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An Introduction to Logic and Logical Fallacies, Study notes of Logic

Slippery Slope (misuse of 'if-then'). ○ If the first step in a “possible” series of events occurs, the other possible steps in the series must inevitably.

Typology: Study notes

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1
1Critical Thinking: An Introduction to
Logic and Logical Fallacies
Lecture II
Fall 2008
2Truth Tables and Logical Operators
Truth Tables and Logical Operators
zFace it…some things are either true or false (specifying this formally is called “propositional calculus”)
zA “proposition” is a meaningful statement
zLimited number of operators: (not, and, or, if…then, if and only if)
zTruth tables chart truth value of proposition by laying out state-of-world possibilities
zUse of conditional logic (if certain conditions are met, then a proposition is true)
3
4Forms of Conditional Reasoning,
Forms of Conditional Reasoning,
based on
based on
If P then Q
If P then Q
zValid Forms
Modus Ponens: P, Q
Modus Tollens: not Q, not P
zInvalid Forms
Affirming the Consequent: Q, P
Denying the Antecedent: not P, not Q
5Logical Fallacies
zIt is important to identify common ways of thinking falsely so that you can sharpen your own
logical analyses
zIdentifying source of fallacious reasoning often helps clarify ideas you are trying to
communicate
zTA’s will call you on logical errors (in public)
6Fallacies of Distraction
zFallacy lies in that you are distracted from “true” premises and led to assume something
faulty
zIllegitimate use of a logical operator is key
zYou can identify these fallacies by showing that the main premise doesn’t accurately reflect
what’s really going on
7False Dilemma (misuse of “or”)
zA limited number of options (usually two) is given, while in reality there are more options. A false dilemma is
an illegitimate use of the "or" operator.
zPutting issues or opinions into "black or white" terms is a common instance of this fallacy
zExamples:
You’re either for me or against me.
America: Love it or leave it.
If you ain’t a Gator, you’re Gator bait (this one’s true).
8Slippery Slope (misuse of ‘if-then’)
zIf the first step in a “possible” series of events occurs, the other possible steps in the series must inevitably
occur.
zExamples
If you drink alcohol once, then you’ll want to drink it again, and pretty soon you’ll be an alcoholic and lose your job.
If we pass laws against fully-automatic weapons, then it won't be long before we pass laws on all weapons, and then we
will begin to restrict other rights, and finally we will end up living in a communist state. Thus, we should not ban fully-
automatic weapons.
pf3

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1 Critical Thinking: An Introduction to

Logic and Logical Fallacies

Lecture II

Fall 2008

2 Truth Tables and Logical OperatorsTruth Tables and Logical Operators

z Face it…some things are either true or false (specifying this formally is called “propositional calculus”) z A “proposition” is a meaningful statement z Limited number of operators: (not, and, or, if…then, if and only if) z Truth tables chart truth value of proposition by laying out state-of-world possibilities z Use of conditional logic (if certain conditions are met, then a proposition is true)

4 Forms of Conditional Reasoning,Forms of Conditional Reasoning,

based on “based on“If P then QIf P then Q””

z Valid Forms

  • Modus Ponens: P, ∴ Q
  • Modus Tollens: not Q, ∴ not P

z Invalid Forms

  • Affirming the Consequent: Q, ∴ P
  • Denying the Antecedent: not P, ∴ not Q

(^5) Logical Fallacies

z It is important to identify common ways of thinking falsely so that you can sharpen your own

logical analyses

z Identifying source of fallacious reasoning often helps clarify ideas you are trying to

communicate

z TA’s will call you on logical errors (in public)

(^6) Fallacies of Distraction

z Fallacy lies in that you are distracted from “true” premises and led to assume something

faulty

z Illegitimate use of a logical operator is key

z You can identify these fallacies by showing that the main premise doesn’t accurately reflect

what’s really going on

(^7) False Dilemma (misuse of “or”)

z A limited number of options (usually two) is given, while in reality there are more options. A false dilemma is an illegitimate use of the "or" operator. z Putting issues or opinions into "black or white" terms is a common instance of this fallacy z Examples:

  • You’re either for me or against me.
  • America: Love it or leave it.
  • If you ain’t a Gator, you’re Gator bait (this one’s true).

(^8) Slippery Slope (misuse of ‘if-then’)

z If the first step in a “possible” series of events occurs, the other possible steps in the series must inevitably occur. z Examples

  • If you drink alcohol once, then you’ll want to drink it again, and pretty soon you’ll be an alcoholic and lose your job.
  • If we pass laws against fully-automatic weapons, then it won't be long before we pass laws on all weapons, and then we will begin to restrict other rights, and finally we will end up living in a communist state. Thus, we should not ban fully- automatic weapons.

(^9) Appeals to Motives

z The key here is to appeal to emotions or psychological factors instead of evidence

z In this way, the reasons supporting the belief are not really provided

z Example: "The only reason why she got the part in that movie is because her husband is the

director."

(^10) Appeal to Force

z The listener is told that unpleasant consequences will follow if they do not agree with the

speaker

z Examples:

  • Agree with our position or we’ll vote you out of office
  • Support mental health or I’ll kill you.

z Identify the proposition and the consequence and show they are not necessarily related

(^11) Appeal to Pity

z The listener is told to agree with a statement because of the pitiful state of the speaker

z Examples:

  • (to a referee: “How can you say that ball was out? I’m already down 10-2”!)
  • We hope you'll accept Mr. Smith’s recommendations. He spent the last three months working extra time on the report.

(^12) Prejudicial Language

z Loaded or emotive terms are used to attach value or moral goodness to believing the

proposition.

z Examples:

  • Right-minded individuals vote for Bob!
  • The proposal is favored by the bureaucrats on Capitol Hill.

(^13) Changing the Subject

z The fallacies in this section change the subject by discussing the person making the

argument instead of discussing reasons to believe or disbelieve the conclusion.

z While on some occasions it is useful to cite authorities, it is almost never appropriate to base

the argument on the person instead of the substance

(^14) Attacking the Person

z ad hominem (abusive): instead of attacking an assertion, the argument attacks the person who made the assertion.

  • You may argue that we have to reduce military spending, but you’re just a bleeding-heart liberal. z ad hominem (circumstantial): instead of attacking an assertion the author points to the relationship between the person making the assertion and the person's circumstances.
  • Governor Smith’s endorsement of President Bush is invalid/biased because they served together on the Texas Cattle Board. z ad hominem (tu quoque): this form of attack on the person notes that a person does not practice what he preaches.
  • Senator McCain says he’s for improving the life of families, but he voted against a bill that would have given aid to pregnant mothers

(^15) Appeal to Authority/Anonymous Authority

z While sometimes it may be appropriate to cite an authority to support a point, often it is not. In particular, an appeal to authority is inappropriate if: (i) the person is not qualified to have an expert opinion on the subject (“Dr. Laura says Tide cleans best”) (ii) experts in the field disagree on this issue (“Noted developmentalist Dr. John Smith argues that all a fetus is a human being from the moment of conception”). (iii) the authority was making a joke, drunk, or otherwise not being serious (“We are headed for nuclear war. The President said we will begin bombing Russia in five minutes”) – this actually happened when President Reagan, after a speech about China, quipped “we’ll begin the bombing in 5 minutes” thinking the microphone was off

(^16) Inductive Fallacies

z Hasty Generalizations : the sample is too small to support an inductive generalization about a population