FINAL UNIT LOGIC

wedge symbol- Disjunction

"or" and "unless" Aspen allows snowboards or Telluride does Either Aspen allows snowboards or Telluride does Aspen allows snowboards unless Telluride does Unless Aspen allows snowboards, Telluride does AVT

Do Not confuse these three statement forms

A if B- B ) A A only if B- A ) B A if and only if B - A = B

False Dichotomy

Is committed when a disjunctive premise presents two unlikely alternatives as if they were the only ones available, and the arguer then eliminates the undesirable alternative, leaving the desirable one as the conclusion.

False Cause

Link between premises and conclusion depends on some imagined casual connection that probably does not exist. Whenever an argument is suspected of committing the false cause fallacy, the reader or listener should be able to say that the conclusion depends on the suppostition that X causes Y, whereas X probably does not cause Y at all. Ex During the past two months, every time that the cheerleaders have worn blue ribbons in their hair, the basketball team has been defeated. Therefore, to prevent defeats in the future, the cheerleaders should get rid of those blue ribbons. Successful business executives are paid salaries in excess of $100,000. Therefore, the best way to ensure that Ferguson will become a successful executive is to raise his salary to at least $100,000. There are more laws on the books today than ever before, and more crimes are being committed than ever before. Therefore, to reduce crime we must eliminate the laws. The first argument depends on the supposition that the blue ribbons caused the defeats, the second on the supposition that a high salary causes success, and the third on the supposition that laws cause crime. In no case is it likely that any causal connection exists. The first argument illustrates a variety of the false cause fallacy called post hoc ergo propter hoc ("after this, therefore on account of this"). This variety of the fallacy presupposes that just because one event precedes another event, the first event causes the second. Obviously, mere temporal succession is not sufficient to establish a causal connection. Nevertheless, this kind of reasoning is quite common and lies behind most forms of superstition. (Example: "A black cat crossed my path and later I tripped and sprained my ankle. It must be that black cats really are bad luck.") The second and third arguments illustrate a variety of the false cause fallacy called non causa pro causa ("not the cause for the cause"). This variety is committed when what is taken to be the cause of something is not really the cause at all and the mistake is based on something other than mere temporal succession. In reference to the second argument, success as an executive causes increases in salary—not the other way around—so the argument mistakes the cause for the effect. In reference to the third argument, the increase in crime is, for the most part, only coincidental with the increase in the number of laws. Obviously, the mere fact that one event is coincidental with another is not sufficient reason to think that one caused the other. A third variety of the false cause fallacy, and one that is probably committed more often than either of the others in their pure form, is oversimplified cause. This variety occurs when a multitude of causes is responsible for a certain effect but the arguer selects just one of these causes and represents it as if it were the sole cause. Here are some examples:

Missing the point

Missing the point illustrates a special form of irrelevance. the fallacy occurs when the premises of an argument support one particualr conclusion, but then a different conclusion, often vaguely related to the correct conclusion, is drawn. Whenever one suspects that such a fallacy is being committed, he or she should be able to identify the correct conclusion. the conclusion that the premises logically imply. ignoration elenchi means- ignorance of the proof Crimes of theft and robbery have been increasing at an alarming rate lately. The conclusion is obvious: We must reinstate the death penalty immediately. Abuse of the welfare system is rampant nowadays. Our only alternative is to abolish the system altogether. At least two correct conclusions are implied by the premise of the first argument: either "We should provide increased police protection in vulnerable neighborhoods" or "We should initiate programs to eliminate the causes of the crimes." Reinstating the death penalty is not a logical conclusion at all. Among other things, theft and robbery are not capital crimes. In the second argument the premises logically suggest some systematic effort to eliminate the cheaters rather than eliminating the system altogether.

