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.
Central concepts
• Central concepts
– Argument v. non-argument
– Deduction v. Induction
– Validity & Soundness v. Strength & Cogency
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 author’s
point?
• Declarative statements & rhetorical questions
(which can masquerade as declarative statements)
• Implicit statements (as opposed to explicit)
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
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
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
Deductive arguments are
intended to be sound [to
succeed] but they may not be
[successful].
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.
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--there’s no
avoiding it!)
• “Invalid” if the premises,
whether true or false,
cannot guarantee the
truth of the conclusion
(I.e., the conclusion
doesn’t necessarily
follow--there are other
ways to explain the
outcome).
Caveats
• To say an argument is valid, however,
doesn’t mean that it is sound or that it’s
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, it’s conclusion must
necessarily follow), but the conclusion is false
and the argument is unsound because one or
more of the premises is false.
Caveats, cont’d.
• 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 we’ll 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).
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.
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.
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”
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]
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 aren’t
inclined to think about the truth of the
propositions, but rather only the structure of
the argument.
Chapter 1.2: Argument forms
• Commercial break
• Some deductive arguments take very
familiar forms.
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Modus Ponens, aka Affirming the Antecedent
Modus Tollens, aka Denying the Antecedent
Hypothetical Syllogism
Disjunctive Syllogism
Constructive Dilemma
Forms method
• If we can reduce an argument to one of the
forms, its validity is very easy to establish.
– Simplify
– Substitute
– Compare
Demonstrations
• Modus Ponens
– aka Affirming Antecedent
• Modus Tollens
– aka Denying Consequent
• Fallacy of Denying Antecedent
• Fallacy of Affirming Consequent
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
Chapter 1.3:
Testing Deductive Arguments
• What are two informal ways of testing
deductive arguments?
– [Informal] refutation
– [Informal] proof
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
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.
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?
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).
① Substitute variables for statements or terms.
② Substitute new, logically sensitive statements or terms for
variables, beginning with a clearly false conclusion.
③ Substitute new logically sensitive statements or terms for
corresponding variables to yield clearly true premises.
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.
Chapter 1.3:
Categorical Statements
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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
Chapter 1.4:
Induction (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
Chapters 2.1 & 2.2 (2.3 EC) Preview
• WARNING: This chapter may seem “squishy.”
– Chapter 2.1—Arguments & Non-arguments
• Distinguishes arguments from other kinds of passages, including
unsupported assertions, like reports, illustrations, explanations, and
conditionals.
– Chapter 2.2—Well-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 2.3—Argument 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.
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.
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.
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.
Preview of 3.1 - 3.3
• Problem areas
– 3.1
• Proposition
– 3.2
• Subtlety of definitional terms
– 3.3
• Largely unproblematic
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 __________.”
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
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
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?
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
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 . . . .]’
Chapter 3.2, cont’d.
• 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?
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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
Ways of defining: terms
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‘definiendum’: word to be defined
‘definiens’: words doing the defining
‘extension’: set of objects in defined class
‘intension’: properties of objects in class
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.
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
Preview of Chapter 4:
Concepts that may present difficulty
• 4.1 “Fallacies of Irrelevance”
– English/Latinate names
• 4.2 “Fallacies Involving Ambiguity”
– Amphiboly is sort of like equivocation—but it’s not the
same.
– Composition and division are similar—but they’re not
the same.
• 4.3 “Fallacies Involving Unwarranted Assumptions”
– “Begging the Question” is not what it sounds like.
Chapter 4.1: Fallacies of Irrelevance
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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
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
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
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