Logical Fallacies and Arguments: Paradoxes, Inductive Reasoning, and More
Logical Fallacies and Paradoxes
Paradox: Contradiction
A logical falsehood is any statement that is not logically consistent or consists of a logical incompatibility between two or more propositions. This sentence is false.
Infinite Regress
A sequence of reasoning or justification that never comes to an end. Reason —> Reason —> Reason Ad infinitum. Example: Turtle, Turtle.
Circularity
A logical fallacy where the reasoner begins with what he or she is trying to end up with. Example: Joe is really smart because he thinks so well.
Paradox Example
The following sentence is true.
The previous sentence is false (circular).
The Cretan Liar
Epimenides: All Cretans are liars.
Epimenides is a Cretan (He is a liar).
Example 2
All Cretans are liars.
Epimenides is a Cretan.
Therefore: Epimenides is a liar (Self-reference) – referring to himself.
Achilles + The Hare (Zeno)
Infinite Mathematics
The Paradox of the Sorites/Jockeys and Basketball Players (Eubulides)
Pile of grain – 1 grain, how many does it take to make a pile?
1 Grain of wheat/sand 2 3 4
Vagueness
Where a concept is lacking in clarity, certainty, or precision, especially in so-called borderline cases. Example: How tall someone is 6’11 ————————— 5’2
The Ship of Theseus
Replacing the ship, does it still make it the Theseus?
The Temptations
An old music group that has new members/not the original cast.
Barber of Seville (Russell)
In the town of Seville, there are two types of men:
- Those who shave themselves, and only themselves.
- The others do not shave themselves but are only shaved by the barber of Seville.
Paradox
Who shaves the barber of Seville?
Epistemological: Kyburg’s Paradox
Low 1 = 100%
Probability vs. Certainty
Inductive Deductive
LOOK IN MODULES!!!!
Inductive Logic
12.1 Generalizing
- A positive instance may confirm a generalization but does not prove it true.
- A negative instance or counter-example decisively refutes a general statement (all you need is one counter-example).
Example
The basketball team is great.
But all the teammates are dumb.
A player on the team is valedictorian.
12.1 A Three Rules for Generalization
- The sample should be sufficiently numerous + various (sources).
- Look for disconfirming as well as confirming instances of the generalization.
- Consider whether the generalization is plausible in light of other knowledge we possess. Example: Swans are only white/false.
12.2 Causality
Cause —> Effect Relationship
Distinction Between Necessary and Sufficient Conditions
Cause: You drop an egg.
Effect: The egg breaks (mess).
—————————–
Hardness of the floor
Hardness of the eggshell
Egg is heavier than air
Definition: A necessary condition for some state of affairs is a condition that must be satisfied for S to obtain.
Definition: A sufficient condition for some state of affairs S is a condition, if satisfied, guarantees that S obtains.
Example
A necessary condition of getting an A is handing in a paper.
A sufficient condition is getting an A on the paper means an A in the class.
12.3 Agreement and Difference
- Agreement + Difference
- Concomitant Variations
- Residues
1. Method of Agreement is identifying the cause of an effect by isolating a factor common to a variety of cases in which an effect occurs. Example: Homicide detective and serial murders.
Method of Difference is identifying a cause of an effect by isolating a factor in whose presence the effect occurs and in whose absence the effect does not occur, all other factors remaining constant (joint method). Example: Doctors – new drug/placebo, change before and after.
2. Concomitant Variations (Degrees)
Identifying a cause of an effect by isolating a factor whose variations are correlated with variations in the effect, all other factors remaining constant. Example: Sugar, stock market, employment.
3. Residue – Identifying causes and effects by isolating that portion of the effect explained by known causal relationships. Example: Vet, weighing you and an object, subtracting your weight.
Chapter 13: Argument by Analogy (Strong or Weak?)
Examples
Jim is an intellectual like Fred.
Fred does not like sports.
So Jim probably does not like them either. Inductive = Probably
Inductive Generalization: Weak Argument
Lincoln’s Gettysburg Address
2 minutes long, all men are created equal.
Analysis
- Argument of authority: Declaration of Independence, Founding Fathers
- Overall structure
- Abstract nature of the address
- Dedication
- Birth + Death imagery (new birth of freedom/death of slavery)
- Impact of address: 13th Amendment to the Constitution (1865) Abolition of Slavery/14th Amendment (Equal Rights under the law regardless of race)/15th Amendment (Extension of voting rights for all men)
Major Premise: All men are created equal.
Minor Premise: African-Americans are men.
Conclusion: Therefore, African-Americans are created equal = and endowed by their creator with certain inalienable rights (deductive).
Inductive
Argument: How strong or weak is the claim that black Americans were truly equal to white Americans after the Civil War?
Strength: Weak —> Very Weak
Martin Luther King, I Have a Dream Speech
- Argument from authority, legal, historical, religious
- Argument by analogy
- Impact of the speech, Civil Rights Act of 1964, Voting Rights Act of 1965
Deductive
Major Premise: The U.S. Constitution and the Declaration of Independence guarantee unalienable rights.
Minor Premise: All African Americans are citizens of the United States.
Conclusion: African Americans are guaranteed these rights.
Inductive
Argument: Did it achieve what MLK’s dream was?
Strength: Strong
*Test: List similarities between Lincoln and MLK:
- Argument by authority
- Logicians
- Master orators
- Equality
- Optimistic + Forward-looking
- Rebirth
- Rebirth
- National heroes and martyrs
Gettysburg, Pennsylvania