Your Argument is Valid, and You’re Still Wrong

How to argue your way out of a paper bag

Image by ElisaRiva from Pixabay

In this article, I’m going to show you how to strengthen your reasoning skills so that you can have more successful and interesting argumentative discussions online and otherwise in real life. To do this, I’m going to distinguish between two senses of the word ‘argue’ and then show you how the sense important for critical thinking is related to reasoning in general.

Intro

I recently watched an panel discussion between a handful of scientists and philosophers on the nature of information. At one point in the discussion, the philosopher (James Ladyman) was asked a question about whether or not information was physical, according to him. He replied that before answering directly it was necessary to make a distinction between a few things one might mean by those terms. One of the scientists playfully interjected, “Philosophers….” Ladyman mostly shrugged off the joke, intent on making his point, and the discussion moved on.

Philosophers are notorious for being pedantic and nitpicky about the meanings of things, which sometimes results in the misunderstanding that they are only interested in insubstantial semantic issues. That’s wrong, but it only takes a short time hanging around philosophers to see where the misconception comes from. Philosophers are nitpickers.

While philosophical nitpicking can be annoying, when used properly it’s really invaluable. Sometimes when people who aren’t experts start nitpicking by making apparently philosophical semantic distinctions, the results can be disastrously irrelevant arguments, myopic self-important disquisitions, or complicated and irrelevant red herring arguments. Take a moment and reflect on whether you have seen this happen in real life on the internet (probably in the comments section of just about anywhere).

I’d bet real money that you have.

Source: https://knowyourmeme.com/memes/ackchyually

The difference between the expert and the novice is that the expert, unlike the novice, knows when a distinction is relevant to the conversation, and she wields her nitpicking appropriately.

Let’s get nitpicky

If you want to do any serious philosophy, you need to be able to distinguish two senses of the word argue.

The first sense of the word is the ordinary, colloquial meaning. An argument in this sense is a kind of heated debate between two or more people. Often this kind of argument is a sort of fight. At its worst it could involve exchanging acts of violence, but usually an argument in the first sense ranges from a playful debate to heated bickering, possibly involving petty name calling, depending on how anonymous the interlocutors are to one another.

While professional philosophers often engage in arguments of this ordinary kind (they are human, after all), usually when a philosopher says she has an argument for something or other, or when she says that such-and-such is or is not a good critique of her argument, she doesn’t mean the word ‘argument’ to refer to this colloquial meaning.

What the philosopher normally means is by ‘argument’ is a special piece of reasoning with a structure. To distinguish an argument in the philosophical sense from one in the ordinary sense, I’m going to call the philosopher’s sense a logical argument. Here’s a working definition that most philosophers and logicians will accept.

Logical Argument (definition): A logical argument is a series of connected propositions consisting of at least one premise and one conclusion, where the premises are intended to support or conclusively demonstrate the truth of the conclusion.

That’s pretty technical, so lets break it down.

Logical arguments are made up out of propositions. Without going into too much detail, a proposition is much like a declarative sentence. You can read more about propositions in the first Beetle Inbox ‘philosophical tools’ post, here. Propositions are the kinds of things that can be either true or false. Questions and commands are not propositions.

Here are some propositions:

  • (A) The earth is an oblate spheroid.
  • (B) The earth is flat.
  • (C) The moon is made of cheese.
  • (D) Medium is a blogging platform.
  • (E) Dinosaurs are super awesome.

I said propositions are the kinds of things that can be true or false. That doesn’t mean we always know whether or not a proposition is true or false. Propositions (A) and (D) above are true, but (B) and (C) are false. What about (E)? I think it’s true. But maybe it’s false. The fact that it has the form of an opinion is irrelevant as to whether it is a proposition. It’s also irrelevant as to whether it is a fact. Some opinions are facts. However, just because I happen to think (E) is true doesn’t mean it is. We would have to decide what we mean by ‘awesome’ and whether or not dinosaurs classify as being in the category of things that are awesome to decide that. But whether or not (E) is true or false, it is a proposition either way, because it is the kind of statement that can be true or false.

