Critical Thinking

Anatomy of an Argument: How to Spot Invalid Logic

In logic, an argument is a set of statements that work together to support a conclusion. But not all arguments are equally logical. Here’s how to recognize sound arguments, so you’ll be better equipped to identify flawed reasoning when you see it.

Trick question: which of the following scenarios portray(s) an argument?

  1. Two young siblings are tugging on the same toy.
  2. Several fans of rival sports teams are each shouting that their team is superior.
  3. A hostile exchange of words is turning into a brawl in an old western movie.

All these scenes do involve arguments in the sense of disagreements between people. But in logic, an argument is something more specific. It’s a set of statements known as premises which are meant to support another statement called the conclusion. For example,

  • Premise 1: DNA contains information.
  • Premise 2: Information comes only from intelligent sources.
  • Conclusion: Therefore, DNA originated from an Intelligent Source.

While this argument follows sound and valid reasoning, not all arguments are equally logical. Let’s see how to characterize different types of arguments so you can more easily discern trustworthy messages from persuasive deceptions.

Deductive Arguments1

Deductive arguments, including the above example about DNA, try to prove a conclusion is certainly true. We consider deductive arguments valid if their conclusions logically follow from their premises. If the premises are true, then the conclusion must be true. The conclusions of invalid arguments, however, do not necessarily follow from their premises, resulting in logical errors known as fallacies. For example,

  • Premise 1: If you have a cat, then you are a pet owner.
  • Premise 2: You do not have a cat.
  • Conclusion: Therefore, you are not a pet owner.

Clearly, the conclusion you are not a pet owner does not necessarily follow from these premises because there are other ways to be a pet owner besides having a cat. So, this argument is invalid, involving a fallacy called denying the antecedent.

So, are all valid arguments safe to believe? Not necessarily. For example,

  • Premise 1: All mammals are fire-breathing creatures.
  • Premise 2: Squirrels are mammals.
  • Conclusion: Therefore, squirrels are fire-breathing creatures.

Although Premise 1 is (thankfully) false, this argument is logically valid because if all its premises were true, its conclusion must also be true. If an argument is valid and all its premises are true, the argument is considered sound. However, if even one false premise appears in a valid argument, the argument is unsound. As another example,

  • Premise 1: If a loving God exists, then the world would not be full of death and suffering.
  • Premise 2: The world is full of death and suffering.
  • Conclusion: Therefore, a loving God must not exist.

This argument follows a logically valid structure called denying the consequent. Does that mean its conclusion is trustworthy? Not unless all its premises are true. And Premise 1 claims that a loving God and a world of suffering could not coexist within the same reality. But, as other articles explain, the Bible reveals that God is loving, and suffering does exist because human sin corrupted the perfect universe God created.2 Therefore, this argument is unsound.

Subtler Errors

Watch out, now. Invalid or unsound arguments may seem believable if their conclusions are true. For instance,

  • Premise 1: If a creature is a bird, then it can fly.
  • Premise 2: Goldfish cannot fly.
  • Conclusion: Therefore, goldfish are not birds.

This argument does have a true conclusion and a logically valid structure. Yet it’s nevertheless unsound because its first premise is false (some birds do not fly). How about this example?

  • Premise 1: If humans evolved from apes, then apes would not exist today.
  • Premise 2: Apes do exist today.
  • Conclusion: Therefore, humans did not evolve from apes.

We can infer from Scripture and observational science that this conclusion is not true, so this argument might seem reasonable. Yet its first premise is false because apes could still exist today even if humans did evolve from a small population of them—and evolutionists do not believe that humans evolved from modern apes anyway. That’s why this argument ranks high among arguments creationists should avoid.

Ultimately, invalid or unsound logic can be used to argue for true conclusions, and valid logic can be used to argue for false conclusions. Regardless of its believability, then, a deductive argument is only trustworthy if its conclusion necessarily follows from all true premises.

Inductive Arguments

While deductive arguments try to prove a claim is certainly true, inductive arguments try to imply a claim is probably true. For example,

  • Premise 1: Most fossils were buried in the global flood.
  • Premise 2: Archeopteryx is a fossil.
  • Conclusion: Therefore, Archeopteryx was likely buried in the global flood.

Instead of being valid or invalid, inductive arguments are called strong or weak. The more probable the conclusion (assuming all true premises), the stronger the inductive argument. For example,

Inductively strong:Inductively weak:
Premise: 99% of patients say vitamin X improved their symptoms.Premise: 49% of patients say vitamin X improved their symptoms.
Conclusion: So, if you have symptoms, you’ll likely benefit from vitamin X too.Conclusion: So, if you have symptoms, you’ll likely benefit from vitamin X too.

If an inductive argument is strong and its premises are true, the argument is cogent. One or more false premises, however, make inductive arguments uncogent.

This may seem like a lot of vocabulary to keep track of, but Figure 1 can help with keeping things straight:Argument+

Summing Up

Okay, time for a quick recap. In logic, arguments contain sets of premises meant to support a conclusion. Deductive arguments try to prove a conclusion is true, with the conclusion necessarily following from the premises in a valid argument. Such arguments are only sound if they’re logically valid and all their premises are true.

Inductive arguments, meanwhile, try to imply a conclusion is probably true, with the strongest arguments containing the most likely conclusions. To be cogent, an inductive argument must be strong and contain only true premises.

Ultimately, being able to recognize a sound deductive argument will help you avoid falling for weak, invalid, or unsound lines of reasoning—and, not to mention, some trick questions.

Footnotes:

  1. Deductive and inductive arguments are different from deductive and inductive reasoning. Deductive and inductive arguments try to prove a claim is certainly true or imply a claim is probably true, respectively. But deductive and inductive reasoning involve arguing from universal to particular or particular to universal, respectively.
  2. Is it circular reasoning for Christians to begin with Scripture as our ultimate authority for truth? No. To find out why not, see Critical Thinking Scan Episodes 3637, and the associated resources.

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