Critical thinking

Successful arguments

For an argument to be successful it must satisfy two conditions, 1. All the premises must be *true*, 2. The premises must *support* the conclusion.

Counter-example

Some A are not B, Therefore, Not all A are B.

Evaluating sources

*1. Is the source in a position to know?* i. Do they have relevant expertise, qualifications or training? ii. If they are a witness, were they in a position to have the relevant experience? *2. Is there any reason to suspect the reliability of the source?* i. What is the source's reputation for reliability? ii. Does the source have a motive for not telling the truth? iii. Are there other factors that might effect the reliability of the evidence? *3. Is there any corroborating evidence from independent sources?*

Identifying assumptions

1. *The lonely premise rule*. An argument with only one premise usually depends on an unstated assumption. 2. *The rabbit rule*. If the conclusion contains a significant word or phrase that does not appear in any of the premises, then the argument usually depends on an unstated assumption that will make use of the missing word or phrase. 3. *Holding hands rule*. If a premise contains a significant word or phrase that does not appear in the conclusion, then the argument usually depends on an unstated assumption. The assumption will be a co-premise of the stated premise and will make use of the missing word or phrase.

Evaluating statistical generalisations

1. Does the claim need *clarification*? Can it be made more specific? 2. How was the statistic *derived*? What is the evidence or argument? Is the argument cogent? 3. What might *explain* the statistic? 4. What is the *significance* of the statistic? Is it surprising or important? Or is it what you might expect? 5. Are there any *other relevant statistics*? 6. If it was true, what further *implications* would it have? 7. Are there plausible conclusions which it would be *tempting*, though *unwarranted* to draw?

Testing validity with counter-example

1. Isolate the form of the argument, 2. Try to find a counter-example, an argument with the same form that has true premises and a false conclusion, 3. If no such argument can be found, then the original argument is deductively valid, 4. It will match one of the valid argument forms below.

Problems with inductive arguments

1. The sample was not large enough. 1A. Is the sample size large enough to support the conclusion? 2. The sample was selected in a biased way. 2A. Could the selection process introduce bias? 2B. Was the sample self selected? 2C. Was the sample based on memorable cases? 2D. What was the response rate? 3. The target property was measured in a biased or unreliable way. 3A. What questions were asked? 3B. Are people likely to respond untruthfully? 3C. Could the wording introduce bias?

Necessary and sufficient conditions.

A *sufficient condition* is one which, if it holds, will cause an event to take place. However, a sufficient condition is not necessary for an event to take place. Said event may occur even if a sufficient condition doesn't hold. E.g. striking a match in the correct conditions is *sufficient* to cause it to light, but there are other ways to light a match. There are also some additional *necessary conditions* to take into account in this case, such as the presence of oxygen. A *necessary condition*, in contrast, must hold in order for an event to take place. However, a necessary condition alone is not always enough to cause an event to take place. E.g. it is *necessary* for a professional bike rider to have good lung capacity, but this is not a *sufficient condition* for them to be able to race. They also need to be conditioned and well trained.

Inductive arguments

A special type of evidence used to support a conclusion. Involves reasoning for a sample, a subclass of people or things, to a population, the class of people or things as a whole. They can be effective or not. They are distinct from the formal 'inductive argument' form discussed earlier but they are also related, as any such argument from a sample can only ever be inductively valid and will never be deductively valid.

Evaluating universal generalisations

A universal generalisation is false if there is a relevant counter example. A true generalisation will have no counter examples.

Affirming the consequent universal form

All A are B, X is B, Therefore, X is A.

Denying the antecedent universal form

All A are B, X is not A, Therefore, X is not B.

False dichotomy

Also known as the black or white fallacy. Occurs when an argument paints things as either one way or another, while failing to take a third relevant option into account.

Appeal to authority

An argument that appeals to an authority in a particular domain is an *appeal to authority*. An argument may be an *illegitimate appeal to authority* if said authority is not a reliable or relevant source.

Begging the question

An argument which assumes something which is the very point at issue in context commits the fallacy known as begging the question. E.g. 'same-sex adoption is wrong because the welfare of children is more important than satisfying the parental cravings of gay and lesbian couples'. In this instance the argument is assuming that same-sex adoption is a bad thing for children and using this assumption to argue that sex adoption is a bad thing for children.

Assumptions

An obvious premise that has not been stated, but which the argument clearly relies upon. E.g. the for argument 'Nellie is an elephant. So she has a trunk which she uses to pick things up' the assumption would be 'elephants have trunks which they can use to pick things up. Represented in an argument map like so: 1. Nellie is an elephant. A2. Elephants have trunks which they can use to pick things up. Therefore: C. Nellie has a trunk which she uses to pick things up.

Universal generalisations

Claims about what is true of *all* things of a certain kind, or in *all* of a number of different situations or cases. Can take the form of statistical generalisations, e.g. X percent of A are B. The label of a generalisation is not inherently bad. Generalisations can be uncontroversially true, controversial/unknown or simply false.

