- "The reason why most bachelors are timid is that their mothers were domineering." (The illogical reasoner attempts to explain why most bachelors are timid, but it can be shown that his generalization is based on two bachelors he once knew, both of whom were timid. This form of evidence is often called "anecdotal evidence".)
- "The reason why I get four or better on my evaluations is that my students love me." (This is a fallacy if the evaluations which score four or less are discarded on the grounds that the students did not understand the question.)
- "The reason why Alberta has the lowest tuition in Canada is that tuition hikes have lagged behind other provinces." (Lower tuitions in three other provinces - Quebec, Newfoundland and Nova Scotia - were dismissed as "special cases" [again this is an actual example])
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A Guide to Logical Fallacies
- Truths+Propositions (3)
- Logical Operators (6)
- Fallacies of Distraction (5)
- Appeals to Motive (5)
- Changing the Subject (5)
- Inductive Fallacies (6)
- Statistical Confusion (3)
- Causal Fallacies (6)
- Missing the Point (4)
- Fallacies of Ambiguity (4)
- Category Errors (4)
- Non Sequitur (4)
- Syllogistic Errors (7)
- Fallacies of Explanation (6)
- Fallacies of Definition (6)
An explanation is a form of reasoning which attempts to answer the question "why?" For example, it is with an explanation that we answer questions such as, "Why is the sky blue?" Explanation can be based on a scientific theory, on agency, or purpose (teleology). In this case, the explanation of why the sky is blue might begin in terms of the composition of the sky and theories of reflection. Of course, blue, as we commonly refer to it, does not refer to a wavelength of light but to that color we see in our mind's eye (qualia) when we look at the sky, a blueberry, or iodine. And the phenomenelogical answer to why the sky appears blue to our minds will be of a different sort. If one is open to the idea that the universe was created or designed for a purpose or with intentionality, one might also venture an answer in terms of teological or aesthetics.
An explanation is intended to explain why some phenomenon happens. In this case, there is evidence that the phenomenon occurred, but it is trumped up, biased or ad hoc evidence.
Examples:
Proof: Identify the term being defined. Identify the conditions in the definition. Find an item which is an instance of the term but does not meet the conditions.
An explanation is intended to explain who some phenomenon happens. The explanation is fallacious if the phenomenon does not actually happen or if there is no evidence that it does happen.
Examples:
- The reason why most bachelors are timid is that their mothers were domineering. (This attempts to explain why most bachelors are timid. However, it is not the case that most bachelors are timid.)
- John went to the store because he wanted to see Maria. (This is a fallacy if, in fact, John went to the library.)
- The reason why most people oppose the strike is that they are afraid of losing their jobs. (This attempts to explain why workers oppose the strike. But suppose they just voted to continue the strike, Then in fact, they don't oppose the strike. [This sounds made up, but it actually happened.])
Proof: Identify the phenomenon which is being explained. Show that the evidence advanced to support the existence of the phenomenon was manipulated in some way.
The theory advanced to explain why some phenomen occurs cannot be tested. We test a theory by means of its predictions. For example, a theory may predict that light bends under certain conditions, or that a liquid will change colour if sprayed with acid, or that a psychotic person will respond badly to particular stimuli. If the predicted event fails to occur, then this is evidence against the theory. A thoery cannot be tested when it makes no predictions. It is also untestable when it predicts events which would occur whether or not the theory were true.
Examples:
- Aircraft in the mid-Atlantic disappear because of the effect of the Bermuda Triangle, a force so subtle it cannot be measured on any instrument. (The force of the Bermuda Triangle has no effect other than the occasional downing of aircraft. The only possible prediction is that more aircraft will be lost. But this is likely to happen whether or not the theory is true.)
- I won the lottery because my psychic aura made me win. (The way to test this theory to try it again. But the person responds that her aura worked for that one case only. There is thus no way to determine whether the win was the result of an aura of of luck.)
- NyQuil makes you go to sleep because it has a dormative formula. (When pressed, the manufacturers define a "dormative formula" as "something which makes you sleep". To test this theory, we would find something else which contains the domative formular and see if makes you go to sleep. But how do we find something else which contains the dormative formula? We look for things which make you go to sleep. But we could predict that things which make you sleep will make you sleep, no matter what the theory says. The theory is empty.)
Proof: Identify the theory. Show that it makes no predictions, or that the predictions it does make cannot ever be wrong, even if the theory is false.
The theory doesn't explain anything other than the phenomenon it explains.
Examples:
- My cat likes tuna because she's a cat. (This theory asserts only that cats like tuna, without explaining why cats like tuna. It thus does not explain why my cat likes tuna.)
- Ronald Reagan was militaristic because he was American. (True, he was American, but what was it about being American that made him militaristic? What caused him to act in this way? The theory does not tell us, and hence, does not offer a good explanation.
- You're just saying that because you belong to the union. (This attempt at dismissal tries to explain your behaviour as frivolous. However, it fails because it is not an explanation at all. Suppose everyone in the union were to say that. Then what? We have to get deeper - we have to ask why they would say that - before we can decide that what they are saying is frivolous.)
