Ch.9 Flashcards
Statistical syllogism
Reasoning from a premise about a group to one of its members.
•Almost all students attending this college or pacifists. Wei-en Attends the college. Therefore, Wei-en Is probably a pacifist. 
Enumerate induction
Reasoning from premises about individual members of a group to conclusions about all members of the group.
1) X percent of the observed members from group a have Property P.
2) Therefore, X percent of all members of the group A probably have property P. 
Target group (Target population)
The whole collection of individuals understudy
Sample (Sample member)
The observed members of the target group
Relevant property (Property in question)
The property, or characteristic, that is of interest in the target group.
Example
1. 40% of the observed pickles from the barrel are exceptionally good.
2. Therefore, 40% of all the pickles in the barrel are probably exceptionally good.
Target population or target group: Pickles in the barrel.
Simple members or sample:
Observed pickles.
Property: Quality of being exceptionally good.

Weak enumerative inductive arguments
•Sample is too small
•Sample is not representative
•Hasty generalization: The fallacy of drawing a conclusion about target group based on an inadequate sample size. 
Example
1. All the corporate executives Jacques has worked for have been crooks
2. Therefore, all corporate executives are probably crooks.
Target group: Corporate executives.
Sample: Corporate executives Jacques has worked for.
Property: Being a crook.
Is it strong or weak?
•We don’t know how many corporate executives Jacques has worked for, but it’s probably a small number of the total number of corporate executives.
•So the sample is too small.
•Jacques also may have only worked in one sector or one region, and so it would not be representative.
Example
1. All of the blue herons that we have examined at many different sites in the nature preserve (about 200 birds) have all had birth defects.
2. Therefore, most of the blue herons in the nature preserve probably have birth defects.
Target group: Blue herons in the nature preserve.
Sample: 200 blue herons examined.
Property: Having birth defects.
Sample is sizeable, different sites means it is representative. So a strong enumerative induction, especially given the way the conclusion is phrased. 
Enumerative induction
Opinion polls
•Random sampling: Selecting a sample to ensure every member of target group has an equal chance of selection.
•Self-selecting sample: A non-random sample in which subjects choose themselves.
Sample size and random sampling
•Samples don’t have to be huge to be representative if it is a truly random sample.
•Target group can be American adults (187 million)
•Sample size can only be 1,000 to 1,500 individuals.
•Can Assign numbers to members of the population and use random number generator’s. 
Self-selecting samples
•Suppose we ask a question to the readers of a magazine. This is already a narrow population, but then only those who bother to write in will actually participate in the survey. 
•We are going to get skewed results because we’ll tend to hear more from people who are strong opinions and/or people who like to take questionnaires and send them in.
Margin of error and confidence level
The variation between the values derived from a sample and the true values of the whole target group. 
•Candidate X will receive 62% of the popular vote with a margin of error of + or -3 points. 
•Means a range, candidate X will receive between 59% and 65% of the vote.
The probability that the sample will accurately represent the target group within the margin of error. 
•95% confidence level is most common
•Means a 95% chance that the sampling results will accurately reflect the target group.
Analogical induction
Analogy: Comparison of two or more things using (“like” or “as”)
•”…The evening is sprout out against the sky… like a patient etherized upon table…” [T.S Eliot]
Argument by analogy: Reasoning that because two or more things are similar in several respects, they are similar in some further respect. 
1) Thing A has properties P1, P2, P3 plus the property P4.
2) Thing B has properties P1 P2 and P3.
3) Therefore, thing B probably has property P4. 
Evaluating Analogical induction
-The more relevant similarities between the things compared, the more Probable the conclusion. 
•The more properties they share, the better.
•Only one similarity is noted in the war example, so weak.
-The more relevant dissimilarities between the things compared, the less probable the conclusion.
•The more properties for two things compare don’t share, the worse for the argument.
•For example, Vietnam and Afghanistan have vastly different populations, terrain, political ideologies, leaders, generals, the wars are separated by decades and so technological differences, etc.
-The greater the number of instances showing relevant similarities, the stronger the argument.
•For example, if you were drawing a conclusion about the next war, it’s better if you have five different wars going on, not just one previous war.
•Only pointing to Vietnam
-The greater the diversity among cases showing relevant similarities, the stronger the argument.
•If we were talking about many US wars that all lacked clear rationales in many different places of the world that the US all lost, then this would make the argument stronger.

The problem of other minds
•How do I know all of you are conscious? It seems that I can only provide an argument using an analogical induction.
I have a nervous system, use language, and make a noise or grimace if suddenly stabbed.
You have a nervous system, use language, and make a noise or grimace if suddenly stabbed.
I am conscious.
Therefore, you are probably conscious.
Casual arguments
Is an inductive argument made to support a casual claim, a statement about the causes of things. 
•Reasoning to casual conclusions can take several inductive forms: enumerative induction, analogical induction, or inference to the best explanation.
•John Stuart Mill noted several ways of evaluating casual arguments, now known as “mill methods” of inductive inference.
•We already use this all the time, part of common sense, just identifying and giving names to them
Mill methods of inductive inference
Method of agreement: If two or more occurrences of a phenomenon have only one relevant common factor, that factor is the cause.
•Let’s say dozens of people stop in to Elmo’s corner bar after work as they normally do and 10 come down with intestinal issues. What’s the cause?
•Could be a lot of things. But if they all had a drink from the same bottle of wine, then that’s probably what made them sick.
Method of difference: The relevant factor present when a phenomenon occurs and absent when the phenomenon does not, is the cause.
•Everyone of an excellent team footballers has been playing well, except for six. The only thing the six are doing differently is taking brand X herbal supplements. So that’s probably what is making them sick.
Joint method of agreement and difference: The cause is isolated by identifying the relevant factors common to occurrences of the phenomenon and discarding any of these that are present when there are no occurrences.
•So say we have 10 patrons at the Elmo’s bar who’ve gotten ill, and they all had the wine and the tacos. It is probably one of these then that made them sick (agreement, what they all have in common). But let’s say you find many other people who had the tacos and are not sick (difference, what the not sick people have that is different from the sick people). So we can conclude that it was the wine.

Method of concomitant variation 
When 2 events are correlated they are probably casually related.
•If you see that the longer you boil eggs, the harder they get, then you can conclude that the boil and causes the hardening.
•The 2 happen together as far as you’ve already seen, so they are probably casually related, though might not be of course. 
-Correlation doesn’t prove causation
-Home PC sales increased at the same time as AIDS increased in Africa.
-Not conceivably casually linked
Common errors in casual reasoning
-Misidentifying relevant factors. 
•What if everyone who became ill had black hair? Might be so, but not relevant.
-Miss handling multiple factors.
•Might not be able to narrow things down.
-Confusing coincidence with cause.
-Confusing cause and effect
-Post hoc fallacy: Reasoning that just because B followed A, A must have caused B.
•Just because crime rates dropped after policing was increased doesn’t necessarily mean one caused the other. Need evidence of a casual link. 
Necessary and sufficient conditions
-A necessary condition for the occurrence of an event is one without which the event cannot occur. 
•If you do not live in the United States, then you do not live in New Jersey.
•Oxygen as needed for a fire. But just the presence of oxygen is not enough to bring about the fire.
-Sufficient condition for the occurrence of an event is one that guarantees that the event occurs.
•If you live in New Jersey, then you live in the United States.
•Depriving a goldfish of food is enough to kill it. 
