Logic and Moral Reasoning: Validity, Fallacies, and Conditional Statements

Moral Reasoning

A set of reasons and a conclusion they are meant to support.

Argument (Logic)

A chain of thought where premises are offered to support a conclusion.

Tests for Good Moral Reasoning

Avoid false beliefs and maintain rigorous, error-free logic.

Logically Valid Argument

When the truth of premises guarantees the truth of the conclusion.

Sound Argument

An argument that is valid and has true premises.

Sufficient Condition

A condition that acts as a guarantee.

Necessary Condition

A condition that acts as a requirement.

Biconditional

A claim supplying both necessary and sufficient conditions.

Modus Ponens

If P then Q; P; therefore Q.

Modus Tollens

If P then Q; Q is false; therefore P is false.

Hypothetical Syllogism

If P then Q; if Q then R; therefore if P then R.

Fallacy

A mistake in reasoning.

Fallacy of Denying the Antecedent

If P then Q; P is false; therefore Q is false.

Fallacy of Affirming the Consequent

If P then Q; Q is true; therefore P is true.

Ad Hominem Fallacy

Undermining a position by attacking the person advancing it.

Straw Man Fallacy

Distorting an opponent's position to make it easier to refute.

Appeal to Ignorance

Assuming a claim is true just because there is no contrary evidence.

Hasty Generalization

Illicitly drawing a general lesson from a small handful of cases.

Meaning of 'Unless' in Logic

It means 'if not'.

Contrapositive

Found by reversing and negating the original conditional statement.

Implicit Premises

Premises omitted by authors because they are considered self-evident.

Complex Argument

An argument that contains one or more intermediate conclusions.

Intermediate Conclusion

A proposition supported by premises that in turn acts as a premise for a further conclusion.

Conditional Arrow Notation

Expressing conditional statements as P -> Q, where the antecedent leads to the consequent.

Evaluating Validity

Determining whether an argument's logical structure ensures that true premises guarantee a true conclusion.

Every political philosopher of the early twentieth century who was either a socialist or a communist was influenced by

Rosa Luxemburg. No one who was influenced by Rosa Luxemburg advocated a totalitarian state. If the statements

above are true, which one of the following must on the basis of them also be true?

(A) No early twentieth-century socialist political philosopher advocated a totalitarian state.

Soundness

An argument is sound when it satisfies two conditions

It is valid

It has all true premises

Validity

An argument is valid if it satisfies the following condition:

If the premises are true then the conclusion must be true

Order of premise

dont matter but standard is conditional is premise 1

Biconditional

A claim that supplies necessary and sufficient conditions is called a biconditional

If and only if p, then Q

Unless

=if not

Only if

=if p then q