study of the methods and principles used to distinguish correct from incorrect reasoning.
building blocks of arguments. Propositions assert that something is the case.
-either T v F; as opposed to questions, commands and exclamations, which have no truth value.
-may be simple (e.g. "The Hills is scripted") or compound (propositions composed of at least two simple propositions; e.g. "Either the Hills is scripted or it is unscripted")
any group of propositions of which one (conclusion) is claimed to follow from the others, which are regarded as providing support for the conclusion.
proposition of an argument that is affirmed on the basis of the other propositions (premises).
-conclusion can appear at the beginning, middle or end of an argument.
-conclusion indicators; 'therefore', 'hence', 'for this reason', 'thus', etc. (*see page 23)
propositions of an argument used to provide support for the conclusion.
-premise indicators; 'since', 'because', 'as indicated by', etc. (*see page 24)
-some premises may be assumed, yet unstated within an argument
e.g. 1) Bob is a native-born American
Therefore, Bob is an American Citizen
*Hidden Premise: All native-born Americans are citizens
it is claimed that the conclusion necessarily follows from the premises.
-every deductive argument is either valid or invalid
a deductive argument is valid iff, when its premises are true, its conclusion must also be true. In other words, if its premises are all true, its conclusion can't be false.
it is claimed that the conclusion follows only with high probability, as opposed to deductive necessity.
-inductive arguments can only be better or worse, more or less probable—not valid/invalid.
Validity and Truth
Truth and falsity are attributes of individual propositions (premises and conclusions); validity and invalidity are attributes of deductive arguments.
a deductively valid argument is sound when all its premises (along with the conclusion) are true.
-technically, inductive arguments cannot be sound
-in everyday discourse, people generally aspire to offer arguments that are not only valid, but sound as well.
committed when threat of force or punishment, either implicit or explicit, is relied on to win consent.
Argument from Ignorance
committed when a conclusion is supported by an illegitimate appeal to ignorance; as when it is claimed that a proposition is true because we cannot prove that it is false, or that a proposition is false because we cannot prove that it is true.
-e.g., There is no evidence proving God doesn't exist. Therefore, God Exists."
-"You can't prove God exists. Therefore, God doesn't exist."
committed when the support offered for some conclusion is an inappropriate appeal to pity.
committed when the primary support offered for some conclusion is the purveyor's desire for it to be true.
occurring in arguments involving an illegitimate appeal to authority, since the supposed authority has no rightful claim to expertise regarding the issue at hand.
-e.g. "You ought to vote. I know this is the case, because Paris Hilton says so (Paris is only a legitimate expert regarding what is hot).
arises from accepting as the cause of an event what is not really its cause.
-e.g. "The Earth rotates on its Axis because Zeus is spinning it in space."
-whether or not something is the cause of an event/phenomenon is often a matter of controversy, especially with regards to correlational studies and findings (e.g. "Hillary Clinton is a woman. She did not win the primary, while Obama, a male, did. Therefore, Hillary was the victim of sexism.")
attempting to establish a conclusion primarily on the basis of popular opinion.
"Obviously, the Foo Fighters are a good rock band. They have sold a ton of records."
committed when a question is asked in such a way as to presuppose the truth of some proposition buried in the question.
-e.g. Sean Hannity, staunch Republican news personality, to any democratic guest on his show, "what explains your misguided, ignorant worldview, which is leading to the downfall of civilized society?"
Begging the Question
committed when the conclusion of an argument is stated or assumed in one of the premises.
-e.g. Michael Moore, ardent Democrat: "Bush is a liar. He intentionally deceived us in the lead up to war, pretending the conflict was about self-defense rather than oil."
-"The future is going to be like the past, because, in the past, the future has always been like the past."
-the popular expression "begs the question" is widely misused as synonym for "raises the question," which is technically incorrect.
committed when one attacks the character of the person offering an argument, rather than the argument itself.
