The Logic of Argument

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The Logic of Argument

• Rodolfo Celis
• EN101.11

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Logic and inference

• Inferences involve the process of deriving the
  logical consequences of assumed premises also,
  the process of arriving at some conclusion that,
  though it is not logically derivable from the
  assumed premises, possesses some degree of
  probability relative to the premises also, a
  proposition reached by a process of inference.

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Logics

• Formal logic e.g. truth-conditional logic
• Informal logic pragmatics

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Truth-conditional logic

• Seeks to better understand the conditions under
  which some sentence is true.
• Philosophers and linguists call these "truth
  conditions."
• These are the conditions under which a sentence
  is true, in any given possible world.
• Thus, sometimes called "possible worlds
  semantics."
• A "truth value" is a sentence's being true or
  false.

relative to any given choice of denotations of
indexical elements
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Truth-conditional logic

• In propositional logic, a kind of
  truth-conditional logic, philosophers study the
  effects of operators or functions performed upon
  sentences. Examples of operators are things like
  negation (symbolized by ) and conjunction
  ("and," symbolized by ).

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Truth-conditional logic

• To figure out the effect of operators,
  philosophers use a tool known as "truth tables"
  that simply itemize all the different sorts of
  possibilities that can obtain with a given
  logical function (operation performed upon a
  sentence whose outcome is contingent upon the
  truth value of the constituent element they
  combine in special ways depending on the
  operator).

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The logic of

• p p
• T F
• F T
• "Your car has been stolen." If it is true that
  your car has been stolen, then it is false to say
  that "Your car has not been stolen."
• If it is false that your car has been stolen,
  then the sentence that it is not the case that
  your car has been stolen is true.

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The logic of

• p q pq
• T T T
• T F F
• F T F
• F F F
• e.g. (to illustrate 3rd line) "My dog just ran
  away and my leg itches" this sentence is not
  "true" if it is not true that your dog just ran
  away. Cf. the disjunctive operator "or"
  symbolized ?.

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Formal logic

• These are types of formal logics.
• Formal logic is concerned with, at a basic level,
  with figuring out the principles of valid
  argument and inference.

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Formal logic

• If Socrates is a man, then he is mortal.
• Socrates is a man.
• Therefore, he is mortal.
• This is known as modus tollens associated with
  Aristotle. This sort of logic is known as
  "deductive logic." In valid deductive arguments,
  the conclusion necessarily follows from the
  premises.
• Most of the arguments encountered in conversation
  and in essays are not strict deductions. That is
  ok human knowledge tends to be imperfect. But
  your job is to recognize this as such, and
  identify the missing information.

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Formal logic - syllogisms

• This sort of argument is known as a "syllogism."
  A syllogism is an argument in which the
  conclusion is supported by two premises, of which
  one (major premise)contains the term (major
  term)that is the predicate of the conclusion, and
  the other (minor premise) contains the term
  (minor term)that is the subject of the
  conclusion common to both premises is a term
  (middle term)that is excluded from the
  conclusion. A typical form is "All A is C all B
  is A therefore all B is C.'

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Formal logic

• The problem is that ordinary language is rife
  with complications. It pays to be aware of these
  complications and perhaps how they work where
  these "complications" behave somewhat
  consistently. This is what linguistic-pragmatics
  does studies the logic of natural language a
  logic that is often different from formal
  symbolic logic, but, nevertheless, displays some
  consistent principles of reasoning.
• This is one of the domains of linguistics.

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The logic of ordinary language pragmatics

• Consider "and" and "but." According to strict or
  formal logic, they have the same truth table
  they mean the same thing
• p q pq
• T T T
• T F F
• F T F
• F F F

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The logic of ordinary language pragmatics

• The problem is, in ordinary language, "and" and
  "but" don't seem to "mean" the same thing.
• Cf. "My dog ran away and my leg itches."
• "My dog ran away but my leg itches."
• Even "and" seems to have a slightly different
  meaning of implication in natural language.
• The Search For The Adamic Tongue Philosophers
  Languages

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The logic of ordinary language pragmatics and
problems in artificial intelligence

• Nigel has 14 children.
• We conclude that Nigel has only 14 children. In
  fact, according to a possible worlds semantics,
  this sentence is not inconsistent with a world in
  which Nigel has 21 children. Where did this only
  come from? These are the sorts of mysteries
  linguists and scientists in artificial
  intelligence explore.

