Author Archive

Fallacies of Vacuity

Circular Reasoning

  • To remember what a circular argument is, think of a P.I.E.
  • In circular arguments, a Premise Is Equivalent to the conclusion.
  • Definition: Circular Argument
  • An argument is circular if and only if there is a premise of the argument that is equivalent to, or simply is the conclusion of that argument.

Examples of Circular Arguments:

  • 1. Drugs that make people hallucinate should be banned.
  • Therefore, hallucinogenic drugs should be banned.
  • 2. Individuals that use the threat of violence in order to make others succumb to their demands should be tortured.
  • Therefore, terrorists should be tortured.

Question Begging

  • To remember what question begging is, think of a P.A.C.
  • In question begging arguments, Premises Assume Conclusions.
  • Definition: Question Begging
  • An argument is question begging if and only if there is a premise of the argument that assumes the conclusion of that argument without any independent reasons for accepting that premise.

Example of Begging the Question

  • Background: a debate over whether alcoholic beverages should be banned.
  • Foods and beverages that make people intoxicated should be banned.
  • Therefore, alcoholic beverages should be banned.


  • To remember what self-sealing is, think of N.E.A.T.
  • For self-sealing arguments, there is No Evidence Against Them.
  • Definition: Self-Sealing
  • An argument (position) is self-sealing if and only if no evidence can possibly be brought against it no matter what.

Three Ways to be Self-Sealing

  • 1. By universal discounting.
  • 2. By going upstairs.
  • 3. By definition.

Universal Discounting

  • dismiss every possible objection, usually in an ad hoc or arbitrary way.

Example of Self-Sealing: Universal Discounting

  • Conspiracy Theorists:
  • Suppose someone thinks that a select group of universities controls all NCAA football.
  • As evidence in support of their position, they point to the select group of universities that get ranked in the top ten year after year despite not having won a national championship within the last decade.
  • Of course, that select group has allowed some non-members to be ranked in the top ten. For example, they let Boise State into the top ten. However, that’s just to conceal their total domination over NCAA football.

Going Upstairs

  • dismiss objections as an indication that the objector is not in a position to grasp the argument, or that by objecting, the objector actually provides evidence that the argument is on the right track.

Example of Self-Sealing: Going Upstairs

  • Psychoanalysis
  • Suppose that Joe meets Fred the Freudian.
  • Fred tells Joe, “you want to sleep with your mother and kill your father.”
  • Joe replies, “That’s absurd!”
  • Fred responds, “You just aren’t aware of your Oedipus complex yet.”
  • Fred tells Joe, “all of this just shows that you really do want to sleep with your mother and kill your father.”
  • Joe replies, “Tell that to my wife!”
  • Fred responds, “maybe someday you’ll come to terms with your Oedipus complex, but your responses indicate that today is definitely not that day.”

By Definition

  • Make a substantive claim. Then, cleverly redefine a crucial term in a way that guarantees that the claim will be true. By doing so, this deprives the claim of any substantive content.

Example of Self-Sealing: By Definition

  • Selfishness
  • Suppose that someone claims that all human actions are selfish.
  • This is an interesting claim, but let’s try to think of some counterexamples involving self-sacrifice.
  • In response to proposed counterexamples based on self-sacrifice, a defender of the claim that all human actions are selfish might respond by saying that by performing an act of self-sacrifice, what one wants to do is to help others. Hence, even acts of self-sacrifice are ultimately selfish.


Categories: Lectures

Fallacies of Vagueness Notes

Fallacies Lecture 1: Fallacies of Vagueness.

What is a Fallacy?

  • A Fallacy is simply an inference that is defective in some way.
  • It is important to study fallacies because many fallacious arguments seem persuasive and can fool us into thinking that they are good arguments.
  • Some types of defective arguments are repeated so often that they have been identified and given particular names.


  • A word is vague when there are borderline cases where it is unclear whether the term applies or not.
  • Specifically, issues of vagueness often occur when a term applies on a continuum of small changes.
  • Consider a term like ‘old’:
  • We can divide up age as finely as we desire from the broad categories of year and month all the way down to very fine categories of minutes and seconds.
  • A clear case of old is Sean Connery at 81.
  • A clear case of not old is Justin Bieber at 17.
  • It is unclear whether Brad Pitt, at 47, old or not.

