# Introduction to LOGic

INTRODUCTION TO LOGIC Building Blocks and Application PART 1: The Building Blocks LOGIC True Valid REASONING Inductive Deductive SYLLOGISMS Categorical Hypothetical Disjunctive LOGIC Definition of logic: Reasoning according to strict principles of validity Other definitions to know:

Truth = Accurate, factual Validity = Quality of arguments; proof of conclusion Premise = A proposition used as evidence in an argument Conclusion = Logical result of the relationship between the premises; the thesis of the argument Argument = The assertion of a conclusion based on logical premises Premise + Conclusion = Argument REASONING Inductive = specific to general Example: You eat at 3 Mexican restaurants, and they are all good. Based on this, you conclude that all Mexican food is good. This is inductive (3 specific examples led to a general conclusion).

Deductive = general to specific You know the food at El Rancho will be good before you go because all Mexican food is good. This is deductive (You used your general conclusion to apply to a specific example). SYLLOGISMS Syllogism is the form in which all deductive reasoning is worked out in Aristotelian logic. All syllogisms consist of 3 parts: Major premise (general statement) Minor premise (specific example) Conclusion Syllogisms and Validity/Truth Example #1:

All cows eat grass Bessy is a cow Therefore, Bessy eats grass This syllogism is _____ and _____ Example #2: All cows are blue Bessy is a cow Therefore, Bessy is blue This syllogism is _____ and _____ 3 TYPES OF SYLLOGISMS Categorical: MP is universal Hypothetical: MP uses if Disjunctive: MP uses either/or

* MP = Major Premise Categorical Syllogism (CS) Rules MP is universal An entire class or category is under consideration Universal affirmative = all, every, everyone, everybody Universal negative = no, not, not any, never, none, nothing For validity in a CS: If both premises are positive, the conclusion must be positive If one of the premises is negative, the conclusion must be negative A conclusion cannot be drawn from 2 negative premises

CS EXAMPLES cows = A blue = B Bessy = C Fill in the blank: ______ like to chase mice. Tinkerbell is a cat. Therefore, Tinkerbell likes to chase mice. A=B

C=A Therefore, C = B Fill in the blank: Some celebrities are very shy. Angelina Jolie is a celebrity. Therefore, _____ . Hypothetical Syllogism (CS) Rules MP uses if Expresses a hypothetical, uncertain, or conjectural relationship Expresses cause and effect If clause = antecedent

Then clause = consequent The minor premise must either: Affirm the antecedent, or Deny the consequent HS EXAMPLES If someone comes to the door, the dogs will bark. Someone came to the door. Therefore, the dogs barked. Fill in the blank:

If Tom asks Jen to the dance, she will go. _____ . Therefore, _____ . If someone comes to the door, the dogs will bark. The dogs did not bark. Therefore, nobody came to the door Fill in the blank: If unemployment does not increase, Obama will make history. _____ . Therefore, _____ . Disjunctive Syllogisms (DS) Rules

MP uses either/or Two possibilities being proposed must be mutually exclusive A valid DS always denies one of the disjuncts DS EXAMPLES Valid: He is either dead or alive. She is either a singer or not a singer. Fill in the blank:

Either P or Q. Not Q. _____ . Not Valid: Either you can vote Republican or bankrupt the country. She is either a singer or a dancer. Fill in the blank: Either P or Q. P. _____ . MY SOAPBOX

If truth is factual accuracy, then it cant be argued for or against. Truth is factual accuracy. Therefore, truth cant be argued. (Therefore, we argue validity.) PART 2: The Application THE ENTHYMEME FALLACIES THE ENTHYMEME Definition: A shortened, informal syllogism in which one of the premises or conclusion is implicit. Appositive:

Participial Phrase: Example syllogism: All whales are mammals. Moby Dick is a whale. Therefore, Moby Dick is a mammal. As a whale, Moby Dick is also a mammal. Adverb clause: Being a whale, Moby Dick is also a mammal. Prepositional Phrase:

Moby Dick, a whale, is also a mammal. Because Moby Dick is a whale, it is also a mammal. Compound sentence: Moby Dick is a whale; therefore, Moby Dick is a mammal. Syllogism Change syllogism into enthymeme: Summers in Scotland are rainy and cool. Edinburg is in

Scotland. Summers in Edinburg are rainy and cool. Change syllogism into enthymeme: Doctors are rich My brother is a doctor Enthymeme Change syllogism into enthymeme: Students who spend a lot of time as school are good students. Riley spends a lot of time at school Riley is a good student.

