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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.

Vagueness

  • 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.
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