Sorites Argument

  • The Sorites argument is an argument that draws upon the borderline cases of vague terms
  • The name comes from an ancient form of the argument about heaps of sand. (soros = heap)
  • Essentially, the argument claimed that, no matter how many grains of sand you had, they would not be a heap (of sand).
  • Consider this argument about whether a room is cold:

1. A room at 100 °F is not cold.

2. If a room at 100 °F is not cold, then a room at 99 °F is not cold.    

3. Therefore, a room at 99 °F is not cold

  • Given the conclusion of the last argument, this argument now seems plausible:

4. A room at 99 °F is not cold.

5. If a room at 99 °F is not cold, then a room at 98 °F is not cold.

6. Therefore, a room at 98 °F is not cold.

  • We can generalize the above argument into this general form:
  1. A room at 100 °F is not cold.
  2. For any number, n, if a room at n °F is not cold, then a room at n – 1 °F is not cold.
  3. Therefore, a room at any temperature is not cold.

Slippery Slope

  • One type of fallacy that we will be examining is called a Slippery Slope.
  • Each form of the Slippery Slope fallacy exploits a similar form of reasoning to the Sorites argument.
  • There are three forms of the Slippery Slope:
  • Conceptual Slippery Slope
  • Fairness Slippery Slope
  • Causal Slippery Slope

Conceptual Slippery Slope

  • A Conceptual Slippery Slope concludes that there really is no difference between things on opposite ends of a continuum due to vagueness in the middle area between them.
  • This can be used to argue that there is no difference between:
  • Living and non-living things
  • People who are sane and people who are insane
  • Amateur athletes and professional athletes.
  • Consider this example:

A human egg one minute after fertilization is not very different from what it is one minute later, or one minute after that, and so on.  Thus, there is really no difference between just-fertilized eggs and adult humans.

  • More formally, the argument is:

1. For any minute after fertilization, t, there is no significant difference between the fertilized egg at t and the same fertilized egg at t + 1.

2. Therefore, there really is no difference between just-fertilized eggs and adult humans.

  • When we looked at the sorites argument, there was an additional premise in the argument.
  • Similarly, there are two additional principles that are needed for this argument to be a good argument:
  • We should not draw a distinction between things that are not significantly different.
  • If A is not significantly different from B and B is not significantly different from C, then A is not significantly different from C.
  • We should not draw a distinction between things that are not significantly different.
  • In some cases, it does make sense to draw a distinction between things that are not significantly different.
  • For example:
  • Driving at the speed limit and one mile per hour over the speed limit.
  • Drinking when you are 20 and 11 months and when you are 21.
  • If A is not significantly different from B and B is not significantly different from C, then A is not significantly different from C.
  • This can cause troubles if you repeat it like in the sorites argument.
  • Although one penny is not significantly different than two pennies, it is significantly different from one billion pennies.

Fairness Slippery Slope

  • A fairness slippery slope concludes that there should not be a line drawn that produces very different consequences assigned to either side of the line when there really isn’t much difference between what is on one side and what is on the other side.
  • This is different from the conceptual slippery slope argument because it concedes that real differences do exist on either side of the line (even though they can be very small).
  • Consider this example:

Since no moment in the continuum of development between an egg and a baby is especially significant, it is not fair to grant a right to life to a baby unless one grants the same right to every fertilized egg.

  • More formally, the argument is:

1. For any moment after the fertilization of an egg, there is no especially significant difference in development immediately before and after that moment.

2. Therefore, if we were to draw any developmental line as to when an entity is conferred the right to life, it would be unfair to the entities that are just on the other side of that line.

3. Therefore, it is not fair to grant a right to life to a baby unless one grants the same right to every fertilized egg.

  • The way that you can avoid a fairness slippery slope argument is to provide an additional argument saying that there needs to be a line drawn, even if there isn’t much difference on either side of the line and the placement seems arbitrary.
  • Some examples:
  • There really should be a speed limit on most streets.
  • It seems reasonable to have a legal drinking age.
  • There should be a difference between passing and failing.

Causal Slippery Slope

  • A causal slippery slope argument takes a claimed relationship between a seemingly innocent initial step and a undesirable consequence as a reason why the initial step should not be taken.
  • This differs from the other forms of slippery slope because it deals with a chain of similar events instead of small differences along a continuum.
  • Consider this example:
  • You can eat that chocolate chip cookie if you want, but I say you’re asking for trouble.  Next you’ll be eating ice cream, then hot fudge sundaes.  Soon it’ll be double cheeseburgers, fried chicken, and layer cakes!  Stroke and a heart attack are waiting for you without a doubt.
  • More formally, the argument is:

1. If you eat that chocolate chip cookie, then you’ll start eating ice cream and hot fudge sundaes.

2. If you start eating ice cream and hot fudge sundaes, then you’ll start eating double cheeseburgers, fried chicken, and layer cakes.

