Induction

• Inductive arguments (or simply induction) – Reasoning from particular cases to general conclusions. – In general, supported by statistical analysis or probability.

• Causal inductive arguments – Special type of induction in which the premises suggest the conclusion that there is a causal relation between two properties or factors. Characteristics of Inductive Arguments 1. Premises and conclusions are all empirical propositions – Descriptions of matters of fact – Not definitions – Not value judgements.

2. Conclusion is not deductively entailed by the premises

3. Underlying reasoning is that the regularities described in the premises will persist throughout the range described in the conclusion

4. Conclusion is either: (a) that unexamined case will resemble the examined ones (b) the premises support an explanatory causal hypothesis Populations, Sample Size and Bias

• Inductive conclusions generalize. We sometimes say that they extrapolate. This just means that inductive conclusions give more information than the information stated in the premises. – For example, “3,356 crows were observed to be black, so all crows are black.”

• The conclusion makes a statement about some population or group based on a sample that is smaller that is smaller than the population or group.

• For an inductive conclusion to be reasonable, the premises must be a representative sample of the whole population. – An unrepresentative sample is called a biased sample. – Biased sampling is a serious problem, and it often arises unintentionally because of a lack of understanding of the population being sampled. Representative Samples

• Evaluating whether or not a sample is representative is difficult and is not straightforward. • It involves a variety of factors, including population size, population homogeneity, and the particular property being sampled. • To understand this more completely TAKE A STATISTICS COURSE before leaving university!!!

• That said, three things to keep in mind: 1) Sampling works best when it is a random sample of the total population. Biased sampling leads to misrepresentative inductive generalization. 2) For a population in the millions, a random sample of about 1,000 can provide a perfectly representative picture of a populations. 3) In order to achieve a representative sample, small populations require the sample to be a greater proportion of the population than for larger populations. (Small populations tend to exhibit more variability.) Evaluating Inductive Arguments

• By definition, the representativeness of a sample can never be proven in an inductive argument. – Representativeness needs to be evaluated using good sense and good judgment. – In statistics, confidence is the metric used to evaluate this question. – If you don’t know any statistics, then you need to make a good guess about whether the sample is representative of the population being sampled.

• Key question: How likely is it that the target population resembles the sample population in the relevant respects? – Same question expressed succinctly: Is the sample population representative? Evaluating Inductive Generalizations

Four steps:

1) Identify the sample and target populations as precisely as possible (relying on contextual cues if necessary).

2) Identify the size of the sample.

3) Reflect on the degree of variability of the trait or property which is extrapolated in the conclusion.

4) Reflect on the sampling process. • Have techniques been used to minimize the possibility of bias? • e.g., increasing sample size, stratified sampling, and so forth. Two General Problems with Inductive Arguments

• Pseudoprecision – The attempt to make a conclusion seem to be justified by expressing premises with numerical exactness. – “Ignatieff is now 27.6 percentage points ahead of Harper.”

• Questionable definition – “Studies prove that over 95% of communication is non-verbal, body language”. Four Inductive Fallacies

1) Hasty inductive generalization: a sample is grossly inadequate so that it is guaranteed to be unrepresentative, and hence, unacceptable.

2) Anecdotal arguments: a common, special case of a hasty inductive generalization, which involves basing an inductive generalization entirely on one (gripping or compelling) story. Again, unrepresentative, and hence, unacceptable.

3) Genetic fallacy: premises offer information about the origins of something, and a conclusion is inferred from this about the thing’s fundamental properties or value. A fallacy of relevance.

4) Fallacies of composition and division: Attributing to the wholes the properties of parts. A fallacy of relevance. Genetic Fallacy

• “86% of people in the world believe that God exists, so God must exist.” – This example involves incorrect reasoning from a (presumably) correct fact about the number of people who believe in god to the existence of god. The number of people who believe in god tells us nothing about the putative properties of god.

• “America will always be a maverick state. The majority of the Founding Fathers were simply rabble rousers.”

• But becareful: In many cases, the origin of a claim is relevant to the evaluation of the acceptability of the claim. – Consider assessment of testimony of texts or experts. Fallacy of Composition and Division

• Two sides of the same coin:

– The fallacy of composition is committed by arguing that because something is true of members of a group, it is true of a group as a whole.

– The fallacy of division is committed by arguing that if something is true of a group, then it is also true of the individuals belonging to the group. Example: Fallacy of Composition

• Classic illustration: – “Atoms are not visible to the naked eye, and humans are made up of atoms, so humans are not visible to the naked eye.”

