Logic: Chapter 1- What Logic Studies

counterexample

a counterexample to a statement is evidence that shows the statement is false. a counterexample to an argument shows the possibility that premises assumed to be true do not make the conclusion necessarily true. a single counterexample to a deductive argument is enough to show that the argument is invalid

argument

a group of statements of which one (the conclusion) is claimed to follow from the others (the premises)

statement

a sentence that is either true or false

inference

a term used by logicians to refer to the reasoning process that is expressed by an argument

deductive argument

an argument in which it is claimed that the conclusion follows necessarily from the premises. in other words, it is claimed that under the assumption that the premises are true, it is impossible for the conclusion to be false

inductive argument

an argument in which it is claimed that the premises make the conclusion probable. in other words, it is claimed that under the assumption that the premises are true, it is improbable for the conclusion to be false

valid deductive argument

an argument in which, assuming the premises are true, it is impossible for the conclusion to be false. in other words, the conclusion follows necessarily from the premises.

invalid deductive argument

an argument in which, assuming the premises are true, it is possible for the conclusion to be false. in other words, the conclusion does not follow necessarily from the premises.

weak inductive argument

an argument such that if the premises are assumed to be true, then the conclusion is not probably true

strong inductive argument

an argument such that if the premises are assumed to be true, then the conclusion is probably true. in other words, if the premises are assumed to be true, then it is improbably that the conclusion is false

explanation

an explanation provides reasons for why or how an event occurred. by themselves, explanations are not arguments; however, they can form part of an argument

cogent argument

an inductive argument is cogent when the argument is strong and the premises are true

uncogent argument

an inductive argument is uncogent if either or both of the following conditions hold; the argument is weak, or the argument has at least one false premise

truth value

every statement is either true or false; these two possibilities are called truth values

unsound argument

if a deductive argument is invalid, or if at least one of the premises is false (truth value analysis) then the argument is unsound

inferential claim

if a passage expresses a reasoning process-that the conclusions follows from the premises- then we say that it makes an inferential claim

proposition

the information content imparted by a statement, or, simply put, its meaning

premise

the information intended to provide support for a conclusion

conclusion

the statement that is claimed to follow from the premises of an argument

logic

the study of reasoning

sound argument

when logical analysis shows that a deductive argument is valid, and when truth value analysis of the premises shows that they are all true, then the argument is sound

premise indicator

words and phrases that help us recognize arguments by indicating the presence of premises (statements being offered in support of a conclusion)

conclusion indicator

words and phrases that indicate the presence of a conclusion (the statement claimed to follow from premises)