Critical Thinking Toolkit: External and Internal Contradictions

When developing critical thinking skills, learning to recognize falsehood is as important as learning to recognize truth. This is important for many reasons. Recognizing falsehood helps you realize when you are making mistakes, when others might be making mistakes or using confusing language, and can help you find out the truth by process of elimination. One key tool for identifying false information are contradictions. A contradiction happens when some kind of conflict emerges between different beliefs or conclusions drawn from beliefs. If that conflict cannot be resolved in a reasonable way, then one of the components (i.e. your beliefs or the evidence being used to justify beliefs) led to that flaw, and that component should now be rejected.

The goal of this article is to discuss a few different ways that contradictions manifest themselves, how to locate these contradictions, and some possibilities of how to resolve them. For our discussion, we will split the discussion into three different kinds of contradictions – internal and external – and work out some of these distinctives

External Contradiction

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How to Identify External Contradictions

Identifying an external contradiction is fairly straightforward. If you hear that X is true by some source, and if from some other source you hear that not X, then these are in external contradiction to one another. The important point here is that the sources of the information are different. Maybe one comes from science and the other from sociology, or one from a conservative news network and one from a liberal news network, ,or from different religious traditions. Whatever it may be, it is critical that the sources be genuinely separate from one another.

How to Resolve External Contradictions

In the case of external contradictions, the goal would be to evaluate the evidence for each of the two opposing options and to do the best we can in determining which has better evidence supporting it. How this evidence is evaluated will, of course, depend on the context and what kind of claim is being evaluated. That is a level of detail that has to be treated case-by-case, and which I do plan to write about on a case-by-case basis later.

Internal Contradiction

An internal contradiction is different. Whereas the external contradiction involves two different viewpoints in opposition to one another, an internal contradiction involves a viewpoint turning against itself, destroying its own validity in some way. I will discuss two similar, but somewhat different, ways I see that the idea of internal contradiction manifests in both day-to-day and academic spheres of thought.

Type 1: Reductio Ad Absurdum

The method of reductio ad absurdum is used frequently throughout philosophy and especially in mathematics. The idea here is to show that a particular viewpoint, when combined with simple rules of logic, will result in an obviously false conclusion. Since true statements combined with logic always result in truth, if you show by logic that X results in some absurd conclusion, then X cannot be true.

How to Utilize Reductio Ad Absurdum

Generally, a method such as reductio ad absurdum only applies in a context where it is fairly clear that the rules of logic are the obvious tools to use. This is true with mathematics in particular (see my article in citation [1] for how this works). To summarize the method, if you can use a claim X to demonstrate that some other statement Y is both true and false, then X must be a false claim. If you hear someone make a claim that has some kind of weird double-sided nature (that seems to suggest both one idea and its opposite) then you might want to see whether a reductio ad absurdum is an appropriate response to that idea.

Type 2: Self-Defeating Claims

Some reductio ad absurdum reasoning also fits into this category, but not all of it – which is why I make this a separate category. A self-defeating claim is any idea or combination of ideas that undermine their own credibility if taken seriously. Self-defeating claims contain a very strange and confusing kind of circularity, and so examples will help. I’ll start with an easy one.

Suppose that someone walks up to you and says “There are no English sentences with more than seven words.” Is this true? Well, not it isn’t true – in fact, the very sentence that person just said has ten words, which is more than seven. This, the sentence “there are no English sentences with more than seven words” undermines its own credibility, because it is an English sentence with more than seven words. This is an example of a self-defeating statement – the very statement exposes itself as a falsehood.

This is a classic example of a self-defeating statement. This example happens to operate on a purely logical/mathematical level – all we need to know is how to read English and how to count. There are more subtle examples of self-defeating statements, however, that operate on levels other than pure logic. There are examples of self-defeating statements in many other realms of thought. For example, the claim that “it is morally wrong to say someone is doing something wrong” is itself an example of calling other people wrong, and in that way it is self-defeating. It is also self-defeating to claim that you are incapable of rational thought – because you can only arrive at true beliefs by rational thought.

If you want to understand self-defeating claims better, try coming up with some of your own or contemplating these three examples for a more extended period of time. If you understand the previous examples, try to see if you can determine whether “only science tells us what is true about reality” is a self-defeating claim.

How to Identify a Self-Defeating Claim

The thing to look for in a self-defeating claim is any notion of self-reference. For example, if you are reading a sentence about sentences (as in the first example of this section), you might ask whether this sentence itself satisfies whatever the content of the sentences says. Or if someone says “the only way to know something is XYZ,” then you can ask the person whether they know that by XYZ.

Citations

[1] https://mathematicalapologist.com/2020/04/24/proof-by-contradiction/(opens in a new tab)

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