• “A US battleship consumes more fuel than a 9.9hp motor boat, so all the battleships consume more fuel than 9.9hp motor boats.” Example: Fallacy of Division

• Classic illustration: – “Humans are visible, and humans are made up of atoms, so atoms are visible.”

• “Canadians use more electricity per capita than Americans. So, Joe Bloggs in St. John’s uses more power than American, Lee Pippa.” Causal Inductive Arguments

• Causal inductive argument: – An inductive argument in which the conclusion is that there is a causal relation between two factors or properties. – E.g., Smoking causes cancer. Green-house-gas emissions from industry cause global climate change.

• Causal inductive arguments are ubiquitous: – Arguments in science commonly suppose the identification of causes.

• But, this kind of argument leads to a number of distinctive complications and problems. In particular, it is difficult to distinguish between: 1. Constant conjunction, i.e., correlation of factors 2. Necessary connection, i.e., a causal connection between factors Causes

• We say things in the form of “C caused E” and “E was caused by C”. – As noted in the discussion of the logical conditional, when we say “If C then E” we tend to suppose (incorrectly) that we are talking about a causal relationship.

• That said, the nature of causation, and related problem of verifying causal claims, are vexing questions to philosophers.

• Saying that “C caused E” could be explained in, at least, one of three things:

1) Event: C caused E means at least that C happened and then E happened, but in addition that something about C engendered or brought into being E.

2) Counterfactual conditional: C caused E, if and only if, C had not occurred, then E would not have occurred.

3) Law of nature: C caused E, if and only if, it is a law of nature that Cs always cause Es. Five Different Interpretations of ‘C causes E’

1. C is a necessary condition for E: without C, E would not occur. (The presence of oxygen is a necessary condition for human life.)

2. C is a sufficient condition for E: C is enough by itself to produce E. (Massive heart failure is a sufficient condition for death.)

3. C is a necessary and sufficient condition for E. (Having diabetes is necessary and sufficient for having a malfunctioning pancreas.)

4. C is an especially important causal factor, leading to E: Individually necessary part of a jointly sufficient causal chain. (The carelessly discarded cigarette butt caused the fire.)

5. C is a causal factor, contributing to the likelihood of E. (Smoking causes lung cancer.) Correlation and Cause

• The premises of a causal induction typically establish, among a sample group, a correlation between two properties or factors.

• The conclusion of a causal induction extrapolates beyond this data in two ways.

1) Like all inductive arguments, it extrapolates that the regularity observed between factors the sample will persist in the target population.

2) It adds the further conjecture that the regularity will persist because there is a causal connection or relation between the factors.

• Why does (2) present a special problem? Example: Allergies and Asthma

• In recent decades, certain kinds of allergies (e.g., peanut) and asthma have been drastically on the rise in Western nations, though not elsewhere in the world.

• The evidence that they are significantly correlated is overwhelming. – If you have these kinds of allergies, then there is a statistically significant increase in the chance that you are prone to develop asthma. – Likewise, if you have asthma, then there is a statistically significant increase in the chance that you are prone to develop these kinds of allergies.

• But, is there a causal relation between allergies and asthma? No amount of correlation will distinguish among these three possibilities:

1) Allergies cause asthma.

2) Asthma causes allergies.

3) Both allergies and asthma are caused by some third property or factor. Correlation Words: Association, Link

• We often confuse correlations with causes, and science reporting often encourages to make this confusion. – “Associations” and “links” among factors suggest a correlation not a causal relation. – Finding a significant correlations, associations and links is often (incorrectly) taken to imply the existence of a causal connection. • Down this road lies conspiracy theories and Dan Brown novels!

• Example: an insurance agent may charge you a higher premium for driving a red sports car, because red sports cars tend to be in more accidents than sports cars in other colours. – There is just a correlation, association or link between red sports car and accidents. – Clearly, the colour of the car does not cause the accident.

• In general, you need strong correlation between factors for the correlation to be significant. Further, a significant correlation is necessary (required for) but not sufficient (not enough for) to establish a causal relation. – Again, just because there is a significant correlation between factors, it does not mean that there is a causal relation between the factors. Three Fallacies of Causation: (1) Post hoc ergo propter hoc

Short form: Post hoc Fallacy – Latin for ‘after this, therefore because of this’.

• To commit the post hoc fallacy is to conclude that A caused B from solely the fact that A happened before B.

