Logic

A logical argument must meed three conditions:

  1. The terms must be clear.
  2. The form must be valid.
  3. The premises must be true.

A basic syllogism looks like this:

  • Premise #1.
  • Premise #2.
  • Conclusion.

If the terms are clear and the form is valid, the conclusion must be true. Channel your inner Vulcan and put your feelings away, for no amount of hurt feelings will make the illogical logical or the logical illogical. There is no tantrum of any size that will make the true conclusion false or the false conclusion true.

What do each of these conditions look like?

Terms

  1. All men have XY chromosomes.
  2. Marie Antoinette is a man.
  3. Marie Antoinette has XY chromosomes.

When the terms are not clear, the argument is said to equivocate the terms.  In this argument, both premises are true and the form is valid, but the term men/man is equivocal. In premise #1, “men” means “of the male sex,” whereas in premise #2, “man” means “mankind” or “human,” as in the classic “All men are mortal./Socrates is a man./Socrates is mortal.” syllogism.

Validity

The form of an argument refers to its structure. In logic text books, the terms are represented with p’s and q’s.  There are many examples of valid and invalid forms, but I’ll stick to the most basic for now.

  1. If P, then Q. (If a person is a man, he has XY chromosomes.)
  2. P. (Marie Antoinette is a man.)
  3. Therefore, Q. (Therefore, Marie Antoinette has XY chromosomes.)

This is a valid form known as modus ponens.  It is the form of the syllogism above.  When I write out the argument using if-then statements, the equivocation becomes more apparent.  A common error related to this form is below.

  1. If it rains outside, the ground will be wet.
  2. The ground is wet.
  3. Therefore, it rained outside.

Written in logical form, it looks like:

  1. If P, then Q.
  2. Q.
  3. Therefore, P.

In logical forms like this, P is known as the antecedent and Q is known as the consequent.  This formal fallacy, which makes the argument invalid, is known as “affirming the consequent.”  I may infer or induce that the ground is wet because of rain, and I may be correct, but logic is the science of deduction.  There are other reasons the ground may be wet such as sprinklers or a busted water main.

Premises

If the terms are clear and the form is valid, we have a valid argument.  That means that IF the premises are true, we must believe the conclusion.  If the premises are, in fact, true, the argument is sound.  It is important to note that a valid argument does not necessarily mean that the conclusion is true. All sound arguments are valid, but not all valid arguments are sound.

Consider this example:

  1. All buildings are marsupials.
  2. The Empire State Building is a building.
  3. Therefore, the Empire State Building is a marsupial.

This syllogism has no unclear terms and it takes the same form as the above arguments, so it is valid.  However, it is not sound.  Premise #1 is false.  A marsupial is an animal that carries its young in a pouch, such as kangaroos and possums.  Buildings are not marsupials.  Thus we need not believe the conclusion based on this argument.

One final note is that an argument may be valid and unsound, but the conclusion may be true.  Consider the following example.

  1. All Vulcans are mortal.
  2. Socrates is a Vulcan.
  3. Therefore, Socrates is mortal.

Again, there are no unclear terms (unless you have never heard of Star Trek [?seriously?]), and the form is valid.  Premise #2 is untrue, and premise #1 is true in fiction but not real life (though Vulcans live much longer than humans). Since the premises are not true, I am not bound to believe the conclusion on account of this argument.  However, I know independently that it is true, because Socrates did, in fact, die (see the painting above of the moments before his death).

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