Quizlet #7 - Chapter 13 -> Deductive Reasoning

more clarifying example of why previous syllogism was wrong

-A: all the students live in Tucson (all A are B) -B: some people who live in Tuscon are millionaires (some C are D) -C: Some of the students are millionaires (Some A are D) **using this new wording while keeping the form the same makes it easier to see that the people in the second premise do not have to include students --can't say this for sure if there are students who are millionaires --possible that no students are millionaires

Difference between validity and truth can make it hard to judge if logical!

-Difference between validity and truth can make it hard to judge whether reasoning is logical or not bc not only can valid syllogisms result in false conclusions, but syllogisms can also be invalid even though each of the premises and the conclusion could be true -So syllogism can have validity but not truth

SO new content -> easier to get this same problem right -> beer paradigm

-Four cards are show and each has an age on one side and the name of a beverage on the other. Imagine talking to officer and apply the rule 'if a person is drinking beer, then he or she must be over 19 years old' -Task: which of cards must be turned over -beer/drinking age version = identical to abstract version Wason had but in concrete terms -Findings: 73% of participants gave correct answer -> it is necessary to turn over the 'beer' and the '16 years old' cards --Necessary to turn over "beer" and "16 year old" --In contrast, none of participants answered the abstract task correctly

BUT if you put some of these in different forms, people can get it easier. Example of easier to notice affirming the consequent

-If i live in Tucson, then I live in Arizona -I live in arizona -Therefore, I live in Tucson *much more obvious that this does not follow from the premises

Conditional syllogism template

-If p then q -P -Therefore, q

Affirming the consequent conditional syllogism (invalid)

-If there is lightning then there are clouds in the sky -there are clouds in the sky -therefore there is lightning **doesn't follow **but 60% accept this incorrectly **invalid bc you are saying if there is lightning then there are clouds NOT if there are clouds then there is lightning

Denying the antecedent

-If there is lightning then there are clouds in the sky -there is not lightning -therefore there are no clouds in the sky **invalid **60% accept this incorrectly

Belief bias experiment

-Participants read valid and invalid syllogisms that had either believable or unbelievable conclusions -Task = indicate whether conclusion was valid -See belief bias -> when syllogism was valid, participants accepted its conclusion 80% of the time if it was believable but only 56% of time if unbelievable -Interesting: invalid syllogisms that had believable conclusions were judged as valid 71% of the time -Therefore the belief bias can cause faulty reasoning to be accepted as valid especially if conclusion of invalid syllogism is believable

looking out for cheaters

-Study suggesting that real-world versions are easier to solve bc people are on the lookout for cheaters -Reasoning behind this explanation is based on idea that from an evolutionary point of view, being aware of people's cheating is important for survival

Mental model

-a specific situation represented in a person's mind that can be used to help determine the validity of syllogisms in deductive reasoning

Modus ponens

-affirming the antecedent (modus ponens) -> valid form example: -If there is lightning then there are clouds in the sky -There is lightning -Therefore there are clouds in the sky --97% accept this --called modus ponens which is latin for 'the way that affirms by affirming' is valid -> the conclusion follows logically from premises

Why is the beer problem so much easier?

-bc involves regulations people are familiar with --anyone who knows there is a minimum age for drinking knows that if someone looks 16, they need to be checked --but it's not specific familiarity unless you've worked as a bouncer -More likely to be schemas -Also specific preparation to detect cheaters

Why do people think that syllogism 3 is valid?

-belief bias - the tendency to think a syllogism is valid if its conclusion is believable -for syllogism 3, the idea that some students are irritable is believable but when we change the wording to create number 4, the new conclusion isn't believable --belief bias works both ways: --ex: syllogism 2 makes an unbelievable conclusion and makes it more likely the syllogism will be considered invalid

Valid

-conclusion follows logically from premises --the conclusions follows by putting in premises and turning the crank

True

-conclusion is true --if its valid it doesn't necessarily have to be true bc premise could be false

how can we understand the difference between two types of reasoning (inductive vs deductive)

-consider the scope of the info being processed -in inductive, starts with specific cases and generalizes to broad principles -in contrast, deductive reasoning starts with broad principles to make logical predictions about specific cases

Syllogism

-consists of two broad statements or premises followed by a third statement called the conclusion (based on rules of logic) --basic form of deductive reasoning -2 forms: --categorical syllogism --conditional syllogism

Modus tollens

-denying the consequent (modus tollens) -If there is lightning, then there are clouds in the sky -there are not clouds in the sky -therefore there is no lightning **only 60% accept this **saying conclusion is false and based on that we can conclude that the second premise is false *valid conclusion

Deductive Reasoning

-determine whether a conclusion logically follows from statements -dif than inductive reasoning which is drawing conclusions based on observations ! -classic example = the syllogism

Conditional Syllogisms

-have two premises and a conclusion like categorical syllogisms, but first premise has the "If ... Then" -this kind of deductive reasoning = super common in everyday life

So conclusions reached are ...

