Lecture Notes by Christopher Lay

Los Angeles Pierce College

Department of History, Philosophy, and Sociology

Mathew Van Cleave's 2016 Introduction to Logic and Critical Thinking

https://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=457

Chapter 3: "Evaluating Inductive Arguments and Probabilistic and Statistical Fallacies" 

Statistical Generalizations

"Statistical generalizations are generalizations arrived at by empirical observations of certain regularities."

Universal and Partial Generalizations

"Universal generalizations assert that all members (i.e., 100%) of a certain class have a certain feature." 

"[P]artial generalizations assert that most or some percentage of members of a class have a certain feature."

Evaluating Generalizations in Arguments

"[I]n evaluating statistical generalizations [we seek to determine] whether the premise in our argument is true (or at least well-supported by the evidence)."

Representative Sample 

"When a sample is representative, the characteristics of the sample match the characteristics of the population at large."  

The Truth of Good Statistical Generalizations

"We can assess whether or not a statistical generalization is true by considering whether the statistical generalization meets certain conditions."  

"Adequate sample size: the sample size must be large enough to support the generalization."

"Non-biased sample: the sample must not be biased." 

Getting it Wrong: Inadequate Sample Size

"First, consider a case in which the sample size is too small (and thus the adequate sample size condition is not met)."  

The Fallacy of Hasty Generalization

"One commits the fallacy of hasty generalization when one infers a statistical generalization (either universal or partial) about a population from too few instances of that population." 

"Hasty generalization fallacies are very common in everyday discourse, as when a person gives just one example of a phenomenon occurring and implicitly treats that one case as sufficient evidence for a generalization." 

Getting it Wrong: Biased Sample

Recall that bias, according to the New Oxford American Dictionary, is "prejudice in favor of or against one thing, person, or group compared with another, usually in a way considered to be unfair." 

Consider a generalization about the kinds of food eaten in Los Angeles based off of the food eaten on this campus. 

Questionnaire Bias

"[B]ias can creep into a statistical generalization through a biased way of asking a question." 

With biased ways of asking a question, polls can fail to be properly representative "because the responses would be skewed by the biased phrasing of the options." 

Random Sampling

"Random sampling is a common sampling method that attempts to avoid any kinds of sampling bias by making selection of individuals for the sample a matter of random chance (i.e., anyone in the population is as likely as anyone else to be chosen for the sample)."

"Inference to the Best Explanation and the Seven Explanatory Virtues" 

"Inference to the best explanation is a form of inductive argument whose premises are a set of observed facts, a hypothesis that explains those observed facts, and a comparison of competing explanations, and whose conclusion is that the hypothesis is true." 

Reasonable

"[I]n order to make a strong inference to the best explanation, the favored explanation must be the best (or the most reasonable)." 

To determine the best explanation, it is useful to compare two or more explanations. 

Explanatory Virtues

"There are certain conditions that any good explanation must meet." 

"The more of these conditions are met, the better the explanation." 

Explanatoriness

Depth

Power

Falsifiability

Modesty

Simplicity / Ockham’s Razor

Conservativeness

Explanatoriness

"[T]he hypothesis proposed must actually explain all the observed facts." 

My take: of two explanations, the one that can explain more of the observed facts is superior to one that cannot explain as many.  

Depth

"Explanations should not raise more questions than they answer." 

An "explanation [that] raises as many questions as it answers ... lacks the explanatory virtue of 'depth.'" 

Power

"Explanations should apply in a range of similar contexts, not just the current situation in which the explanation is being offered." 

Of two competing explanations, if one can explain the observed facts in question, and other, similar observable facts, then it is superior to the explanation that only explained the observed facts in question. 

Falsifiability

"Explanations should be falsifiable—it must be possible for there to be evidence that would show that the explanation is

incorrect."

If a hypothesis appeals to unobservable, or unverifiable evidence, then there is a problem with falsifiability. 

Modesty

"Explanations should not claim any more than is needed to explain the observed facts." 

"Any details in the explanation must relate to explaining one of the observed facts." 

If the "details [do not] help us to understand why the observed facts occurred" then there is a problem with modesty. 

Simplicity

"Explanations that posit fewer entities or processes are preferable to explanations that posit more entities or processes. All other things being equal, the simplest explanation is the best. This is sometimes referred to as “Ockham’s razor” after William of Ockham (1287-1347), the medieval philosopher and logician."

"The explanatory virtue of 'simplicity' tells us that all other things being equal, the simplest explanation is the better explanation."

"More precisely, an explanation that posits fewer entities or processes in order to explain the observed facts is better than an explanation that posits more entities and processes to explain that same set of observed facts." 

Conservativeness

"Explanations that force us to give up fewer well- established beliefs are better than explanations that force us to give up more well-established beliefs." 

"[B]etter explanations are ones that force us to give up fewer well-established beliefs."

"[C]onservativeness is an explanatory virtue only when we are considering two explanations that each explain all the observed facts, but where one conflicts with well-established beliefs and the other doesn’t."

"In such a case, the former explanation would lack the explanatory virtue of conservativeness, whereas the latter explanation would possess the virtue of conservativeness." 

Analogical Arguments

"In an argument from analogy, we note that since some thing x shares similar properties to some thing y, then since y has characteristic A, x probably has characteristic A as well." 

Analogical arguments often begin by showing how two things share some qualities.  The next step is to show other qualities are also shared. 

