Definition:Invalid Argument
Definition
An invalid argument is a argument in which the premises do not provide conclusive reasons for the conclusion.
Also known as
An invalid argument is also known as a fallacy.
Some authors use the term unsound argument to mean invalid argument.
However, because of the confusion about the meaning of sound argument, which can be used to mean either valid argument or proof, it is recommended that this term not be used.
Examples
Socrates is Mortal
This argument is technically invalid:
Moon is Yellow
- The moon is yellow.
- Therefore, the moon is made of cheese.
I am Not Famous
The following is an invalid argument with true premises and a true conclusion:
- If I am President then I am famous.
- I am not President.
- Therefore I am not famous.
Rockefeller was Not Famous
The following is an valid argument with true premises and a false conclusion:
- If Nelson Rockefeller was President then he was famous.
- Nelson Rockefeller was not President.
- Therefore Nelson Rockefeller was not famous.
Also see
Linguistic Note
The word invalid, as used in the logical context, has the stress on the second syllable: in-val-id.
Pronounced in-val-id, with the stress on the first syllable, the word means a person who is being treated for an illness.
There are plenty of apocryphal tales on the internet where furious users have called the helpdesk to tell the staff that their computer is calling them bad, and an invalid.
So let's be careful out there.
Warning
In natural language, especially when a person is attempting to sound more learned than they are, it is commonplace to discuss the nature of statements as being valid or invalid.
What is really meant, of course, is that a statement is either true or false.
Sources
- 1959: A.H. Basson and D.J. O'Connor: Introduction to Symbolic Logic (3rd ed.) ... (previous) ... (next): Chapter $\text I$ Introductory: $3$. Logical Form
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $1$ The Nature of Logic
- 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $1$ Introduction: Logic and Language: $1.2$: The Nature of Argument
- 1980: D.J. O'Connor and Betty Powell: Elementary Logic ... (previous) ... (next): $\S \text{I}: 1$: The Logic of Statements $(1)$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): argument: 2.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): valid
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): argument: 2.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): valid