John: I think that Coronavirus is not real! It’s just a hoax to scare people…

Anne: Well, here are some peer-reviewed papers on cases all over the world. Have a look and let’s talk tomorrow.

Next Day…

John: I’ve read the papers. Now I think that this is the worst virus we’ve ever seen and it will probably kill 80% of all humanity.

Anne: …

So it turns out that John is open minded, but not a critical thinker.

What does this have to do with necessary and sufficient conditions?

The necessary conditions represent the supporting reasons that must be included to demonstrate that an argument is true.

Certain arguments could require many necessary conditions in order to be proven as true. If some or all are missing, then the argument is not proven. Here is a helpful example:

The sufficient conditions represent the group of all the requirements necessary for an argument to be proven as true.

When checking the necessary and sufficient conditions to see if the argument holds, it is helpful to assess the argument by rephrasing the conditions.

Unproven argument 1

Anna is a teenager because she is over 12.

Although the reason “Anna is over 12” is a necessary condition, this argument is not proven because the reason is not a sufficient condition. We need more reasons to prove it. For example, if Anna is 36, she is still over 12, but she is definitely not a teenager.

Unproven argument 2

Anna is a teenager because she is under 20.

Here, similarly, although the reason “Anna is under 20” is a necessary condition, it is also not sufficient. Anna could be 5 and therefore not a teenager.

Proven argument

Anna is a teenager because she is over 12 and under 20.

Necessary but Not Sufficient

To better understand this concept of necessary but not sufficient, we will use the idea of open-mindedness being a necessary but not sufficient condition for critical thinking. We came across this argument when reading this paper written by Harvey Siegel.

Siegel argues that critical thinking is the more fundamental ideal for education when compared to open-mindedness.

Otherwise put, education systems should focus their efforts on ensuring that as many people as possible are critical thinkers by the time they leave school. And these people should continue leading their lives in a critical thinking spirit- not only having skills such as identifying fallacies, or arguing efficiently, but also having and exercising the tendency to apply these skills in their daily lives and having or gaining background knowledge to better apply those skills. Being open to hear reasons for opposing ideas is also one such skill. But in and of itself this skill is not sufficient to be a critical thinker. As already pointed, many other conditions are required.

So the argument here is that education should be focused on developing critical thinking as a whole, rather than aiming solely towards open mindedness.

There are two reasons which support this claim:

1. Open-mindedness is a necessary (but not sufficient) condition of critical thinking. Indeed, imagine a friend who is generally willing to reconsider her position and adapt her beliefs. But this friend might not be very good at assessing the reasons presented to her. So despite her open-mindedness, we cannot say that this friend is a critical thinker, because she might be lacking important argumentation skills and/or background knowledge.
2. Critical thinking is a sufficient (but not necessary) condition of open-mindedness. Being a critical thinker already embeds being open minded. But it is not necessary to be a critical thinker in order to achieve this quality.

From the two reasons above it follows that critical thinking is the more fundamental ideal for education when compared to open-mindedness.

To sum up, always check the arguments presented carefully: are their reasons both necessary and sufficient?