Phil 140 Chapter 8: Inductive Reasoning

Is this a good analogy?

"Doctors are allowed to look up difficult diagnoses in their medical textbooks, so students should be able to look up tough test questions in their textbooks" -Relevant dissimilarities: Students are being tested, which is relevant to the issue of whether looking up material should be allowed. Doctors are not being tested. Is this a good analogy? You wouldn't steal a car, you wouldn't steal a handbag, downloading pirated films is stealing, you wouldn't download pirated films -Is downloading pirated films similar or dissimilar in relevant ways to stealing a car/handbag? -Relevant Similarities/Dissimilarities: Dissimilarity: a person has lost something/someone has not lost something, physical items/non-physical Similarity: gained something without paying for it when they would have expected payment, against the law

Correlation and Causation

'Worldwide non-commercial space launches' is correlated with 'Sociology doctorates awarded (US)'. Does space launches cause sociology doctorates? Answer is no. -When two events are correlated (when one varies in close connection with the other) they could be casually related -However, correlation does not necessarily imply causation -Correlation without causation can occur due to: (1) coincidence (2) common causes

What are the three problems to a weak enumerative inductive argument?

(1) too small a sample size; (2) sample size not representative of the overall population; (3) drawing too strong a conclusion

Is this argument deductive or inductive? "if Calgary faces Montreal in the final, Calgary will probably win because they have a stronger record on the regular season."

(inductive: uses probability, and goes beyond given evidence to make a prediction about something that has not yet happened.)

Is this argument deductive or inductive? "according to CRL rules, the teams that win next weekend's games will advance to the Grey Cup."

(more deductive: because it merely spells out what is in the rules of CFL football)

Mill's Methods: Method of Agreement

-"If two or more occurrences of a phenomenon have only one relevant factor in common, that factor must be the cause." -If C occurs, and E occurs, so C causes E -Example: Ten of twelve people who visit Elmo's bar get sick. Why? The funky taco meat? The yellowish ice cubes? The stinky wine? -Four sick people had no ice cubes. All sick people drank the same wine and had tacos. So the wine and/or tacos probably caused the sickness.

Mills Methods: Joint Method of Agreement and Difference

-"The likely cause is the one isolated when you identify the relevant factors common to occurrences (Agreement) and discard any of these that are present even when there are no occurrences (difference)" -If C occurs E occurs, and if C does not occur E doesn't occur, so C causes E. -Example: if fire occurs and the smoke occurs, and we remove the fire and no more smoke occurs, then the fire causes the smoke

Mill's Methods: Method of difference

-"The relevant factor that is... absent when the phenomenon does not occur must be the cause. Here we look not for factors that the instances have in common, but for factors that are points of difference" -If C does not occur, E does not occur, so C causes E -Example: Healthy and sick people ate the tacos, so tacos did not cause the sickness. Healthy people did not have the wine, and sick people all had wine, so the wine probably caused the sickness.

Mill's Methods: method of Concomitant Variation

-"When two events are correlated- when one varies in close connection with the other - they are probably causally related" -If C occurs the chance of E raises, if C is absent the chance of E lowers, so C causes E. -Example: The more you boil an egg, the harder it gets, so boiling an egg causes egg hardness -Example: the more/less you study the better/worse grade, so studying causes good grades

Post Hoc Ergo Propter Hoc Fallacy

-"after that, therefore because of that" The fallacy of reasoning that just because B followed A that A must have caused B -Believing that one event is cause of a second event because the first event occurs prior to the second. But, many past events are causally unrelated -Example: a cold clears up in a few days after taking a herbal tea, but most colds clear up in a few days, anyway

Evaluating Statistical Syllogisms: (3)

-(1) Acceptable Premises: is P1 justified? -P1: Most Canadians prefer baseball to basketball. How do we know this? According to a recent poll of 60 Canadians, 64% of Canadians said they prefer baseball to basketball -(2) Statistical Strength: how strong is the generalization? -P1: Most Canadians prefer baseball to basketball. "Most" or 64% is somewhat strong but not really strong -(3) Typical Individual: is the individual randomly selected? -P2: Sally is a Canadian. Sally is just a person we met at school. (is probably random enough)