There are two kinds of propositions in a logical argument: premises and a conclusion. You can’t decide whether a proposition is a premise or a conclusion of an argument just by looking at the proposition all by itself. Propositions become either premises or conclusions depending on how they are related to other propositions in the whole logical argument. Let’s start with the conclusion of an argument.

The whole point of creating a logical argument is to either conclusively prove or else strongly support the truth of some idea. Whatever idea it is that you’re interested in supporting or proving as true should be stateable in the form of a declarative sentence that could be either true or false. That statement, the one you’re trying to prove or get to is the conclusion of the argument. Every logical argument must have a conclusion (or, if you will, a point). Also, every logical argument has exactly one conclusion. No argument has more than one conclusion.

Let’s say you wanted to prove that the earth is flat. That is the conclusion of your argument. It’s what you’re trying to establish. How do you establish “The earth is flat” as true? It’s not enough to simply state the conclusion. You have to support it with other propositions. Those other propositions are the premises of your logical argument.

Here is a proposition that could act as a premise for an argument whose conclusion is that the earth is flat: The earth looks flat.

Now we can form a full argument. It looks like this:

(Premise) The earth looks flat.

(Conclusion) The earth is flat.

If we wrote out the argument in ordinary English, we might say, “The earth is flat, because it looks flat.” That’s an argument. It meets the definition.

“But that argument isn’t logical”

A common response to seeing an argument like the one above is to claim that it is not a logical argument. But that’s wrong. It’s a perfectly logical argument. It’s just a bad argument. What’s the difference?

Here’s a way to get clear about this distinction. Consider the situation the opposite way around. What would be an illogical argument? An illogical argument would be either (1) a series of propositions that are not connected into the right format discussed above, consisting of premises intended to support a conclusion, or (2) a series of propositions with the right structure but such that there is not relevant connection between the premises and conclusion. An argument is logical if, and only if, it is not illogical. So any argument that fails to satisfy either (1) or (2) or both is perfectly logical according to our definition. But it still might be a terribly bad piece of reasoning.

Take a look at the argument above again. Is it in the right format? Yes. It has two propositions, a premise and a conclusion, connected in a way so that the premise is intended to support the conclusion. So it can’t be illogical because of (1). What about (2)? Is there a connection between the premise and conclusion of the argument above? Yes. It’s not a very good connection, but on the face of it (and taken in isolation from any other available evidence) the fact that the earth looks flat is a reason to think that it is flat. It’s not the only reason, and it’s not a very good reason all by itself, nor is it a reason that couldn’t be defeated by much better reasons to the contrary. But it’s a reason. That’s all that is needed to get a connection between the premise of the argument and the conclusion.

But wait. The argument above is still a pretty bad argument. How do we talk about when arguments are good or bad? Let’s see.

VALID vs INVALID and STRONG vs WEAK

Logical arguments come in two basic kinds: formal and informal. The difference is that whereas formal arguments are created with the intention of conclusively proving their conclusion to be true, informal arguments are intended to make their conclusion likely. Most of the arguments you will encounter in day to day life are informal arguments, but it’s worthwhile to take a quick look at formal arguments, too.

Formal Arguments

The reason formal arguments are called ‘formal’ in the first place is because their goodness/badness is determined on the basis of the form they take. When a formal argument is a good argument, it is called valid, and when it’s bad, it’s invalid. The validity or invalidity of a formal argument is a purely structural affair. It has nothing to do with the truth of the propositions involved, except in as much as the truth of the premises does or does not guarantee the truth of the conclusion.

Here is, hands down, the most important concept you need to know about formal arguments: validity.

What is validity? It doesn’t just mean good.

Validity (definition): A formal argument is valid just in case it is impossible for the premises of the argument to be true and the conclusion be false at the same time.

