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Definition

• Two pages of Boolean Logic (Gates) examples. Perfect to laminate 30 double sided and use these as hand outs in lesson. Or to print these out for each student to keep a copy in their folders. Includes the four main logic gates with rules, diagrams, truth tables and expressions.
• Let’s take a look at an example! If you took the June 2007 LSAT and got a raw score of 15 on the first Logical Reasoning section and 19 on the second, 20 in Logic Games, and 17 in Reading Comp, that adds up to a raw score of 71. That translates to a scaled score of 156.

A fallacy is the use of invalid or faulty reasoning.

A quick reference guide for PHP, with functions references, a regular expression syntax guide and a reference for PHP's date formating functions. As of 28/6/14, the cheat sheet now includes popup links to the appropriate PHP manual pages.

Some fallacies are committed intent­ionally to manipulate or persuade by deception, while others are committed uninte­nti­onally due to carele­ssness or ignoranceAristotle was the first to system­atize logical errors into a list, as being able to refute an opponent's thesis is one way of winning an argumentRichard Whately defines a fallacy broadly as, 'any argument, or apparent argument, which professes to be decisive of the matter at hand, while in reality it is not'https:­//e­n.w­iki­ped­ia.o­rg­/wi­ki/­Lis­t_o­f_f­all­acies
The first principle is that you must not fool yourself and you are the easiest person to fool
Richard P. Feynman

Types of Fallacies

Formal An error in logic in the argument's form.
Non Sequiturs Propos­itional fallacies Quanti­fic­ation fallacies Syllog­istic fallaciesInformal Reasons other than struct­ural, require examin­ation of the argument's content Faulty genera­liz­ations Red herring fallaciesCond­itional or questi­onable Arguments disregard or confusionOther systems of classi­fic­ation
The most famous are those of Francis Bacon and J. S. Mill
Bacon divided fallacies into 4 Idola (Idols, False Appear­ances), summarize the kinds of mistakes the human intellect is prone.

Free Cheat Sheets

Offend­icula of Roger Bacon
Opus maius,J. S. Mill book of his Logic,
Jeremy Bentham's Book of Fallacies (1824).
Whateley's Logic, A. de Morgan, Formal Logic (1847)
Sidgwick, Fallacies (1883)

Mindmap

Formal fallacies

Appeal to probab­ilityTakes something for granted because it would probably be the case Something can go wrong (premise). Therefore, something will go wrong (invalid conclu­sion)Argument from fallacyAka fallacy fallacy, assumes that if an argument is fallac­ious, then the conclusion is false If P, then Q. P is a fallacious argument. Therefore, Q is falseBase rate fallacyMaking a probab­ility judgment based on condit­ional probab­ili­ties, without taking into account the effect of prior probab­ilities Police officers have breath­alyzers displaying false drunke­nness in 5% of the cases the driver is sober. However, the breath­alyzers never fail to detect a truly drunk person. One in a thousand drivers is driving drunk. The police officers stop a driver at random, and force the driver to take the test. The test is positive. You don't know anything else about him or her. How high is the probab­ility he or she really is drunk? Many would answer as high as 0.95, but the correct probab­ility is about 0.02. To find the correct answer, one should use Bayes's theoremConjun­ction fallacyAssumption that an outcome simult­ane­ously satisfying multiple conditions is more probable than an outcome satisfying a single one of them Linda is 31 years old, single, outspoken, and very bright. She majored in philos­­ophy. As a student, she was deeply concerned with issues of discri­­mi­n­ation and social justice, and also partic­­ipated in anti-n­­uclear demons­­tr­a­t­ions. Which is more probable? Linda is a bank teller. Linda is a bank teller and active in the feminist movement. The majority of those asked chose second option. However the probab­ility of two events occurring together is always less than or equal to the probab­ility of either one occurring aloneMasked-man fallacySubsti­tution of identical design­ators in a true statement can lead to a false one Lois Lane believes that Superman can fly. Lois Lane does not believe that Clark Kent can fly. Therefore Superman and Clark Kent are not the same personProp­osi­tional fallacies
A propos­itional fallacy is an error in logic that concerns compound propos­itions. For a compound propos­ition to be true, the truth values of its consti­tuent parts must satisfy the relevant logical connec­tivesand, or, not, only if, if and only ifAffirming a disjunctConcluding that one disjunct of a logical disjun­ction must be false because the other disjunct is true Max is a mammal or Max is a cat. Max is a mammal. Therefore, Max is not a catAffirming the consequentThe antecedent is claimed to be true because the consequent is true; if A, then B; B, therefore A If someone owns Fort Knox, then he is rich. Bill Gates is rich. Therefore, Bill Gates owns Fort KnoxDenying the antecedentThe consequent is claimed to be false because the antecedent is false; if A, then B; not A, therefore not B If you are a ski instru­ctor, then you have a job. You are not a ski instru­ctor, Therefore, you have no jobQuan­tif­ication fallacies
A quanti­fic­ation fallacy is an error in logic where the quanti­fiers of the premises are in contra­diction to the quantifier of the conclu­sionExiste­ntial fallacyAn argument that has a universal premise and a particular conclusion ^{Every unicorn definitely has a horn on its forehead}