Opinion polls must satisfy further conditions as well (3)

-(1) Phrasing of questions -Example: "Are you in favour of Quebec tearing Canada in half by separating?" -(2) Order of questions: Example: Pew research, the order of overall satisfaction than bush approval or bush approval then overall satisfaction, the second had lower overall satisfaction -(3) Restricting Choices: Example: "Should abortion be allowed? Yes or no?" vs. "Should abortion always be allowed, never be allowed, only be allowed when the life of the mother is at stake, only be allowed in the case of rape, only be allowed in the first trimester"

Deductive Reasoning vs. Inductive Reasoning Inductive reasoning

-A cogent inductive argument provides probably true conclusions if we have reasoned strongly from true or probably true premises. Conclusions of inductive arguments go beyond the information given in the premises, they are ampliative -"The deductive method is the mode of using knowledge, and the inductive method the mode of acquiring it" - Henry Mayhew

Hasty Generalization and Availability Bias

-Availability bias: giving extra credence to examples that come easily to mind since they were recently seen, or personally seen -Putting too much weight on examples that come to mind to draw a conclusion is a hasty generalization, and judging based on too small a sample size -Example: Homicide rates in the US going down, though we hear of murders in media and remember the murders, not the stories where no one was murdered

Causation without Causation: (1) Coincidence

-Coincidence: the occurrence of events that remarkably seem related, but are not causally related at all -If a correlation occurs, ask: 'is it likely that these are causally connected, or do they seem causally unconnected?' -Two events may be causally unconnected if far apart in space (far apart physically) and time and not traditionally associated (ex: fire and smoke).

Correlation without Causation: (2) Common cause

-Common cause: one event regularly causes two effects, so these two effects have a common cause, rather than one of the effects causing the other -Example: when you walk the dog on a sunny day, so does your shadow the dog on a sunny day. Does your shadow cause the dog to be walked? -No. The shadow is caused by your self, which also causes the dog walk

Deductive Reasoning and the Regress Problem

-Deductive reasoning (categorical logic, propositional logic) preserves the truth that is already present in the premises -Problem: How do we know the premises of a deductive argument are true? -Possible Answer: They are conclusions from prior valid deductive arguments -Example: All humans are mortal, Socrates is human, so Socrates is mortal. How do we know 'all humans are mortal'. From a prior deduction: 'all animals are mortal, humans are animals, so all humans are mortal'. A regress ensues

Judging Analogical Reasoning: (4) Diversity Among Cases

-Diversity among cases: the greater the diversity among the cases showing the relevant similarity, the stronger the argument. The diversity of cases shows us that it is not coincidence, so the analogy really holds. -Example: When Mrs. X left the conservatives for the liberals, there was a public backlash. When Mr. Y left the liberals for the conservatives, there was a public backlash. If Joe leave the Liberals for the NDP, there will likely be a backlash

Hasty Generalization and First Impressions

-First impression: our impression of someone after meeting them once. We put a lot of value on our first impression of a person, our gut reaction to a person -Putting too much weight on what a person did/said on one occasion is a hasty generalization and judging based on too small a sample size -Overcoming: listen to your gut, but be open minded while gathering more info

Necessary/Sufficient Conditions and 'If"

-If C is sufficient for E, then the conditional 'if C then E' is true -If C is necessary for E, then 'only if C then E' is true, or, 'if C doesn't occur, E doesn't occur' is true -If C is necessary & sufficient for E, then 'if and only if C, then E' is true

(3) Drawing too strong a conclusion

-If the premises say something occurs X% of the time, the conclusion should be that that thing is X% probable -We draw too strong a conclusion when we reason from premises saying a thing occurs X% of the time to the result that is more than X% probable -Example: 'Over 50% say Pepsi tastes better' in premise to 'Pepsi tastes better' in the conclusion (but what is over 50%?)

