Critical Thinking: Formal Fallacies


Formal Fallacies

Formal fallacies are so called because the mistake in reasoning stems from the structure or the form of the argument.

An argument is called “valid” when it’s form is correct and does not lend to a mistake in reasoning due to a faulty structure. An argument is deemed “cogent” when its form is valid and its premises are sound. In logic, “valid” means that if the premises are true, the conclusion is also true.

A fallacy can occur when the form is adulterated to reach a false conclusion.

modus ponens

Consider the proposition, “If she walks, then she moves.” This proposition has the basic form: “If a, then c.” Any proposition that has that form (“if a, then c”) is called a “hypothetical proposition.” This is because it’s not asserting either a or c; it is merely stating that if a hypothetically were true, then c would have to be true as well. If an argument has two premises, only one of which is hypothetical, then it is called a “mixed hypothetical syllogism.” Example:

  • If she walks, then she moves.
  • She walks.
  • Therefore, she moves.

In a hypothetical proposition the first part (a) is called the antecedent, and the second part (c) is called the consequent. In the example, “If she walks” is the antecedent, and “then she moves.” is the consequent.

In this argument, the first premise (if a, then c) is hypothetical. The second premise (a) is not hypothetical. It asserts that she is indeed walking. The conclusion is c. Since the second premise affirms that a is true, this type of argument is called “affirming the antecedent” and is perfectly valid. In notation, this would appear as follows:

  • If a, then c.
  • a is true
  • Therefore c

In Latin this is modus ponens, which means the “method of affirming.”

Fallacy of Affirming the Consequent

Consider the fallacy that can occur by altering the form. In notation, this would appear as follows:

  • If a, then c.
  • c is true
  • Therefore a

The example would read thusly:

  • If she walks, then she moves.
  • She moves.
  • Therefore, she walks.

Clearly, her being in motion does not mean that she is limited to walking. So, this argument is invalid. The second premise affirms that the consequent (c) is true, instead of affirming the antecedent. This fallacy is called “affirming the consequent.” Here is a paraphrased example of an argument authored by Dr. Jason Lisle:

  • If Darwinism were true, we would expect to see similarities in DNA of all organisms on earth.
  • We see similarities in DNA of all organisms on earth.
  • Therefore, Darwinism is true.

Of course there are similarities in the DNA of all organisms on earth. So what?

There are similarities in Java code, C++ code, and Visual Basic code — in fact, they share 100% of their letters, numbers, and symbols in uncompiled form and 100% of their bits in compiled form. They are remarkably similar though they are utterly different in both form and utility. A telephone directory and the collected works of William Shakespeare also share 100% of letters and numbers in common.  They are even both printed on paper!  So what?

Ultimately, all of these similarities are irrelevant. All of these things were CREATED (designed) by man. We should expect to see similarities and commonalities.

Likewise, because all living things were created (designed) by God, it would be foolish to expect not to find similarities in our design. The argument is utterly fallacious.

modus tollens

Another mixed hypothetical syllogism has the following form:

  • If a, then c.
  • Not c.
  • Therefore, not a.

This is a valid argument as can be seen by substituting the phrases for the symbols.

  • If she walks, then she moves.
  • She is not moving.
  • Therefore, she is not walking.

Since the second premise denies that the consequent (c) is true, this valid argument is called “denying the consequent” or, in Latin, modus tollens, which means the “method of denying.”

The Fallacy of Denying the Antecedent

As with modus ponens, there is an argument that is superficially similar to modus tollens, but is actually a fallacy. It has this form:

  • If a, then c.
  • Not a.
  • Therefore, not c.

We can see that this is fallacious by substituting the phrases for the symbols:

  • If she walks, then she moves.
  • She is not walking.
  • Therefore, she is not moving.

But clearly, she could not be walking and still be moving. So, the argument is invalid. Since the second premise denies that the antecedent (a) is true, this fallacy is called “denying the antecedent.” Here is another great example authored by Dr. Jason Lisle:

  • If we found dinosaur and human fossils next to each other in the same rock formation, then they must have lived at the same time.
  • We do not find them next to each other in the same rock formation.
  • Therefore, they did not live at the same time.

The argument denies the antecedent and is fallacious in its form. There could be thousands of reasons why dinosaur fossils are not normally found next to human fossils. Perhaps dinosaurs weigh a lot more than human beings (imagine that!) and their corpses settled first after they drowned in the global flood.  That is merely one possibility.

As an aside, I find it fascinating that whenever human and dinosaur fossils DO co-exist, Darwinists do not consider it convincing evidence. I wonder what the meaning is there — the intent.
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As Christians, we are expected to think in a way that is consistent with God’s logical nature (Romans 12:2). Recognizing fallacious arguments is part of donning the whole armor of God. Scripture promises that if we chose to believe lies, we will be damned.  It is the obligation of the Christian to be rational and to pattern our thinking after God’s own thinking (Isaiah 55:7–8).

It is important for us to teach our children how to recognize fallacies in arguments so that they can better hear, recognize, and know the truth. Even more important than knowing the truth for ourselves is the ability to give a truthful and cogent answer for the joy that is in us, the ability to share the truth with the lost.


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