Logic for Metaphysics Vocabulary

Vocabulary flashcards covering fundamental logical concepts, argument structures, and notation used in metaphysics.

Argument

A series of statements in which someone is presenting reasons in defense of some claim.

Premise

A statement offered as part of an argument as a reason for accepting a certain claim.

Conclusion

The part of an argument that is being argued for, for which reasons are being offered.

Theism

The thesis that God exists.

Atheism

The thesis that God does not exist.

Numbered premise form

A way of stating arguments so that each premise as well as the conclusion are given a number and presented each on their own line.

Deductively valid

An argument is deductively valid when there is no possible way for the premises of the argument to all be true while its conclusion is false.

Deductively invalid

An argument is deductively invalid when it is possible for the premises of the argument to all be true while its conclusion is false.

Contradiction

Any sentence or statement of the form $P$ and not-$P$.

Counterexample

An example that shows an argument is invalid, by providing a way in which the premises of the argument could be true while a conclusion is false; or an example that shows a statement is false, by providing a way in which it could be false.

Sound

An argument is sound just in case it has all true premises and is deductively valid.

Minor conclusion

A statement that is argued for on the way to arguing for an argument's major conclusion.

Major conclusion

The final conclusion of an argument.

Principle of charity

A convention of philosophical debate to, when reasonable, try to interpret one's opponent's claims as true and her arguments as valid.

Enthymeme

An argument that is incomplete as stated and invalid, although it is easy to supply the missing premises that the argument would need to be valid.

Logical connectives

Symbols used to build complex propositions out of simpler ones.

Modus ponens

The logical form: If $A$, then $B$; $A$; Therefore, $B$, where $A$ and $B$ are any propositions.

Variables

Symbols like $x$, $y$, $z$, etc. used to stand in for other things in a sentence, called the values of the variable.

Existential quantifier

$\exists$, a symbol of first-order predicate logic. When combined with a variable, it can be used to represent a statement to the effect that something exists that is a certain way.

Scope (of a quantifier)

The part of the sentence containing the variables the quantifier is binding.

Bound variable

A variable that is within the scope of some quantifier phrase.

Domain of quantification

The set of objects over which the quantifiers range in a given context, the set of possible values the variables can take.

Universal quantifier

$\forall$, a symbol of first-order predicate logic. When combined with a variable, it can be used to represent a statement to the effect that everything is a certain way.