Could You Give an Example of a Valid Argument with False Premises and a True Conclusion?

Consider the following syllogism:

All things that are made of cardboard are edible and taste of cheese. Pizza is made of cardboard. Therefore, pizza is edible and tastes of cheese.

In this example, both the major premise and the minor premise are false. It is not true that all cardboard items are edible or taste of cheese, and it is not true that pizza is made of cardboard. However, the conclusion may still be true because pizza is indeed edible and does taste like cheese. The argument is valid because the conclusion logically follows from the premises, even though the premises are false.

A More Complex Example

The following syllogism involves a logical fallacy known as Affirming the Consequent:

If tigers are striped then leopards are striped. Leopards are striped. Therefore, tigers are striped.

Both of the premises in this argument are false, but the conclusion is true. This represents a case where a valid logical structure coincides with a true conclusion, but it does not imply that such a conclusion will always be true. For instance, if one were to use this same form of argument incorrectly, it might lead to a false conclusion.

Another Instance: Common Misconceptions

Consider a classic statement that can be exemplified by a common phrase: "It is always in the last place you look..."

“Well, no shit.” Do this with answers... Run off with the first one that sounds good... No wonder it is counter-intuitive... Find what you are looking for and then stop looking.

This phrase highlights a common human behavior, but its truth does not necessarily mean it is useful or accurate in all situations. Often, the intuition that a thing is in the last place checked is misleading, leading to immediate answers or quick decisions that may overlook the true solution.

Example of a Valid Argument with False Premises and a True Conclusion

An example of a valid argument with false premises and a true conclusion is:

All cats are birds. All birds can fly. Therefore, all cats can fly.

In this case, both premises are false because cats are not birds, and not all birds can fly. However, the conclusion is true since all cats, by definition, can fly (in our hypothetical premises). This demonstration shows that the validity of an argument is determined by the logical structure rather than the truth of the premises. It also clarifies that the truth or falsity of the premises is a separate issue from the validity of the argument.

The Relevance in Science and Philosophy

Even in science and philosophy, arguments can have logical validity despite premises that are false. For example, consider a simplified physics argument:

The general physics community’s point of view is that... The argument is valid and has true premises... The conclusion is false based on the accepted community’s perspective...

This scenario illustrates that an argument can be logically valid and have true premises, yet still have a false conclusion. This distinction is important in understanding the nature of logical reasoning and the importance of empirical evidence over pure logical structure.