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Chapter Notes (Final Exam)
Part 3: Arguments
Chapter 8: Inductive Reasoning (270-324)
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Chapter Notes (Final Exam) Part 3: Arguments Chapter 8: Inductive Reasoning (270-324) -Deductive argument is intended to provide logically conclusive support for its conclusion; such an argument is valid or invalid, sound or unsound. Inductive argument is intended to supply only probable support for its conclusion, strong if it succeeds and weak if it fails. -The conclusion of an inductively strong argument is simply more likely to be true than not. If the argument’s premises are true, it is said to be cogent. Unlike valid deductive arguments, an inductively strong argument cannot guarantee that the conclusion is true but it can render the conclusion probably true, even highly likely to be true. -Inductive arguments, cannot give us certainly but they can give us high levels of probability. Inductive reasoning gives us most of what we know about the empirical workings of the world, allowing us in science to soar reliably from what we know to what we don’t. -Inductive arguments come in several forms (4) including enumerative, analogical and casual. Also inference to the best explanation (ch9). 1) Enumerative Induction -Sometimes an inductive argument reasons from premises about a group, or class, of things to a conclusion about a single member of the group. Enumerative Induction: An inductive argument pattern in which we reason from premises about individual members of a group to conclusions about the group as a whole. -Far more inductive arguments do the enumerative induction pattern. In such cases, we begin with observations about some members of the group and end with a generalization about all of them. It’s a way of reasoning that we all find both natural and useful. -Enumerative induction has this form: X per cent of the observed members of group A have property P. Therefore, X per cent of all members of group A probably have property P. -Enumerative induction comes with some useful terminology:

Target population (target group): In enumerative induction, the whole collection of individuals under study. Sample members (sample): In enumerative induction, the observed members of the target group. Relevant property (property in question): In enumerative induction, a property, or characteristic, that is of interest in the target group. -Remember that an inductive argument cannot only be strong or weak, but it can also vary in its strength in the degree of support that the premises give to the conclusion. So the strength of the argument depends on the premises as well as on how much is claimed in the conclusion. -Enumerative inductive arguments can fail to be strong in the two following major ways. Its sample can be 1) too small or 2) not representative. It’s possible for an enumerative induction to be perfectly strong but to have false premises, in which case the argument isn’t cogent. The data (or evidence) stated in the premises could have been misinterpreted, fabricated, or misstated. Sample Size -Just about everyone at one time or another probably makes this kind of mistake, which is known as hasty generalization. Hasty generalization: The fallacy of drawing a conclusion about a target group on the basis of too small a sample. -People regularly make this mistake when dealing with all sorts of enumerative inductive evidence; political polls, consumer opinion and surveys, scientific and medical studies, etc. -In general, the larger the sample, the more likely it is to reliably reflect the nature of the larger group. In many cases our common sense tells us when a sample is or is not large enough to draw reliable conclusions about a particular target group. A rule of thumb is the more homogenous a target group is in relevant to the property in question, the smaller the sample can be. The less homogenous, the larger the sample should be. -In social, psychological and cultural properties, people are too diverse to judge a large target group by just a few of its members. In biological properties, however, Homo sapiens are relatively uniform. We need to

survey only one normal member of the species to find out if humans have ears. Representativeness -In addition to being the proper size, a sample must be a representative sample. If it doesn’t properly represent the target group, it’s a biased sample. Representative sample: In enumerative induction, a sample that resembles the target group in all relevant ways. Biased sample: A sample that does not properly represent the target group. -An enumerative inductive argument is strong only if the sample is representative of the whole. -Many arguments using unrepresentative samples are ludicrous (ridiculous); others are more subtle (thoughtful). -To be truly representative, the sample must be like the target group by 1) having all the same relevant characteristics and 2) having them in the same proportions that the target group does. The ‘relevant characteristic’ is features that could influence the property in question. -We are often guilty of biased sampling in everyday situations. One way this happens is through a phenomenon called selective attention (we notice certain things and ignore others, usually without even being aware that we’re doing it. We may ignore facts that contradict our beliefs and search out facts that support them). Opinion Polls -Enumerative inductions reach a high level of sophistication in the form of opinion polls conducted by professional polling organizations. Opinion polls are used to arrive at generalizations about everything. Opinion polls are still essentially inductive arguments and must be judged accordingly. -So as inductive arguments, opinion polls should 1) be strong and 2) have true premises. Any opinion poll worth believing must 1) use a sample that is largely enough to represent the target population accurately in all the relevant population features and 2) generate accurate data.

-A poll can fail to meet this latter (final) requirement through dataprocessing errors, botched (messed up) polling interviews, poorly phrased questions, restricted choices and order of questions. -(Ex: polling organizations such as Environics and IpsosReid regularly conduct polls in which the target group is Canadian adults (more than 25 million) and the representative sample consists of only 1000-1500 individuals). How can this be? By using random sampling. Random sample: A sample that is selected randomly from a target group in such a way as to ensure that the sample is representative. In a simple random selection, every member of the target group has an equal chance of being selected for the sample.

