Philosophy%20103%20Linguistics%20103%20Introductory%20Logic:%20%20Critical%20Thinking%20%20Fall%202007

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Philosophy 103Linguistics 103MoreIntroductory
Logic Critical Thinking

• Dr. Robert Barnard

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Last Time

• Syllabus
• Home.olemiss.edu/rwbjr/rbphil103.htm
• Basic Concepts
• Arguments ( Premise/Conclusion)
• Propositions (Simple/Complex)
• - Conditional Props. (Antecedent/Consequent)
• -Truth values

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Why Logic?

• One way to support a theory is to offer an
  argument in its favor.
• One way to criticize a theory is to offer an
  argument against that theory.
• Which arguments should we take seriously? Logic
  answers this Question!

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Talking about Arguments

• We need to have a specific vocabulary for talking
  about different kinds of arguments and when an
  argument works and when it doesnt work.
• We will use different terms to describe failures
  of structure and failures of content.

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Deduction

• In DEDUCTIVE ARGUMENTS the CONCLUSION is supposed
  to follow NECESSARILY from the PREMISES.
• A DEDUCTIVE INFERENCE is one which takes us from
  evidence or reasons to a conclusion with
  necessity.

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A Deductive Argument

• All Cars have engines
• My Honda is a car
• Therefore,
• My Honda has an engine.

Premise 1
Premise 2
Conclusion INDICATOR
THE CONCLUSION!

• Note
• If I tell you what the premises are, you know
  what the conclusion would be before I told you!!!
  It is impossible for the conclusion to be
  false, given these premises!

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Induction

• In INDUCTIVE ARGUMENTS the CONCLUSION is supposed
  to follow with HIGH PROBABILITY from the
  PREMISES.
• An INDUCTIVE INFERENCE is one which takes us from
  evidence or reasons to the likelihood of the
  conclusion.

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An Inductive Argument

• Every person I have met from Poland loves potato
  soup.
• Karlov is from Poland.
• Therefore,
• i) Karlov will love potato soup.
• ii) Karlov will probably love potato soup.

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A Quick review

• Deductive vs. Inductive Arguments
• Deductive The truth of the premises is supposed
  to require the truth of the conclusion (Necessary
  Support)
• Inductive The truth of the premises is supposed
  to increase the probability of the conclusion
  (Probability)

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Good vs. Bad Arguments

• Deductive Validity IF the premises are true
  THEN the conclusion MUST be true.
• Inductive Strength IF the premises are true
  THEN the conclusion WILL BE PROBABLE.
• Deductive Soundness the deductive argument is
  valid AND premises are all true
• Inductive CogencyThe inductive argument is
  strong and the premises are all true

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Argument Family Tree
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Deductive Arguments

• Deductive Validity IF the premises are true
  THEN the conclusion MUST be true.
• Deductive Soundness the deductive argument is
  valid AND premises are all true
• Failure of Structure INVALID
• Failure of Content UNSOUND

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Validity

• Validity is the central concept in deductive
  logic. Validity is related to structure or form.
• Validity df A deductive argument is valid iff
  it is impossible for the premises to be true and
  the conclusion false (at the same time).

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Soundness

• Soundness is the secondary mode of evaluation in
  deductive logic. Soundness is related to
  content.
• Soundness df A deductive argument is sound iff
  the argument is valid and the premises are all
  true (at the same time).

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Kinds of Deductive Arguments

• Arguments from Mathematics
• Arguments from Definition
• Categorical Syllogism
• Hypothetical Syllogism
• Disjunctive Syllogism

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Argument Family Tree (D)
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Evaluating Deductive Arguments

• To determine VALIDITY you must first identify the
  form of the argument.
• Try to develop counter-examples with the same
  logical form, or
• Employ methods of formal logical analysis.
• Determining SOUNDNESS depends upon the truth of
  the premises (beyond logic)

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Inductive Arguments

• Inductive Strength IF the premises are true
  THEN the conclusion WILL BE PROBABLE.
• Inductive CogencyThe inductive argument is
  strong and the premises are all true
• Failure of Structure WEAKNESS
• Failure of Content NON-COGENT

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Strength

• Inductive STRENGTH is the central mode of
  evaluation for inductive arguments.
• Strengthdf An inductive argument is strong iff
  it is improbable that the conclusion is false
  when the premises are all assumed to be true.

