Good and Bad Arguments

Good and Bad Arguments

Deductive and inductive arguments can both be evaluated by asking (1) whether the premises support the conclusion in the required way and (2) whether all the premises are true. Failure on either test undermines the argument’s support for its conclusion; it does not by itself establish that the conclusion is false.

In the deductive realm, that a conclusion follows from premises means that the argument is valid – it is invalid if the conclusion does not follow. Strictly speaking, in the deductive realm, an invalid argument is one where a formal fallacy has been committed. When an argument is valid and all the premises are true in the deductive realm, the argument is said to be a good, sound argument. If the argument is invalid or any of the premises are false, then the argument is unsound – thus, both conditions, validity and truth of all of the premises, must be met. A sound deductive argument guarantees a true conclusion.

So, the "Our sun is cube‑shaped" argument is valid but still unsound because the second premise is false. It is thus a bad argument and should be rejected.

This is true →	(1) Our sun is a star.
This is false →	(2) All stars are cube‑shaped.	←Valid, but not all premises
Does follow →	(3) Therefore, our sun is cube‑shaped.	are true, so unsound

On the other hand, the "The mind is a computer" argument has true premises but is still unsound because it’s invalid. It, too, is a bad argument and should be rejected.

This is true →	(1) Computers can calculate things.
This is true →	(2) The mind can calculate things, too.	←All premises are true, but
Doesn’t follow →	(3) Therefore, the mind is a computer.	invalid, so unsound

In the inductive realm, that a conclusion likely will follow from premises means that the argument is strong – it is weak if the conclusion likely does not follow. An informal fallacy can make an inductive argument weak. When an argument is strong and all the premises are true in the inductive realm, the argument is said to be a good, cogent argument. If the argument is weak or any of the premises are false, then the argument is uncogent – thus, both conditions, strength and truth of all of the premises, must be met. A cogent inductive argument makes its conclusion probable rather than certain.

So, the 5,000‑calorie‑a‑day weight loss argument is strong but still uncogent because the first premise is false. It is thus a bad argument and should be rejected.

False →	(1) In over 1 million controlled studies, it was shown consistently that people lost 10% of their body weight in a month on a 5,000‑calorie‑a‑day diet.
True →	(2) You are starting that same diet at the beginning of next month.
Follows →	(3) Therefore, all things being equal, you too will likely lose 10% of your bodyweight in a month on a 5,000‑calorie‑a‑day diet.	←Strong, but not all premises are true, so uncogent

On the other hand, the following argument has true premises but is still uncogent because it’s weak – a fallacy has been committed. It’s an example of the informal fallacy known as appeal to inappropriate (or false) authority or inappropriate appeal to authority. It, too, is a bad argument and should be rejected.

This is true →	(1) He is an accountant by trade.
This is true →	(2) In his opinion, global warming occurs.	←All premises are true ,
Doesn’t follow →	(3) Therefore, global warming occurs.	but weak, so uncogent

The first diagram summarizes the requirements for good arguments. A deductive argument is sound when it is (1) valid and (2) based on true premises. An inductive argument is cogent when it is (1) strong and (2) based on true premises.

The second diagram summarizes failures. A deductive argument is unsound if it (1) is invalid, (2) has a false premise, or (3) both. An inductive argument is uncogent if it (1) is weak, (2) has a false premise, or (3) both.