1) Establish shared, non-controversial similarities between X and Y. 

2) Show how controversial target feature is found in X. 

3) Assert that controversial target feature must also be found in Y. 

Conditions of Strength

"[A]n argument from analogy is [inductively] strong only if the following two conditions are met:" 

A) There must be enough relevant similarities

B) There should not be any significant, relevant dissimilarities 

Handling Analogical Arguments

Differences: object to an analogical argument by showing "that there are relevant differences between the two things being compared in the analogy." 

Similarities: object to an analogical argument by showing that there are not enough relevant similarities shared by the two things being compared in the analogy.

Causal Reasoning

Identifying the condition that serves as the cause of an effect will sometimes depend on the context of the event. 

Complexity / Background Conditions

"[A]ny cause is more complex than just a simple event that produces some other event."

"[T]here are always multiple conditions that must be in place for any cause to occur.  These conditions are called background conditions."

"[W]e often take for granted the background conditions in normal contexts and just refer to one particular event as the cause." 

Conditions Necessary

"For just about any cause, there are a number of conditions that must be in place in order for the effect to occur.  These are called necessary conditions (recall the discussion of necessary and sufficient conditions from chapter 2, section 2.7)."  

"A sufficient condition is a condition that suffices for some other condition to obtain." 

"A necessary condition is a condition that must be in present in order for some other condition to obtain."  

"To say that x is a necessary condition for y is to say that if x were not present, y would not be present either."  

Conditions Sufficient

"[A] sufficient condition is one which if present will always bring about the effect."

Causal Generalizations

"Because the natural world functions in accordance with natural laws (such as the laws of physics), causes can be generalized."  

"Causal generalizations have a particular form: For any x, if x has the feature(s) F, then x has the feature G."  

"Being able to determine when causal generalizations are true is an important part of becoming a critical thinker."

Mill's Method of Agreement

"If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or effect) of the given phenomenon."  

"[B]y comparing together different instances in which the phenomenon occurs," we have evidence pertaining to an effect's cause.  

Where ever we have an effect present in all instances, we can see how they further agree, and thus have evidence that the cause may be identical to that further agreement.  

Mill's Method of Difference 

"If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former; the circumstance in which alone the two instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon." 

"[B]y comparing instances in which the phenomenon does occur, with instances in other respects similar in which it does not," we have evidence pertaining to an effect's cause.  

Where ever we have an effect present in merely one instance, we can see how that instance is further different, and thus have evidence that the cause may be identical to that further difference.  

Mill's Agreement and Difference 

"If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance, the circumstance in which alone the two sets of instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon."  

Where ever we have an effect present in more than one instance, and less than all of the instances, we can see how those instances are in some further agreement and some further difference, and thus have evidence that the cause may be identical to that further agreement and difference.  

Mill's Concomitant Variation 

"Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation."  

Concomitant Variations

"In concomitant variation we look for how things vary vis-à-vis each other." 

"When two things are positively correlated, as one increases, the other also increases at a similar rate (or as one decreases, the other decreases at a similar rate)."

"In contrast, when two things are negatively correlated, as one increases, the other decreases at similar rate (or vice versa)."

Correlation ≠ Causation

"[W]e cannot directly infer causation from correlation. Correlation is not causation."

"If A and B are positively correlated, then there are four distinct possibilities regarding what the cause is:  A is the cause of B; B is the cause of A; [s]ome third thing, C, is the cause of both A and B increasing; or [t]he correlation is accidental." 

Background Knowledge

"In order to infer what causes what in a correlation, we must rely on our general background knowledge (i.e., things we know to be true about the world), our scientific knowledge, and possibly further scientific testing."

Some Third Thing

"Sometimes two things can be correlated without either one causing the other. Rather, some third thing is causing them both." 

"For example, suppose that Bob discovers a correlation between waking up with all his clothes on and waking up with a headache. Bob might try to infer that sleeping with all his clothes on causes headaches, but there is probably a better explanation than that. It is more likely that Bob’s drinking too much the night before caused him to pass out in his bed with all his clothes on, as well as his headache. In this scenario, Bob’s inebriation is the common cause of both his headache and his clothes being on in bed." 

Accidental Correlations

"Sometimes correlations are merely accidental, meaning that there is no causal relationship between them at all."  

"What makes [a correlation] accidental is that we have no theory that would make sense of how they could be causally related." 

"This just goes to show that it isn’t simply the correlation that allows us to infer a cause, but, rather, some additional background theory, scientific theory, or other evidence that establishes one thing as causing another." 

"We can explain the relationship between correlation and causation using the concepts of necessary and sufficient conditions (first introduced in chapter 2): correlation is a necessary condition for causation, but it is not a sufficient condition for causation." 

False Cause Fallacy

"Our discussion of causes has shown that we cannot say that just because A precedes B or is correlated with B, that A caused B. To claim that since A precedes or correlates with B, A must therefore be the cause of B is to commit what is called the false cause fallacy."

"As we’ve seen, false cause fallacies occur any time someone assumes that two events that are correlated must be in a causal relationship, or that since one event precedes another, it must cause the other."

Avoiding the False Cause Fallacy

"To avoid the false cause fallacy, one must look more carefully into the relationship between A and B to determine whether there is a true cause or just a common cause or accidental correlation."

"Common causes and accidental correlations are more common than one might think."