(2) Representative Sample Size

-One can have a large sample size, but still have a weak inductive argument, if the sample size is not representative -Your sample must represent the overall population in all relevant ways (if age is relevant, make it age representative, etc...) or it is a biased sample -To avoid bias, have a random sample size, or ensure that your sample represents the population -Example: if the issue is whether condoms should be distributed to students, we should not only interview those practicing abstinence/promiscuity -Example: informal polls on news sites, but the news site is left/right, so only left/right people go to the site, so only left/right people vote

Enumerative Induction and Opinion Polls

-Opinion Polls are common and well established examples of enumerative induction -Good opinion polls have a large sample size and representative sample -Sample size: a poll of 1000 subjects is sufficient for a population of 25 million -Representation: random sampling is preferable, self-selection often entails that those passionate about the issue will participate -Margin of Error: 33% support Conservative party, +/- 4.4% -Confidence level: 33% support Conservative party +/- 4.4%, 19/20 times

Small Sample Size and the Fallacy of Hasty Generalization

-Recall, the fallacy of hasty generalization: making conclusions about a group of people/things too hastily (i.e., with too small a sample size) -Example: reading one review on Amazon to decide on the product -Example: Michael's thought experiment on convicts

Statistical Syllogisms

-Recall: categorical syllogisms: all dogs are animals, all animals are mortal, so all dogs are mortal -Statistical syllogisms: lead from statistical generalizations about a group of people to a conclusion about one member of that group -Statistical syllogisms argue from a group to a particular, where enumerative induction argues from particulars to groups -Example: "80% of Canadians live in cities, you are Canadian, so you probably (80% likely) live in a city" -Example: Most pro basketball players are over six feet tall. Terrence is a pro basketball player, so Terrence is probably over six feet tall. Example: Most (the proportion) pro basketball players (the group) are over six feet tall (the characteristic). Terrence (the individual) is a pro basketball player, so Terrence is probably over six feet tall.

Judging Analogical Reasoning: (2) Relevant dissimilarities

-Relevant dissimilarities: if there are (many) dissimilarities between the items being compared, and these dissimilarities are relevant to the conclusion, then the conclusion is probably not true

Cause and Effect

-Things happen in the world, things happen to us. How do they happen? -Example: The house burned down... why? Joe got cancer... why? Jennie broke up with Fred...why?

Argument by analogy (analogical induction)

An argument making use of analogy, reasoning that because two or more things are similar in several respects, they must be similar in some further respect.

Example of Not relevant similarities:

Birds have two legs, two eyes, breathe air, and can fly. Humans have two legs, two eyes, breathe air, so humans can fly. -How many items in common do they have? Three -How relevant are the common items to the conclusion? Being able to breath, having eyes, in no way determines one's ability to fly, so not relevant.

Example of Relevant Similarities:

Birds have wings and can fly, planes have wings, so planes can probably fly. -How many items in common do they have? Only one. -How relevant are the common items to the conclusion? The conclusion states planes can fly, wing are relevant to the ability to fly, so quite relevant.

Analogy

Compares two things. An argument from analogy compares two things and suggests they must be alike in some further way as well. -Formally: A has property w, x, y, and z. B has property w, x, and y. So, B probably has property z. -Example: Love is sweet and messy like chocolate, and chocolate doesn't last, so love probably doesn't last either. -Chocolate has the properties of being sweet, messy and not lasting. Love has is sweet and messy. So, love probably has the property of not lasting

Problem: How do we know the premises of those prior arguments are true? What's the solution?

Inductive Reasoning -We need a way to generate true statements that is not true based on prior deductive reasoning -Inductive reasoning is an alternate form of reasoning that generates likely or probably true statements without appealing to deductive reasoning.

Analogies are?