Weak analogy

Not strong enough to support the conclusion that is drawn EX) Amber's dog is similar in many ways to Kyle's cat. Both like being petted, they enjoy being around people, they beg for food at the dinner table, and they sleep with their owners. Amber's dog loves to romp on the beach with Amber. Therefore, Kyle's cat probably loves to romp on the beach with Kyle. In this argument the similarities cited between Amber's dog and Kyle's cat probably have nothing to do with the cat's attitude toward romping on the beach. Thus, the argument is fallacious. The basic structure of an argument from analogy is as follows: Entity A has attributes a, b, c, and z. Entity B has attributes a, b, c. Therefore, entity B probably has attribute z also. Evaluating an argument having this form requires a two-step procedure: (1)Identify the attributes a, b, c,... that the two entities A and B share, and (2)determine how the attribute z, mentioned in the conclusion, relates to the attributes a, b, c,... If some causal or systematic relation exists between z and a, b, or c, the argument is strong; otherwise, it is weak. In the given example, the two entities share the attributes of liking to be petted, enjoying people, begging for food, and sleeping with their owners. Because it is highly probable that none of these attributes is systematically or causally related to romping on the beach, the argument is fallacious.

Negated statements

Rolex does not make computers It is not the case that Rolex makes computers It is false that rolex makes computers all represent by ~R

Division

The fallacy of division is the exact reverse of composition. As a composition foes from parts to whole, division goes from whole to parts. The fallacy is committed when the conclusion of an argument depends on the erroneous transference of an attribute from a whole onto its parts. Salt is a nonpoisonous compound. Therefore, its component elements, sodium and chlorine, are nonpoisonous. This airplane was made in Seattle. Therefore, every component part of this airplane was made in Seattle. The Royal Society is over 300 years old. Professor Thompson is a member of the Royal Society. Therefore, Professor Thompson is over 300 years old.

fallacies of presumption

These fallacies arise not because the premises are irrelevant to the conclusion or provide insufficient reason for believing the conclusion but because the premises presume what they purport to prove begging the question, complex question, false dichotomy, and suppressed evidence.

Appeal to ignorance (agumentum ad ignoratiam)

When the premises of an argument state that nothing has been proved one way or the other about something, and the conclusion then makes a definite assertion about that thing, the argument commits an appeal to ignorance. The issue usually involves something that is incapable of being proved or something that has not yet been proved. EX People have been trying for centuries to provide conclusive evidence for the claims of astrology, and no one has ever succeeded. Therefore, we must conclude that astrology is a lot of nonsense. Conversely, the following argument commits the same fallacy. People have been trying for centuries to disprove the claims of astrology, and no one has ever succeeded. Therefore, we must conclude that the claims of astrology are true. The premises of an argument are supposed to provide positive evidence for the conclusion. The premises of these arguments, however, tell us nothing about astrology; rather, they tell us about what certain unnamed and unidentified people have tried unsuccessfully to do. This evidence may provide some slight reason for believing the conclusion, but certainly not sufficient reason.

California's having a gold rush is a sufficient condition for its being admitted into the Union; moreover, Alaska's having a gold rush and its being purchased from Russia is a sufficient condition for its being admitted into the Union and its having two senators

You should begin by identifying the statement's main operator. In this case, the given statement is a conjunction, and so the main operator is a dot. The first conjunct is the conditional statement C ⊃ L, and the second conjunct is the conditional statement (A • R) ⊃ (U • S). Therefore, the correct translation is: (C ⊃ L) • [(A • R) ⊃ (U • S)].

fallacy

a defect in an argument that arises from either a mistake in reasoning or the creation of an illusion that makes a bad argument appear good. non sequitur (it does not follow)

truth function

any compound proposition whose truth value is completely determined by the truth values of its components

statement forms

are an arrangement of statement variables and operators such that the uniform substitution of statements in place of the variables results in a statement. EX) For example, and are statement forms because substituting the statements A and B in place of p and q, respectively, results in the statements and . For a slightly more complicated example, is a statement form, because substituting A, B, and C in the place of p, q, and r, respectively, results in the statement . These statements are substitution instances of the respective statement forms.

informal fallacies

are those that can be detected only . by examining the content of an argument. The Brooklyn Bridge is made of atoms. Atoms are invisible. Therefore, the Brooklyn Bridge is invisible

