Can an Argument Be Partially True but the Rest False?

Arguments, often considered in terms of truth or falsehood, are more accurately evaluated based on their logical structure and the truth of their premises. Here, we explore the nuances of an argument that has some true premises and yet leads to a false conclusion, delving into the realm of philosophical inquiry.

Understanding Logical Validity and Truth

Arguments are neither inherently true nor false. They are logical structures that are either valid or invalid, determined by the arrangement of their premises and the form of their conclusion. A logically valid argument is one where if the premises are true, the conclusion must also be true. The truth or falsity of the premises, however, is a separate issue.
For instance, an argument is logically valid if it follows a valid logical form, such as:

All men are mortal. Socrates is a man. Therefore, Socrates is mortal.

Here, the premises "All men are mortal" and "Socrates is a man" are premises that can be considered true (assuming the premises hold in their general or specific context). However, the argument remains valid even if the premises are false. In logical terms, an invalid argument is one where the conclusion does not necessarily follow from the premises.

False Premises and Logical Validity

Even when an argument is logically valid, the conclusion is only guaranteed to be true if all premises are true. If some or all of the premises are false, the argument becomes useless, regardless of its logical structure. For example:

The sky is blue. The ocean is blue. Why is the sky blue? Because it's water. Why doesn't the water of the sky flood us? Because there’s a transparent crystalline dome holding the water back. We call that dome the ‘firmament’.

This argument has two true premises ("The sky is blue" and "The ocean is blue"), but the conclusion is entirely false. The premise that "the sky is a body of water" is also false, as the sky is not composed of water. Thus, this argument is logically valid, but has a false conclusion.

Partial Truth in Arguments

Arguments can be partially true but still be logically invalid. Let's consider another example:

Rain makes the pavement wet. The pavement is wet. Therefore, it rained today.

The premises "Rain makes the pavement wet" and "The pavement is wet" may be true, but the conclusion "It rained today" does not necessarily follow. There are other potential causes for the wet pavement, such as sprinklers or morning dew. This argument is valid in its logic (it could be true if rain is the only cause of a wet pavement), but the conclusion is not necessarily true, making the overall argument invalid.

Philosophical Insights on Partial Truth

Philosophically, arguments with partially true premises can still be considered flawed if the conclusion does not logically follow. Despite the premises being true in a certain context, the argument may still be invalid if the conclusion does not emerge naturally from the premises. For example:

All cats are furry. Fido is a dog with fur. Therefore, Fido is a cat.

The premises "All cats are furry" and "Fido is a dog with fur" are true in a philosophical or formal logic sense, but the conclusion "Fido is a cat" is false. This demonstrates that while premises can be true, the logical structure of the argument can still be invalid.

Conclusion

In summary, an argument can have some true premises and yet be logically invalid, leading to a false conclusion. Understanding the distinction between the truth of premises and the validity of the logical structure is crucial in evaluating arguments. Recognizing and addressing these nuances helps in constructing more robust and reliable arguments.