What is a Good Argument?

As you are now familiar with the structure of an argument, there are now finer details that need to be addressed. First, arguments can primarily be categorized as either deductive or inductive, which derive their names from the types of reasoning used to construct them. Second, we'll discuss the concepts of validity and soundness for deductive arguments. Next, concerning inductive arguments, we'll discuss the concepts of strength and cogency. Last, after discussing all of these facets of logic, we'll conclude with a discussion on how to determine whether an argument is good or bad.

Deductive versus Inductive Arguments

While there are number of categories that exist for arguments out there, deductive and inductive are the dominant types you will encounter regularly. The formal definitions are:

  • A deductive argument is an argument in which it is thought that the premises provide a guarantee of the truth of the conclusion. In a deductive argument, the premises are intended to provide support for the conclusion that is so strong that, if the premises are true, it would be impossible for the conclusion to be false.

  • An inductive argument is an argument in which it is thought that the premises provide reasons supporting the probable truth of the conclusion. In an inductive argument, the premises are intended only to be so strong that, if they are true, then it is unlikely that the conclusion is false.

It's worth noting that a deductive argument will always be more believable than an inductive argument as the conclusion is guaranteed to be true. Now, an example of a deductive argument is as follows:

  • The color of Stephanie’s shirts are either blue or yellow.

  • Stephanie is not wearing a blue shirt today.

  • Therefore, Stephanie’s shirt is yellow.


Here, the premises are “The color of Stephanie’s shirts are either blue or yellow” and “Stephanie is not wearing a blue shirt today.” The conclusion is the statement “Stephanie’s shirt is yellow.” This is a deductive argument as both of the premises are structured in a way as to guarantee the truth of the conclusion if the premises are true. In other words, if we can guarantee that Stephanie only wears blue or yellow shirts, then it is impossible for the conclusion of our argument to be false if we observe that Stephanie is  not wearing a blue shirt today. 

Observe, deductive arguments tend to be quite precise or mathematical in nature. For example, I could very easily reformulate the above argument to one dealing with variables such as:

  • A is equal to B.

  • B is equal to C.

  • Therefore, A is equal to C

  • Mathematically, A = B, B = C. Hence, A = C.


Next, for an example of an inductive argument:

  • It has snowed in Chicago every winter in recorded history. Ergo, it will snow in Chicago this upcoming winter


where, “It has snowed in Chicago every winter in recorded history” is the premise and the conclusion is the statement “it will snow in Chicago this upcoming winter.” As you can see, the premise is true and the conclusion is most likely true, however, it is possible for it to be false. For example, with current global warming trends, it is probable that Chicago will have a winter without snowfall sometime this century.


Validity & Soundness

Before discussing validity and soundness, it is important to understand the concept of truth. Truth is a property of statements that determines loosely if the statement should be trusted or not. How one goes about this is a highly debated core topic within philosophy known as Truth Theory, which is not within the scope of this post. Thus, to avoid confusion, the theory of choice for this discussion will equate truth with a fact (i.e., when I say truth, I am implying it is a fact).


Validity is a property of deductive arguments where the conclusion and premises are related in such a way that it is absolutely impossible for the premises to be true unless the conclusion is also true. Succinctly, an argument is valid if and only if the truth of the premises logically guarantees the truth of the conclusion. For example:

  • Tom either walks or drives his car to work.

  • Tom has chosen to not walk today.

  • Therefore, Tom is driving his car to work.


This is a valid argument as it is impossible for the premises (i.e., “Tom either walks or drives his car to work” and “Tom has chosen to not walk today”) to be true and the conclusion (i.e., “Tom is driving his car to work”) false.


It is important to note that the premises of an argument don't actually have to be true for the argument to be valid. An argument is valid if the premises and conclusion are related to each other in such a way so that if the premises were true, then the conclusion would have to be also true. Consider the following argument:

  • All gardens have gnomes.

  • Gnomes create mischief wherever they are.

  • Therefore, gardens are places of mischief.


Here, as is probably obvious to you, the premises are not true. While it may be hard to imagine these premises being true, if they were, it is easy to see how the truth of the conclusion is logically guaranteed. Last, if an argument fails to meet the requirements to be considered valid, then it is invalid.


The previous example is clearly a poor argument as it is predicated on false premises. Nonetheless, the argument is still valid even though it produces a false conclusion. Therefore, when we are constructing an argument, not only should we aim for a valid argument, but for one that is sound. Soundness is a property of arguments that requires that an argument is both valid and contains true premises. For example:

  • When it rains, the roads become wet.

  • It is raining.

  • Therefore, the roads are wet.


Clearly, both of the premises are true and the argument is also valid. Ergo, this argument is sound. Note, all invalid arguments are also unsound.


Let's examine a few more examples:

  • All humans are mammals.