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Premise

• A premise is a starting point. The person making
  the argument would have us believe it is true,
  though you should always check. A premise is one
  of the reasons adduced in an argument for
  concluding something.
• When we reason, we combine two or more premises
  and draw a conclusion based on their connection.

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Premise

• Premise 1 Super glue can be tasty.
• Premise 2 I just ate some super glue.
• Conclusion Boy, I must have just had a tasty
  experience/meal/snack.

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Premises and conclusions

• Note that even true premises may not justify a
  conclusion. Among other things, the premises
  need to be relevant to the conclusion.
• You should ask yourself are all the premises in
  this argument true? Are they relevant? What are
  the premises actually? What is the conclusion?
  What sort of evidence is adduced to back up these
  premises anyway? (Note that evidence may not
  always be possible but its lack should at least
  be noted where relevant.)

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Premises and conclusions

• When we analyze inferences, and their
  relationship to one another in an argument, we
  are evaluating whether or not the reasoning from
  them to the conclusion is justified. In large
  part, this will be your task when reading
  critical or argumentative essays.

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Premises and conclusions

• Consider some of the following statements, which
  include a premise or premises, and some sort of
  inference or conclusion drawn from these premises.

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Premises and conclusions

• I sent my English teacher an email but he never
  answered. He must really hate me.
• A course in linguistics provides the basis for a
  more coherent understanding of some of the
  unspoken processes we use when we converse.
  Therefore, all students should be required to
  take linguistics.
• Rodolfo's jeep has Alabama tags. Therefore, the
  rules of Philadelphia roads do not apply to him.

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Insinuations

• Sometimes things are not stated, but insinuated.
  You should be very aware of insinuations.
  Consider the following
• Serbs hate Croations. Milovich is a Serb.
• Insinuated
• Milovich hates Croations.
• When a conclusion like this is missing, the
  argument is called an enthymeme. Such an
  argument is an "enthymemic" argument.
  "Enthymeme" is classical Greek for "to hold in
  mind."

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Common logical fallacies the undistributed
middle

• A syllogism won't work unless the assertion found
  in the major premise is true of all members of
  the group.
• In the Socrates syllogism, "mortality" is true of
  "all men."
• But look at the following syllogism on the next
  slide.

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Common logical fallacies affirming the
consequent

• The State of Pennsylvania punishes English
  professors who chase after cars.
• The State of Pennsylvania punished Rodolfo.
• Therefore, Rodolfo chases after cars.
• Here you are merely "affirming" a consequence.
  But this consequence, in the absence of further
  specification, does not follow.

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Common logical fallacies circular reasoning or
begging the question

• Involves "arguing in a circle" using as a
  premise what in fact is trying to be proved
  burying a conclusion in a premise.
• Examples
• Freud's investigations were truly scientific
  because they were based on Freud's own clinical
  research.
• This car doesn't work because something is wrong
  with it.

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Common logical fallacies non sequitur

• Latin for "does not follow." Applies to any
  argument whose conclusion simply has nothing to
  do with its premises, at least logically
• Examples
• Rodolfo will make an excellent governor because
  he grew up in the fine state of South Carolina.

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Common logical fallacies Post hoc, ergo propter
hoc

• Latin for "after this, therefore because of
  this."
• We commit this fallacy when we argue, without
  other reasons, that because X occurred before Y,
  X caused Y.
• Example
• Last spring Rodolfo was elected president of the
  Elks Club and world hunger disappeared. What
  more can I say? This argument is partially
  enthymemic.

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Common logical fallacies ad hominem

• Latin for "to the man."
• Someone guilty of this fallacy argues by making
  irrelevant assertions such as character
  assassinations about an opponent, rather than
  attacking the opponent's reasoning.

Fun with etymology assassin comes from the
Arabic word hasasin missing diacritics,
literally "hashish users," denoting a group of
11th century Ismali Muslims who murdered
Christian leaders. The Ismali Muslims were active
in Persia and Syria from about 1090 to 1272 and
were reputed to attack the Crusaders.
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A checklist of questions and suggestions for comp
students

• What are the premises?
• What are the conclusions?
• Are all the premises there?
• Are they true?
• Do they have evidence?
• Does the author at least admit that there is no
  evidence, or is this matter avoided?
• Do you agree with all the premises?
• Sketch out the argument in its skeletal form.
• Is the conclusion highly probable given the
  premises?
• Are the statements made statements of fact or
  are they statements of value? (Not that there is
  anything inherently wrong with statements of
  value!)
• Any logical fallacies?