(Ex: When conducting a poll and you know very little about the characteristics of this target population. Best bet for getting a representative sample of the group is to choose the sample members at random). -Selecting a sample in truly random fashion is easier said than done (humans have a difficult time selecting anything in a random way). Researchers and pollsters use various techniques to help them get close to true randomization. They may for example, assign a number to each member of a population then use a random number generator to make the selections. -One approach that does not produce a random sample is allowing survey subjects to choose themselves. The result of this process is called a selfselecting sample, a type of sample that usually tells you very little about the target population. (Ex: getting a self-selecting sample from a questionnaire in a magazine, TV or radio news broadcast casting a vote on a particular issue). In such cases, the sample is likely to be biased in favour of subjects who, just happen to be especially opinionated or passionate, who may have strong views about the topic of the survey, or who may like to fill out questionnaires. -So a well conducted poll using a random sample of 1000-1500 people can reliably reflect the opinions of the whole adult population. If a second well conducted poll is done in exactly the same way, the results will not be identical to that of the first poll. (Ex: the reason is that every instance of sampling is only an approximation of the results that you get if you polled every single individual in a target group. And by chance, each attempt at sampling will produce slightly different results). Such differences are referred to as the margin of error for a particular sampling or poll. Competently executed opinion polls will state their results along with a margin of error. Connected to the concept of margin of error is the notion of confidence level. Confidence level refers only to sampling errors, that is, the probability that the sample does not accurately reflecting the true values in the target population. Margin of error: the variation between the values derived from a sample and the true values of the whole target group. Confidence level: in statistical theory, the probability that the sample will accurately represent the target group within the margin of error. -Sample size, margin of error, and confidence level are all related in interesting ways:

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Up to the point, the larger the sample, the smaller the margin of error because the larger the sample, the more representative it is likely to be.

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The lower the confidence level, the smaller the sample size can be. If you’re willing to have less confidence in your polling results, a smaller sample will do.

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The larger the margin of error, the higher the confidence level can be. You can have more confidence in your enumerative inductive argument if you qualify, or decrease the precision of the conclusion

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The following shows roughly the relationship between sample size and margin of error for large populations (95% confidence level): 10000 ss-1% me, 2000-2%, 1500-2.5%, 1000-3%, 500-4.5% and 100-10%.

Statistical Syllogisms -Very often we have incomplete, but reasonable reliable, information about a group or category of things, and on the basis of that knowledge we can reach conclusions about particular members of that group or category. -In chapter 7, we dealt with categorical syllogisms, which were deductive arguments considering of 3 elements: two categorical premises and a categorical conclusion. But there are also statistical syllogisms, which are inductive arguments that apply a statistical generalizations a claim about what is true of most members of a group or category to a specify member of that group or category. -Here is the pattern that all statistical syllogisms follow, when spelled out fully: Premise 1: A proportion X of the group M have characteristic P. Premise 2: Individual S is a member of group M. Conclusion: Individual S has characteristic P. -It is important, in analyzing a statistical syllogism, to be able to identify: • • • •

The The The The

individual being examined. group to which that individual is said to belong. characteristic being attributed. proportion of the group said to have that characteristic.

-Sometimes, the proportion will take form of an actual statistic. That’s where the term statistical syllogism comes from. It might be stated as a percentage or it could also be a fraction. Sometimes specific numbers aren’t available and an arguer will use a word like ‘most’ or ‘almost all’ or ‘most of the time’.

The point is that the first premise is a generalization -a statement about the members of a group or class. -Because they are a type of inductive argument, statistical syllogisms (even good ones) with acceptable premises cannot guarantee their conclusion. Sometimes they can lead us off course. Evaluating Statistical Syllogisms -Since statistical syllogisms, though very useful, are never closed, we need a method for evaluating them. Acceptable Premises The first thing to consider is whether we have good reason to believe the premises. How is it that the generalization expressed in the first premise was arrived at? Is it common knowledge? It is based on a careful survey, one with a large enough randomly selected sample? If the grounding of the generalization is weak then the argument is weak? Statistical Strength -Perhaps most obviously, we should ask ourselves: just how strong is the generalization being offered? We should clearly ask questions, then, when vague words such as ‘most’ or ‘lots of’ are used in statistical syllogisms. ‘Most’ might just mean 51% of. And that’s a pretty weak basis for a conclusion about any particular member of that group. Typical or Randomly Selected -Statistical syllogisms take a generalization about a group or class and apply that generalization to a specific, individual member of that group or class. This will make most sense for members that we have reason to believe are typical of that group or class. It is most reasonable to assume that the individual is typical when he/she or it is selected randomly from the population. Thus we should always consider whether the individual person or item under consideration is likely to be a typical member of the group, or whether you have reason to believe that he/she or it is an exception to the rule. 2) Analogical Induction Analogy: A comparison of two or more things alike in specific respects. -In literature, science, and everyday life, analogies are used to explain or describe something. Analogies (often in form of similes) can be powerful literary devices, both unforgettable and moving.