  • No mammals are animals with scales.

  • Therefore, no humans are animals with scales.

  • All humans are dogs

  • No dogs are animals with scales.

  • Therefore, no humans are animals with scales.


Both of these arguments share the same form:

  • All A's are B.

  • No B are C.

  • Therefore, No A are C


Both of these arguments are valid, but only the first argument is sound as the second argument contains the false premise “All humans are dogs.” As you can see, the goal with deductive arguments is to structure them so as they are sound. Only then can the conclusion be trusted.

Strength & Cogency

Strength is a property of inductive arguments that indicates the likeliness that the conclusion is true. This term correlates loosely with validity for deductive arguments except that with inductive arguments strength comes in a spectrum (i.e., an argument can be mostly strong, weak, or somewhere in between). In general, if there is at least a 50% probability that the conclusion follows from the truth of the premises, then it is strong. However, if the argument fails to meet this criterion then it is considered weak. For example:

  • Most people who are from an African country have dark skin (put more scientifically, this is just a higher concentration of melanin in the skin, which protects our skin from UV rays).

  • Julian is from Uganda.

  • Therefore, Julian has dark skin.


This is clearly an inductive argument as the conclusion is not guaranteed by the truth of the premises (i.e., there are light-skinned people from Africa, but they make up a small percentage. Note, lightness and darkness are subjective, which complicates this argument. A more precise argument would be structured from experimental data examining melanin concentrations taken from skin samples). Based off of the premises, I think it's fair to classify the conclusion here as strong. Here's another example:

  • Most people who are from an African country have dark skin.

  • Julian has dark skin.

  • Therefore, Julian is from an African country.


Now, this is similar to our previous argument, except this time, we are expected to infer from the premises that just because Julian's skin is dark, that he's from an African country. The probability of this is going to be significantly less likely as there are dark-skinned people who live all over the world, not just on the continent of Africa. I would classify this argument as weak.


Similar to the concept of soundness for deductive arguments, cogency is when a strong inductive argument has true premises. To label an inductive argument cogent is to say that there is good evidence that the conclusion is true. An argument cannot be cogent if it is either weak or strong with a false premise(s). For example:

  • Bobby is usually late to work.

  • Bobby is scheduled to work tomorrow.

  • Therefore, Bobby will be late.


Here, we're going to assume the premises are true – we have a credible source of information - and that “usually” indicates at least 50% of the time. Thus, the argument is cogent as it is both strong and the premises are true. Now, let's suppose that the premise “Bobby is usually late to work” came from an untrustworthy source, we then fact check the claim and it turns out to be a lie. In this case, this would render the premise false and the argument is no longer considered cogent.

Yoda.png

What is a good Argument?

Up to this point, we've discussed the two different argument types (i.e., deductive versus inductive) along with the structural terminology that go with each. Now, while being able to identify an argument is important, it is secondary to knowing when it is reasonable or not to accept the conclusion. When you are presented with an argument, the presenter is attempting to persuade you of something. With that in mind, how do you decide whether or not you should accept the conclusion? Other people attempting to persuade us to believe or do something is a situation that we all face daily. Therefore, improving our ability to distinguish between good and bad arguments is tremendously valuable to our everyday lives.


A good argument is one where the premises sufficiently support the belief that the conclusion is true. Diametrically, a bad argument is one where the premises do not provide good reasons to support the conclusion. Note, a convincing argument is not the same as a good argument. It may be the case that an argument sounds very convincing, but nonetheless, is still a bad argument. Most of us encounter arguments of this type on a daily basis. From used car salesman to politicians, the world is full of people attempting to convince us without providing good reasons. Furthermore, it's also important to note that a bad argument doesn't automatically render the conclusion false. It is possible for the conclusion to be true without premises that sufficiently support it.


For an argument to be considered good, it must obey two criteria:

  1. The premises are plausible. That is, you must have sufficient evidence to believe that the premises are true.

  2. The argument must be valid or strong.


These two criterion coupled with all of the terminology that we've discussed up to this point will help you to determine whether or not an argument is good or bad. Essentially, an argument can be considered good when it is either sound or cogent.

Conclusion

Arguments are something that we all encounter on a daily basis. Sometimes it's your significant other trying to convince you to agree on that new car purchase, a co-worker trying to persuade your boss into a promotion, a company who wants you to buy their latest and greatest product, you even construct arguments internally when you're attempting to make an important decision. The fact is, arguments are unavoidable and determining a good argument from a bad one is incredibly important to all of us.

The tools needed to complete such a task have all been provided to you within this post. The primary argument types, the terminology that goes along with each and last, that a good argument is one that is either sound or cogent. With a firm understanding of these concepts, you are now better armed to protect yourself against the bad arguments of the world and, more importantly, you will know how to structure a good argument of your own.


Video