Notice the definition of validity says nothing at all about the premises or conclusion happening to be true or false. What matters is the connection between the premises and conclusion. Here are some examples of valid arguments.

Argument A

All chihuahuas are dogs.

All dogs are mammals.

Therefore, All chihuahuas are mammals.

Argument B

If the moon is made of cheese, then the Queen’s glasses are made of rubies.

The moon is made of cheese.

Therefore, The Queen’s glasses are made of rubies.

Both arguments A and B are valid. Yes, really. They are perfectly good logic. The fact that in argument B both premises are false is irrelevant. Remember, validity is all about the connection between the premises and conclusion. Argument B is valid because it is impossible for the premises to both be true and the conclusion false. In other words, IF the statement “If the moon is made of cheese, then the Queen’s glasses are made of rubies” is true AND the statement “The moon is made of cheese” is true, THEN the statement, “The Queen’s glasses are made of rubies” must also be true.

For validity, the structure is what matters. There is a sense in which the conclusion of a valid argument is already contained in the premises in a hidden form. That’s why it’s possible to prove the conclusion definitively assuming the premises are true.

Validity is cheap

It’s important to realize what validity is and how cheap it really is. Getting a valid argument is not difficult. Here’s a valid argument:

Argument C

The earth is flat

Therefore, The earth is flat.

That’s a perfectly good argument, logically speaking. At least if we judge goodness by validity. Every circular argument is valid. Why? Because it’s impossible for the premises to be true and the conclusion false (the definition of validity), since the premise and conclusion are identical and every proposition is either true or false but not both.

Informal Arguments

Most of the arguments you will ever encounter are informal arguments. That means they are not designed to definitively prove their conclusion in the way formal arguments do. In “real life” you will probably hear people tossing around the terms ‘valid’ and ‘invalid’ when they’re talking about informal arguments. Technically, this is incorrect.

Since informal arguments are not intended to prove the truth of their conclusion by showing that the conclusion is really already conceptually contained in the premises, validity doesn’t strictly apply. But that doesn’t mean we can’t evaluate informal arguments on the basis of non-structural or extra-structural features.

To be a good informal argument, the premises should be connected to the conclusion in such a way as to be relevant and to make the conclusion likely. Arguments that have premises backed by good evidence and that are relevantly connected to the conclusion are called strong and those that aren’t are called weak.

Consider the argument at the beginning of this article:

The earth looks flat.

Therefore, The earth is flat.

This is an informal argument. It’s not appropriate to say that it’s invalid, because that only applies to formal arguments, but we can definitely say it is a very weak argument. The premise is connected to the conclusion, but the connection is extremely weak as it is stated, because there is an unstated assumption that is an implicit background premise. Think about what is unstated in the argument for a minute.

The unstated premise is: Things are the way they look. If we supplement the argument with this premise, it becomes:

Things are the way they look

The earth looks flat

Therefore, The earth is flat.

This is still an informal argument, and it’s still very weak, but it’s not fallacious. The reason we should reject it is because it has a highly questionable premise. That things are the way they look is common sense, but common sense is usually based on how humans perceive things at human-sized scales, and common sense often turns out to be wrong when we zoom in to smaller scales or zoom out to larger scales.

Formalizing informal arguments

It’s not always possible to do it in a straightforward way, but often informal arguments can be formalized. For example, we can take the first argument about the flatness of the earth and formalize it as:

If the earth looks flat, then it is flat.

The earth looks flat.

Therefore, The earth is flat.

This is a perfectly valid argument. So what’s wrong with it?

Remember: validity is cheap.

Your argument is valid, and you’re still wrong

A strong informal argument is a good argument in general. Even without formalization, if you can show that some premises are connected to the conclusion of an argument in a relevant way, and you can show that the premises are very probably true, then you’ve demonstrated with a high degree of certainty that the conclusion is true. And if you could formalize that argument, you would get something even better: a sound argument.

