Formal Versus Informal Logic Deductive Versus Inductive Forms

Formal Versus Informal Logic Deductive Versus Inductive Forms of Reasoning

What is Logic? • Logic is the study of valid reasoning. • That is, logic tries to establish criteria to decide whether some piece of reasoning is valid or invalid. • OK, so then what do we mean by ‘valid reasoning’?

Reasoning • A piece of reasoning consists of a sequence of statements, some of which are claimed to follow from previous ones. That is, some are claimed to be inferred from others. • Example: Either the housemaid or the butler killed Mr. X. However, if the housemaid would have done it, the alarm would have gone off, and the alarm did not go off. Therefore, the butler did it.

Valid Reasoning • While in every piece of reasoning certain statements are claimed to follow from others, this may in fact, not be the case. • Example: If I win the lottery, then I’m happy. However, I did not win the lottery. Therefore, I am not happy. • A piece of reasoning is valid if the statements that are claimed to follow from previous ones do indeed follow from those. Otherwise, the reasoning is said to be invalid.

In Short: Logic helps us distinguish good arguments from bad arguments. • Two questions: • 1. Are the premises true? • 2. Do the premises provide good reasons to accept the conclusion?

Two basic categories of human reasoning • Deduction: reasoning from general premises, which are known or presumed to be known, to more specific, certain conclusions. • Deductive arguments (try to) PROVE their conclusions • Both deductive and inductive arguments occur frequently and naturally…both forms of reasoning can be equally compelling and persuasive, and neither form is preferred over the other (Hollihan & Baske, 1994). • Induction: compiling of evidence /reasons/examples that support an argument: the amassing of reasons. Reasoning from specific cases to more general, but uncertain, conclusions. • Inductive arguments (try to) show that their conclusions are PLAUSIBLE or LIKELY.

DEDUCTIVE REASONING commonly associated with “formal logic. ” involves reasoning from known premises, or premises presumed to be true, to a certain conclusion. the conclusions reached are certain, inevitable, inescapable. All human beings are mortal. TRUE general/known Socrates is a human being. TRUE more specific/known Therefore, Socrates is mortal. TRUE very specific/known

INDUCTIVE REASONING commonly known as “informal logic, ” or “everyday argument. ” involves drawing uncertain inferences, based on probabilistic reasoning. the conclusions reached are probable, reasonable, plausible, believable. “Wow! My dog smells terrible. She was outside all night, and around midnight I smelled skunk at the back of the house. I heard her barking loudly, too. That’s definitely a skunky smell on her. She must have tangled with that skunk. ” • My dog smells terrible! • She was outside all night • • At 12: 00 I smelled skunk I heard her bark She’s smell like skunk She must have fought with the skunk. A very plausible conclusion!

Deductive Versus Inductive Reasoning Deduction It is the form or structure of a Example: deductive argument that determines its Everyone has one and only validity biological mother TRUE the fundamental property of a valid, Full sisters have theifsame deductive argument is that the premises are true, then the. TRUE conclusion biological mother necessarily No onefollows. is her own biological Themother. conclusion is said to be “entailed” TRUE in, contained in, the premises. or Therefore, there is no one whose biological mother is also her sister. Conclusion necessarily follows Induction By contrast, the form or structure of an inductive argument has little to do with its perceived believability or credibility, apart from making the argument seem more clear or more well-organized. The receiver (or a 3 rd party) determines the worth of an inductive argument Every ruby discovered thus far has been red. So, probably all rubies are red.

THE DIFFERENCE Key: deductive inductive • If the premises are true the conclusion is necessarily / probably true. • The premises provide conclusive / good evidence for the conclusion. • It is impossible / unlikely for the premises to be true and the conclusion to be false. • It is logically inconsistent / consistent to assert the premises but deny the conclusion.

Sample Deductive and Inductive Arguments Example of Deduction • major premise: All tortoises are vegetarians • minor premise: Bessie is a tortoise • conclusion: Therefore, Bessie is a vegetarian • Certain Example of Induction • Boss to employee: “Biff has a tattoo of an anchor on his arm. He probably served in the Navy. ” • probably

Syllogistic Reasoning Deduction • The syllogism is a common form of deductive reasoning. • There are different types of syllogisms • Categorical (universal premises) • Hypothetical (if-then premises) • Disjunctive (either-or premises) • All follow the basic form: • Major premise • Minor premise • Conclusion

Syllogistic Reasoning • The terms used in a syllogism must be defined precisely. • Major Premise: • All pitchers hold water. • Minor Premise: • The term “pitcher” has two different meanings in this argument, so no valid conclusion can be reached. • Tom Glavin is a pitcher. • Conclusion: • Therefore, Tom Glavin holds water

Example of a valid deductive argument • Major Premise : All cats have 9 lives • Minor Premise: “Whiskers” is a cat • Conclusion: Therefore, Whiskers has 9 lives • It doesn’t matter whether cats really have 9 lives; the argument is premised on the assumption that they do.

Enthymeme *An argument in which one premise is not explicitly stated * One or more of the major premise, minor premise or the conclusion is omitted. When a part of an argument is missing, it is assumed not only to be true, but so obvious that it is not worth including. This makes it very difficult to challenge, as questioning the obvious is an admission of ignorance, which opens oneself to attack. When the unsafe part of the argument is left out, then people may not realize that it has been omitted. Advertisements and politicians make great use of enthymemes.

