Logical Yet False
Does it surprise you that an argument can be logical but false?
It’s a common misconception that a logical argument must be true, but indeed, an argument can be logically sound in its form yet lead to a false conclusion if the premises are untrue. Logicians describe a deductive argument as valid if the conclusion logically follows from the premises. However, the argument is considered sound only if it is valid and the premises are true. Overlooking this distinction often hampers our ability to discern good arguments from bad ones.
Examples
Mars Example
Consider the premises “Mars is blue” and “Mars is a planet.” Together, they logically lead to the conclusion, “Mars is a blue planet.” This argument is valid because the conclusion follows logically from the premises, but it is not sound because the premise “Mars is blue” is false. Therefore, despite being logically valid, this argument does not provide a true conclusion that can be relied upon for further logical thought.
Deport Immigrants Example
Some people conclude that immigrants should be expelled based on the following logical argument: “Immigrants who commit crimes should be expelled” and “Immigrants have committed crimes.”
The English language allows us to state, “Immigrants have committed crimes,” which can be interpreted as “some immigrants” or “all immigrants.” This ambiguity can lead to the mistaken generalization “immigrants commit crimes,” when the factual statement is that some, or a very few, immigrants commit crimes. Consequently, the premise “Immigrants commit crimes” and the conclusion “Immigrants should be expelled” are broader than the evidence supports. The conclusion is false because the premise does not apply to all immigrants.
Real-World Implications
The distinction between valid and sound arguments is not just an academic exercise. It has real-world implications in various fields, from politics and law to science and everyday decision-making. For instance, consider how policies are formed based on arguments that may be valid but not sound. If policymakers rely on flawed premises, the resulting policies might be misguided or harmful.
Counterarguments
Some might argue that focusing on the logical form of an argument is sufficient for practical purposes. However, this overlooks the importance of truth in premises. A valid argument with false premises can lead to false conclusions, which, in turn, can result in real-world consequences that are detrimental.
Additional Example: Economic Policy
Consider an economic argument based on the premises “All government spending is wasteful” and “The government is spending money.” The conclusion, “The government is wasting money,” follows logically. However, the first premise is a sweeping generalization and not necessarily true. While the argument is valid, it is not sound, as the premise oversimplifies a complex issue. Policies based on this flawed premise could lead to harmful austerity measures.
Reflective Questions
Can you think of any government outlays that benefit you and society? How do these benefits illustrate the importance of sound arguments in policy-making?
Citation: Rubik’s Cube in head from wikimedia. By Simon Child – https://thenounproject.com/search/?q=logical&i=63409, CC BY 3.0 us, https://commons.wikimedia.org/w/index.php?curid=52500113.
Additional Information
Fake News and Free Speech
