Phil 102 Unit 3

Strong inductive arguments

A strong inductive argument with true premises is termed cogent. To say an argument is cogent is to say it is good, believable; there is good evidence that the conclusion is true.

Weak inductive arguments

A weak argument cannot be cogent, nor can a strong one with a false premise(s).

Inductive argument

An argument in which it is thought that the premises provide reasons supporting the probable truth of the conclusion. In an inductive argument, the premises are intended only to be so strong that, if they are true, then it is unlikely that the conclusion is false.

Sound argument

An argument is sound if and only if it is valid and all its premises are true.

Cogent argument

By definition non-deductive, which means that the premises are intended to establish probable (but not conclusive) support for the conclusion. Furthermore, a cogent argument is strong, so the premises, if they were true, would succeed in providing probable support for the conclusion.

Enumerative induction

Enumerative induction or, as the basic form of inductive inference, simply induction, reasons from particular instances to all instances, thus an unrestricted generalization. If one observes 100 swans, and all 100 were white, one might infer a universal categorical proposition of the form All swans are white.

Invalid arguments

Remember that an argument is valid if it is impossible for the premises to be true and the conclusion false at the same time. To show that an argument is invalid, we must give an example of a possibility in which the premises could be true and the conclusion false at the same time.

Modus ponens

the rule of logic stating that if a conditional statement ("if p then q ") is accepted, and the antecedent ( p ) holds, then the consequent ( q ) may be inferred.

Invalid argument forms

-Modus Ponens* -Modus Tollens*

Valid argument forms

-Modus Ponens* -Modus Tollens* -Disjunctive Syllogism -Hypothetical Syllogism

Principle of simplicity

A common paraphrase of Ockham's principle, originally written in Latin, is "All things being equal, the simplest solution tends to be the best one."

Generalization from a sample

A generalization is defined as a broad statement or an idea that applies to a group of people or things. Oftentimes, generalizations are not entirely true, because there may be examples of individuals or situations wherein the generalization does not apply.

Substition instance

A statement in logic derived from a statement form by substitution of constants for variables.

Valid arguments

An argument is valid if and only if it is necessary that if all of the premises are true, then the conclusion is true; if all the premises are true, then the conclusion must be true; it is impossible that all the premises are true and the conclusion is false.

Deductive argument

An argument that is intended by the arguer to be deductively valid, that is, to provide a guarantee of the truth of the conclusion provided that the argument's premises are true.

Argument by analogy

Argument from analogy is a special type of inductive argument, whereby perceived similarities are used as a basis to infer some further similarity that has yet to be observed. Analogical reasoning is one of the most common methods by which human beings attempt to understand the world and make decisions.

Hypothetical syllogism

In classical logic, hypothetical syllogism is a valid argument form which is a syllogism having a conditional statement for one or both of its premises. If I do not wake up, then I cannot go to work. If I cannot go to work, then I will not get paid. Therefore, if I do not wake up, then I will not get paid.

Modus tollens

In propositional logic, modus tollens (or modus tollendo tollens and also denying the consequent) (Latin for "the way that denies by denying") is a valid argument form and a rule of inference. It is an application of the general truth that if a statement is true, then so is its contra-positive.

Inference to the best explanation

Inference to the Best Explanation. Inference to the Best Explanation is a kind of abductive reasoning identified by Gilbert Harman in 1965 . He called it abductive reasoning, but Harman's definition of abduction did not correspond exactly to Charles Sanders Peirce's triple of Deduction, Induction, and Abduction.