Why logical arguments are bad arguments

Some people think that logical deduction is the gold standard of reason, but most good arguments are actually fallacies.

By Lars Harhoff Andersen

It is common for people to wish for better arguments in public debates. While the general sentiment might be a good one, it is often accompanied by the idea that we should “use more logic” or that the problem is that people are using logical fallacies. This idea is implicit in the title of videos like Charlie Kirk Destroys Race Baiting Student With Facts and Logic and MAGA Logic Explained By Trump Supporters, but is also sometimes explicit, like in the list of logical fallacies below.

Not only are such appeals generally accompanied by hostility and condescension, but they also often lack any real understanding of what it means to make a good argument. In this post, I will therefore explain what it means to make a logical argument and why fallacies often make for better arguments. 

What is a logical fallacy?

The technical definition of a logical fallacy is making a logically invalid argument. Therefore, in order to understand what a logical fallacy is, we first need to understand what it means to make a logically valid argument. While terms such as “reason” or “rationality” are incredibly hard to pin down, the definition of a logical deduction is actually quite clear. A logical argument is valid if it is impossible that the conclusion is false while the assumptions are true. Thus, “All poodles are mortal” follows from the premises “all dogs are mortals” and “poodles are dogs”, because it would be impossible for some dogs - such as the poodles - to be immortal if all dogs are mortal. We would be contradicting ourselves if we denied the conclusion while believing the assumptions. However, while it is surely virtuous to avoid contradicting oneself, it is also insufficient as a rule for argumentation. To understand why we need to look at a bit of philosophy.

During the age of enlightenment, philosophers discovered that all true (or false) sentences could be classified as either synthetic or analytical.¹ On the one hand, a sentence can be synthetic, which means that it is true if it describes some fact about the world correctly and false if it does not. “The Eiffel tower is more than one meter tall” and “All cats are black”, are both synthetic sentences, one true, the other false. Synthetic sentences work by putting two logically unrelated terms (such as “cat” and “black”) together and thereby say something new about cats that we did not include in the definition. It could be that all cats are black, they might all be white, or they might have many colors. The only way to know is to go out and check. On the other hand, a sentence can be analytical, which means that it is true if it correctly describes the relationship between different terms and false if it does not. Thus, “All cats are animals” is true, not because someone went out and checked if all cats were animals, but because the (technical) definition of cat is “animal of the species Felis Catus”. If it were wrong, it would imply that “animal of the species Felis Catus are not animals”, which is a contradiction in terms. We do not need empirical evidence to confirm or deny analytical sentences because they actually don’t say something about the world. “All wizard can use magic” is a (true) analytical sentence, but it doesn’t say anything about the world because wizards (probably) don’t exist. “A wizard cannot use magic” is wrong the only way an analytical sentence can be wrong – it is a contradiction in terms.

Logical deductions are the prime examples of analytical sentences. They are not themselves statements about the world, but instead lay out the relationship between different words and concepts.² The assumptions are doing all the heavy lifting, and logic is only playing the role of analyzing what we assumed. Logical deduction is an act of translation rather than one of exploration.

Language and Logic

Since a logical deduction can’t lead us to any conclusion that we have not already (explicitly or implicitly) assumed in the premise of the argument, it follows that a logical deduction is only interesting if it tells us something about our assumptions that isn’t obvious.  From the premise “All my children are tall” the conclusion “my oldest child is tall” does follow, but I am sincerely hoping that a logical argument wasn’t necessary for you to come to that conclusion. The problem is that besides such simple examples it is almost impossible to make logically binding deductions with the terms we use in science or everyday speech.

In order to understand why this is so hard in practice, let us look at the definition of a common word in social science like “state”:

State: A nation or territory considered as an organized political community under one government.

Let us now go on to assume something like “Denmark is a state”, which is clearly true. What can we derive from this? Using the definition we can derive that “Denmark is a political community” or perhaps that “Denmark is under one government”, but for anybody who knows what a state is such arguments would be trivial. But, what happens if we try to derive something more substantive? Let us imagine that someone were to say “The state of Denmark is really unorganized”. Could we prove them wrong with logic? Well in some sense we can. We could argue that since the person acknowledges that Denmark is a state, they must also accept that Denmark is an organized political community, and since nothing can be both organized and not organized, Denmark can’t be unorganized. While this deduction seems formally correct, it is also clearly wrong. While both people in this scenario use the term “organized” correctly the term itself is so vague that all logical deductions outside of the trivial will end up producing nonsense like what I showed.

