Philosophy - Proofs

Terminology

Logic: “the study of methods for evaluating whether the premises of an argument adequately support its conclusion.”

· Very broadly, the study of the principles of good reasoning.

Reasoning: A psychological state where one or more beliefs are derived from one or more (typically distinct) beliefs.

Argument: In philosophy, an argument is the fundamental unit of reasoning. It is a series of statements, at least one of which is a premise and at least one of which is a conclusion. The conclusion is always related to the premises by way of an inference.

Inference: The relation between premises and a conclusion. Conclusions are inferred from premises (but never vice versa).

Statement: A statement is a sentence that is either true or false, or “has truth value”. (e.g. declarative sentence, assertion, claim, proposition) It is distinct from questions, commands, and exclamations (which do not have truth value).

Premise: A statement that supports a conclusion; the evidence provided for a claim.

Conclusion: A statement that is supported by premises, the claim that is being made.

Validity: “A valid argument is one in which it is necessary that, if the premises are true, then the conclusion is true.”

· Informally, in a valid argument, the conclusion follows from the premises.

· A property of arguments but not statements.

· Validity is almost always determined by the form of the argument, and not the content.

Formally Valid: An argument that is valid in virtue of its form.

Deduction: A deductive argument is one in which the premises are intended to guarantee the truth of the conclusion

· Deductive arguments are valid or invalid, not strong or weak.

Induction: “An inductive argument is one in which the premises are intended to make the conclusion probable, without guaranteeing it.”

· Inductive arguments are strong or weak, not valid or invalid.

Inductive Strength: An inductive argument is inductively strong if and only if, should all the premises be true, then the conclusion is likely to be true.

Truth (informally):A property of statements but not arguments. A statement is true when it corresponds to reality.

· e.g. “Ronald Reagan is the 44th and current president of the U.S.A.”

· e.g. “Barrack Obama is the 44th and current president of the U.S.A.”

Soundness (informally): A sound argument is one in which all of the premises are true and it is a valid argument.

· If an argument is sound, then the conclusion must be true.

· An unsound argument is one that is either invalid, has at least one false premise, or both.

· A property of arguments but not statements.

Tautology: A statement is a tautology when it cannot possibly be false.

Contradiction: A statement is a contradiction when it cannot possibly be true.

Contingency: A statement is contingent when it can be either true or false.

Logical Consistency: Two statements are consistent when they can both be true.

Logical Equivalence: Two statements are logically equivalent if the truth of either one entails the truth of the other, and the falsity of either one entails the falsity of the other.

e.g. P ↔ ∼∼P

Fallacy: An error in reasoning. (Only applies to arguments, not statements)

Equivocation: “A fallacy that occurs when a word (or phrase) is used with more than one meaning in an argument, but the validity of the argument depends on the word’s being used with the same meaning throughout.”

Circularity (Begging the Question): A fallacy that occurs in an argument when the truth of one or more premises depend upon the truth of the conclusion.

Counterexample: A counterexample to an argument form is a substitution instance in which the premises are true and the conclusion is false.

Premise Indicator Words Conclusion Indicator Words

because since for as evidenced by seeing that in that the reason being given that indicated by owing to due to is inferred from

therefore so hence consequently thus accordingly implies that entails that follows that in conclusion proves that we may infer that deduce that