Red Herring

associated with missing the point committed when the arguer diverts the attention of the reader or listener by changing the subject to a different but sometimes subtly related one. He or she then finishes by either drawing a conclusion about this different issue or by merely presuming that some conclusion has been established. By doing so the arguer purports to have won the argument, the fallacy gets it sname from a precedure used to train huntng dogs to follow a scent. A red herring is dragged cross the trial with the aim of leading dogs astray. arguer must change the original subject of the argument without the reader or listener noticing it. EX Environmentalists are continually harping about the dangers of nuclear power. Unfortunately, electricity is dangerous no matter where it comes from. Every year hundreds of people are electrocuted by accident. Since most of these accidents are caused by carelessness, they could be avoided if people would just exercise greater caution. There is a good deal of talk these days about the need to eliminate pesticides from our fruits and vegetables. But many of these foods are essential to our health. Carrots are an excellent source of vitamin A, broccoli is rich in iron, and oranges and grapefruit have lots of vitamin C Both arguments commit the red herring fallacy. In the first, the original issue is whether nuclear power is dangerous. The arguer changes this subject to the danger of electrocution and proceeds to draw a conclusion about that. The new subject is clearly different from the possibility of nuclear explosion or meltdown, but the fact that both are related to electricity facilitates the arguer's goal of leading someone off the track. In the second argument, the original issue is pesticides, and the arguer changes it to the value of fruits and vegetables in one's diet. Again, the fact that the second topic is related to the first assists the arguer in committing the fallacy. In neither case does the arguer draw a conclusion about the original topic, but by merely diverting the attention of the reader or listener, the arguer creates the presumption of having won the argument.

accident

committed when a general rule is applied to a specific case it was not intended to cover. Typically the general rule is cited in the premises and tehn wrongly applied to the specific case mentioned in the conclusion. general rule missaplied to the specific case

begging the question

committed whenever the arguer creates the illusion that inadequate premises provide adequate support for the conclusion by leaving out a possibly fake (shaky) key premise, by restating a possibly false premise as the conclusion, or by reasoning in a circle. petitio principii (request for the source) the actual source of the support for the conclusion is not apparent so the argument is said to beg the question Murder is morally wrong. This being the case, it follows that abortion is morally wrong. the first of these arguments begs the question "How do you know that abortion is a form of murder?"

fallacies of illicit transference

composition and division

fallacies of ambiguity

equivocation and amphiboly ambiguity in the premises or conclusion

Hasty generalization

fallacy that affects inductive generalizations. inductive generalization is an argument that draws a conclusion about all members of a group from evidence that pertains to . selected sample. The fallacy occurs when there is a reasonable liklihood that the sample is not representative of the group. EX Today's money managers are a pack of thieves, every last one of them. Look at Bernie Madoff and Robert Allen Stanford. They ripped off billions of dollars from thousands of trusting clients. And Raj Rajaratnam profited to the tune of millions of dollars through illegal insider trading. The mass shooting in a Colorado movie theater was carried out by a young, white male. The school shootings in Roseburg, Santa Barbara, and Newtown were all carried out by young, white males. The evidence is clear. Young, white males are a serious threat to public safety. In these arguments a conclusion about a whole group is drawn from premises that mention only a few instances. Because such small, atypical samples are not sufficient to support a general conclusion, each argument commits a hasty generalization.

Suppressed evidence

if an inductive argument does indeed ignore important pieces of evidence, then the argument commits the fallacy of suppressed evidence.

Composition

is committed when the conclusion of an argument depends on the erroneous transference of an attribute from the parts of something onto the whole. in other words, the fallacy occurs when it is argued that because the parts have a certain attribute, it follows that the whole has an attribute too. Maria likes anchovies. She also likes chocolate ice cream. Therefore, it is certain that she would like a chocolate sundae topped with anchovies. Each player on this basketball team is an excellent athlete. Therefore, the team as a whole is excellent. Each atom in this teacup is invisible. Therefore, this teacup is invisible. Sodium and chlorine, the atomic components of salt, are both deadly poisons. Therefore, salt is a deadly poison.

triple bar symbol bi-conditional

is used to translate the expressions if and only if, and is a sufficient and necessary condition for EX) JFK tightens security if and only if Ohare does JFKS tightening security is a sufficient and necessary condition for O'hares doing so

Appeal to pity

occurs when an arguer attempts to support a conclusion by merely evoking pity from the reader or listener. This pity may be directed toward the arguer or toward some third party different from argument from compassion. these supply information about why the person is genuinely deserving of help or special consideration.

amphiboly

occurs when the arguer misinterprets an ambiguous statement and then draws a conclusion based on this faulty interpretation. The original statement is usually asserted by someone other than the arguer, and the ambiguity usually arises from a mistake in grammar or punctuation- a missing comma, a dangling modifier, an ambiguous antecedent of a pronoun, or some other careless arrangement of words. because of this ambiguity, the statement ma be understood in two clearly distinguishable wats. The arguer typically selects the unintended interpretations and proceeds to draw . conclusion based on it.

