Dr. Young Addresses The Big Question

Chapter 1: Deductive and Inductive Logic

In order to understand my argument, one needs to be familiar with some concepts of deductive and inductive logic.

Logic is “the study of methods for evaluating whether the premises of an argument adequately support its conclusion” 3. If one claims to be “logical,” he or she must then provide support for his or her opinions. Science involves studying phenomena in the universe and learning their causes. Science has to be logical in order to persuade others and to provide a basis for further learning and reasoning.

In logic, people offer arguments. An argument is a set of statements where some of the statements are intended to support another statement. Statements that are intended for support are premises, and the statement to be supported is the conclusion. Premises can be offered in any order in an argument, but the conclusion typically is at the end of a chain of premises.

A statement is a declarative sentence that is either true or false. Truth or falsehood are the only possible truth values. If a sentence is neither true or false (like a command: Get out of town!, or a question: What time is it?), then the sentence is not a statement.

A deductive argument is one in which the premises are intended to guarantee the conclusion — to make the conclusion certain. An inductive argument is one in which the premises are intended to make the conclusion probable, without guaranteeing truth.

Here is an example of a deductive argument, with two premises and a conclusion:

  1. If one is added to one, then the sum is two.
  2. One is added to one.
  3. Therefore, the sum is two.

The conclusion is set off with the word, “therefore.” If premise number 1 is true (which it is), and premise number 2 is true (which it is), then the conclusion can be guaranteed to be true (which it is).

Once again, the premises may be listed in any order. For example:

  1. One is added to one.
  2. If one is added to one, then the sum is two.
  3. Therefore, the sum is two.

Here is an example of an inductive argument:

  1. Most people like ice cream.
  2. John is a person.
  3. Therefore, John most likely likes ice cream.

There, of course, is no guarantee that John likes ice cream — only the probability of it.

In deductive logic, deductive arguments are either valid or invalid. In inductive logic, inductive arguments are either strong or weak. We will cover inductive arguments in a later chapter.

A valid argument is “one in which it is necessary that, if the premises are true, then the conclusion is true” 3. The example above of a deductive argument — of adding one to one — is a valid argument. One way to guarantee if an argument is valid is to use a valid argument form. If an argument is in a valid argument form and the premises are true, then the conclusion is guaranteed to be true.

One such valid argument form is modus ponens. Modus ponens (MP) is:

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

P and Q are variables that represent statements in English. The adding-one-to-one example is in the form of MP, and so is the example where the premises are re-ordered. P represents “one is added to one” and Q represents “the sum is two.”

Note that premise 1 of MP is in the form of “If…, then…” This is a conditional statement or a “conditional.” The portion of a conditional statement that follows the word, “if,” is the antecedent, and the portion of a conditional statement that follows the word, “then,” is the consequent. In logical operator notation, a conditional statement can be symbolized as P → Q, with the operator of a conditional symbolized as an arrow. MP is symbolized as:

  1. P → Q
  2. P
  3. ∴ Q

Another famous valid argument form is modus tollens (MT). It is:

  1. P → Q (If P, then Q)
  2. ~Q (Not Q)
  3. ∴ ~P (Therefore, not P)

The operator for a negation is a tilde (a “squiggle”). Here is an example of MT:

  1. If one is added to one, then the sum is two.
  2. The sum is 3 (not two).
  3. Therefore, one is not added to one.

Now an argument may be valid, but it may not necessarily be a true or a sound argument. Consider this argument, in the form of MP:

  1. If one is added to one, then the sum is three.
  2. One is added to one.
  3. Therefore, the sum is three.

The argument is valid because it is in a valid argument form, but it is not sound because the first premise is incorrect or false. If any premise (or at least one premise) is false, then the argument is unsound even though it is a valid argument.

Another way to make an argument unsound is to use an invalid argument form. Even if all the premises are true, the conclusion may be false if an invalid argument form is used. An argument where the conclusion can be false even though the premises are true is by definition an invalid argument. If the argument is invalid, it is also unsound, regardless of the truthfulness of the premises.

Consider the following argument:

  1. If one is added to one, then the sum is two.
  2. The sum is two.
  3. Therefore, one is added to one.

The argument is both invalid and unsound. There are many ways to get the sum of two besides adding one to one. 1.5 could be added to 0.5. Negative 98 could be added to 100. .0001 could be added to 1.9999. The combinations are endless and only limited by the imagination.

The following represents the famous invalid argument form known as affirming the consequent (remember, P is the antecedent and Q is the consequent in a conditional statement):

  1. P → Q
  2. Q
  3. ∴ P

I put a single line through #3 to indicate that it is an improper conclusion. One cannot deductively determine the antecedent from the consequent. To do so is both logically invalid and unsound.

We have reached the end of Chapter 1. Please read the above carefully and make sure you understand it because you will need to understand these concepts to understand what I will tell you next.

Also, before beginning Chapter 2, please carefully study the photograph of the damaged car. After carefully studying it, write down on a piece of paper your answer for how the car got into this condition. Think hard now, and good luck!

Crumpled Car

Download Dr. Young Addresses The Big Question (PDF)