Logic and Validity: Key Concepts in Deductive Arguments

Valid Argument

A deductive argument is valid if it is logically impossible for the conclusion to be false while all the premises are true.

Test for Validity

Try to imagine a situation where all the premises are true but the conclusion is false.

Logical Possibility

A situation is logically possible if it is coherent, conceivable, and non-contradictory.

Example of Logical Possibility

"Dogs breathe underwater" is logically possible (we can imagine it), even though it's biologically impossible.

Logical Impossibility

A situation is logically impossible if it is incoherent, inconceivable, or contradictory.

Example of Logical Impossibility

"Paris is in France and Paris is not in France" is a contradiction and is logically impossible.

Validity vs. Truth

Validity is NOT about the actual truth of the premises or conclusion.

Valid Argument with False Premises

An argument can be valid even if its premises and conclusion are false.

Example of Valid Structure with False Premises

"All birds are mammals. All mammals are fish. Therefore, all birds are fish." (Valid structure, false premises, false conclusion)