-But an analogy can also be used to argue inductively for a conclusion. Such an argument is known as an analogical induction or simply an argument by analogy. Argument by analogy (analogical induction): An argument that makes use of analogy by reasoning that because two or more things are similar in several respects, they must be similar in some further respect. -Analogical induction has this pattern: Thing A has properties P1, P2 and P3, plus the property P4. Thing B has properties P1, P2, and P3. Therefore, thing B probably has property P4. -Argument by analogy, like all inductive reasoning, can establish conclusions only with a degree of probability. The greater the degree of similarity between the two things being compared, the more probable the conclusion is. -The most obvious difference between these two forms of induction is that enumerative induction argues from some members of a group to the group as a whole but analogical induction reasons from (one or more) individuals to one further individual. Looking from another way, enumerative induction argues from the properties of a sample to the properties of the whole group; analogical induction reasons from the properties of one or more individuals to the properties of another individual. -Arguments by analogy are probably used and misused in every area of human effort but especially in law, science, medicine, ethics, archaeology, and forensics. -Arguments by analogy are easy to formulate, too easy. To use an analogy to support a particular conclusion, all you have to do is find two things with some similarities and then reason that the two things are similar in yet another way. You could easily reach some very silly conclusions. -Fortunately, there are some criteria we can use to judge the strength of arguments by analogy: 1) Relevant similarities, 2) Relevant dissimilarities, 3) The number of instances compared, 4) Diversity among cases. Relevant Similarities -The more relevant similarities there are between the things being compared, the more probably the conclusion.

-Notice that this first example involves relevant (suitable) similarities. The similarities cited in an analogical induction can’t strengthen the argument at all if they have nothing to do with the conclusion. A similarity (or dissimilarity) is relevant to an argument by analogy if it has an effect on whether the conclusion is probably true. -Of course, it’s not always obvious what counts as a relevant similarity. In order to be relevant, a similarity cited as part of an analogical argument clearly has to be connected in some significant way to the conclusion being argued for. (Ex: there is no connection between the colour of the soldier’s eyes and their success in war. In some cases, an explanation may be required to show why a particular similarity is actually relevant. In this regard, the burden of proof (the weight of evidence/argument required by one side in a debate/disagreement) is on the person putting forward the argument. Relevant Dissimilarities -Generally, the more relevant dissimilarities there are between the things being compared, the less probable the conclusion. Dissimilarities weaken arguments by analogy. -Pointing out dissimilarities in an analogical induction is a common way to undermine the argument. Sometimes finding one relevant dissimilarity is enough to show that the argument should be rejected. The Number of Instances Compared The greater the number of instances, or cases, that show the relevant similarities, the stronger the argument. (Ex: in the war argument, there is only one instance that has all the relevant similarities: the Vietnam War. But what if there were 5 additional instances, 5 different wars that have the relevant similarities to the present war? The argument would be strengthened). Diversity among Cases - As we’ve seen, dissimilarities between the things being compared weaken an argument by analogy. Such dissimilarities suggest that the things being compared are not extremely analogues. And we’ve noted that several cases that exhibit the similarities can strengthen the argument. -Focus on a very different point. The greater the diversity among the cases that exhibit the relevant similarities, the stronger the argument.

-As you know, an inductive argument cannot guarantee the truth of the conclusion, and analogical inductions are no exception. 4) Casual Arguments -Our world is shifting, numerous, complicated web of causes and effects and that’s an oversimplification. The normal human response to the apparent casual chaos is to jump and ask what causes what. What causes breast cancer? What brought the universe into existence? -When we answer such questions (or try to) we make a casual claim and when we try to prove or support a casual claim, we make a casual argument. Casual Claim: A statement about the causes of things. Casual Argument: An inductive argument whose conclusion contains a casual claim. -Casual arguments, being inductive, can give us only probably conclusions. If the premises of a strong casual argument are true, then the conclusion is only probably true, with the probability varying from slightly likely to highly probable. The probabilistic nature of casual arguments, however, is not a failing or weakness. -Casual reasoning is simply different from deductive reasoning and it is our primary method of acquiring knowledge about the workings of the world. (Ex: science is concerned mainly with casual processes and casual arguments. We now have very strong inductive arguments, in favour of the claim that cigarettes cause cancer, that the HIV virus causes AIDS). Each of those casual conclusions is very reliable and constitutes a firm basis for guiding individual and collective behaviour. -Casual arguments can come in several inductive forms, some of which you already know about. (Ex: we sometimes reason about cause and effect by using enumerative induction).

More often, though, we use another type of induction in which we reason to a casual conclusion by pinpointing the best explanation for a particular effect. This is a very powerful and versatile form of inductive reasoning called inference to the best explanation. It’s the essence of scientific thinking and a mainstay of our everyday problem solving and knowledge acquisition (whether casual or non-casual). Inference to the Best Explanation: A form of inductive reasoning in which we reason from premises about a state of affairs to an explanation for that state of affairs: Phenomenon Q. E provides the best explanation for Q. Therefore, it is probable that E is true. Testing for Causes -An English philosopher John Stuart Mill noted several ways of evaluating casual arguments and formulated them into what are known as ‘Mill’s Methods’ of inductive inference. The methods are basically common sense and are used by just about everyone. Th...