Logic 1.4

Evaluation of every argument consists in evaluating either the factual claim or the inferential claim of an argument, or sometimes both. Succeeding in proving the inferential claim makes an argument valid, but the conclusion may still be false, or the argument may not be sound.

Valid Deductive Arguments: an argument in which it is impossible for the conclusion to be false given that the premises are true and the conclusion follows from the premises.

Invalid Deductive Arguments: an argument in which it is possible for the conclusion to be false given that the premises are true.

How to test validity: Assume the premises are true. If it is possible to deny the conclusion given the premises, then the argument is invalid.
Ex: All teachers are lunatics.
Mr. Nicholson is a lunatic.
Therefore, Mr. Nicholson is a teacher.

* Validity is not determined by the truth or falsity of premises and conclusions, but by the relationship between premises and conclusion.

* An argument with true premises, but a false conclusion is obviously invalid. This is the foundation of logic.

Sound Argument: A deductive argument that is valid and has all true premises.

Unsound Argument: A deductive argument that is invalid, has one or more false premise, or both.

*The addition of a false premise to an already sound argument does not make it unsound. For an argument to be unsound, it must have a false premise as needed by the argument, or be invalid.

Inductive Arguments: It is improbably that the conclusion be false and the premises be true.

Strong Inductive Arguments: it is improbable that the conclusion be false given that the premises are true.

Weak Inductive Arguments: it is not improbable that the conclusion be false given that the premises are true, but it is claimed to be probable.

Testing Inductive Validity: Assume the premises are true, then consider whether the conclusion is probably true.
E.g., All emeralds examined up to this point have been green, therefore, the next emerald we examine will be green.

E.g., During the last 2000 years, Christianity has been a dominant force in Western Civilization. Therefore, the American presidency will probably continue to be a secular office.

A Cogent Argument is an inductive argument that is strong and has all true premises. It is the inductive analog of a sound deductive argument.
An Uncogent Argument is an inductive argument that is weak, has one or more false premises, or both.

The most an inductive argument can prove is probability.

Total Evidence Requirement: unlike deductive arguments, the premises of an inductive argument must not only be true, but they must not ignore evidence to the contrary.

Statements: true or false;
Groups of Statements: arguments or non-arguments;
Arguments: Inductive or Deductive;
Deductive Arguments: Valid or Invalid;
Valid Deductive Arguments: Sound or Unsound;
Inductive Arguments: Strong or Weak;
Strong Inductive Arguments: Cogent or Uncogent.