¬ -e,g., "You are an ugly, miserable, liar!"
dismissing a person's argument based on his/her personal or professional affiliations
-e.g., "That's an interesting point, but you're a student. All students are hopelessly naïve; so your conclusion is without merit."
the opposite of the fallacy of Hasty Generalization, the fallacy of accident is committed when a general principle is mistakenly applied to a particular case for which the principle does not hold.
-e.g. "Reality show stars are generally despicable human beings. Therefore, Patti Stanger from Millionaire Matchmaker is a despicable human being (Patti makes dreams come true).
the opposite of the fallacy of Hasty Generalization, the fallacy of hasty generalization is committed when a principle holding for a particular case or set of cases is mistakenly assumed to apply to a very broad range of cases when there is not enough evidence to warrant this inference.
-e.g. "The Situation is a despicable human being. Therefore, all Jersey Shore cast members are despicable human beings."
committed when the support offered for a conclusion does not, in fact, support that conclusion, but rather some other conclusion that is not at issue.
¬-catchall class for fallacies of relevance, reserved for cases that do not fit readily into other categories. In some sense, every example of a relevance fallacy (hasty generalization, character, etc.) also commits the irrelevant conclusion fallacy.
-e.g., "You should go out with me because your boyfriend sucks and he cheated on you."
Fallacies of Ambiguity
category of logical fallacies encompassing cases where words or phrases within an argument are used in a vague or misleading way.
committed when two or more meanings of the same word or phrase have been confused within the same argument.
-e.g. "All banks are beside rivers. Therefore, Bank of America is beside a river."
Two different meanings of bank: riverbank versus financial institution.
-look out for arguments utilizing 'relative' terms, 'small,' 'heavy,' 'good,' etc. (e.g. "She is a heavy baby. Therefore, she is a heavy person." Heaviness is context-dependent)
committed when an argument contains a premise that can be understood in multiple ways, usually due to the premise's awkward grammatical construction.
-e.g. "Apparently, Hank crashed into another car running from the police. It sounds like Hank deserves to be prosecuted" (perhaps it was the other car that was running from the police and ran into Hank).
committed when the meaning of a word or phrase differs in the premise(s) and conclusion, due to a shift in emphasis.
-includes cases of misleading advertising involving the manipulation of print size, font type, etc (e.g. "Doctor James says, 'You must BUY THIS SUPPLEMENT NOW if you are interested in the possible benefits.' So follow Doctor James' advice and pick up our product now.")
committed when the attributes of the parts of a whole are mistakenly attributed to the whole itself.
-e.g. Margaret, Brigitte and Jean, members of the USA softball team, have high batting averages. Therefore, the USA softball team has a high batting average."
committed when the attributes of a whole are mistakenly attributed to parts of the whole.
-e.g. "The American political system is flawed and corrupt. Hence, Obama is flawed and corrupt."
Negation; symbolized "~"
-If P = T then ~P = F, and if P = F then ~P = T
"not," "it is false that," "it is not the case that," etc. (e.g. "not" P, symbolized as ~P)
Conjunction; symbolized as " * " , or "&"
-composed of 'conjuncts' (simple or compound statements)
-T iff both conjuncts are T (Truth Table, pg. 115)
"and," "but," "yet," "also," "however," etc.
( "both" P "and" Q, symbolized as P & Q)
( P "and" Q "not both", symbolized as ~(P & Q); e.g. Paul and Queen are not
( P "and" Q "both not", symbolized as ~P & ~Q; e.g. Paul and Queen are
both not birds.)
Disjunction; symbolized "v"
-composed of 'disjuncts' (simple or compound statements)
-T iff one (or both) of the conjuncts is T
(e.g. "either" P "or" Q, symbolized as P v Q)
( P "unless" Q, symbolized as P v Q)
( "neither" P "nor" Q, symbolized as ~(P v Q), or as ~P & ~Q)
Universal affirmative, 'A,' propositions
All A is B.
Universal Negative, 'E', propositions.
No A is B.
Particular Affirmative, 'I', propositions
Some A is B.
Particular Negative, 'O,' propositions
Some A is not B.