3. If you start eating double cheeseburgers, fried chicken, and layer cakes, then you’ll get a stroke and a heart attack

4. A stroke or heart attack is really bad.

5. Therefore, you shouldn’t eat that cookie.

  • The general form of the argument is:

1. Taking a seemingly innocent first step will lead to a chain of events ending with consequence X.

2. Consequence X is bad.

3. Therefore, you should not take the seemingly innocent first step.

  • There are three questions about an argument that has the form of a causal slippery slope argument that all have to be answered with “yes” or the causal slippery slope argument is fallacious:
  • Are any of the claimed effects really very bad?
  • Are any of these effects really very likely?
  • Do these dangers outweigh all the benefits of what is being criticized.
Categories: Uncategorized

Lecture 10/18: Taking Chances

October 18, 2011 1 comment

Notes on taking chances

Guy using fallacious reasoning.

Probability Theory (Chapter Ten)
I. Gambler’s fallacy and the law of large numbers
A. Examples
B. Law of Large numbers:  The difference between the observed value of a sample and its true value will diminish as the number of observations in the sample increases.


O: after a billion flips of a coin, we counted 48% heads, 52% tails.
H1: Fair coin
H2: coin is weighted towards tails

Which hypothesis is predicted by the law of large numbers?
answer:  H2, due to the Law of Large Numbers

O: after ten flips of a coin, we counted 6 heads and 4 tails
H1: Fair coin
H2: Coin is weighted towards heads?

Which hypothesis is predicted by the law of large numbers?

answer: predictively equivalent (H1 = H2)

Random sequences:
A. 1, 1, 1, 1, 1, 1, 2, 1, 1, 2
B. 1, 2, 1, 2, 2, 1, 2, 1, 1, 2
C. 1, 2, 2, 2, 2, 1, 2, 1, 1, 2
D. 1, 2, 2, 2, 1, 2, 1, 2, 2, 1

Which one was generated by a “randomizer” ? A—form.htm

Question: Suppose you flip a fair coin three heads in a row. What is the
probability that a head will come up a fourth time?
answer: 1/2

...because it's FAIR.

C. Misapplication of law of large numbers
Example 1 and 2:
law of large numbers does not support the idea that a gambler will experience runs of good luck after a run of bad luck.  For coins and casino machines the probability of any outcome is independent of the number of trails you have experienced.  All bets are off if the trials are dependent rather than fair (but then no one would play at such a casino where the outcomes are rigged).

D. Examples outside of gambling

– Hot streaks in basketball:  give the ball to the buy who has made a bunch of shots in a row.  But, statistically, hitting three or shots in a row is statistically insignificant.

– “market beaters” in fund managing:  you swap out of your underperforming funds and into the hot fund.  But, given that the market is pretty efficient, past performance is not a good guide to future performance (there will be streaks for any fund over long enough period of time).

II. Common judgements and their fallacious foundations

The Path of Folly.

A. Confirmation bias:  you are convinced beforehand that a stock picker or basketball player can “get hot” (due to media attention or your own feelings about the person).  So, you ignore the fact that streaks are likely in the short term (given law of large numbers).

B. Over optimism
How often does a college basketball team that is trailing at halftime come back to win?
answer: (less than 20%) (people typically guess 30%-60%)
data: 3300 games in Nov-Jan.

Why are we often wrong?
We are optimistic and media gives most attention to comeback victories.

C. Irrationality due to desire to win
Suppose 50% chance of scoring on a two-point shot. 33% for a three-point shot.  A team is down by two points and it has time for one last shot. What play should the coach call?
answer: if the team makes the two-point shot, it still has to play overtime, where its chances of winning are 50%. Have to win on two 50% gambles = 25%
overall. So, should go for 3-points.

Apply this to stocks: many investors shy away from stocks because of the potential for short-term sting (like the sting of losing from a 3-point shot at the
buzzer). But, in the long run stocks are best investment (over its history).

D. Representative heuristic
question #1 on Tversky teasers.
People tend to say that Hand #2 is much more unlikely than Hand #1. But, each is equally likely in a fair game.
Representative heuristic: Hand #2 is more unimpressive so it is more likely to represent an ordinary hand.

question #2 on “teasers”
89% of students said that it is more likely that Linda was both a bank teller and a feminist than that she was simply a bank teller.
can’t be true: the probability of two things being true can never be higher than the probability that just one of them is true (one is true if both are).


Welcome to the blog

This is the official blog corresponding to Philosophy 1200 Logic and Reasoning for the Fall of 2011.