Fallacy of sweeping generalisation

Defective reasoning in the opposite direction, from population to sample, ignoring specific conditions that may be relevant to the individual case. E.g. everyone has a right to his or her own property. Therefore, even though Crosby was blind drunk, you had no right to take away his Uzi.

Modus ponens

If A then B, A, Therefore, B.

Affirming the consequent

If A then B, B, Therefore, A.

Denying the antecedent

If A then B, Not A, Therefore, Not B.

Modus tollens

If A then B, Not B, Therefore, Not A.

Support in arguments

If all the premises are true, would they provide good reason for thinking the conclusion is also true? Note that true premises do not guarantee a successful argument if they do not support the argument. The premises must *imply* or *entail* the conclusion, which *follows from* the premises.

Questionable assumptions

If an argument depends on a questionable assumption, one that we have strong reason to believe isn't true, then the argument is unsuccessful.

Hypothetical syllogism

In A then B, If B then C, Therefore, If A then C.

Deductive validity

In a *deductively valid* argument it is impossible for the argument to be false if all of the premises are true. Note that *inductively valid* arguments can still be strong arguments, but not to the same extent as a *deductively valid* one.

Heuristic of representativeness

Judging the probability that A has feature B by judging how similar is to a paradigm or stereotypical example of B. Associated bias in reasoning: 1. *Base rate neglect*, tendency to ignore base rate, generic information and focus on specific information. 2. *Conjunction effect*, tendency to assume that specific conditions are more probable than general ones, e.g. 'harry is a professional actor who likes going to classic concerts' presumed more likely than 'harry enjoys going to classical' concerts despite the latter being a larger and class and therefore more likely. 3. Belief in the *'law of small numbers'*, e.g. coin toss pattern HTHTHT is more likely than HHHHHH. 4. *Gambler's fallacy*, tendency to assume that the probability of an event is affected by previous events. 4. *Insensitivity to sample size.* 5. *Jumping to casual conclusions*. 6. *Illusion of control*, tendency to assume that we have control over external events.

Ambiguity and equivocation

Lexical ambiguity can make analyzing arguments problematic, e.g. 1. Our radio station has a responsibility to serve the public interest. 2. There is an overwhelming public interest in the private lives of local celebrities. Therefore: C. Our radio station has a responsibility to publicize the private lives of local celebrities. The definition of 'public interest' differs between 1 and 2, but the two uses in conjunction with 'publicize' in 3 make this argument appear more convincing than it is.

Post hoc ergo propter hoc

Literally 'after which therefore because of which'. Fallacious assumption that temporal correlation always equals causation. Note that outside of the fallacy temporal correlation along with a plausible connection can be reason to argue causation.

Evidence

Many arguments fail because they handle evidence, or the search or it, improperly. This can be because, 1. The strength of the evidence is misjudged, 2. Not all potential evidence is considered and/or an argument does not take other possibilities into account.

Relevance of motive and bias

Note that motive and bias is not always relevant. It is only ever legitimate to dispute a claim on the basis of these considerations when you are being asked to believe a claim solely on that person's say-so. If they have given an independent argument for their claim it is generally not legitimate to dispute it by referring to their motives or past unreliability.

Correlation and causation

Reasoning with causation is problematic. Temporal correlation can be a good indicator of causation, but this is not always the case. Correlation of two events can occur because they are being caused by a third variable, for instance.

Independent/convergent premises

Support a conclusion without relying on each other. Each premise by itself provides some support for the conclusion. *1.* Premise 1. *2.* Premise 2. *Therefore:* *C.* Conclusion. C / \ 1 2

Heuristics and biases

System 1 automatically produces an answer to most questions. If it cannot find an answer, it often finds an easier question and answers that instead. In other words, system 1 often uses heuristics. A heuristic is a procedure or rule of thumb for quickly and easily generating the answers to questions. This use of heuristics leads to cognitive biases and illusions.

Believing and unbelieving

System 1 is 'biased to believe'. To comprehend a claim we construct a mental model of a world in which that claim is true. Believing is an automatic System 1 process. Only system 2 can unbelieve. When system 1 is inactive or busy, people become more credulous.

Association and priming

System 1 is an associative machine, e.g. completing phrase 'bread' to 'bread and butter' or filling in the word fragment SO blank P as SOAP. Once an idea has been activated, it makes it easier for related ideas in the system of associations to be activated. This is called a priming effect. E.g. hearing EAT rimes the idea of SOUP while hearing WASH primes the idea of SOAP

Cognitive processes - System 2

System 2: 1. Critical thinking, reasoning. 2. Slow, voluntary control. 3. Lazy, easily distracted. 4. Rule-following. 5. Supports system 1. System 2 normally runs in 'low effort' mode and is only it is mobilised when there is a question System 1 cannot easily answer or when something happens that violates the model built by System 1. System 2 monitors the assessments produced by System 1 and if it endorses them, they become beliefs, judgments, decisions or actions. Skill acquisition involves a gradual transfer of ability from system 2 to system 1.