Inductive arguments (also known as analogical induction), so they lead to probable conclusions. Humans use analogical reasoning in learning and in decision making about novel circumstances. -Example: Baby Sally hears "ball" for many different kinds of objects, so she finds similarities between the balls. When a new object is presented to her, she judges it similar to previous balls she has experienced. -Example: going down a dark alley, you judge it is not safe based on its similarity to other experiences of dark alleys

A strong enumerative inductive argument

Might still not be cogent. In order to be cogent, an argument must be probabilistically strong and also have true or very probably true premises

Enumerative induction

Reason from individual members of a group to conclusions about all members of the group -Example: 12/12 squirrels we studied love nuts, so, probably all squirrels love nuts

Weak inductive reasoning

Similar to 'invalid', an inductive argument is weak if its true (or probably true) premises provide little support for the truth (probable truth) of the conclusion

Strong inductive reasoning

Similar to 'valid', an inductive argument is strong if its true (or probably true) premises provide strong support for the truth (probable truth) of the conclusion

Hasty generalization

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

Necessary and Sufficient Conditions Define 'Having Sex'. You are having sex when...?

When defining terms, we often try to make our definition include every and all true cases. A definition captures necessary/sufficient conditions. -Example: 'Sex is genital contact with at least one other person" So, if genital contact with at least one other person happens (sufficient condition), sex happens. If genital contact with at least one other person doesn't happen (necessary condition), sex doesn't happen.

Reasoning in deductive argument is what? Reasoning in inductive argument?

While the reasoning in a deductive argument is valid/invalid, the reasoning in a inductive argument is strong/weak -Valid/invalid is all or nothing, perfect reasoning vs entirely failed reasoning -Strong/weak is a matter of degree: very strong, strong, weak, very weak

Enumerative induction formally written parts

X% of the sampled members have the property in question, therefore X% of the target group as a whole has the property in question -Sampled members = 12/12 squirrels we studied -Target group = all squirrels -property in question = love nuts

Analogy definition

a comparison between two things alike in specific respects

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

Cogent vs. Not Cogent Inductive Arguments In inductive reasoning:

all true premises and inductively strong reasoning = a cogent argument

Cogent vs. Not Cogent Inductive Arguments In deductive reasoning:

all true premises and valid reasoning = a sound argument

Causal argument

an inductive argument whose conclusion contains a causal claim

A condition can be necessary but not sufficient

example: oxygen is necessary for life but not sufficient since we need water and food as well.

Causal arguments

is an argument that has a causal claim in the conclusion -Causal argument are inductive. They reason from many similar past instances to a present instance. Hence, they give us probably conclusion. -They are similar to statistical syllogisms, since they reason from a group of similar instances in the past to a conclusion about what happened now. -example: the last ten times I put my finger in a spinning fan, I hurt my finger, so my hurt was cause by putting my finger in the spinning fan -They are similar to analogical reasoning, since they compare previous relevantly similar instances to make conclusions about the new instance -Example: I put my finger in a fire, causing a burn; I put my finger on the hot stove, causing a burn; so if I put my finger in a hot toaster it will cause a burn

Statistical syllogism

reason from premises about the group to conclusions about the individual Example: most Canadians like hockey, Jan is Canadian, she probably likes hockey

Judging Analogical Reasoning: (1) Relevant Similarities

the similarities being compared must be relevant to the conclusion being drawn. The greater the number of relevant similarities between the items, the stronger the conclusion

1) Small Sample Size

the size of the sample that is studied is the sample size. The sample size can be too small to accurately reflect the group at large -The smaller your sample, the greater the chance you have selected outliers (atypical specimens). The larger the sample size, the easier it is to see the true nature of the specimen

Margin of error

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

Necessary/Sufficient Conditions and Causation To prevent an effect

we focus on necessary conditions. If a condition is 'necessary' for the effect, then taking it away will take away the effect -Example: remove the necessary condition of oxygen, the fire goes out

Necessary/Sufficient Conditions and Causation To cause an effect

we focus on sufficient condition. If a condition is 'sufficient' for the effect then making it happen makes the effect happen -Example: assuming the car is working, and gas is in the tank, turning the ignition key is sufficient for starting the car

Confidence level

In statistical theory, the probability that the sample will accurately represent the target group within the margin of error.