Equivocation

occurs when the conclusion of an argument depends on the fact that a word or phrase is used, either explicitly or implicitly, in tow different senses in the argument

fallacy of appeal to force

occurs whenever an arguer presents a conclusion to another person and tells that person either implicitly or explicitly that some harm ill come to him or her if she does not accept the conclusion

Compound statement

one that contains at least one simple statement as a component. EX) it is not the case that al-Qaeda is a humanitarian organization represent like It is not the case that A D and C Either P Or E If N then F B if and only if R >> Negative statements are interpreted as compound units consisting of an affirmative statement and the phrase "it is not the case that".

simple statement

one that does not contain any other statement as a component Ex) fast foods tend to be unhealthy Any uppercase letter may be selected to represent each statement

formal fallacy

one that may be identified by merely examining the form or structure of an argument. Fallacies of this kind are found only in deductive arguments that have identifiable forms. >> Categorigcal syllogism ex All bullfights are grotesque rituals. All executions are grotesque rituals. Therefore, all bullfights are executions. This argument has the following form: All a are b all c are b all a are c INVALID >> hypothetical syllogism ex If apes are intelligent, then apes can solve puzzles. Apes can solve puzzles. Therefore, apes are intelligent. If A then B B A.

Fallacies of Relevance

share the common characteristic that the arguments in which they occur have premises that are logically irrelevant to the conclusion. the premiss may appear to be psychologically relevant, so the conclusion may seem to follow from the premises, even though it does not follow logically.

Propositional logic

the fundamental elements are whole statements. Statements represented by letters, and these letters re combined by means of the operators to form more-complex symbolic representations

Main operator

the operator that has as its scope everything else in the statement. if there are no parentheses in the statement, the main operator will either be the only operator or, if there is more than one, it will be the operator that is not a tilde. If there are parentheses, brackets, or braces in the statement, the main operator will be the operator that lies outside all parentheses, brackets, and braces; if there is more than one such operator, the main operator will be the one that is not a tilde. o(J V K) the dot is the main operator

straw man

the straw man fallacy is committed when an arguer distorts an oppenents argument for the purpose of more easily attacking it, demolishes the distorted argument, and then concludes that the opponents real argument has been demolished. By doig so, the arguer is said to have set up a straw man and knocked it down, only to conclude that the real "man" has been knocked down as well. Mr. Goldberg has argued against prayer in the public schools. Obviously Mr. Goldberg advocates atheism. But atheism is what they used to have in Russia. Atheism leads to the suppression of all religions and the replacement of God by an omnipotent state. Is that what we want for this country? I hardly think so. Clearly Mr. Goldberg's argument is nonsense.

complex question

this fallacy is committed when two or more questions re asked in the guise of a single question and a single answer is given to both of them. Let us suppose the respondent answers "yes" to the first question and "under the bed" to the second. The following arguments emerge: You were asked whether you have stopped cheating on exams. You answered, "Yes." Therefore, it follows that you have cheated in the past. You were asked where you hid the marijuana you were smoking. You replied, "Under the bed." It follows that you were in fact smoking marijuana

Horse Shoe- Conditional

translate "if... then" statements EX) If purdue raises tuition then so does Notre Dame Notre dame raises tuition if purdue does Purdue raises tuition only if Notre Dame does Cornell cuts enrollment provided that Brown does Cornell cuts enrollment on condition that Brown does Brown's cutting enrollment implies that Cornell does A)B is not equivalent to B)A The horseshoe symbol is also used to translate statements phrased in terms of sufficient conditions and necessary conditions. Event A is said to be a sufficient condition for event B whenever the occurrence of A is all that is required for the occurrence of B On the other hand, event A is said to be a necessary condition for event B whenever B cannot occur without the occurrence of A. EX) having the flu is a sufficient condition for feeling miserable, whereas having air to breathe is a necessary condition for survival, but without air, survival is impossible. In other words, air is necessary.

