Ash
TNPer
Logic Lesson 4
Some Application
We'll now look at formal fallacies (and even then, only on the type of logic we've covered).
Wikipedia says that : "In philosophy, a formal fallacy is a pattern of reasoning that is always wrong. This is due to a flaw in the logical structure of the argument which renders the argument invalid. A formal fallacy is contrasted with an informal fallacy, which may have a valid logical form, but be false due to the characteristics of its premises, or its justification structure." (http://en.wikipedia.org/wiki/Formal_fallacy)
The first fallacy we'll look at is Affirming a Disjunct. This is known with a variety of names like :
Affirming One Disjunct
The Fallacy of the Alternative Syllogism
Asserting an Alternative
Improper Disjunctive Syllogism
This happens when the argument takes the form :
PREMISES
A or B
A
CONCLUSION
Therefore, it is not the case that B
Or in our symbolic form (where we'll use ? to mean "Therefore" , a logical assertion).
PREMISES
A V B
A
CONCLUSION
? ~B
Can you see what's wrong here? Wikipedia says "The fallacy lies in concluding that one disjunct must be false because the other disjunct is true; in fact they may both be true. This results from 'or' being defined inclusively rather than exclusively." There are occasions when this is valid and for those occasions visit : http://www.fallacyfiles.org/afonedis.html.
For the next few fallacies I'll lift a section from a wonderful site that you all should visit ((http://www.legalargument.net/argumentnotes.html#difficult)
We'll first consider the form of Affirming the Consequent by comparing it to the form of Modus Ponens. Modus Ponens takes the form:
PREMISES
If P then Q
P
CONCLUSION
Q
This is a deductively valid argument form. That means that if the premises ("If P, then Q,'" and "P") are true, then the conclusion ("Q") is necessarily true. Let's compare Modus Ponens to the form of Affirming The Consequent:
PREMISES
If P then Q
Q
CONCLUSION
P
This is a deductively invalid argument form. That is because the truth of the premises does not necessarily make the conclusion true. Consider this example:
PREMISES
If it rains, then the river rises.
The river rises.
CONCLUSION
It rains.
The truth of the premises does not guarantee the truth of the conclusion. It may be true that the river rises, but it may be false that it rains. Maybe the river rises because an upstream dam has broken sending more water into the river below. But that does not mean that it is raining when this happens.
Here is an-easy-to-understand example given by the Texas Court of Appeals: "The court says that reasonable doubt makes you hesitate to act; therefore, if you hesitate to act, you have a reasonable doubt. That is like saying, 'Pneumonia makes you cough; therefore, if you cough, you have pneumonia. This is the logical fallacy called 'affirming the consequent'." (Culton v. State (Tex. App. 2002) 95 S.W.3d 401, 405.) For examples of other recent cases where appellate court judges point out the fallacy of affirming the consequent see Gilliam v. Nevada Power Co. (9th Cir. 2007) 488 F.3d 1189, 1197, fn. 7; In re Stewart Foods, Inc. (4th Cir. 1995) 64 F.3d 141, 145, fn. 3; City of Green Ridge v. Kreisel (Mo. App. 2000) 25 S.W.3d 559, 563-564.)
An example of what happened in the High Court recently went something like this:
PREMISES
If Person A is a Senator then Person A can vote in General Elections.
Person A can vote in General Elections.
CONCLUSION
Person A is a Senator.
In fact, Person A may be a standard non-office holding citizen.
Youtube link for affirming the consequent
Now we'll consider Denying The Antecedent, and we will contrast it to the deductively valid argument form of Modus Tollens. Modus Tollens takes this form:
PREMISES
If P, then Q
Not Q
CONCLUSION
Not P
Denying The Antecedent takes this invalid form:
PREMISES
If P, then Q
Not P
CONCLUSION
Not Q
For examples of recent cases where appellate court judges point out the fallacy of denying the antecedent see e.g., Edwards v. Riverdale School Dist. (Or. App. 2008) 188 P.3d 317, 321; Agri Processor Co., Inc. v. N.L.R.B. (D.C. Cir. 2008) 514 F.3d 1, 6;Iams v. Daimler Chrysler Corp. (Ohio App. 2007) 883 N.E.2d 466, 478-479.
United States Supreme Court Justice Antonin Scalia is one of the most logically rigorous judges in American legal history. And while he is justly criticized by many, his critics could learn something about logical analysis from him. Judge Scalia is quite up on the subject of Denying The Antecedent, and we'll see another example in a later note. For now, I want to analyze one of his statements to get a better understanding of why Denying The Antecedent is a formal fallacy.
In Crawford v. Washington (2004) 541 U.S. 36 Justice Scalia countered an argument based upon Lee v. Illinois (1986) 476 U.S. 530. Scalia noted an argument in Lee about the admissibility of statements by criminal defendants and accomplices that are interlocked. Justice Scalia cited the following quotation from Lee as the holding in that case, "when the discrepancies between the statements are not insignificant, the codefendant's confession may not be admitted." (See Washington v. Crawford, supra, 541 U.S. at p. 58.) Next Scalia quoted the State of Washington's argument based upon Lee: "[t]he logical inference of this statement is that when the discrepancies between the statements are insignificant, then the codefendant's statement may be admitted." (See Washington v. Crawford, supra, 541 U.S. at pp. 58-59.) Washington's argument can be reconstructed as follows:
PREMISES
If the discrepancies between the statements are not insignificant, the codefendant's confession may not be admitted.
The discrepancies between the statements are insignificant.
CONCLUSION The codefendant's statements may be admitted.
Justice Scalia gave the following response to this Denying The Antecedent, "But this is merely a possible inference, not an inevitable one, and we do not draw it here." (Id. at p. 59.)
As the truth-table shows, this form allows for the case of an unreliable inference: line three contains all true premises with a false conclusion. Therefore, arguments that rely on this form are not valid! They will not work as deductive arguments.
The lesson is clear : be careful in your reasoning!
You can also you the techniques learnt in this course in legal drafting:
In informal speech, people do not always honor logic. Drafters try to honor logic, but when
they use complex logical constructions, they may confuse readers or even themselves.
A common problem involves using negatives like "not" with conjunctions like "and" or
disjunctions like "or". In logic textbooks you will find,
not(A or B) = (not A) and (not B).
Similarly,
not(A and B) = (not A) or (not B).
For drafters, that means,
DO NOT WRITE:
The contractor shall not
(a) eat spinach, and
(b) drink beer.
IF YOU REALLY MEAN:
(a) The contractor shall not eat spinach.
(b) The contractor shall not drink beer.
A contractor who eats spinach without beer can argue it is in compliance with the first
provision. The contractor is clearly in violation of the second. If you want to separately prohibit each item in a list, use "or" ...
The contractor shall not
(a) each spinach, or
(b) drink beer.
... or repeat the "not" and use "and".
The contractor shall
(a) not eat spinach, and
(b) not drink beer.
Not every reader of your draft will intuitively grasp the logical fine points of combining "not"
with a conjunction or disjunction. An alternative approach is to avoid the use of "and" or "or":
The contractor shall not do any of the following:
(a) eat spinach.
(b) drink beer.
Now, there is a whole bunch of informal fallacies. For a discussion on these (and this is required reading) see : http://www.unc.edu/~ramckinn/Documents/NealRameeGuide.pdf
For a general overview of formal and informal fallacies, see: http://www.logicallyfallacious.com/index.php/logical-fallacies
