Continued : from Halpern's "Thought and Knowledge"
Logic Inductive Reasoning: observations are collected that support or suggest a conclusion. It is a way of projecting information from known examples to the unknown or in other words, inferring the general from the particular. If every person we have met has one head, we can infer that everyone in the world has one head. If one ever finds out someone who has more than one head, then the conclusion will be proved wrong. Thus with inductive reasoning, one cannot prove (with absolute certainty) that the conclusion or hypothesis is correct, but can disprove it.
Deductive Reasoning: This type of reasoning proceeds from some assumptions/facts/beliefs and inferences are drawn in particular cases based on the starting hypothesis.
A distinction between inductive and deductive reasoning may not be particularly useful to describe real life thinking behavior. In everyday contexts, we switch from inductive to deductive reasoning in course of our thinking.
Illicit Conversion Consider the following statements from a logical point of view
a) If she is rich, she wears diamonds. She is rich. Therefore she wears diamonds.
b) If she is rich, she wears diamonds. She is not wearing diamonds. Therefore she is not rich.
c) If she is rich, she wears diamonds. She is wearing diamonds. Therefore she is rich.
d) If she is rich, she wears diamonds. She is not rich. Therefore she is not wearing diamonds.
Which of the four conclusions are valid given the premise? Please take a moment to figure this out.
One of the common logical thinking errors is called illicit conversion. When it is stated that
"if {A} then {B}" is true, we automatically assume the reciprocal relationship "if {B} then {A}" is true.
A tree diagram is helpful. From the start point there are 2 nodes - "rich" and "not rich". The "rich" node, there is a connection to "wears diamonds". Since it is not stated that "if she is rich,
sometimes she wears diamonds, we go with "if she is rich,
always she wears diamonds." So there is no branch from the "rich" node to "does not wear diamonds".
The "not rich" node will have branches to both "wears diamonds" and "does not wear diamonds" since we are not told anything about this condition.
We can conclude
a) and b) are valid.
c) and d) are not valid.
In real world examples, we need to think critically to figure out whether we are falling prey to illicit conversions. Take for example an advertisement where some healthy centenarian people in a remote location are shown and we are told that they eat yogurt. (Assume for the moment that the previous statement is true). The advertisers are hoping that we will draw the conclusion that eating yogurt is good for health and longevity.
Take an example from a legal context. A person is being accused of murder. He has an alibi from after 11PM. Now the prosecutor is trying to prove through coroner's reports that the murder happened before 11PM - say at 10:30 to convince the jury that the accused is guilty. But even if the murder happened at 10:30, by itself does it say anything conclusive about the guilt of the accused?
Confirmation BiasThe
confirmation bias has been already covered in other threads, but here is an interesting example which (may) illustrate this in a different way.
Four cards are lying face up on a table in front of you. Every card has a letter on one side and a number on the other. Your task is to decide if the following rule is true "If a card has a vowel on one side, then it has an even number on the other side". Which card or cards would you need to turn over to find out whether the rule is true or false. You may turn over only the minimum number necessary to determine if this rule is true.
The four cards are
A D 4 7
If interested, take a few minutes to think about the problem.
Most people answer "A only" or "A and 4" according to Halpern. But the right answer is "A and 7".
Syllogisms and Missing Quantifiers Syllogisms are commonly encountered logic problems. A syllogism usually consists of two statements called premises and a third statement called conclusion. In categorical syllogisms, quantifiers (eg all, some etc) are used in the premises and conclusion. The task is to determine if the conclusion follows logically from the premises.
The typical way to check for validity of categorical syllogisms are through Venn/circle diagrams. G00gling syllogisms and Venn diagram will bring up pages illustrating the formal process.
Example
1. Premise 1 : All people on welfare are poor.
Premise 2: Some poor people are dishonest
Conclusion: Some people on welfare are dishonest
If one can work through the various combinations and find one case where the conclusion is not valid (though it could be valid for most cases), then the syllogism is said to be not valid.
