Understanding the Validity of Arguments: Beyond Premise Truth

When evaluating the validity of an argument, one must consider the logical structure rather than the truth of the premises. This article explores the relationship between the truth of the premises and the validity of an argument, and highlights several real-world examples to clarify misunderstandings surrounding logical statements.

The Role of Premises in Argument Validity

To determine if an argument is valid, one needs to examine the logical relationship between its premises and conclusion. An argument is valid if the conclusion necessarily follows from the premises, regardless of whether the premises themselves are true or false. If the premises are not just false, but also impossible to be true, the validity of the argument remains unaffected.

Example: Unicorns and the Sky

Consider the following argument:

Premise 1: All unicorns are green.
Premise 2: There are unicorns.
Conclusion: Therefore the sky is blue.

In this example, the premises are clearly false and impossible to be true as unicorns do not exist. However, the argument is valid because if the premises were true, the conclusion would follow logically. This demonstrates that the validity of an argument does not depend on the actual truth value of its premises.

Validity and Testability

An argument is considered valid if it can be tested and not proved illogical. Just because an argument is based on false premises does not make it invalid. For instance, the logical statement x 1 in mathematics is a valid argument because it can be tested and its logic is sound.

However, an invalid hypothesis is a statement that logically contradicts itself, making it trivial to disprove. On the other hand, a theory is a hypothesis that can be tested to determine its truth value. Not all valid theories are necessarily valid arguments, as they may be too broad or under-specified to be falsifiable.

The Relationship Between Valid Arguments and Valid Theories

A valid argument is a logical statement that holds under certain conditions, whereas a valid theory is a well-specified hypothesis that can be tested to either confirm or deny its validity. All valid arguments are, in essence, valid theories because they can be tested for truth or falsehood within a single statement.

For example, the theory that life naturally evolves by natural selection of natural variance is not fully specified enough to be definitively falsified or proven. However, this does not mean the argument itself is invalid; it simply reflects the need for further specification. The modern theory of natural biological evolution, on the other hand, is a collection of valid arguments based on evidence such as the fossil record and genetic changes.

Illogical Premises: Invalidity and Falsifiability

When the premises of an argument are false, the argument may still be valid if the conclusion logically follows from the premises. However, if the premise is determined to be false, the argument becomes illogical despite remaining valid.

For instance, the statement "my sister is a boy and therefore I am not her sister" is illogical because the premise "my sister is a boy" is false. Despite this, the logical structure of the argument remains valid, as the conclusion does not directly depend on the false premise.

Conclusion

In conclusion, the validity of an argument is determined by the logical relationship between its premises and conclusion, not by the truth value of the premises themselves. While some arguments based on false premises may be considered valid, the truth or falsity of the premises is crucial for determining the validity of the argument.