However, terms like “state” are just the tip of the iceberg. Most words don’t even have definitions in the strict sense. If you look up the definition of “chicken” you might see something like “a domestic fowl kept for its eggs or meat, especially a young one.”, which gives us a problem. Most turkeys are “domestic fowls”, most are “kept for their meat” and some are young. Does that mean that (some) turkeys are chickens? Of course not. The problem is that terms like “chicken” or “turkey” are defined ostensively. Their definitions do not say what is necessary or sufficient to be a chicken, but rather point to something in the world and say “chickens are those birds over there we get eggs from.” While this works very well for practical purposes, it makes it more or less impossible to use such terms in a logical deduction. It might be very hard to derive anything meaningful from the definition of the word “state”, but it is downright impossible to do so from something that is defined as “those things over there”. If something does not have a clear definition, it does not make much sense to try to investigate that definition with logic.³ When people insist on investigating the words of natural language through logical analyses, the results often end up being farcical.

Back in January, the Canadian psychologist Jordan B. Peterson was a guest on the podcast The Joe Rogan Experience where he made the following comments about climate science:

Well, that’s ‘cause there’s no such thing as climate. Right? “Climate” and “everything” are the same word. […] It’s like, climate is about everything. Okay. But your models aren’t based on everything. Your models are based on a set number of variables. So that means you’ve reduced the variables, which are everything, to that set. Well how did you decide which set of variables to include in the equation, if it’s about everything? That’s not just a criticism, that’s like, if it’s about everything, your models aren’t right. Because your models do not and cannot model everything.⁴

Peterson was afterwards widely ridiculed, but I think for the wrong reasons. He was mostly ridiculed for making logical fallacies, which of course he did, but the real problem was that he tried to use logical deductions to show how a model of the climate should look. The strangeness of the arguments comes not from a lack of logical ability, but from the fact that he needs to change the definitions of words in order to make his logical deduction work. The word “Climate” is clearly both more specific and vastly more vague than the word “everything”, but the actual definition of climate does not really have any neat logical properties with which to derive anything.

While such blatant misuses of logic might seem embarrassing, Peterson is in some sense in good company. Much pre-modern philosophy seems silly to modern eyes, not because they did not use logical analysis, but because they used it too much and on words that could not bear its weight. Thus, the logic of platonic metaphysics and rigid scholastic proofs of the existence of God today mostly inspire snickers in those who are not paid to read them, while the softer existential musings of Marcus Aurelius are read for pleasure and contemplation. Peterson might be making a terrible argument, but it is not because he is too stupid for logical syllogism, but because the ideology of logic corners him into committing the platonic hubris.

There is one language where logical deduction plays a useful and important role, and it is the one that originally inspired Plato: Mathematics. In mathematics, we do not use the vague and ostensive definitions of everyday speech, but instead make clear and unambiguous definitions from which we can construct long and clear chains of reasoning. The logical deductions of mathematics are far from trivial, but the elegance of mathematics comes at the cost of abstraction. Mathematics is however so abstract a language that most of our ideas about the world cannot be spoken in it. This is at the core of many of the arguments over the role of assumptions in economic models – something I hope to return to in a later post.

Are all arguments attempts at logic?

A typical counterargument against the assertion that logic is useless in real discussions is that we are overlooking the role of hidden assumptions. Consider the following argument: ”John put a gun to his head and pulled the trigger, therefore John is now dead”. While this is somewhat simple it is also clearly an example of good reasoning. It is, however also a logical fallacy. After all, there is no logically necessary reason why pulling the trigger would kill John. The gun might not have bullets in it or it might be a broken gun. The idea that although it seems as if the argument is a logical fallacy, this is only because the implicit assumption, that the gun is loaded and unbroken, has been omitted.

The problem with this line of argument is that in order to make everyday arguments logically valid you need a whole lot of hidden assumptions. Even if the gun works, it is still logically possible that John would survive if someone pushed the gun right when the trigger was pulled, so we also have to assume that didn’t happen. We also need to assume that John wasn’t wearing a helmet that stopped the bullet. It is also – logically – possible that the laws of physics change for a few seconds such that the bullet did not move, so we need to assume away that possibility as well. And so on and so forth. We could of course say that the implicit assumption is “if John puts a gun to his head and pulls the trigger, then he will die”. This would make the argument valid, but it would also be a trivial statement. If we assume that “all I say is true” it also follows that John dies if I say he does, but we would never call that a good argument. The larger problem is that assuming that we all run around and have these implicit assumptions which we keep secret is simply begging the question. If we assume that all good arguments have hidden assumptions that make them logically valid, then it does follow logically that all good arguments are indeed valid. If you assume that everything is a nail you don’t have to regret that your only tool is a hammer.

When we are making good arguments, it is not because we have found out that ours is the only possible conclusion, but because we have found good reasons to believe something. A good argument takes what you already know and tries to find some possible connections you might have missed. If logical deduction is a form of translation, then most good arguments are those that read between the lines. Reading between the lines is hard and we often get it wrong, but sticking only to logically valid arguments means that we do not even try.

In the end, the obsession with logic is a tragic one. It comes from a dream that we can finally find objective rules to decide who is right and who is wrong. But, this is not possible. The closest thing we have to a universal methodology for truth is logic, but it only works by taking us out of the real world. As Wittgenstein in his later works said of the world of logic:

“We have got onto slippery ice where there is no friction and so in a certain sense the conditions are ideal, but also, just because of that, we are unable to walk. We want to walk so we need friction. Back to the rough ground!”⁵

We might marvel at the skills of a figure skater, but those of us that are on the ground should not be wearing ice skates.