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

Deductive Reasoning vs. Inductive Reasoning Deductive reasoning

A sound deductive argument provides indisputably true conclusions if we have reasoned validly from true premises. Conclusions of deductive arguments preserve the truth of the premises

Causal claim

A statement about the causes of things or an assertion about the cause of something. X cause Y -Example: the short circuit caused the house to burn down -Example: smoking caused Joe to get lung cancer -Example: Fred said a bunch of mean things to Jennie so she dumped him

Example of inductive reasoning

-This squirrel likes nuts, that squirrel likes nuts, the next ten squirrels like nuts, so, probably all squirrels like nuts -Is this a strong or weak inductive reasoning? -12/12 in our sample of 1 billion squirrels like nuts, so we conclude, probably, all 1 billion squirrels like nuts -Issues: sample size (very small), results of the sample (all similar) -Example: 95% of humans have been heartbroken less than five times in their lives, Socrates is human, so, probably, Socrates was heartbroken less than five times in his life -Premise 1 (true), Premise 2 (true), the inductive reasoning is reasoning from a 95% likelihood in the premise, to a probable (51-99%) likelihood in the conclusion -This is a strong inductive argument -Example: 60% of people know if they are with Mr. or Mrs. Right within ten weeks, John has been with Sally for ten weeks, so, John probably knows if Sally is Mrs. Right -Premise 1 (true), Premise 2 (true), the inductive reasoning is reasoning from a 60% likelihood in the premise, to a probable likelihood in the conclusion -This is a somewhat strong inductive argument.

Individually Necessary and Jointly Sufficient

-When a set of necessary conditions together constitute a sufficient condition for an event we call them 'individually necessary and jointly sufficient' -Example: to keep a goldfish alive, water, plus food, plus warmth is (roughly) an INJS condition

Judging Analogical Reasoning: (3) Number of Instances Compared

-the greater number or cases that show the relevant similarities, the stronger the argument. After all, this shows us that the similarity is not coincidental -Example: The previous 20 times we observed this blood splatter pattern, we learned the gunshot victim was four feet from the gun. In this crime, we have this exact pattern of blood, so the victim was four feet away from the gun.

What is the 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

Sufficient condition:

A condition for the occurence of an event that guarantees that the event occurs a condition that guarantees the event will occur. If C occurs, E occurs, so C is sufficient for E -Example: being red is a sufficient condition for being a colour

Necessary Condition:

A condition for the occurrence of an event without which the event cannot occur or a condition that is needed in order for the event to occur. If C does not occur, E does not occur, so C is necessary for E. -Example: oxygen is a necessary condition for staying alive

Biased sample

A sample that does not properly represent the target group

Evaluating enumerative inductive arguments

Enumerative inductive arguments can be strong or weak, or can vary in strength.

A condition can be sufficient but not necessary

Example: being red is sufficient for being colour, but not necessary, since brown and green are colours too

Relevant property (property in question)

In enumerative induction, a property, or characteristic, that is of interest in the target group.

Representative sample

In enumerative induction, a sample that resembles the target group in all relevant ways

Sample (sample member)

In enumerative induction, the observed members of the target group

Target group (target population)

In enumerative induction, the whole collection of individuals, under study

Inductive reasoning example?

This squirrel likes nuts, that squirrel likes nuts, the next ten squirrels like nuts, so, probably, all squirrels like nuts -The conclusion is only probably, as we have not studied every squirrel, so we are not sure they are like nuts. But, the conclusion is probably true, as every squirrel we studied likes nuts, so, probably, they all do. -Inductive reasoning is ampliative: from facts about ten squirrels, we conclude something about all squirrels.