cognitive lecture 16- logical reasoning

What are the factors affecting conditional reasoning?

1. Linguistic problems (linguistic of the negative, people get confused transferring to logic), e.g., whether the problem contains negative statements. 2. Abstractness of the problem e.g. P&Q rather than more realistic problems, people are more likely to get confused.

What are the factors affecting syllogisms?

1. Linguistic: As before, Syllogisms are more difficult if they include negatives; furthermore, they're easier to solve if they use the active voice: If all plants need water, And all flowers are plants; then.... compared to passive voice: If water is needed by all plants, And all flowers are plants; then... (Lippman, 1972). 2. Time: Galotti et al. (1986) found that with little time, participants give their first impressions. Even experts make errors when time is limited.

What is deduction?

A formal process by which sequence of rules of inference produced by a set of premises, from, which a conclusion necessarily follows. In other words: reasoning from general premises, which are true or presumed to be true, to more specific, certain conclusions. o E.g.: IF THEN statement. o Must be true if the premises are true.

What is an argument?

A sequence of propositions, starting with premises, which allegedly justifies another proposition, called a conclusion. - Premise: the U.S. military budget is the largest in the world - Conclusion: it is probable that the US military will remain one of the largest for several years

What is soundness of an argument?

A sound argument is a valid argument in which the premises are true.

What is validity of a syllogism or argument?

A syllogism, or any argument, is valid if the conclusion(s) drawn logically follow from the premises; otherwise it is invalid. In a valid argument if the premises are true, the conclusion is necessarily true.

What is Abductive reasoning?

Abductive reasoning: (type of inductive reasoning), typically begins with an incomplete set of observations and proceeds to the likeliest possible explanation for the set. Abductive reasoning yields the kind of daily conclusions that does its best with the information at hand, which often is incomplete. Doesn't give an absolute conclusion. Most relevant to everyday life. Conclusions not definitely true. The bowl is filled with apples You have an apple in your hand You took the apple out of the bowl

What is the belief bias error in syllogisms?

Belief bias - occurs when people make judgements based on prior beliefs, rather than on the rules of logic; í i.e. they accept invalid conclusions if they are believable and reject valid conclusions when they are unbelievable.

What is Induction?

Coming to a conclusion that is likely from the premises. Usually coming to conclusions about a universal or a particular from previous instances of particulars. In other words: reasoning from specific cases to more general, but uncertain, conclusions. "Both inductive and deductive arguments occur frequently and naturally... Both forms of reasoning can be equally compelling and persuasive, and neither form is preferred over the other" (Hollihan & Baaske, 2015, p. 97).

What is conditional deductive reasoning?

Conditional - if X is older than Y, and C is younger than X, then who is the eldest? X, but can we tell who is the youngest? We cannot tell.

What does deductive reasoning. include?

Deductive reasoning: originates from philosophy and mathematics and is the most obvious form of reasoning. Deduction is a method of applying a general rule (major premise) in specific situations (minor premise) of which conclusions can be drawn. All humans are mortal Socrates is human Socrates is mortal (true syllogisms) All Martians are icnoc Ehhny are martians (less concrete example) Ehhny are icnoc Icnoc are Mortal All Icnoc are humans (not correct and true to internal logic)

What are the criticisms of Scribner (1977) study?

However, o This may not be due to no-schooling, but rather due to specific type of group -thinking. o In two studies, with members of a traditional indigenous Maya members from Guatemala, Castelain et al. (2016), showed that group discussion improved individual reasoning performance for a wide variety of tasks. o Observed improvement in the reasoning skills was attributed to two features: o Reduction of the myside bias, which precludes individuals from improving their performance on their own, and o the ability to soundly evaluate others' arguments, which allows individuals to benefit from group discussions.

What are some examples of invalid conclusions?

If it is raining, Alan gets wet. P > Q Alan gets wet. Thus it must be raining. Q > P (wrong) INVALID because he may have gotten wet a number of other ways, e.g. someone threw a bucket of water over him, he jumped in a pool etc. "affirmation of the consequence". It is not raining. Thus Alan does not get wet. No P > No Q (wrong) INVALID because he may still get wet otherwise... "denial of the antecedent".

What is inductive reasoning?

Inductive reasoning: a logical process in which multiple premises, all believed true or found true most of the time, are combined to obtain a specific conclusion 'the sun rose yesterday, the sun rose the day before etc.' so probably, 'the sun will rise tomorrow' (highly likely conclusion).

