PHIL 110 - Lec #10/11 Inductive Reasoning

Define 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

What is the form for enumerative induction?

X% of the observed members of group A have property P

Therefore, X% of all members of group A have property P

What are the three factors in an enumerative induction?

Target group (target population): The whole collection of individuals under study

Sample (sample member): The observed members of the target group

Relevant property (property in question): A property, characteristic, that is of interest in the target group

How can enumerative induction be strong or weak?

1. The sample size

2. If the sample is representative of the target group

Define hasty generalization

The fallacy of drawing a conclusion about a target group on the basis of a sample that is too small

How can a sample be representative of the target group?

1. Having all the same relevant characteristics

2. Having them in the same proportions that the target group does

3. Random sampling can be used

What is self-selecting sample

The process by which you allow survey subjects to choose themselves

define margin of error

The variation between the values derived from a sample and the true values of the whole target group

define confidence level

The probability that the sample will accurately represent the target group within the margin of error

• A 95% confidence level means that there is a 95% chance that the results will accurately reflect the frequency in the total population

Define statistical syllogism

Inductive arguments that apply a statistical generalization—a claim about what is true of most members of a group or category—to a specific member of a group or category

What is the form of statistical syllogisms

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

What do we need to be able to identify in order to analyze a statistical syllogism

• The individual being examined

• The group to which that individual is said to belong

• The characteristic being attributed

• The proportion of the group said to have that characteristic

What are some hints to tell if an argument is a statistical syllogism

• If the argument has three statements, 2 premises and 1 conclusion

• The first premise is a generalization—a statement about the members of a group or class

• Very often, the first premise of a statistical syllogism will be arrived by an argument using enumerative induction

How can we evaluate if a statistical syllogism is strong or weak?

1. Acceptable premises

   • Do 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?

   • Is it based on a careful survey, one with a large enough, randomly selected sample?

2. Statistical strength

   • Just how strong is the generalization being offered?

   • Ask questions when vague words such as “most” or “lots of” are used

3. Typical or randomly selected

   • When apply a generalization about a group or class to a specific member of that group or class, we must have reason to believe that members are typical of that group

   • The individual is considered typical when he/she is selected randomly from the population

Define analogical induction

An analogy is a comparison of two or more things alike in specific respects. An analogy can be used to argue inductively for a conclusion

An analogical induction (or argument by analogy) reasons this way: because two or more things are similar in several respects, they must be similar in some further respects

What is the form of analogical induction?

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

What is the criteria for judging the strength of arguments by analogy?

1. Relevant similarities

   • The more relevant similarities there are between the things being compared, the more probable the conclusion

2. Relevant dissimilarities

   • Generally, the more relevant dissimilarities there are between the things being compared, the less probable the conclusion is

3. The number of instances compared

   • The greater the number of instances, or cases, that show the relevant similarities, the stronger the argument

4. Diversity among cases

   • The greater the diversity among the cases that exhibit the relevant similarities, the stronger the argument

Define causal claim

A statement about the causes of things

Define causal argument

An inductive argument whose conclusion contains a causal claim

Explain causal arguments

• Causal arguments, being inductive, can give us only probable conclusions

• If the premises of a strong causal argument are true, then the conclusion is only probably true

• Causal arguments can come in several inductive forms

Define 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

What is the form for inference to the best explanation

Phenomenon Q

E provides the best explanation for Q

Therefore, it is probable that E is true

What are the 4 Mill’s methods for evaluating causal arguments

1. Agreement

2. Difference

3. Both agreement and difference

4. Correlation (concomitant variation)

Explain agreement (mill’s method)

If two or more occurrences of a phenomenon have only one relevant factor in common, that factor must be the cause

Schematic of an argument based on the method of agreement:

• Instance 1: Factors a, b, and c are followed by E

• Instance 2: Factors a, c, and d are followed by E

• Instance 3: Factors b and c are followed by E

• Instance 4: Factors c and d are followed by E

• Therefore, factor c is probably the cause of E

Only factor c consistently accompanies effect E. The other factors are sometimes present and sometimes not. We conclude then, that factor c brings about E.

Explain difference (mill’s method)

The method of difference says that the relevant factor that is present when the phenomenon occurs and that is absent when the phenomenon does not occur must be the cause

Schematic of an argument based on the method of difference:

• Instance 1: Factors a, b, and c are followed by E

• Instance 2: Factors a and b are not followed by E

• Therefore, factor c is probably the cause of E

Explain both agreement and difference (mill’s method)

Joint method of agreement and difference: apply both methods simultaneously. This generally increases the probability that the conclusion is true

The likely cause is the one isolated when you:

• identify the relevant factors common to occurrences of the phenomenon (the method of agreement) and

• discard any of these that are present even when there are no occurrences (the method of disagreement)

The schematic for arguments based on the joint method of agreement and difference:

• Instance 1: Factors a, b, and c are followed by E

• Instance 2: Factors a, b, and d are followed by E

• Instance 3: Factors b and c are not followed by E

• Instance 4: Factors b and d are not followed by E

• Therefore, factor a is probably the cause of E

Factors a and b are the only relevant factors that are accompanied by E. But we can eliminate b as a possibility because when it’s present, E doesn’t occur. So, b can’t be the cause of E; a is most likely the cause

Explain correlation (mill’s method)

When two events are correlated—when one varies in close connection with the other—they are probably causally related

In many cases, relevant factors aren’t merely entirely present or entirely absent during occurrences of the phenomenon—they are closely correlated with the occurrences

The schematic for arguments based on concomitant variation

• Instance 1: Factors a, b, and c are correlated with E being present

• Instance 2: Factors a, b, and increased c are correlated with increased E

• Instance 3: Factors a, b, and decreased c are correlated with decreased E

• Therefore, factor c is causally connected with E

What are the three causal confusions?

