Video Module 27: Reasoning Flashcards
deductive reasoning
reasoning by using general statements to reach a logically certain conclusion
- guaranteed to be correct when adhering to the rules
- using logical constructions to reach conclusions about specific cases
inductive reasoning
reasoning by using specific examples to arrive at general conclusions
- constructing or evaluating general propositions derived from specific examples
- probable guesses made on the basis of prior evidence
- not always guaranteed to be correct
syllogisms
a type of reasoning where a conclusion is drawn from two or more premises, which are both assumed to be true
- If, given that 2 premises are true, a conclusion must be true, then an argument is valid
- If, given that 2 premises are true, a conclusion does not necessarily have to be true, then an argument is invalid
- e.g.
—Premise 1: Starfire is an alien
—Premise 2: Robin likes some aliens
—Conclusion: Robin likes Starfire
—‘Robin likes Starfire’ is an invalid argument because, given that both premises are true, the conclusion does not necessarily have to be true. Since Robin likes ‘some aliens’ and not ‘all aliens,’ one may assume that it is possible for Starfire to not be included in the aliens that Robin likes.
How is a conclusion logically valid?
A conclusion is logically valid if it must be true given that the premises are true.
- If a conclusion doesn’t necessarily have to be true given that two premises are true, then the conclusion is logically invalid (because it doesn’t follow the line of reasoning)
belief bias
the tendency to accept invalid conclusions if they are believable, or to reject valid conclusions if they are not believable
- e.g. #1
—Premise 1: Starfire is an alien
—Premise 2: Robin likes some aliens
—Conclusion: *Robin likes Starfire.
—Given that someone has knowledge of Robin and Starfire’s relationship, they may accidentally decide that “Robin likes Starfire” is a valid conclusion. However, this is not a logically valid conclusion.
- e.g. #2
—Premise 1: Robin wears a mask.
—Premise 2: Starfire hates all people who wear masks.
—Conclusion: Starfire hates Robin.
—People may accidentally say that ‘Starfire hates Robin’ is an invalid conclusion because of their outside knowledge.
truth vs. validity
truth: depends on the relationship between an assertion and the state of the world
validity: depends on the relationship between the form of the argument and the conclusion
What is the relationship between truth and validity of an argument?
The truth and validity of an argument are independent and are not mutually exclusive.
- An argument can be true in the real world (e.g. ‘Robin likes Starfire’), but logically invalid given the premises (e.g. ‘Starfire is an alien’ and ‘Robin likes some aliens’)
- An argument can be false in the real world (e.g. ‘Starfire hates Robin’), but logically valid given the premises (e.g. ‘Starfire hates all people who wear masks’ and ‘Robin wears a mask’)
modus ponens
If A, then B. A, therefore B.
—If A is true, then B is true.
—A is true, therefore B is true.
—this conditional syllogism is logically valid
—e.g. “If Gojo is the strongest, then Geto will defect. Gojo is the strongest, therefore Geto will defect.”
modus tollens
If A, then B. Not B, therefore not A.
—If A is true, then B is true.
—B is not true, therefore A is not true.
—this conditional syllogism is logically valid
—e.g. “If Geto acts evil, then Gojo will kill him. Gojo has not killed Geto, therefore Geto has not acted evil.”
affirming the consequent
If A, then B. B, therefore A.
—If A is true, then B is true. B is true, therefore A is true.
—this conditional syllogism is logically invalid
—the consequent is what follows a given situation
—e.g. “*If Yuji is evil, then Gojo will kill him. Gojo will kill Yuji, therefore Yuji is evil.”
This is a logically invalid argument because Gojo killing Yuji will certainly follow Yuji being evil, however it is not necessarily the case the Yuji has been evil if Gojo does kill him. Gojo may also kill Yuji on other terms.
denying the antecedent
If A, then B. Not A, therefore not B.
—If A is true, then B is true. A is not true, therefore B is not true.
—this conditional syllogism is logically invalid
—the antecedent is the given situation
—e.g. *“If Nanami dies, then Yuji will kill Sukuna. Nanami does not die, therefore Yuji will not kill Sukuna.”
This argument is logically invalid because it is not necessarily the case that Yuji will not kill Sukuna if Nanami is alive. Yuji may kill Sukuna for other reasons.