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Cogency

• Inductive COGENCY is the secondary mode of
  evaluation for inductive arguments.
• Cogencydf An inductive argument is cogent iff
  it is inductively strong and the premises are all
  true.

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Kinds of Inductive Arguments

• Prediction
• Arguments from Analogy
• Generalization
• Arguments from Authority
• Arguments based upon signs
• Causal Inferences

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Argument Family Tree (I)
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Evaluating Inductive Arguments

• To determine STRENGTH you must evaluate whether
  the truth of the premises would in fact enhance
  the probability of the conclusion. This requires
  knowledge of how things work and how they are
  related.
• To determine COGENCY you must know the truth of
  the premises (beyond logic)

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Induction?

• The evaluation of inductive arguments is less
  clear. If you can give determinate quantitative
  values to probabilities, then the rules of
  statistics apply.
• Otherwise you need to try and reflect on the
  probabilities to the best of your ability.

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Induction

• Some factors to keep in mind about inductive
  data
• Typicality (How common?)
• Generality (How General?)
• Frequency (How Frequent?)
• Analogy / Dis-analogy?

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Arguments

1. All ARGUMENTS have a CONCLUSION and PREMISES that
   are supposed to support the conclusion.
2. Deductive and Inductive arguments differ with
   respect to the type of support they are intended
   to provide.
3. Deductive arguments provide NECESSARY SUPPORT
4. Inductive arguments provide PROBABLE SUPPORT

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Pause and reflect
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New TopicInformal Fallacies

• The study of informal fallacies goes back to
  Ancient Greece, where the first philosophers and
  logicians sought to control the demagogues and
  their teachers (the so-called Sophists).

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What is a Fallacy?

• A fallacy is a mistake in an argument which
  consists in something other than merely false
  premises.

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Formal Fallacies

• A formal fallacy is simply an invalid deductive
  argument form.

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Informal Material

• Informal fallacies depend on the content of the
  fallacious argument either the argument depends
  upon a shift or ambiguity in linguistic meaning
  or the substitution of an non-logical basis for a
  logical justification. There are many varieties.

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Fallacies of Relevance

• Fallacies of Relevance
• The conclusion is logically irrelevant to the
  premises, even if it is psychologically or
  emotionally relevant.
• The key to spotting a fallacy of relevance is to
  distinguish genuine evidence from emotional
  appeal.

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1. Appeal to Force (Argumentum Ad Bacculum)

• Arguing via threat "I deserve a good grade,
  wouldn't you agree? If you don't agree, I'm
  afraid about what might happen I just can't
  control Bruno here".

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2. Appeal to Pity(Argumentum ad Misericordium)

• Trying to support a conclusion by evoking pity in
  the listener. I need to pass this class in order
  to graduate, if I don't graduate,, my parents
  will kill me. Therefore, I should receive a
  passing grade in the class".

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3. Appeal to the People (argumentum ad populum)

• Attempting to convince by appealing to the
  natural desire we all have to be included, or
  liked, or recognized. This type of fallacy breaks
  down into several sub-types.
• Bandwagon Of course God exists. Every real
  American believes that. Other related types
  Appeal to Vanity Appeal to Snobbery ("Of course
  you should cheat all the cool people are doing
  it").

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3. Appeal to the People (argumentum ad populum)
(2)

• In general, accepting a claim only because
  someone else believes it is a fallacy (not
  because you find them to be a credible source for
  instance . . .). So, we could say that another
  example of an ad populum is
• Appeal to Belief. Example "90 of those surveyed
  think we should not convict Clinton, so you
  should too".
• Closely related is the
• Appeal to Common Practice. Example "Hey,
  everyone speeds. So speeding isn't wrong".