Change syllogism into enthymeme: Snakes with triangle-shaped heads are poisonous. Copperheads have triangleshaped heads. Therefore, Copperheads are poisonous. Enthymeme Syllogism Change enthymeme into CS and HS: As an athlete, Anna Sharapova is careful about what she eats. Change enthymeme into CS and HS:

The kangaroo, with a pouch for its young, is a marsupial. Change enthymeme into CS and HS: The sketches, are signed by Van Gogh; therefore, they will bring high dollars at auction. Change enthymeme into CS and HS: Because Yogi is a bear, he will hibernate during the winter. FALLACIES

Rhetorical fallacies dont allow for the open, twoway exchange of ideas upon which meaningful conversations depend. Instead, they distract the reader with various appeals instead of using sound reasoning. Rhetorical fallacies can be divided into 3 categories: Emotional fallacies: Unfairly appeal to the audiences emotions. Ethical fallacies: Unreasonably advance the writers own authority or character. Logical fallacies: depend upon faulty logic. Keep in mind that rhetorical fallacies often overlap. EMOTIONAL FALLACIES Sentimental Appeals use emotion to distract the audience from the facts.

Red Herrings use misleading or unrelated evidence to support a conclusion. That painting is worthless because I dont recognize the artist. Scare Tactics try to frighten people into agreeing with the arguer by threatening them or predicting unrealistically dire consequences. The thousand of baby seals killed in the Exxon Valdez oil spill have shown us that oil is not a reliable energy source. If you dont support the partys tax plan, you and your family will be reduced to poverty. Bandwagon Appeals encourage an audience to agree with the writer because everyone else is doing so. Paris Hilton carries a small dog in her purse, so you should buy a hairless Chihuahua and put it in your Louis Vuitton. Emotional Fallacies Continued

Slippery Slope arguments suggest that one thing will lead to another, oftentimes with disastrous results. Either/Or Choices reduce complicated issues to only two possible courses of action. If you get a B in high school, you wont get into the college of your choice, and therefore will never have a meaningful career. The patent office can either approve my generator design immediately or say goodbye forever to affordable energy. False Need arguments create an unnecessary desire for things. You need an expensive car, or people wont think youre cool. ETHICAL FALLACIES

False Authority asks audiences to agree with the assertion of a writer based simply on his or her character or the authority of another person or institution who may not be fully qualified to offer that assertion. Using Authority Instead of Evidence occurs when someone offers personal authority as proof. Trust me my best friend wouldnt do that. Guilt by Association calls someones character into question by examining the character of that persons associates. My high school teacher said it, so it must be true. Saras friend Amy robbed a bank; therefore, Sara is a delinquent. Dogmatism shuts down discussion by asserting that the writers beliefs are the only acceptable ones.

Im sorry, but I think penguins are sea creatures and thats that. Ethical Fallacies Continued Moral Equivalence compares minor problems with much more serious crimes (or vice versa). Ad Hominem arguments attack a persons character rather than that persons reasoning. These mandatory seatbelt laws are fascist. Why should we think a candidate who recently divorced will keep her campaign promises? Strawperson arguments set up and often dismantle easily refutable arguments in order to misrepresent an opponents argument in order to defeat him or her Person A: We need to regulate access to handguns.

Person B: My opponent believes that we should ignore the rights guaranteed to us as citizens of the United States by the Constitution. Unlike my opponent, I am a firm believer in the Constitution, and a proponent of freedom. LOGICAL FALLACIES Hasty Generalization draws conclusions from scanty evidence. Faulty Causality (or Post Hoc) arguments confuse chronology with causation: one event can occur after another without being caused by it. A year after the release of the violent shoot-em-up video game Annihilator, incidents of school violence tripledsurely not a coincidence. Non Sequitur (Latin for It doesnt follow) is a statement that does not logically relate to what comes before it.An important logical step may be missing in such a claim.

I wouldnt eat at that restaurantthe only time I ate there, my entree was undercooked. If those protesters really loved their country, they wouldnt question the government. Equivocation is a half-truth, or a statement that is partially correct but that purposefully obscures the entire truth. Logical Fallacies Continued The Gambler's Fallacy is committed when a person assumes that a departure from what occurs on average or in the long term will be corrected in the short term. Begging the Question occurs when a writer simply restates the claim in a different way; such an argument is circular. His lies are evident from the untruthful nature of his statements. Faulty Analogy is an inaccurate, inappropriate, or misleading comparison between two things.

"You see that horse over there? He lost his last four races. I'm going to bet on him." Example: Letting prisoners out on early release is like absolving them of their crimes. Stacked Evidence represents only one side of the issue, thus distorting the issue. Cats are superior to dogs because they are cleaner, cuter, and more independent.

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