More than one person has believed that all good arguments are logically sound, but this is a mistake. Not all good arguments are logically sound. Even so, understanding why not all good arguments are logically sound can help us better understand what good arguments are. I will discuss what good arguments are, I will explain what it means for an argument to be logically sound, explain the distinction between deductive and inductive arguments, and present an argument that proves that not all good arguments are logically sound.

What are good arguments?

For our purposes here a good argument is one that is rationally persuasive and does not make use of informal fallacies (informal errors in reasoning). Good arguments give us a sufficient reason to rationally agree with a conclusion. I will not discuss “informal fallacies” in detail here.

However, it is not entirely clear what a “good argument” is because it is not entirely clear when an argument is rationally persuasive. What exactly “rationality” consists of is a controversial topic that is studied by epistemologists (philosophers who study reasoning, justification, and knowledge).

Even so, there are uncontroversial examples of good arguments. A common example of a good argument is the following:

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

(“Socrates” refers to a real historical figure discussed by Plato and other ancient philosophers and Socrates is said to have died by drinking hemlock.)

This argument gives us a sufficient reason to rationally agree with the conclusion that “Socrates is mortal” because the premises are highly justified, and anyone who believes the premises are true has no choice but to think that the conclusion is true. A person would not be irrational to believe the conclusion and it might even be rationally required for us to believe the conclusion—perhaps anyone who knows about this argument yet believes that Socrates is immortal (or is even undecided about it) is irrational considering how highly rationally persuasive this argument is.

What does it mean for an argument to be logically sound?

“Logical soundness” requires that an argument is both logically valid and that all the premises are true.

What’s a valid argument?

Logically valid arguments have a form that guarantees that the argument can’t have true premises and a false conclusion at the same time. For example, consider the following valid argument:

If all dogs are mammals, then all dogs are animals. If all dogs are animals, then all dogs are flowers. Therefore, if all dogs are mammals, then all dogs are flowers.

This argument is logically valid because we can’t imagine that the premises are true and the conclusion is false at the same time. If we imagine that both the premises are true, then the conclusion must also be true.

To better understand why an argument is logically valid, it can be a good idea to consider the logical form. In this case the logical form is the following:

If a, then b. If b, then c. Therefore, if a, the c.

All arguments with this logical form are logically valid. Each variable (a, b, and c) can stand for any proposition. Keep in mind that valid arguments can have false premises or conclusions. However, if an argument with this form has true premises, then it’s logically sound—and we are guaranteed that the conclusion is also true. Why? Because valid arguments can’t have true premises and a false conclusion at the same time.

It can also be a good idea to consider an invalid argument to see how it differs from a valid one. An example of an invalid argument is the following:

If all dogs are mammals, then all dogs are animals. All dogs are animals. Therefore, all dogs are mammals.

In this case we can imagine that the premises are true but the conclusion is false insofar as both premises could be true even if not all dogs are mammals.

The logical form of this invalid argument is the following:

If a, then b. b. Therefore, a.

Any argument with this form is invalid. We can replace the variables with new propositions to show that an argument with this form can have true premises and a false conclusion at the same time. Let’s replace a with “all cats are reptiles” and b with “all cats are animals.” In that case we get the following invalid argument:

If all cats are reptiles, then all cats are animals. All cats are animals. Therefore, all cats are reptiles.

Now both premises are true, but the conclusion is false. The problem with invalid arguments of this kind is not that a premise or conclusion is false. The problem is that the premises do not give us a sufficiently good reason to think the conclusion is true—even if the premises are true, the conclusion can still be false.

What’s a sound argument?

An example of a sound argument is plausibly the following:

If all dogs are mammals, then all dogs are animals. If all dogs are animals, then all dogs have DNA. Therefore, if all dogs are mammals, then all dogs have DNA.

One problem with just about any example of a “sound argument” is that there’s some uncertainty involved. Our best science tells us that the premises are true, but there’s a chance that the science is wrong. We can say that this argument is “probably sound” but we can’t say we know it is sound for absolute certain. It is possible that one of the premises are false and that the conclusion is false as a result.

If it were true that all good arguments are logically sound, that would imply that we almost never know for sure if an argument is good. The best we could do is say that it’s probably a good argument.

What’s the difference between inductive and deductive arguments?

Inductive arguments are meant to give us a conclusion that’s probably true based on limited data, but deductive arguments are meant to guarantee that the conclusion is true. Deductive arguments are meant to be valid, but inductive arguments are not meant to be valid. The above arguments were all deductive, but not all good arguments are deductive. For example, consider the following good inductive argument:

The laws of nature existed throughout human history. Therefore, the laws of nature will probably exist tomorrow.

This argument could be considered to be logically invalid, but it’s not meant to be logically valid. It’s only meant to tell us what is probably true based on limited information. This is how scientific arguments for theories work. Science makes predictions based on limited data. The predictions could always have a chance of being false. For example, it is possible that the laws of nature will not exist tomorrow. We predict they will, but we can’t prove they will for absolute certain.

The fact that we can have good inductive arguments is potential proof that not all good arguments are logically sound. If all good arguments are logically sound, then the above argument about the laws of nature would fail to be a good argument—and all scientific arguments for theories would be also fail to be good arguments. And yet many of the most persuasive rational forms of reasoning to believe anything is based on science (and inductive arguments).

Proof that not all arguments are logically sound

An argument against the belief that all good arguments are logically sound is the following:

At least some good scientific theories were proven to be false. If at least some good scientific theories were proven to be false, then not all good arguments are logically sound. Therefore, not all good argument are logically sound.

Premise 1 – Is it true that “at least some good scientific theories were proven to be false?” Yes. For example, I think Newton’s theory of physics is a good example. It was believed that Newton’s theory of physics was complete and could predict any physical motion, but it failed to predict the motion of Mercury. However, Einstein’s theory of physics was able to predict the motion of Mercury and is now considered to be a better (and more complete) theory of physics.

Premise 2 – Is it true that “if at least some good scientific theories were proven to be false, then not all good arguments are logically sound?” Yes. Scientists give good arguments in favor of good scientific theories. If all good scientific theories are proven to be true by sound arguments, then they can’t be proven to be false. Sound arguments would guarantee the theories are true because the premises would be true and the arguments for the theories would be valid—valid arguments can’t have true premises and false conclusions at the same time.

Given that we should accept these justified premises, the conclusion should also be accepted. We seem to know the premises to be true, so we have no choice but to think we can know the conclusion is also true. Why? Because this argument uses a valid logical form. The logical form is “a. If a, then b. Therefore, b.” This valid logical form is well-known to be valid and is called “modus ponens.”

Conclusion

I am all for good arguments, and I think people should know more about what good arguments are. I want them to know more about what it means to give people a sufficient reason to rationally agree with a conclusion. Saying that not all good arguments are logically sound doesn’t mean we shouldn’t try to present sound arguments now and then. However, it does mean that we can’t condemn all arguments that fail to be sound.

(Updated 11/21/13 to add clarification.)

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