Soundness is the crème de la crème of argumentative reasoning. Here’s the definition of soundness.

Soundness (definition): An argument is sound if, and only if, it is both valid and has all true premises.

Soundness is as good as you can get. Here’s why. If you know that an argument is valid, then you already know that if the premises are true, then the conclusion also has to be true. That’s just the definition of validity. So if you add on top of that the fact that the premises really are true, what do you get? You get that the conclusion is definitely true as well. Success!

How to pick apart arguments online

Alright, if you’ve made it this far, congratulations, you’ve successfully passed the intro to logic class I used to teach. (This is mostly a joke, but it is true that the whole course was really just about getting students to understand validity and soundness.)

You now have the distinctions necessary to completely crush your illogical opponents online. Make sure to internalize the differences between:

  • Formal arguments
  • Informal arguments
  • Validity versus invalidity (applies to formal arguments)
  • Strong versus weak (applies to informal arguments)
  • Soundness

Once you have the concepts down, you’re ready to go. Usually, if someone is making a bad argument on the internet, either one of two things is wrong with it.

Either (1), the argument is structurally bad, or (2) the argument has false premises.

First, you must decide what kind of argument your opponent is making. In all likelihood, they are making an informal argument. If you can formalize their argument without losing the meaning, it can be helpful to do that, because then it will be much easier to see whether the problem is with questionable premises or whether the structure is bad. But be very careful doing this. People don’t like words being put in their mouth, and they may not accept your formalization. (Tip: a good practice is to formalize their argument slowly by asking them if they agree with certain statements, which are formalizations of the propositions of their argument. Then, string together the propositions into an argument, and ask them if they agree with it. If they do, then you can show why it’s wrong.)

More often than not, it is just not possible to reformulate an informal argument as a formal one without losing some of the meaning. You can still show your opponent that the argument is bad by figuring out if the problem lies in false premises or with the connection between the premises and conclusion.

A lot of times people will come up with pieces of reasoning that are just logically bad but which involve true premises — problem (1). A good practice is to let your opponent know that you agree with the truth of the premises, but show them that the premises are not connected to the conclusion in a relevant way, so that even though they are true, the conclusion just doesn’t follow.

On the other hand, if your opponent’s argument is logically okay but has false or questionable premises — problem (2) — a good idea is to directly confront this honestly. You can tell your opponent that their reasoning is good but that you think a premise (or all the premises) are false or unlikely, and ask them to provide evidence for them. This helps them to not feel stupid so they will actually think about your reasoning.

A final word of caution

If you’re careful about it, you can come away from an online argument (in the first sense of ‘argue’!) as the rational party. In the best case scenario, you elevate the level of rational discourse of your opponent as well.

Be careful about your distinction mongering. People don’t like to hear that they are using the words ‘valid’, ‘invalid’, ‘sound’, etc., incorrectly. If you bring up this point, do it gently, and keep in mind that these are technical notions, and it’s completely understandable that a lot of people might not know about them. Also, even though the concept of soundness technically only applies to formal arguments, since many informal arguments can be formalized, it’s usually okay to talk about the soundness of an informal argument in ordinary discourse. (But I’m sticking to my guns about validity. The only way that should be used is when referring to its logical meaning or the common scientific usage ‘empirically valid’, which is a different thing.)

Lastly, don’t be a dick, and make sure to check yourself. It’s all too easy to slide into false moral superiority in the name of good reasoning. Be kind to people, and help them understand what’s gone wrong with their reasoning, and make sure they know that their mistakes in reasoning are understandable and tempting for everyone. Check yourself, too. Be brutal on your own reasoning and arguments, and be kind to yourself when you screw it up, because you will. It’s hard, but thinking clearly is really worth it, and by actively reasoning carefully, together we can genuinely make the world a better place one argument at a time.

I’m a PhD candidate in philosophy. Get my free ebook How Philosophy Pays (and more) by subscribing to my newsletter: https://joshuajarrott.substack.com/

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