Every Logical Argument You Ever Made Was Wrong

Isn’t Logic Great?

Who doesn’t like logic? We idolize Sherlock Holmes’ ability to solve mysteries by “eliminating the impossible.” In arguments with friends, we try to prove we’re right using logic, rather than intuition or emotions. And we especially enjoy pointing out others’ logical fallacies–preferably using latin terms.

Don’t pat yourself on the back just yet. Finding logical fallacies is actually much less impressive than you might think. That’s because in the real world, all arguments violate the principles of formal logic.

Yes, perhaps every logical argument you have ever encountered was flawed.

What Is Logic?

What is logic anyways? Logic, or specifically Deductive Reasoning, is the process of using several true statements (premises) to demonstrate that another statement (the conclusion) is true. In theory, logic can help you reach profound conclusions, by compounding an unlimited number of premises. That’s why it appeals to so many rational thinkers. However, logic only works for theoretical or philosophical matters. Real life is filled with uncertainty, and that uncertainty prevents logic from working.

Don’t believe us? Here’s a simple challenge. Try to craft a useful logical argument–i.e. one in which all the premises and assumptions are true, and they combine through the rules of logic to form a useful conclusion. It’s much harder than you’d think, as the following example will illustrate.

Certainty in an Uncertain World

Let’s see how Wikipedia struggles with this challenge. Here is their attempt at a textbook example of logic:

  1. If it is raining, then there are clouds in the sky.
  2. There are no clouds in the sky.
  3. Thus, it is not raining.

This is a very simple logical argument, which seems practical enough. But there’s a catch. In the real world no premise is 100% true. In this example, they tried to provide premises that are certain, but still managed to fail: Rain without clouds is rare, but it can happen.

Since this premise does not apply 100% of the time, the argument is not sound. This fallacy of claiming a certain conclusion from uncertain premises is called “Appeal to Probability,” and can be found in virtually any non-hypothetical logical argument.

At this point you’re probably thinking that it’s no big deal. The premises are near certain, so the conclusion is near certain, and that’s more than enough for practical purposes. However, although this may work for simplified examples like the one above, that is rarely the case with real-world issues. We don’t need advanced reasoning to predict rain from clouds; we need it to solve tough, complex problems. Now imagine what happens when you try to build a practical logical argument in a discussion on public health, international conflicts, or immigration.

The Health Care Debate

Let’s illustrate this by picking a recent opinion piece from The New York Times, which tries to build an argument against the Affordable Care Act.

The basic points were:

  1. If government increases free-market competition among insurers, insurance prices will be lower.
  2. When prices are lower, more Americans buy their own insurance.
  3. If more Americans buy insurance, more will be covered.
  4. It is good to have more Americans covered by health insurance.
  5. Therefore, we should abolish the ACA.

While the conclusion may be correct, it is not due to the deduction above. Let’s examine the first two premises, which are both incredibly complex and uncertain.

  1. Is it true that increasing free-market competition always results in lower prices?
  2. Does healthcare really behave like a commodity?
  3. Why do countries with no free-market competition have lower health costs than the US? Are health services in those countries better or worse than in the US?
  4. If prices were to go down, would the coverage be equivalent?
  5. What about unintended consequences? For example, if doctors focus on quantity over quality then small problems might turn into large problems, which would ultimately raise the cost of care.
  6. Would more Americans really buy their own insurance if prices were lower? People often don’t make rational economic decisions.
  7. Would having non-mandatory (but cheaper) insurance result in more coverage than under a mandatory system?

Compounding Uncertainty

There are many more such questions, and each can be further broken down into smaller questions. On issues more complex than cloud-rain relationship, there may be hundreds of premises and hidden assumptions, and each comes with some uncertainty. As that uncertainty accumulates, the deduction process becomes increasingly less reliable.

Consider a case with 50 premises, that are each 95% reliable. Can you still rely on the argument? Not a good idea: all the premises will be true simultaneously less than 8% of the time! (0.95 to the 50th power). So, is our confidence that the conclusion is true only 8%? Unfortunately, we can’t even say that. It could be much more or much less. To determine that we need to evaluate many factors and use tools stronger than Logic…

If Not Logic, Then What??

If deductive arguments are useless in the real world, then how do we manage to make successful choices? What do we actually do when we think we’re using “logical arguments”? And is there a better method for drawing conclusions in an uncertain world? Those topics will be covered in part 2 of this post. In the meantime, visit Rootclaim to see analyses that avoid the pitfalls of human reasoning.


  1. This essay is wildly wrong. When premises are untrue, the argument is unsound, not invalid. Validity refers to the formal relationship between terms, and is always defined hypothetically, “…if the premises are true…” Unsound arguments can be formally valid, but have untrue or questionable premises. For example, “Spot is a dog. All dogs have fleas. Spot has fleas” is formally valid, but likely unsound, because the premise “All dogs have fleas” is probably false.

    • Thanks for commenting, Jon.
      As you can tell, we don’t care much for logical reasoning, so we don’t really bother with the formal terms. Please interpret words using their normal spoken meaning.

  2. The article seems to propose that if a statement is based in some way on inductive reasoning then the argument is wrong. Ironically, the article uses inductive reasoning to make this claim. Deductive and inductive reasoning are both logical types of reasoning and two sides of the same coin. In fairness, I have not read part 2 of the article.

    I do have similar convictions about the Sherlock Holmes/Arthur Conan Doyle quote though. I never liked that quote. It ignores inductive reasoning and is a non sequitor. Five contradicting things could still remain after eliminating the impossible.

    • Thanks for commenting, Tim.
      The problem is deeper than that. All logical reasoning, whether deductive, inductive, or abductive, is irrelevant to real life. The whole concept of assigning true/false values to statements collapses under complex reasoning, as it causes uncertainty to accumulate.
      It can only work when discussing theoretical concepts (like we’re doing now) or when uncertainty is negligible (physics, computer science). In all other domains, you must explicitly quantify truthiness (probability), and use mathematical models that can handle it (probability theory).

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