In the above example, all poor people are not on welfare. It is possible for some poor people who are dishonest to not be on welfare. This would make the conclusion logically invalid.
In real life, it is not usually possible to throw Venn diagrams at a syllogism, but working on such tools is helpful in exercizing the critical thinking muscle.
When syllogisms are found in everyday use, the quantifiers are often missing. Sometimes this absence is deliberate in the hope that you will infer one particular quantifier (eg assume "all" instead of the more truthful "some"). Here is an example of categorical reasoning being used in a presidential campaign. A presidential candidate was questioned about his extramarital affairs. He responded this way: I have not been perfect in my private life, but we have had great presidents who were also not perfect in their private lives.
Let us convert this to a categorical syllogism:
Premise1: I am not perfect (in my private life)
Premise 2: Some great presidents were not perfect (in their private lives)
Conclusion: I will be a great president (implied)
In its abstract form this becomes:
A=I (the speaker)
B=people who are not perfect
C=great presidents
or
All A are B
Some C are B
All A are (will be ) C
The conclusion he wanted listeners to draw is that he would also be a great president.
One important factor to keep in mind is that in real life, few things are known for certain. So reasoning is usually probabilistic.
When we reason in everyday contexts, we consider the strength and likelihood of evidence (premises) that support a conclusion and often decide if a conclusion is probable or improbable, not just merely valid or invalid.
Another important point to keep in mind is the
distinction between validity of an argument and truth . Validity refers to a form of argument and is unrelated to content. If a conclusion necessarily follows from the premises, then it is valid. But it may not be true. One should take care to examine if the premises given are true or if significant facts are omitted. A conclusion is valid if it follows from the premises but good reasoning from poor premises will not produce realistic results.
Halpern provides a real life example of a revisionist speaker attempting to convince a group of young adults that slavery in the US was not so bad.
First, listeners were asked if they agreed that people do not harm valuable property. Most nodded in agreement. Then they were told that slaves were valuable property; therefore slave owners took good care of their slaves. The speaker went on to say that "most slaves enjoyed being taken care of", so slavery was not as bad as we had been led to believe. The scary part of this scene was that there were many listeners who seemed to be considering this ludicrous idea or could not figure out what was wrong with it. Can you?
I hope that you are outraged at this attempt to rewrite a disgraceful part of US history and to use what seems like reasoning to do it. It is true that most people do not harm valuable property, but there are massive amounts of historical evidence that slaves were often subjected to the most brutal and dehumanizing conditions. The speaker left out far too many relevant facts to make this conclusion logical. There was a seductiveness to the speaker's "logic" but it was patently wrong.
This brings us to the next topic, analyzing an argument.
Anatomy of an Argument An argument (used in the sense of giving reasons) consists of premises and conclusion. Arguments may also contain assumptions and qualifiers.
Premises are the reasons that support a conclusion- or the "why" part of an argument. To identify a premise in everyday language, it is useful to look for premise markers - though a premise marker is not necessarily always followed by a premise. Some common premise markers are
because, for, if, given that, as shown by, seeing that, whereas .....
Conclusion is the purpose or the "what" of an argument. It is the point of view being supported or defended with the premises. Some common conclusion indicators are
therefore, hence, so, thus, consequently, as a result, it is clear ......
Assumption is a statement for which no proof or evidence is offered. Assumptions are more often implied or unstated.
Take the example of a car advertisement:
More people have bought LaBaroness automobiles than any other American car.
The implied statement is that if more people bought this car, then it must be better in some way. The assumption (unstated) is that when large number of consumers make a choice, it is good. There is no justification for this assumption. The implied conclusion is that buying this automobile would be a good choice.
Qualifiers are constraints or restrictions put on the conclusion. It states the conditions under which the conclusion is supported. Consider the paragraph below
It is important that we have some indicators of what and how much students are learning in college. For this reason, a national college-level testing program is needed. However, if the national assessment is not related to the subjects taught in the college curriculum, then it will not be a valid measure of college-level learning.