How do we use mental rules to make deductions?
Researchers propose that we may use mental rules, which are language-like representations we use for reasoning.
—We may apply syntactic rules of inference to these mental rules
—using the rules of syntax to manipulate representations of reasoning
—Inferences are less complex if we already have a rule for them
—Explains why it is easy for us to see lines of reasoning such as “modus ponens”, but why other lines of reasoning are more difficult
How do we use mental models to make deductions?
Researchers propose that we may use mental models, which are diagrammatic representations of possible states of the world that are compatible with the premises.
—employing mental diagrammatic representations to evaluate the validity of arguments
—explains why we might fall for statements that are logically invalid, if they are believable
Wason 4 card task
A task which researchers use to evaluate people’s conditional reasoning abilities.
—”If there is a G on one side of the card, then there is a 3 on the other side”
—modus ponens: There is a G on one side of the card, therefore there must be a 3
—modus tollens: There is not a 3 on one side of the card, therefore there cannot be a G
—affirming the consequent: *There is a 3 on one side of the card, therefore there must be a G
—denying the antecedent: *There is not a G on one side of the card, therefore there cannot be a 3
How can we improve our performance on the Wason 4 card task?
Researchers found that people’s performance on the Wason 4-Card task improved when they made the cards relevant to people’s actual experiences.
—Participants’ performance improving when the Wason 4-Card task uses examples such as drinking ages and alcohol is evidence that we rely on a mental model of the world rather than a linguistic rule to solve problems that are relevant to our experience
pragmatic reasoning schema
a general, non-abstract rule that relates to a particular kind of goal, such as permission, obligation, or causation
- e.g. When the Wason 4-Card selection task is reframed in terms of beer and age, 61% of college students succeeded, compared for just 19% for the original version of the task
—Show that we might use a pragmatic reasoning schema for the instance of age and beer
What does social contract theory and evolutionary psychology suggest about reasoning?
Social contract theory suggests that moral and political obligations are dependent on a contract or agreement among individuals to form a society.
In accordance with social contract theory and evolutionary psychology, Leda Cosmides (Cosmides & Tooby 1996) argues that people are good at reasoning in particular situations that have been present in evolutionary history.
—This would explain why we’re good at reasoning in situations such as people breaking social norms or detecting cheaters (on tests and in relationships)
—Cooperation is crucial for survival
—Evolution has not selected for the ability to solve abstract logic problems, since these are not necessarily crucial for our survival
—This theory is highly controversial
the problem of induction
Induction does not guarantee a correct answer, however there are many cases in which we cannot rely upon deductive inferences
—Most of the time, we do not have knowledge of general principles
- We can use inductive reasoning (forming universal generalizations from specific instances) in any situation we choose, but that does not guarantee that our reasoning is correct.
—Induction is only guaranteed to be correct is we have experienced all possible instances of something
illusory covariation
a tendency to see patterns between variables that are not really linked
- e.g. Noticing that Academy Award-winning actors tend to live 3.9 years longer than actors who were never nominated for an Academy Award.
—Does this mean that success = longevity? No.
—The reality is that actors who live longer have more time to win an Oscar.
- Focusing on observations that confirm our beliefs, but ignore the base rates of behaviour:
—thinking that two things are related because they stand out when they occur together
- e.g. Noticing that you get good grades when you wear your ‘lucky hair clip’.
—It is easy to think that the hair clip is lucky because you get good grades. However, if you’re a good student, you are likely not making note of the times that you’ve gotten decent grades without wearing the hair-clip because it is a normal occurrence. You are more likely to pay attention to the fact that your grades are high when you’re wearing something that you believe will make them high.
confirmation bias
the tendency to be more responsive to evidence that confirms one’s beliefs, and ignore disconfirming data
- e.g. Using an EVP machine while ghost hunting and taking every speech-like sound as “evidence of ghosts,” while ignoring all of the instances of random sounds that got recorded.
What are some different forms of confirmation bias?
- seeking out evidence which confirms what you already believe
- failing to adjust your belief after seeing disconfirming evidence
- taking confirming evidence at face value, but scrutinizing disconfirming evidence (or reinterpreting disconfirming evidence to diminish its impact)
- having a better memory for confirming rather than disconfirming evidence
- failing to consider alternate hypotheses that are just as possible
