Logicians often break arguments into a formal structure known as standard form. The basic idea is that extracting an argument into standard form allows logicians to analyze the argument in a more thorough and accurate fashion. People often make logical mistakes that go unnoticed while arguing; extracting an argument into standard form is a method used to catch these mistakes. I will give you instructions on how to put an argument in standard form. Consider this argument:

“If you stand by the ocean and see no curvature on the horizon, then the Earth is flat. I drove my car to the beach today. I just stood at the ocean and saw a curvature on the horizon; thus, the Earth is not flat.”

Step 1

Identify the conclusion of the argument and write it down at the bottom of your page:

The conclusion of the argument is always the main point of the argument, or what the arguer is ultimately trying to get you to believe. It seems like the arguer is trying to get us to believe that the Earth is not flat, so that is probably the conclusion.

Additionally, there are some words which will help you determine what parts of the argument are premises and what part of the argument is the conclusion. The first group of words are usually followed by the conclusion. These words are known as conclusion indicators. Examples include:

• Thus
• Therefore
• It follows that
• This implies

Sentences that are premises are generally found before the conclusion indicator and sentences that are conclusions are usually found after. For example:

“Sally is a jerk, so it follows that you shouldn’t date her.”

The premise of this argument is ‘Sally is a jerk’ and the conclusion is ‘you shouldn’t date her’. This general pattern is not always the case; however, these indicators can generally help you find the conclusion.

There are also some words that are usually followed by a premise. We call these premise indicators. For example:

• Because
• Since
• The reason for this is
• Due to

The conclusion is generally found prior to using the premise indicator. For example:

“You shouldn’t date Sally because she is a jerk.”

In the example above, it is clear that the conclusion is ‘you shouldn’t date Sally’ and the premise is ‘she is a jerk’. You can tell this by finding the premise indicator.

In short, conclusion indicators follow this pattern:

{Premise} [Conclusion indicator] {Conclusion}

While premise indicators usually follow this pattern:

{Conclusion} [Premise indicator] {Premise}

Okay, so that is how you figure out what parts of the argument are premises and what parts are conclusions. So, let’s go back to the original argument:

If you stand by the ocean and see no curvature on the horizon, then the Earth is flat. I drove my car to the beach today. I just stood at the ocean and saw a curvature on the horizon; thus, the Earth is not flat.

Notice that “the Earth is not flat” follows “thus,” a conclusion indicator. Thus, it seems like the conclusion is “the Earth is not flat.” We should then write, “Thus the Earth is not flat” at the bottom of your page:

Thus, the Earth is not flat.

Step 2

Identify the premises of the argument and then write them above the conclusion.

So, we know that the conclusion is, “Thus the Earth is not flat.” So, we should go ahead and write any other sentence that seems to be a premise to the argument. We should write these sentences above the argument in the order that seems to flow best. So, this should look like:

If you stand by the ocean and see no curvature on the horizon, then the Earth is flat

I drove my car to the beach today

I just stood at the ocean and saw a curvature on the horizon

Thus, the Earth is not flat

Step 3

Make sure you use consistent terminology

When we evaluate arguments, we are trying to figure out if the premises give reason to believe the conclusion. Unfortunately, inconsistent language can often distract us from this task since people can interpret words in different ways. Thus, it is important to make sure that your argument uses the same words for the same concept. So, what should we do with this argument? Notice that I say “beach” at one point and “ocean” at one point. This distinction seems to be unnecessary for the argument, so we should change the argument to this:

If you stand by the ocean and see no curvature on the horizon, then the Earth is flat

I drove my car to the ocean today

I just stood at the ocean and saw a curvature on the horizon

Thus, the Earth is not flat

Step 4

Remove any unnecessary words or premises

We want to make our arguments as concise as possible. Often when we talk, we put unnecessary filler in, but this only distracts us when we analyze arguments. So, take anything out that seems unnecessary. The premise indicators are generally perceived to be unnecessary, but the conclusion indicators are necessary So, perhaps we could condense this argument to:

If you don’t see a curvature on the ocean’s horizon, then the Earth is flat

I saw a curvature on the ocean’s horizon

Thus, the Earth is not flat

It seems like I took out nothing of importance and only made the argument simpler.

Step 5

Number the propositions

We want to assign numbers to the different propositions (all the statements in the argument) so that we can refer to each individual proposition. Often when we evaluate arguments, we will look at each premise and consider whether it is true. Thus, the argument should look like:

1. If you don’t see a curvature on the ocean’s horizon, then the Earth is flat
2. I saw a curvature on the ocean’s horizon
3. Thus, the Earth is not flat

Before I move on, it is important to note that you should never use the same numbers to refer to different propositions in the same essay, chapter, or document (or if you do, make sure that it is very obvious that they are referring to different arguments).

Step 6

Draw a horizontal line below the last premise and above the conclusion

We draw a line to help us distinguish what part of the argument the premises are in and what part the conclusion is in. So, our argument should look like this:

1. If you don’t see a curvature on the ocean’s horizon, then the Earth is flat
2. I saw a curvature on the ocean’s horizon
3. Thus, the Earth is not flat

This is our final extraction into standard form. It is important to note that there can be multiple good ways to extract arguments into standard form. Thus, this is to some extent more of an art than a science.

Comprehension Questions