What is the definition of logical reasoning?

Logical reasoning is the process which uses formal tools (arguments, statements, premises and axioms) to define whether a statement is true or false.

How can syllogisms be represented?

One way to represent syllogisms is using Venn diagrams - known in this case as Euler's circles 3 circles inside each other, big, medium and small C,B,A respectively from outer circle All A are B All B are C Therefore, all A are C

What are the issues when a problem is abstract?

Try the following example: If an object is not blue, then it is rectangular. This object is not rectangular. Therefore, it is blue. (True or False?) Easier to visualise problems; people struggle when it is abstract; o Individuals have difficulty when the material is abstract (Wason & Johnson-Laird, 1972). o Other research indicates that performance is better if the propositions are high in imagery (Clement & Falmagne, 1986).

What did Wason & Johnson-Laird (1972) find about errors in conditional reasoning?

You need to determine which of the hidden parts of these cards you need to see in order to answer the following: "is it true that if there is a vowel on one side there is an even number on the other side?" You have one chance to make the decision; you must not assume that you can inspect the cards one at a time. Name those cards which it is absolutely essential to see. given set of cards o Wason (1966), found <10 % of their participants chose the correct cards o Wason selection test: deductive reasoning task used in hundreds of studies over the last thirty years or so (Wason, 1966; updated by Evans,1993). o The study shows that people have a tendency to confirm hypotheses. o People have to be taught the rules of logic.

What is a premise?

a proposition that is assumed to be true for the sake of a logical argument premise: 'all tortoises are vegetarians'

What is a syllogism?

a specific type of logical argument that applies reasoning to arrive at a conclusion. It is generally based on two or more propositions that are asserted or assumed to be true, e.g.: - Major premise: All dogs have four legs. - Minor premise: Rover is a dog. - Conclusion: Rover has four legs.

What do syllogisms involve?

o A form of deductive logic invented by Aristotle, often found in intelligence tests. o The goal of syllogistic reasoning is to understand how different premises can be combined to give logically true conclusions. o Often, syllogisms are presented in an abstract form, such as: All A are B. All B are C. Therefore, All A are C. o Inserting words into the syllogism will verify the truth of the conclusion: All mammals have fur. All bats are mammals. Therefore, all bats have fur. o A logical construction often consisting of: o A major premise (e.g. All mammals have fur.) o A minor premise (e.g. A bat is a mammal.) o A conclusion (e.g. a bat has fur.)

What is the definition of reasoning?

o A purposeful mental activity that involves operating on information in order to reach conclusions. o Not using instinct or emotional processing. o Reasoning requires us to draw inferences from observations, facts, or assumptions

What are the two major parts of conditional reasoning?

o Conditional reasoning always contains two major parts: 1. Conditional clause - a statement that expresses some relationship between conditions (e.g. between the moon and needing a torch). 2. Evidence - pertains to the conditional clause (e.g. not being able to see without the torch). Conclusion: Therefore, conditional reasoning involves a logical determination of whether the evidence supports, refutes, or is irrelevant to the stated if - then relationship o If A, then B o If A=true, then follows that B=true (called modus ponens: "the way that affirms by affirming"). o If B=not true, then follows that A=not true (called modus tollens: "the way that denies by denying"). Premise 1: If it is raining, Alan gets wet. P > Q Premise 2a: It is raining. Inference: "Alan gets wet" is true. P >Q (Modus ponens: proving something right) Premise 2b: Alan does not get wet. No Q >No P Inference: "It is raining" is not true. (Modus tollens: proving something wrong)

what is decision making?

o Decision making: Should I email the lecturer for help about my cognition essay? Or, should I call my friend who's finished his essay? o Decision making refers to assessing and choosing among several alternatives o Choices.

in deductive reasoning a conclusion is guaranteed?

o Deductive reasoning moves from the general rule to the specific application: In deductive reasoning, if the original assertions are true, then the conclusion must also be true. o For example, math is also a form of deductive reasoning o If x = 4 And if y = 1 Then 2x + y = 9

What are the fallacies in conditional reasoning?

o Denial of the antecedent (DA): false antecedent implies false consequent o Affirmation of the consequent (AC): true consequent implies true antecedent

What did Evans (1989) suggest about belief bias?

o Evans (1989) argued that individuals 'short-circuit' their usual critical approach when the conclusions are consistent with their prior beliefs.

