The Little Blue Reasoning Book - Brandon Royal [48]
(Parents conversing with their doctor): “Because we already have three boys, the odds greatly favor our having a baby girl.”
The result of one birth has absolutely no influence (almost no influence, biologically speaking) on the gender of future offspring. The odds are still 50-50.
Fallacy of False Precision
The fallacy of false precision consists in making a claim with a level of mathematical precision that is likely impossible to obtain.
“One out of every four people in Shakespeare’s day did not actually like Shakespeare’s plays.”
It is unlikely that such a precise figure could be obtained, particularly during that time period.
4) Fallacies Found in Deductive Logic
Fallacy of Affirming the Consequent
The fallacy of affirming the consequent assumes that in an “If A, then B” scenario, the opposite, “If B, then A,” is also true. This is sometimes called the fallacy of false conversion.
“Whenever I go on vacation, I feel relaxed. I feel relaxed, so I must be on vacation.”
Maybe the pub sells a lot of beer all week long, all year round.
Fallacy of Denying the Antecedent
The fallacy of denying the antecedent assumes that in an “If A, then B” scenario, it is also true that “If not A, then not B.”
“Whenever it rains the ground gets wet. It didn’t rain last night so the ground can’t be wet.”
For all we know, the sprinkler system may have been turned on, causing the ground to be wet.
For a review of both of the preceding fallacies, refer to the discussion of “If … then” type statements in chapter 5.
APPENDIX III – AVOIDING IMPROPER INFERENCES
Developing the mindset to master critical reasoning requires knowing where to “draw the line” between inferable and non-inferable statements. First, let’s contrast the terms inference and assumption. An assumption is an unstated premise which is an integral component of any argument — it is the missing link needed to make an argument work. An inference is a logical extension — a logically inferable statement based on an argument, statement, or passage.
In everyday life we make loose inferences. We make inferences based on what is “most probably true.” For example, the statement, “It’s been raining a lot lately,” begs the inference “umbrella sales are up.” The statement, “The weather’s getting colder,” begs the inference that “ice cream sales are down.” But these are not logically inferable. What is “logically inferable” is a much firmer, tighter noose than what is “most probably true.”
Take the following argument: “Buy our product. It’s the cheapest in the market.” The conclusion is “buy our product.” The evidence is “it’s the cheapest in the market.” The assumption is “price is the dominant factor in a purchasing decision.” The statement “other products in the market are more expensive” is not an assumption but an inference — a logically inferable statement based on the argument.
Problem 40: Little Italy
Antonio is a well-known Italian connoisseur operating the Little Italy restaurant in Devon City. Not only do three out of every four food and beverage consultants recommend his Italian restaurant but a survey by the city’s Food and Beverage Association shows that his restaurant is unsurpassed by any other Italian restaurant in the city. The proof is in the eating. Antonio’s customers prefer his style of Italian cooking by a ratio of 2 to 1.
Which of the statements below are logically inferable based on the brief passage about the Little Italy restaurant above?
Tip #50: The word “unsurpassed,” both technically and legally, does not mean “best.” It is possible that all products, competitors, etc., could be tied at number one and yet all could claim to be unsurpassed.
1. Antonio’s restaurant Little Italy is regarded by the city’s Food and Beverage Association as the best Italian