Fallacy of hasty generalisation

When a noteworthy piece of evidence (such as an experience or testimonial) can lead us to forming a completely general view. Also known as the *Volvo fallacy*, e.g. Volvos are supposed to be safe, but I saw one totalled in an accident. I'll never buy one of those!

Appeal to ignorane

When an argument uses the absence of evidence as a significant point. This is not always fallacious, it may be that studies have been conducted and no evidence was found. An appeal to ignorance occurs when the absence of evidence is cited as significant and no the potential to find evidence has not been ruled out. It applies to any type of argument, not just scientific or casual arguments.

Valid and invalid argument forms

*Valid* = modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, counter-example, *Invalid* = affirming the consequent, denying the antecedent.

Standard form

1. Premise 1, 2. premise 2, Therefore: C. Conclusion.

Statistical generalisations

A special case of generalisations of the form X% of As are B. Can be universal or non-universal. Statistical generalisations which are not universal cannot be refuted by counter examples. Note that exact percentage is not always specified, quantifiers such as 'most', 'some', 'very few' etc. might be used.

Modus ponens universal form

All A are B, X is A, Therefore, X is B.

Modus tollens universal form

All A are B, X is not B, Therefore, X is not A.

Cum hoc ergo propter hoc

As with post hoc fallacy, but refers to events which co-occur rather than occur after each other temporally.

Fallacy of unrepresentative sample

Central to assessing inductive arguments is the question of whether or not the sample is representative of the population in a relevant way. It may be that the sample is unrepresentative or biased. If so, the argument is fallacious.

Cognitive illusion

E.g. optical illusions. When System 1 automatically produces an answer that seems right and we accept it without checking.

Disjunctive syllogism

Either A or B, Not A, Therefore, B.

Arguments and other kinds of discourse

Every argument contains at least two elements, a *conclusion* and some reason for believing said conclusion, also known as a *premise*. An argument is distinct from an assertion or a denial. A passage can also describe an argument without being an argument itself.

Truth in arguments

For an argument to be successful, all the premises must be true. Some questions for determining truth: 1. Does the premise come from an *expert source* or *reliable authority*? 2. Could you confirm that the premise is true by looking it up in a reference book or other reliable source? 3. Is the premise beyond reasonable doubt? Is it common knowledge? 4. Does the premise contradict something else you know to be true? 5. If the premise is a *generalisation*, are there any *counter-examples*?

Heuristic of availability

Judging probability or frequency using the ease to which cases spring to mind. Associated bias in reasoning: 1. *Hindsight bias*, tendency to view events as predictable after they have happened. 2. *Outcome bias*, tendency to judge a decision according to its outcome rather than the quality of the decision at the time. 3. *Biased assessment of likelihood and risk*. 4. *Illusory correlation*.

Co-dependent premises

Premises that rely on each other to jointly support their conclusion. *1.* Premise 1. *2.* Premise 2. *3.* Premise 3. *Therefore:* *C.* Conclusion. C ┌┼┐ 123

Confirmation bias

Related to the fact that system is 1 is biased to believe. Confirmation bias is the tendency we all have to actively seek out or recall cases that are consistent with a claim while avoiding or forgetting cases that are inconsistent with it.

Inductive argument terminology

Sample = e.g. 'The 2000 people polled on the Daily Telegraph website'. Population = e.g. 'All (adult) Australians'. Target property = e.g. 'Opinion on whether or not parents should smack their children.'

Cognitive processes - System 1

System 1: 1. Intuitive. 2. Fast, automatic. 3. Almost effortless. 4. Always running. 5. An associative machine. System 1 maintains an associative model of the current environment and uses it to make fast assessments and predictions. System 2 is only mobilised when System 1 cannot easily answer a question, or when something happens that violates the model built by system 1.

Myside bias

The bias to over-estimate the strength of arguments for conclusions that you believe to be true. System 1 is undisturbed so System 2 is not called in to check.

Good faith and the straw man fallacy

The straw man fallacy involves deliberately representing the opposition's point of view in a slovenly, oversimplified manner. It is appealing because it involves gaining an argumentative advantage without engaging in critical thinking. It is not simply a fallacy because it is a misrepresentation, it is also a breach of good faith, not a worthwhile substitute for rational argument.

Sub-arguments

Two or more arguments can be linked together to establish a conclusion. *A sub-argument* is an argument used to establish a premise of a further argument. The result is known as a *chain of argument*. The conclusion of the sub-argument is known as the *intermediate conclusion*. *1.* Premise 1. *Therefore:* *2.* Premise 2. *Therefore:* *C.* Conclusion. C ↑ 2 ↑ 1