Argument against the person Ad Hominem

two arguers. one of tehm advances a certain argument, adn the other then respons by directing his or her attention not to the first persons argument but to the first person himself. three forms" abusive, circumstantial, and tu quoque. abusive: the second person responds by verbally abusing the first person circumstantial: begins the same way as the ad hominem abusive but instead of verbal abusive on his opponent, the respondent attempt to discredit the argument by alluding to certain circumstances that affect the opponent. By doing so the respondent hopes to show that the opponent is predisposed to argue the way h or she does and should therefore not be taken seriously. Tu quoque- begins the same way as the others, except that the second arguer attempts to make the first appear to be hypocritical or arguing in bad faith. HOW DARE YOU when you have done X in your life!

dot symbol for Conjunctions

used to translate conjunctions such as "and", "also" , "but", "however", "yet", "still", "moreover", "although", and "nevertheless" EX) Tiffany sells jewelry, and Gucci sells cologne Tiffany sells jewelry, but Gucci sells cologne Tiffany sells jewelry, however Gucci sells cologne Tiffany and Ben Bridge sell jewelry

appeal to the people

uses these desires to get the reader or listener to accept a conclusion. Everyone wants to be loved, esteemed, admired, valued, recognized, and accepted by others. Two approaches are involved: one of them direct and the other indirect. The direct approach occurs when an arguer, addressing a large group of people, excites the emotions and enthusiasm of the crowd to win acceptance for his or her conclusion. sort of a mob mentality. Propaganda and demogogue.. appeal to fear-- mob mentality biggie Bandwagon- everyone believes such and such or does such and such; therefore, you should believe or do such and such too. appeal to vanity- linking love, admiration or approval of the crowd with some famous figure appeal to snobbery- appeal to smaller group that is superior in some way appeal to tradition- its been done this way for a long time Ad populum-- you want to be accepted/ included in the group Therefore accept XYZ as tru

Appeal to Unqualified authority

variety of the argument from authority and occurs when the cited authority or witness lacks credibility. several reasons why an authority or witness might lack credibility: requisite expertise, might be biased or prejudiced, might have a motive to lie or disseminate "misinformation," or might lack the requisite ability to perceive or recall. Dr. Bradshaw, our family physician, has stated that the creation of muonic atoms of deuterium and tritium hold the key to producing a sustained nuclear fusion reaction at room temperature. In view of Dr. Bradshaw's expertise as a physician, we must conclude that this is indeed true. This conclusion deals with nuclear physics, and the authority is a family physician. Because it is unlikely that a physician would be an expert in nuclear physics, the argument commits an appeal to unqualified authority.

Slippery Slope

variety of the false cause fallacy. It occurs when the conclusion of an argument rests on an alleged chain reaction and there is not sufficient reason to think that the chain reaction will actually take place. Immediate steps should be taken to outlaw pornography once and for all. The continued manufacture and sale of pornographic material will almost certainly lead to an increase in sex-related crimes such as rape and incest. This in turn will gradually erode the moral fabric of society and result in an increase in crimes of all sorts. Eventually a complete disintegration of law and order will occur, leading in the end to the total collapse of civilization. Because there is no good reason to think that the mere failure to outlaw pornography will result in all these dire consequences, this argument is fallacious.

Statement variables

which are lowercase letters that can stand for any statement. For ex the statement variable p could stand for the statements A, AVB, and so son. Statement variable are used to construct statement forms

5 logical operators

~ negation- tilde o- dot- conjunction V- wedge- disjunction )- horseshoe implication = triple bar- equivalence EX) It is not the case that A ~A-- NEGATION D and C- DoC -- CONJUNCTIVE STATEMENT Either P or E- P V E--- DISJUNCTIVE If N then F -- N ) F -- CONDITIONAL STATEMENT- expresses a material implication - N is the antecedent- and- F is the consequent B if and only if R- B=R - Biconditional statement- expresses the relation of material equivalence