Meta-discussion: Reflections on the Basics of Contradictions and Valid Arguments

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"Meta-discussion": This is the first of what might be a series on this blog (but no guarantees) about foundational principles that are important in many kinds of discussions about controversial matters.

A key piece of groundwork to keep in mind is what constitutes a contradiction.  When talking about the logical problem of evil, Dr. William Lane Craig uses a framework of reflecting on contradictions that is useful.  Most basically, there are two kinds of contradictions:

Explicit contradiction: A simple statement of both a proposition and its negation.  (ex: "God exists." and "God does not exist." explicitly contradict each other)

Implicit contradiction: Two statements that aren't explicitly contradictory, but entail an explicit contradiction when combined with necessarily true premises. (ex: "John is a bachelor." and "John is married." is an implicit contradiction; one is not the direct negation of the other, but "John is a bachelor." combined with the necessarily true premise "All bachelors are not married." entails that "John is not married.", which does in fact make an explicit contradiction with "John is married.")

The key point to keep in mind, here, is that if two claims are implicitly contradictory, there should, in fact, be another "step" (or group of steps) which bring one from the implicit contradiction to an explicit one.

This is an important point to remember, because you may often come across people arguing against each other about a topic, but arguing for central points that may not actually contradict one another.  At the least, to conclude that their central points contradict one another, you may need to insert premises that aren't obviously or necessarily true- and thus it may be a good idea to pursue whether said premise really is true.

Another, related consideration I want to put forward is about the nature of arguments.  Throughout discussions on controversial questions, both sides generally trot out talking points, moral considerations, or evidence that they believe support the position they are trying to defend.  Many times, though, if you try to lay out their argument in a more formal way, there is a major problem with the argument that will be exposed.

A deductive argument (what we'll focus on for now) has four basic requirements to be a good argument:

1. The argument's conclusion should be in line with the position the person making the argument is trying to defend. (If you're trying to argue for X, but your argument's conclusion is Y, then there's a "gap" in your reasoning that needs to be filled.)

2. The argument has to be valid. (The conclusion has to logically follow from its premises.  You can look up the logical rules of inference; you may be scared of logic-speak, but most of them are fairly easy to grasp on an intuitive level.)

3. Every premise has to be reasonable to believe to be true (the more reasonable, the better).  The reasonableness can be explicitly argued for, or it can be an assumption that the interlocutors share.

[I'd argue this condition will depend on the context of the conversation, meaning that some arguments can be better in some contexts than others.  

For example, if a Catholic were to defend a particular doctrine to another Catholic by quoting some Church document, that would be a good argument for that doctrine for the purpose of that discussion.  But if that same Catholic were to quote that same document to a non-Catholic in support of the same doctrine, it wouldn't constitute as good an argument for the purposes of that discussion.

A good argument starts with assumptions that the interlocutors can agree on, and then tries to demonstrate, normally with at least one controversial premise that is argued for, that the arguer’s interlocutor should accept the conclusion.]

4. The reasons for believing the truth of the premises can't be dependent on already believing the conclusion.  This is the criterion Dr. Craig uses for the fallacy of begging the question, and I think it's a good one.  Note that it’s okay if the premises entail the conclusion; in fact, it’s necessary for that to be so, see the second criterion.

Now, I understand that not every argument made in a real-life (or internet) context will be neatly laid out in premise-conclusion form; nor am I suggesting that they should always be.  But you want to keep in mind that every good deductive argument should at least be able to be written as a formal argument that fulfills the above four criteria.  This post is more focused on the first two.

A good exercise you might want to consider is: when you’re in a discussion with someone about a controversial issue (particularly a heated one, where it will be most important of all to parse everything out), try to write down (or type out) what they are saying in premise-conclusion form.  Ask yourself these questions:

1. Is the conclusion something you disagree with in the first place?  [Related: Does the conclusion actually contradict what you were trying to get across?]

2. Does the conclusion logically follow from its premises? [Related: Are they using key terms in the same sense when they use it in multiple premises?]

3. If the answer to 2 is no, try to insert or change premises as needed to try to make the argument valid.  When you do so, is there a premise in the new, valid form of the argument that’s dubious, and that your interlocutor didn’t really argue for?

If the answer to 1 is no, or if the answers to 2 and 3 are no and yes respectively, then while the interlocutor may be rhetorically effective, have a bunch of social media followers as an “amen” choir horde, and even be making true points in support of true conclusions, but none of that actually undermines your central point, and thus their contribution to the discussion is much less valuable than a valid argument that really does attempt to contradict what you are saying.

You may find that you will answer the questions the above way in many instances, and that therefore, you'll be able to have better focus on those arguments that really are relevant to the issues you are interested in debating.

Of course, you should also ask the questions in reverse when thinking about your own arguments, to make sure you are arguing effectively and not engaging in red herrings.

Depending on how I (or others) use this post in the future, it's possible you've been directed here because you're either making an invalid argument, or because you're arguing for a conclusion that I (or your interlocutor) don't actually disagree with, and doesn't actually contradict my beliefs.