Informal Fallacies

Informal fallac­ies
Arguments that are fallacious for reasons other than structural (formal) flaws and usually require examin­ation of the argument's content.Appeal to the stoneargum­entum ad lapidem Dismissing a claim as absurd without demons­trating proof for its absurdity A: Infectious diseases are caused by microbes B: What a ridiculous idea! A: How so? B: It's obviously ridicu­lousArgument from ignoranceargum­entum ad ignora­ntiam It asserts that a propos­ition is true because it has not yet been proven false (or vice versa) There may be seventy kazillion other worlds, but not one is known to have the moral advanc­ement of the Earth, so we're still central to the UniverseArgument from incred­ulityAppeal to common sense 'I cannot imagine how this could be true; therefore, it must be false.'­ Argument from ignoranceArgument from repetitionargum­entum ad nauseam, argumentum ad infinitum signifies that it has been discussed extens­ively until nobody cares to discuss it anymore; sometimes confused with proof by assertionArgument from silenceargum­entum ex silentio conclusion is based on the absence of evidence, rather than the existence of evidenceArgument to moderationad temper­antiam false compro­mise, middle ground, fallacy of the mean. Assuming that the compromise between two positions is always correctArgumentum verbosiumSee: by verbosityBegging the questionpetitio principii providing what is essent­ially the conclusion of the argument as a premise Opium induces sleep because it has a soporific quality A kind of circular reasoningShifting the burden of proofSee: onus probandi I need not prove my claim, you must prove it is falseCircular reasoningcirculus in demons­trando when the reasoner begins with what he or she is trying to end up with; sometimes called assuming the conclusion Whatever is less dense than water will float, because such objects won't sink in waterCircular cause and conseq­uenceThe conseq­uence of the phenomenon is claimed to be its root cause. Correl­ation does not imply causationContinuum fallacyImproperly rejecting a claim for being imprecise Fred is clean-­shaven now. If a person has no beard, one more day of growth will not cause them to have a beard. Therefore Fred can never grow a beardCorrel­ati­ve-­based fallaciesCorr­elation proves causat­ionpost hoc ergo propter hoc a faulty assumption that because there is a correl­ation between two variables that one caused the other.
Supp­ressed correl­ative where a correl­ative is redefined so that one altern­ative is made impossibleDivine fallacyArgument from incred­ulity. Because something is so incredible / amazing / ununde­rst­and­able, it must be the result of superior, divine, alien or paranormal agencyDouble countingCounting events or occurr­ences more than once in probab­ilistic reasoning, which leads to the sum of the probab­ilities of all cases exceeding unityEquivo­cation

Lsat Logic Games Cheat Sheet

Misl­eading use of a term with more than one meaning
Ambiguous middle term a common ambiguity in syllogisms in which the middle term is equivocated
Defin­itional retreat changing the meaning of a word to deal with an objection raised against the original wording.

Draft Version

1 October 2020

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