The Enthymeme • Syllogisms are seldom found in their pure form but instead appear in the form of enthymemes • Resembles a syllogism in that it employs logic • At its starting point is an assumption, statement, or proposition that the writer/speaker presumes the audience accepts • • We recognize that part of the argument goes unstated Based on opinion and formed on deductive reasoning Only two parts where the syllogism has three The enthymeme is applied to specifics, whereas the syllogism is applied to generalities.

How does it work? “I hear you and Elizabeth are getting married. ” “Yes, that’s true. ” • Major Premise: “Well, now that you’ve got a woman too cook for you, maybe you could invite me over for dinner sometime. ” “Why do you think Elizabeth will be doing all of the cooking? ” “Because she’s a woman. ” • Minor Premise • Conclusion:

How do I recognize an enthymeme? • Often compound sentences with the two clauses linked by words such as for, so, therefore, and consequently. • May also be complex sentences with the clauses joined by words such as since or because.

Real-life example “On Meet the Press, [George W. ] Bush [answered] questions about his service in the National Guard during Vietnam. [Tim] Russert [the moderator] reminded Bush, ‘The Boston Globe and the Associated Press have gone through some of their records and said there’s no evidence that you reported to duty in Alabama during the summer and fall of 1972. ’ Major Premise: “Bush replied, ‘Yeah, they’re just wrong. There may be no evidence, but I did report. Otherwise, I wouldn’t have been honorably discharged. ’” (William Saletan, Slate, February 2004) Conclusion: Minor Premise:

Inductive or deductive reasoning? A sample of fifty motorists who were stopped by the CHP at a sobriety checkpoint on a Saturday at midnight revealed that one in four drivers were either uninsured, intoxicated, or both. Thus, if you get involved in an accident on the freeway there is a 25% chance the other motorist will be drunk or uninsured. The Law of the Sea treaty states that any vessel beyond a 12 mile limit is in international waters. The treaty also states that any vessel in international waters cannot be legally stopped or boarded. Therefore, when the U. S. Coast Guard intercepts boats coming from Cuba or Haiti more than 12 miles from the U. S. coast, it is violating the Law of the Sea.

Inductive Reasoning! • A sample of fifty motorists who were stopped by the FHP at a sobriety checkpoint on a Saturday at midnight revealed that one in four drivers were either uninsured, intoxicated, or both. Thus, if you get involved in an accident on the freeway there is a 25% chance the other motorist will be drunk or uninsured. • 50 motorists • Saturday @ 12: 00 • 1 out 4 • Intoxicated • Uninsured • Both • Accident? There is a 25% chance the other motorist is drunk, uninsured, or both.

Deductive Reasoning • The Law of the Sea treaty states that any vessel beyond a 12 mile limit is in international waters. The treaty also states that any vessel in international waters cannot be legally stopped or boarded. Therefore, when the U. S. Coast Guard intercepts boats coming from Cuba or Haiti more than 12 miles from the U. S. coast, it is violating the Law of the Sea. • All vessels 12 miles out are in • international waters. A vessel in international waters cannot be legally stopped or boarded. • Therefore, the Coast Guards violates the Law of the Sea when they intercept boats more than 12 miles out.

Deduction Versus Induction --still more Deductive reasoning is commonly found in the natural sciences or “hard” sciences, less so in everyday arguments Occasionally, everyday arguments do involve deductive reasoning: Example: “Two or more persons are required to drive in the carpool lane. You don’t have two or more persons. Therefore you may not drive in the carpool lane” Inductive reasoning is found in the courtroom, the boardroom, the classroom, and throughout the media Most, but not all everyday arguments are based on induction ◦ Examples: The “reasonable person” standard in civil law, and the “beyond a reasonable doubt” standard in criminal law

Deduction Versus Induction ---continued Deductive reasoning is either “valid” or “invalid. ” A deductive argument can’t be “sort of” valid. If the reasoning Inductive reasoning enjoys a wide range of probability; it can be plausible, possible, reasonable, credible, etc. the inferences drawn may be placed on a continuum ranging from cogent at one end to fallacious at the other. employed in an argument is valid and the argument’s premises are true, then the argument is said to be sound. valid reasoning + true premises = sound argument fallacious cogent

“Validity” vs. “Soundness” • An argument is VALID if its structure conforms to the rules of formal logic. • An argument is SOUND if it is valid, and its premises are true. • Thus validity is a prerequisite for soundness, but an argument needn’t be sound to be valid. • If sound, then valid too. • If valid, not necessarily sound

Validity vs. Soundness • Major Premise: All cats are pink • Minor Premise: Felix is a cat • Conclusion: Therefore, Felix is pink. • Cats aren’t pink, which makes the first premise untrue. Validity, however, presumes the truth of the premises. • Major Premise: Communicable diseases pose the greatest threat to public health. • Minor Premise: Anthrax is not a communicable disease. • Conclusion: Therefore anthrax does not pose the greatest threat to public health. • The premises are true and the conclusion is valid, that is, it necessarily follows from the premises.

Avoiding the Holes Faulty Reasoning ◦ Both induction and deduction demand attention to accuracy and relevance. Induction False conclusions result when specific observations are insufficient or mistaken. Deduction Invalid conclusions result when premises are inaccurate or their relevance to one another is misinterpreted

“I hear you and Elizabeth are getting married. ” “Yes, that’s true. ” “Well, now that you’ve got a woman to cook, maybe you could invite me over for dinner sometime. ” “Why do you think Elizabeth will do all the cooking? ” “Because she’s a woman. ” Implied Major Premise: Minor Premise: Conclusion –