Fallacies and how to use them

If logical deductions do not help us, how should we discuss with one another? Simple: Use logical fallacies! On the list of fallacies that started this post it says in big capital letters “Thou shalt not commit fallacies”, but many of the fallacies it includes are actually pretty good guides for how to argue.

If you think that the sun will rise after the night is done, just because it has done so since the dawn of time, you are committing the inductive fallacy, but would we say that it was a bad argument? Are you willing to bet? We have no idea how Paracetamol works, but we use it because it worked before. Is it irrational to take a Tylenol for your headache? Is it just a habit? Arguing that if we allow A, then we will soon have to allow B and C is the slippery slope fallacy, but are some slopes not slippery? If I were to argue that, the government should not arrest bad people without a trial, because it might lead them to arrest good people later, you would likely agree, but we would then both be making the slippery slope fallacy.

The list says that appealing to authority is a fallacy, but I doubt most of the people reading this has ever seen proof of the discoveries of Newton, the existence of bacteria, or that the capital of Angola is Luanda. We believe these things completely not because of logical arguments, but because we believe what scientists, newspapers, and teachers tell us. We are in other words committing the very reasonable fallacy of appealing to authority. Conspiracy theorists are often right that they have given their ideas more independent thought than those with whom they discuss, but they are wrong to take it as a point of pride. It might be true that many appeals to authority are unreasonable, but so are many denials of authority. None of them are logically valid. In the list of fallacies I included in the beginning of this post, they actually argue that even though appealing to authority is a fallacy, it should “not be used to dismiss the claims of experts”. The makers of the list bring down the fallacies like Moses from Mount Sinai, but do not seem to reflect on what the implications are of the caveats they slap on them. “Thou shalt not commit fallacies, unless I like the results”. The most comical of all the fallacies included is begging the question, which is defined as “an argument where the conclusion is already included in the premise”, which is the literal definition of a logically valid argument! The implication seems to be that an argument is a fallacy in case it is valid and in case it is invalid. It looks like we might have to watch out for what we say.

And this is the crux of the matter. Almost all arguments are technically fallacies, so no one actually believes that we should never make arguments that are logically invalid. Although Sherlock Holmes talks endlessly about the power of logic and deduction, he almost never actually makes any valid logical deductions. In his first meeting with Dr. Watson, Holmes deduces that the doctor recently arrived from Afghanistan because he is tan, wounded, and had the “air of a military man”.⁶ However, this is not a logical deduction, but the very useful fallacy known as “abduction” where one assumes that if A could explain B (better than the alternatives) then A is likely to be true. These long lists of fallacies end up being tools we use to dismiss the views of our opponents without argument, not ways for us to become better at thinking. At the bottom of the list I included here, it even says that if you see someone making a fallacy you should send them a link to the exact fallacy they are making on the website “yourlogicalfallacyis.com”.⁷ I am sure that will convince grandma to take the vaccine.

The obsession with logic and fallacies both lead us to the nonsensical ramblings of Peterson and the condescending double standards of fallacy hunting. There is no simple set of logical rules you can follow that makes you smart. Outside of the narrow world of mathematics, problems in both science and everyday arguments are not solved with logical deduction, but with the myriad of reasonable fallacies that we call thinking.

Lars Harhoff Andersen is the editor of Unreasonable Doubt, where he writes about Culture, Politics, and Philosophy. Lars is a Ph.D. fellow at the Department of Economics at the University of Copenhagen where his research centers on Economic History and the impact of culture on societal development.

1. Although there are some precedents, most notably in the works of John Locke (1632 – 1704), Gottfried Wilhelm Leibniz (1646-1716), and David Hume (1711-1776), the modern distinction between Analytic and Synthetic truth comes to us from the German philosopher Immanuel Kant (1724-1804). It should be noted that Kant argued that mathematics was synthetic truth, but since this view is marginal today I won’t be going into this question any further.

2. Technically the conclusion to a logical deduction can be a synthetic statement, such as “all poodles are mortal” in the example above, but this is only because we implicitly assumed it in the premises. It might seem like we learned a statement about the world from the logic deduction, but we had just implicitly assumed that poodles where mortals, when we said that all dogs where. Thus the deduction itself was analytic, but the conclusions and one of the premises was synthetic.

3. A story goes that Plato, when asked for the definition of a man said that it was a “featherless biped”. The cynic philosopher Diogenes is then said to have gone to the academy with a plucked chicken and said “Behold, Plato’s man!”

4. The Joe Rogan Experience episode 1769

5. Philosophical Investigations, §107

6. A study in Scarlet p. 11

7. Note that the website is called yourlogicalfallacyis.com and not mylogicalfallacyis.com.