How are people highly prone to errors in evaluating the validity of arguments?

o Evans et al., 1995 studied how well people judge these 4 types of statements. o Across three experiment, found that the bias was mostly restricted to DA and MT inferences: suggesting a difficulty with double negation: o If it is raining, Alan gets wet. o Modus tollens (MT): false consequent implies false antecedent e.g. Alan does not get wet. Inference: "It is raining" is not true. o Denial of the antecedent (DA): false antecedent implies false consequent e.g.: If it is NOT raining, Alan does NOT get wet.

What is inductive/abductive reasoning used in?

o Extensively used in scientific methods. Researchers make observations, then draw some conclusions that they think are probably true o It is always important to note that new information may come along that will refute the conclusion. For example the world is flat. Ships sail off and never return because they fall off the edge. When a ship does return the world can no longer be considered flat.

What is the illustration of conditional reasoning?

o Illustration of conditional reasoning: If the moon is shining, I can see without a torch. (conditional clause) I cannot see without a torch. (evidence) Therefore, the moon is not shining.

Why are some people better at syllogisms?

o Johnson-Laird (1985) states that syllogistic reasoning is much more highly correlated with spatial ability than verbal ability. o Suggests that people solve problems involving logical deductions by constructing Mental Models. o Mental models are imagined physical representations of the facts. It has been related to WM capacity Consider the following: A is less than C B is greater than C Is B greater than A? What would your mental model look like?

What did Lord et al (1979) suggest about belief bias?

o Lord et al. (1979) asked people who either supported or opposed capital punishment to read summaries of two studies on the topic. Then they rated how well the study had been conducted, and whether it supported the conclusion. o Half of the summaries supported capital punishment, the other half opposed. o if studies conformed to the participants prior belief, then they rated the studies higher.

What are the valid inferences in conditional reasoning?

o Modus ponens (MP): true antecedent implies true consequent o Modus tollens (MT): false consequent implies false antecedent both valid inferences

What reasoning is used most in everyday life?

o Nearly all our reasoning in everyday life is inductive/ abductive rather than deductive o Refers to the drawing of general conclusions from specific observations; " I just had a bad lecture from X; they must be a bad teacher". o This is a reasoning in which the premises provide support for a certain conclusion, but it is still possible for the conclusion to be false. Use this a lot in science...

How do people differ in solving syllogisms and how do they often make errors?

o People differ widely in their ability to solve syllogisms. o In addition to this, people are not always logical. They will often accept false syllogisms as valid; "All birds have beaks That creature has a beak Therefore, that creature is a bird"? - Not true

What are the cross-cultural differences in syllogistic reasoning?

o Studies suggest that illiterate, unschooled people in remote villages in various places throughout the world are unable to solve syllogistic problems. Scribner (1977), visited various tribes (e.g. Liberia, West Africa and the Kpelle) and presented them with the following: All Kpelle men are rice farmers. Mr Smith is not a rice farmer. Is he a Kpelle man? o Participants tended to reply: 'I don't know the person. If I was to know him in person, then I could answer. If you don't know a person, how can you respond?'

What is the hypothesis testing (confirmation bias) error in syllogisms?

o Wason (1960) told people that the numbers below conformed to a simple relational rule: 2 4 6 o Participants were asked to find out the exact rule that applied by using other three-number series, and getting feedback on each whether the numbers conformed to the rule.

what is logical reasoning?

o We use logical (deductive) reasoning and decision-making on a daily basis. o Logical reasoning: A friend says that if they finish their assignment in time, they'll call you about going out that night. Your friend doesn't call you, so you draw the logical conclusion that he didn't finish the essay! o Reasoning refers to transforming given information to reach a conclusion (Galotti, 1989) o Used to solve problems.

How is syllogistic reasoning applied to real world problems?

o When applying syllogistic reasoning to real-world problems, it is a two step process. 1. Determine whether the syllogism itself is valid. 2. If the syllogism is valid, determine the empirical truth of the premise. o Thus, with syllogisms there are a number of conclusions: true, false, or 'can't say'.

What is a sample Venn diagram of a deductive argument?

see lecture notes for image Errors occur because premises are often reversed: All birds have beaks All beaked animals are birds. Confuse the two statements.

What is Syllogism deductive reasoning?

use of quantitative words such as all, none or some. "All birds have beaks"