Proof: Identify the theory and the phenomenon it explains. Show that the theory does not explain anything else. Argue that theories which explain only one phenomenon are likely to be incomplete, at best.
Theories explain phenomena by appealing to some underlying cause or phenomena. Theories which do not appeal to an underlying cause, and instead simply appeal to membership in a category, commit the fallacy of limited depth.
Examples:
- A society is free if and only if liberty is maximized and people are required to take responsibility for their actions. (Definitions of this sort are fairly common, especially on the internet. However, if a person is required to do something, then that person's liberty is not maximized.)
- People are eligible to apply for a learner's permit (to drive) if they have (a) no previous driving experience, (b) access to a vehicle, and (c) experience operating a motor vehicle. (A person cannot have experience operating a motor vehicle if they have no previous driving experience.)
Proof: Theories of this sort attempt to explain a phenomenon by showing that it is part of a category of similar phenomenon. Accept this, then press for an explanation of the wider category of phenomenon. Argue that a theory refers to a cause, not a classification.
Propositions and their truth values are two elemental ingredients of logical reasoning.
A proposition is an assertion that something is the case. We use sentences to express propositions. A sentence may be made of black ink, be on a page, and be four inches long. But the content of the sentence cannot be found on the page. The proposition it expresses appears to be a non-physical entity which can be in the mind.
Examples:
- The following sentences express the same proposition:
- Il pleut.
- Esta lloviendo.
- It is raining.
- Es regnet.
- The following sentences express the same proposition:
- John loves Mary.
- Mary is loved by John.
Proof: It makes sense to think of a proposition as being the meaning of a sentence. The meaning of a sentence has several components:
- denotation: the state of affairs in the world that the sentence holds to be the case.
- connotation: the feelings, ideas or emotions evoked in the reader by the sentence.
- emphasis: the relative importance the writer ascribes to different elements in the sentence.
For example, in the sentence "The fire raged down the hill" the denotation of the sentence is the assertion that there is a fire buring on a hill and moving down the hill. The connotation is that this is something to be feared (the word "rage" implies anger or danger). The emphasis in this sentence is the fire itself; had we written the same sentence "Down the hill raged the fire" the emphasis would be on the hill.
Philosophers argue a lot about meaning. Some say that the meaning is the denotation only, some say it is a combination of denotation and connotation only, while others say it is all three.
A proposition can have the following truth values: true or false. "P" is true if and only if P. "P" is false if and only if not P. In other words, a proposition is true if and only if what it says about the world is in fact the way the world is. Though this correspondence view of truth has long been questioned, and especially so in these postmodern times, it remains our common sense, everyday understanding of truth.
Examples:
- The proposition "Snow is white" is true if and only if snow is white.
- The proposition "Snow is white" is false if and only if snow is not white.
A logical operator joins two propositions to form a new, complex, proposition. (If you have not read about propositions, you should do so now. Follow the Next links until you return to this page.) The truth value of the new proposition is determined by the truth values of the two propositions being joined and by the operator that joins them.
Any two propositions P and Q can be conjoined, producing the new, complex, proposition:
P and Q
The proposition P and Q is true if and only if both P and Q are true. It is false otherwise.
Examples:
|
P |
Q | P and Q |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
Any two propositions P and Q can be disjoined, producing the new, complex, proposition:
P or Q
The proposition P and Q is true if and only if either P or Q are true. It is false only if both P and Q are false.
Examples:
|
P |
Q | P or Q |
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
Any two propositions P and Q can be joined by a conditional operator, producing the new, complex, proposition:
If P then Q
The proposition If P then Q is true if and only if either P is false or Q is true. It is false only when P is true and Q is false.
Examples:
|
P |
Q | If P then Q |
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
Proof: A special conditional occurs if we flip the P and Q around: we get if Q then P, which is the same as saying P only if Q.
Any proposition P can be converted into its negation with a negation operator, producing the new, complex, proposition:
Not P
The proposition Not P is true if and only if P is false. It is false only if P is true. The truth table for Not P is as follows:
Examples:
|
P |
Q | Not P |
| T | T | F |
| T | F | F |
| F | T | T |
| F | F | T |
Proof: It does not matter whether Q is true or false. Every time, Not P is true if P is false, and false if P is true.
Any two propositions P and Q can be joined with the biconditional operator, producing the new, complex, proposition:
P if and only if Q
The proposition P if and only if Q is true if and only if both P and Q are true, or if both P and Q are false. It is false only when one of them is true and the other false.
Examples:
|
P |
Q | Not P if and only if Q |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | T |
Proof: P if and only if Q is the same as:
( If P then Q ) and ( P only if Q ). This is like saying:
( If P then Q ) and ( If Q then P ).
</dl>
The biconditional is a complex operator, built out of simpler operators. Think of it this way:
<dl>The if and only if operator plays a special role in definitions. When we say P if and only if q, we are saying that P says the same thing as Q.