-in deductive reasoning, the conclusion reached can be definitely true but only if both premises are definitely true and if the form of the syllogism is invalid --but judging the truth and validity isn't easy

What is tricky in conditional syllogisms

-just like in categorical syllogisms, if both the premises are true and the syllogism is valid, then the conclusion is definitely true -BUT also like in categorical syllogisms, assessing validity = tricky

Classical syllogism set up

-major premise -minor premise -conclusion -ex: --all men are mortal --socrates is a man --therefore, Socrates is mortal *valid, true, and sound

Findings

-many participants indicated that the E must be turned over (correct) -46% of participants indicated that in addition to the E, the 4 would need to be turned over --but this gives us no info about whether the rule is true other than it works in this case --what looking for when testing any rule is an example that doesn't work and as soon as we do we conclude the rule is false -> Falsification principle

Mental models of deductive reasoning (one possible mechanism for deduction)

-proposed to aid in judging the validity of syllogisms -idea that people can imagine situations = basis of their proposal that people use mental models to solve deductive reasoning problems

Why are real world problems easier? -> Wason four-card problem

-related to syllogisms and shows similar errors -task: --Each card has a letter on one side and a number on the other --Which of these cards must you turn over to test the following statement? ---if there is a vowel on one side of the card, then there is an even number on the other side -cards: E, K, 4, and 7 --you have to turn over E and 7 but most people want to turn over the 4

what this principle shows us

-shows us the principle behind the mental model theory -> a conclusion is valid only if it cannot be refuted by any model of the premises -Mental model theory is attractive bc it can be used to assess a syllogism's validity without training in the rules of logic bc it makes predictions that can be tested --Ex: theory predicts that syllogisms that require more complex models will be more difficult to solve and this has been confirmed in experiments

Schemas?

-suggested that people think in terms of schemas -> their knowledge about rules that govern their thoughts and actions -one of these = permission schema which states that if a person satisfies a specific condition (being of legal drinking age) then he or she gets to carry out an action (being served alcohol) --if you are 19 then you get to drink a beer -> something most participants had learned -idea that people apply real-life schema like permission one to the card task makes it easier to understand dif between abstract and real world --abstract -> goal = indicate whether abstract statement is true --but in beer / drinking task, goal = be sure that a person has permission to drink alcohol --activating the permission schema helps people focus attention on the card that would test the schema

Basic principle behind mental models

-that people create a model, or an imagined representation of the situation, for reasoning problem --they generate a tentative conclusion based on this model and then look for exceptions that might falsify the model -if they do find an exception, they modify the model -eventually if they can find no more exceptions and their current model matches the conclusion, they can conclude that. the syllogism is valid

Categorical syllogisms

-the premises and conclusions are statements that all begin with All, No, or Some -ex: Premise 1: all birds are animals Premise 2: all animals eat food Conclusion: therefore, all birds eat food

Falsification principles

-to test a rule, it is necessary to look for situations that would falsify the rule -the second card that should really be turned over is 7 and only 4% came up with this

Invalid inferences with conditional syllogisms

-use same example as before -2 kinds: --Affirming the consequent --Denying the antecedent

Sound

-valid + premises are true

So takeaways on syllogisms

-very much type II -> doesn't come naturally! -in language we often don't distinguish clearly between "if" (syllogism) and "if and only if" (biconditional)

use these syllogisms in real life?

-yes -Even though syllogisms seem academic, people use syllogisms to "prove" their points, often without realizing that their reasoning is sometimes invalid --It is easy to fall prey to the belief bias and even conclusions that might sound true are not necessarily the result of good reasoning

Are there other models about how people might assess validity in syllogisms?

-yes -no agreement about which is correct -People can use a variety of dif strategies in reasoning and some people are much better at solving syllogisms than others -So question of how people go about determining validity in syllogisms remains unanswered

Valid but premises and conclusion are not true

1 - All men are purple 2 - Socrates is a man 3 - therefore, Socrates is purple -how can it be valid if conclusion is obviously wrong? --validity is about whether the conclusion logically follows from the premises based on the form or structure of the syllogism --if it does, and the premises are true, as in syllogism 1, then the conclusion is true as well --but if one or both of the premises are not true, the conclusion may not be true, even though syllogism's reasoning is valid

Valid and true but not sound example

1 - All punk rockers live to their 90s 2 - Tony Bennet is a punk rocker 3 - Therefore, Tony Benett has lived into his 90s **the conclusion is true and this is valid, but the premises are not true so it isn't sound

Possibly true but not valid example (syllogism 3)

1 - all students are tired 2 - some tired people are irritable 3- some of the students are irritable **conclusion could be true but doesn't follow from the premises -some people might have a hard time accepting this bc probs know tired and irritable students and students are people --can better understand how this does not logically follow from premise by looking at another syllogism (4)

Valid inferences with the conditional syllogism

1 - modus ponens 2 - modus tollens

Example: beekeepers

1 - none of the artists are beekeepers 2 - all of the beekeepers are chemists 3 - some of the chemists are not artists **So according to mental model, we will imagine that we are visiting a meeting or artists, beekeepers, and chemists society --or you might start building a model in your head like imagining little tokens representing artists, beekeepers and chemists --all have to follow these rules of the first two premises -> no artists can be beekeepers and all of the beekeepers must be chemists --formulate first model, then revise it and then confirm the model

What people are doing here

1 - people turn over the 4 --They are acting as though "if" is the same as "if and only if" 2 - they fail to turn over the 7 --They are confirming when they should attempt to falsify 3 - accuracy depends on content though!