Difference between valid and sound arguments

Note: this is just for my own reference ðŸ™‚

To understand what it means for an argument to be ‘valid’ or ‘sound’, let’s take a step back and consider what the heck an argument is in the first place.

What is an argument?

An argument is a set of statements given to support a conclusion. In philosophy, the fancy word for a statement is a premise. Here’s an example argument where the premises are prefixed as P1 and P2, and the conclusion is prefixed with C:

``````P1: John owns either a BMW or a Mercedes.
P2: John does not own a BMW.
C: Therefore, John owns a Mercedes.``````

Okay, so an argument is basically a set of statements followed by some conclusion.

When considering some of the most important questions in life, we often have to consider the various arguments for and against a certain proposition. How can we evaluate all these arguments and decide which are good and which are bad?

Well, ‘good’ and ‘bad’ are kinda vague terms because a good argument for one person may not be so good for another – it can all be very subjective.

As a result, philosophers prefer to use well-defined terms like ‘valid’ and ‘sound’ to describe more explicitly the properties of arguments. Having these well-defined terms is supposed to bring more clarity to our analysis of arguments and so make the process of distinguishing between ‘good’ and ‘bad’ arguments less subjective.

What does a ‘valid’ argument mean?

An argument is considered valid if the truth of the premises guarantees the truth of the conclusion. In other words, if the premises are true, then the conclusion must also be true.

Validity is not concerned with whether the premises of an argument or even the argument itself is actually true, it’s only concerned with whether the form of the argument is logical in the sense that the premises logically lead to the conclusion.

This process of analyzing the validity of arguments comes under the branch of propositional calculus which in a nutshell checks to see if the form of an argument follows a set of valid forms known as rules of inference.

What does a ‘sound’ argument mean?

An argument is considered sound if it’s both valid and its premises are true. In other words, it’s a stronger type of argument where not only do the premises guarantee the conclusion, but the premises are also shown to be true. When an argument is proved to be sound, it’s very difficult to refute.

An argument can be valid but not sound

It’s important to note that an argument can be valid but not sound. Many fallacious arguments are like this. Here’s an example of an argument that’s valid but not sound:

``````P1: All men love dogs
P2: Socrates is a man
C: Therefore, Socrates loves dogs``````

Here, the argument is valid because the conclusion that ‘Socrates loves dogs’ must be true if premise 1 ‘All men love dogs’ and premise 2 ‘Socrates is a man’ are true. More specifically, this argument is valid because it follows the Universal Modus ponens rule of inference.

However, the argument is not sound because its first premise (‘All men love dogs’) is false and so it doesn’t matter if the conclusion logically follows. If any of the premises are false, the argument is not sound and therefore not any good.

Determining whether an argument is valid or sound is hard work

So when evaluating an argument, it seems we have to do a bunch of things.

Step 1 – Determine if the argument is valid using propositional calculus

Here, we have to be a little analytical and really dissect the argument into its various propositions and logical connectives. It probably helps to be familiar with the fundamentals of propositional calculus to do this step effectively and avoid any logical fallacies. This step seems like a pain in the ass.

Step 2 – Determine if the premises are true

As mentioned earlier, a valid argument is no good if any of its key premises are false. The trouble is that it’s often difficult or impossible to determine whether a given premise is true or not.

Consider the following formulation of the Cosmological Argument.

1. A contingent being (a being such that if it exists, it could have not-existed or could cease to exist) exists.
2. This contingent being has a cause of or explanation for its existence.
3. The cause of or explanation for its existence is something other than the contingent being itself.
4. What causes or explains the existence of this contingent being must either be solely other contingent beings or include a non-contingent (necessary) being.
5. Contingent beings alone cannot provide a completely adequate causal account or explanation for the existence of a contingent being.
6. Therefore, what causes or explains the existence of this contingent being must include a non-contingent (necessary) being.
7. Therefore, a necessary being (a being such that if it exists, it cannot not-exist) exists.
8. The universe is contingent.
9. Therefore, the necessary being is something other than the universe.

Here, one could deny premise 8 by saying that we don’t know enough yet to assume that the universe is contingent – perhaps it’s eternal, who knows!. The whole argument fails if such a key premise is denied.

But the problem is that we can’t conclusively say whether premise 8 is true or not at the moment. This is why scientific evidence is often essential to many philosophical arguments, especially a posteriori arguments. If we don’t have hard evidence to support our premises, it’s difficult to reach sound conclusions.

Step 3 – Be prepared to accept hard truths

It’s often very uncomfortable to accept what seems to be sound and reasonable arguments. Accepting an argument may hurt your ego, threaten your sense of identity, or even shatter your existing worldview.

This step can often be the hardest!

TODO: Need some examples of valid, invalid and sound arguments.

Hello! My name is Sajad. I’m a software developer at Nationwide and an aspiring entrepreneur. Originally from Afghanistan, I moved to London at an early age and have been living here for the past 20 years.

This is my personal website where I blog mostly about programming with occasional thoughts on a bunch of other things. I write mainly for my own benefit as I find that writing helps clarify my otherwise very confused thoughts.