Let's dissect the paragraph into its component parts:
The conclusion is : a national college level test is needed.
A premise is: It is important that we have some indicators of what and how much students are learning in college
An unstated assumption is: A national college level test is a good way to indicate what students are learning.
A qualifier is: the conclusion is valid only when the assessment is related to the curriculum.
Arguments can have convergent structure where multiple premises independently support the conclusion. eg
"Be sure to get plenty of aerobic exercise because it helps build a strong cardiovascular system, helps brain function and lowers the resting heart rate."
Arguments can also have a chained structure where one premise is the reason for a second premise which is the reason for a conclusion. eg
"It is important that you work through all of the problems in the workbook because the problems will help you to learn the skills of critical thinking. We can conclude that working the problems in the workbook will help you to learn the skills based on research that shows that active learning promotes long-term retention."
For arguments having a linked structure, the conclusion is only as strong as the weakest subargument.
For complex arguments with multiple premises and conclusions with interlinks, a simple diagramming approach is suggested to check the validity and strength of the argument.
Evaluating the strength of an argument Arguments are evaluated by how well they meet three criteria.
1) The first criterion concerns the acceptability and the consistency of premises. This often requires personal research, looking at what relevant, credible experts have to say on the topic - evaluating both the source of the information and the information itself. It is useful to make an effort to distinguish between opinions, reasoned judgments and facts.
2) The second criterion concerns the relationship between the premises and the conclusion. Do the premises directly support the conclusion?
Take an example
(a)M and E had a fight this morning. (b) In fact, they fight every day. (c) E is moving out of the apartment and plans to move in with his mother. (d) M has made an appointment with a divorce attorney. Therefore they plan to get a divorce.
Here there are 4 premises (a), (b), (c) and (d) and the conclusion. (a) can be labeled as the weakest by itself as far as supporting the conclusion goes. (b), (c) and (d) get progressively stronger as premises supporting the conclusion.
3) The third criterion concerns the unseen part of the argument. What is missing that could change the conclusion? This is related to the strength of relevant counter arguments that can be found. Going back to the previous revisionist speaker hinting that slavery was not that bad, one can find huge missing portions in facts and counter arguments that blows the argument out of the water.
To assess the soundness of arguments, one has to look out for biases which may lead to rationalization and selectively cherry picking data and analysis preferring a particular conclusion. Halpern sites a study (Lord, Ross and Lepper, 1979) where students were given an essay to write where they argued for or against some controversial issue like abortion or capital punishment. The students were then given the results of experimental studies that supported a "middle of the road" point of view. But after reading the balanced review, students who had written "for" the issue concluded that the objectively neutral paper supported their "pro" position. The students who had written against the issue concluded that the neutral paper supported their "con" position. Instead of bringing the two sides closer, the balanced paper drove them further apart.
Halpern states that the above finding has been repeated in different studies.
So just telling people that we tend to judge information that we favor as stronger than information that we oppose does not work to correct that bias. Is it any wonder why it is so difficult to get people to assess controversial issues in a fair-minded manner? Because we are not aware that we judge reasons in a way that supports what we believe to be true, it is very difficult to change the way we evaluate information.
One successful attempt was accomplished by Koriat, Lichtenstein, and Fischhoff (1980). They required students to list reasons that support a conclusion and reasons that run counter to a conclusion (counter arguments) and to rate the strength of each. This should be familiar because they are steps used in analyzing arguments. They found that the students became more accurate in their assessments after this training in "giving reasons". These results have been replicated in more recent studies in which the bias for information that confirms a prior belief was reduced by requiring people to provide reasons that did not support the preferred conclusion (Lenski, 2001; Flannelly & Flannelly, 2000). The authors of one of the studies summarized their research : " critical thinking skills of students should be fostered so the students come to appreciate the importance of weighting both positive and negative evidence" (Flannelly & Flannelly, 2000).
These sorts of experimental results show that the giving and assessing of reasons can have beneficial results that improve the thinking process.
Edit: Grammar error and clarity