• “The Conservatives were in power for one year when there were significant increase in the high school drop out rate. It must have been Conservative policies that were responsible for students dropping out.” Three Fallacies of Causation: (2) Objectionable cause (I)

• The objectionable cause fallacy is committed when a causal conclusion is reached too hastily. – No attention has been paid to alternative possibilities. – Compelling narratives or beliefs connect the effects with the alleged cause. – Here “objectionable” means open to objections, not nasty.

Example: “I know it is troubling to see all those street people begging for money and looking dirty and depressed, but remember, if you make bad decisions throughout your life these are the consequences you can expect.” Three Fallacies of Causation: (2) Objectionable cause (II)

• The Monte Carlo Fallacy or Gambler’s Fallacy is a variation on the objectionable cause fallacy. • The Monte Carlo Fallacy is committed when it is assumed that past outcomes causally affect future chance outcomes. – Future chance events are independent of past events. If they weren’t independent, then they wouldn’t be chance events!

• Example: “I have been losing to this VLT all night. I will keep playing because it has to start paying out soon.” Three Fallacies of Causation: (3) Causal Slippery Slope

• This fallacy is committed when an claim is rejected on the grounds that while some action might seem harmless and justified on its own, it will cause a series of other events, leading to an undesirable event.”

• Example: “If we grant a building permit for a fast food restaurant, then there will be no limit to the number of building permits we will have to grant to fast food restaurants and it will drive away all the good places to eat.” Moving from Correlation to Causation …

• But, clearly we need to move from correlation to causation! • How else could empirical science get work done?

• John Stuart Mill (1806-1873) recognized that inferring causes from correlations was difficult, if not impossible, to logically sanction.

• Mill’s methods: five tools for mitigating the obvious problems of inferring from correlation to causation. • We accept that there is a causal relation among factors when one of Mill’s methods has been satisfied. Mill’s Methods

1) Method of Agreement 2) Method of Difference 3) Method of Agreement and Difference 4) Method of Residues 5) Method of Concomitant Variation Mill’s Methods (I)

• Assume: Factors A, B, C, D and E and some effects w, x, y and z.

1) Method of Agreement: – The factor that always correlates with the effect is the cause of the effect. – For example: Factors A, B and C occur with effects w, x and z. Factors A, D and E occur with effects w and y. Therefore, A is the cause of y. Mill’s Methods (II)

2) Method of Difference: – The factor that is never present when the effect does not occur is the cause. – For example: Factors A, B and C occur with effects w, x, y and z. Factors B and C occur with effects x, y and z. Therefore, A is the cause of y.

3) Method of Agreement and Difference – The simultaneous use of the method of agreement and the method of difference. – For example: Factors A, B and C occur with effects x, y, z. Factors A, D and E occur with effects w, x, and y, and also B and C occur with y and z Therefore, A is the cause of x. Mill’s Methods (III)

4) Method of Residues – If all factors except one have been matched with an effect, then the remaining effect can be attributed to the remaining factor. – For example: A, B and C occur with effects x, y and z. B is the cause of y C is the cause of z Therefore, A is the cause of z.

5) Method of Concomitant Variations A, B and C occur with effects x, y and z. Changing A results in a change in x only. Therefore, A is the cause of x. Inference to the Best Explanation (IBE)

•Mill’s methods have their limitations. Consider the following: 1) They assume that it easy to make a short-list of candidates for the status of cause 2) They are well-suited for identifying necessary and sufficient conditions but less well-suited to identifying causal factors, etc.

• IBE, also called ‘abduction’ by C.S. Peirce, is a mode of argumentation which also applies in these cases, and which does not oversimplify in the same way (though it faces other problems). IBE (I)

1. Effect E exists. 2. Hypothesis 1 would explain E. 3. H1 is the best explanation of E.

Therefore, it is reasonable to tentatively endorse H1. IBE (II)

Clearly the term “best” is vague, and this makes IBE controversial among philosophers of science.

What can we say about ‘best’ in ‘best explanation’? • Three criteria to evaluate “best”: 1) plausibility (i.e., consistency with relevant background knowledge, scientific theorizing, etc.) 2) simplicity and generality (two key virtues for any hypothesis) 3) falsifiability (it must be consistent with some possible outcomes, and inconsistent with other possible outcomes, of else it does not say anything) IBE (III)

• One particularly prevalent flawed type of explanation is called ad hoc explanation. – ‘Ad hoc’ = after the fact.

•An ad hoc explanation is one that is brought in after a certain counterexample is found, in order to explain away the counterexample.