mean by __________.

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Chapter 3.1

• Which of these concepts/terms were difficult?
• Proposition
• Cognitive meaning
• Emotive force
• For the concepts/terms that were confusing, can
  someone clarify it for us by defining and giving
  at least one example, or the range of examples,
  of it?
• Why is it important to understand these
  concepts/terms?
• Review problematic exercises

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Chapter 3.2

• Which of these concepts/terms were difficult?
• Ambiguity versus vagueness
• Extensional definition
• Ostensive
• Enumerative
• Subclassical
• Intensional definition
• Lexical (genus differentia)
• Stipulative
• Precising
• Theoretical
• For the concepts/terms that were confusing, can
  someone clarify it for us by defining and giving
  at least one example, or the range of examples,
  of it?
• Why is it important to understand these
  concepts/terms?
• Review problematic exercises

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Definition by extension

• Pointing (a.k.a. ostensive)
• actually showing one or more cases
• Enumeration
• listing individual examples
• Subclass
• listing types or categories
• Exhaustive v. non-exhaustive?

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Intensional definition

• Stipulative personal, ad hoc, coined or not
• Lexical positive, descriptive, dictionary-type,
  though not necessarily exclusively so
• Precising minimizes vagueness ambiguity, to
  put a fine point on it, to distinguish precise
  meaning from popular meaning
• Theoretical places a term in a particular
  context may give meaning to both term and
  context
• Persuasive affective, subjective, emotive

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Definition by intension

• Synonym
• Another word (lit. ??? similar ????? name)
• Etymology
• Linguistic genealogy (lit. ?????? true ????s
  account)
• Test
• Establishes criteria to be met
• Genus difference/differentia
• garden variety definition technique x is a y
  that . . . .

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Chapter 3.2, contd.

• Which of these concepts/terms were difficult?
• Genus versus difference/differentia
• Difiniendum versus difiniens
• Counterexample
• For the concepts/terms that were confusing, can
  someone clarify it for us by defining and giving
  at least one example, or the range of examples,
  of it?
• Why is it important to understand these
  concepts/terms?
• What are the criteria for producing a good
  definition?
• Not to wide
• Not to narrow
• Not obscure, ambiguous, figurative
• Not circular
• Not negative if it can be positive
• Not use unsuitable criteria to determine
  extension
• Review problematic exercises

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Ways of defining terms

• definiendum word to be defined
• definiens words doing the defining
• extension set of objects in defined class
• intension properties of objects in class

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Rules

• What is meant by essential characteristics
  (necessary sufficient)?
• How can the definiens be too broad or narrow?
• What is meant by circularity?
• Cite examples of ambiguity, obscurity, figurative
  or emotive language.

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Chapter 3.3

• Which of these concepts/terms were difficult?
• Equivocation versus merely verbal dispute
• Persuasive definition
• For the concepts/terms that were confusing, can
  someone clarify it for us by defining and giving
  at least one example, or the range of examples,
  of it?
• Why is it important to understand these
  concepts/terms?
• Review problematic exercises

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Preview of Chapter 4Concepts that may present
difficulty

• 4.1 Fallacies of Irrelevance
• English/Latinate names
• 4.2 Fallacies Involving Ambiguity
• Amphiboly is sort of like equivocationbut its
  not the same.
• Composition and division are similarbut theyre
  not the same.
• 4.3 Fallacies Involving Unwarranted Assumptions
• Begging the Question is not what it sounds
  like.

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Chapter 4.1 Fallacies of Irrelevance

• Which of these concepts/terms were difficult?
• Fallacy
• Formal
• Informal
• Of irrelevance
• Ad Hominem (Against the Man)
• Personal attack
• Circumstantial
• Tu Quoque
• Straw Man
• Ad Baculum (Appeal to Force)
• Ad Populum (Appeal to the People)
• Ad Misercordiam (Appeal to Pity)
• Ad Ignorantiam (Appeal to Ignorance)
• Ignoratio Elenchi (Red Herring or Missing the
  Point)
• For the concepts/terms that were confusing, can
  someone clarify it for us by defining and giving
  at least one example, or the range of examples,
  of it?
• Why is it important to understand these
  concepts/terms?
• Review problematic exercises

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Chapter 4.2 Fallacies of Ambiguity

• Which of these concepts/terms were difficult?
• Fallacy of Ambiguity
• Equivocation
• Amphiboly
• Composition
• Division
• For the concepts/terms that were confusing, can
  someone clarify it for us by defining and giving
  at least one example, or the range of examples,
  of it?
• Why is it important to understand these
  concepts/terms?
• Review problematic exercises

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Chapter 4.3 Fallacies of Unwarranted Assumption

• Which of these concepts/terms were difficult?
• Unwarranted Assumption
• Begging the Question (Petitio Principii)
• False Dilemma
• Appeal to Unreliable Authority (Ad Verecundiam)
• False Cause
• Complex Question
• For the concepts/terms that were confusing, can
  someone clarify it for us by defining and giving
  at least one example, or the range of examples,
  of it?
• Why is it important to understand these
  concepts/terms?
• Review problematic exercises

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Chapter 5 Categorical Logic Statements

• Chapter 5.1
• Terminology is important we will be coming back
  to it again and again.
• Translation is key grasp the meaning of
  stylistic variants and their translation
• Chapter 5.2
• Chapter 5.3