There are some easy to commit errors regarding causal arguments:

1. Misidentifying relevant factors

2. Mishandling multiple factors

3. Being misled by coincidence

What is misidentifying relevant factors?

• Are the factors preceding an effect truly relevant to that effect?

• Your ability to identify relevant factors depends mostly on your background knowledge. Lack of background knowledge might lead you to dismiss or ignore relevant factors or to assume that irrelevant factors must play a role.

What is mishandling multiple factors?

• Sometimes there are too many relevant factors to consider, and so trying to narrow the possibilities to one is extremely difficult/impossible

• Ordinary causal reasoning is often flawed because of the failure to consider all the relevant antecedent factors

• This is also a function of skimpy background knowledge

What is being misled by coincidence?

• Sometimes ordinary events are paired in unusual or interesting ways

• People are especially prone to think “it can’t just be a coincidence” because they misjudge the probabilities involved

When do you have good reason for suspecting that a causal connection exists?

If the connection passes one or more standard causal tests and if you can rule out any relevant factors that might undermine the verdict of those tests

What is the logical fallacy known as post hoc, ergo propter hoc

A particularly common type of misjudgment about coincidences is the logical fallacy known as post hoc, ergo propter hoc (“after that, therefore because of that”).

• Just because one event precedes another, that doesn’t mean that the earlier one caused the later

• Example: An hour after Julio drank the cola, his headache went away. The cola cured his headache.

Explain ignoring the common causal factor

Sometimes A and B are correlated with each other, and genuinely causally connected, but A doesn’t cause B and B doesn’t cause A. Rather, both A and B are caused by some third factor, C, that they share in common.

Example: There is a correlation between sales in ice cream and deaths due to drowning. When ice cream sales are high, there is also a high number of deaths due to drowning.

• Does this mean that ice cream causes people to drown? Or that drowning causes people to buy ice cream?

• Both of these things are more commo in the summer months. So “summertime” is the common causal factor

Explain confusing cause and effect

Sometimes we may realize that there’s a causal relationship between two factors, but we may not know which factor is the cause and which is the effect.

Example: Does your coffee drinking cause you to feel stressed out - or do your feelings of being stressed out cause you to drink coffee?

Define necessary condition

A condition for the occurrence of an event without which the event cannot occur

Define sufficient condition

A condition for the occurrence of an event that guarantees that the event occurs

Explain necessary conditions

Suppose you drop a water balloon from the top of a building, and it breaks on the pavement. What are the necessary conditions for the breaking of the balloon?

Necessary conditions:

1. You release the balloon

2. The force of gravity acting on the water

3. The breakability of the balloon

4. The hardness of the pavement

If any one of these conditions is not present, the water balloon will not break

Explain sufficient conditions

Suppose you drop a water balloon from the top of a building and it breaks on the pavement. What are the sufficient conditions for the breaking of the balloon?

Sufficient conditions:

• Non of the necessary conditions by itself is sufficient to cause the balloon to break. None guarantees the occurrence of the effect

• But all of the necessary conditions combined are sufficient to guarantee the balloon’s breaking

Ex: Failing to feed a healthy goldfish for a few weeks is a sure way to kill it.

• So, failing to feed the goldfish is a sufficient condition for its death. So removing the water from its fishbowl.

• However, not feeding the goldfish nor draining its bowl of water is a necessary condition for the goldfish’s death because its death can be caused without resorting to either of these methods

What happen in cases in which a complete set of necessary conditions constitutes a sufficient condition for an event?

We say that the conditions are individually necessary and jointly sufficient for an event to occur.

When we’re interested in preventing or eliminating a state of affairs, we often focus on necessary causal conditions

• i.e. Eliminating standing water to prevent mosquito infestations

When we’re interested in brining about a state of affairs, we’re likely to focus on sufficient causal conditions

• i.e. Surgery to remove the blockage in an artery

How do you determine if something is a necessary or sufficient condition in a causal statement?

• The word ”if” by itself signals a sufficient condition

  • In the current situation, the prime minister will call an election if Parliament doesn’t vote in favour of his proposal to cut taxes

• The words “only if” signals that what comes after is a necessary condition

  • In the current situation, the prime minister will call an election only if Parliament doesn’t vote in favour of his proposal to cut taxed

• The words “if and only if” signal that the conditions are both necessary and sufficient

  • The paper will combust if and only if it’s heated to a sufficiently high temperature in the presence of oxygen

What are examples where there is neither a necessary or sufficient condition

A causal connection doesn’t need to be either necessary or sufficient. It could be neither.

• Ex: Late delivery of the package caused John to miss his deadline

• Ex: Ricardo’s stubbornness caused the negotiations to break down