Core Concepts in Critical Thinking, Part I

Critical Thinking
Across the
Curriculum Project Critical Thinking Core Concepts
Contributed by: Lauren Miller and Michael Connelly, Longview Community College

Introducing logical vocabulary-

Statements or propositions-

A statement is a sentence which "has a truth-value" - i.e., one which is either true or false. Your English teacher will refer to these as declarative sentences, which they are called for the obvious reason that they are good for declaring that things are so or not so. What you declare to be so may really be so, in which case the "truth value" of the statement will be T (for True). Or it may not really be so, in which case the truth value of your statement is F (for False).

The truth value of a given statement may be unknown, but that doesn't keep us from telling that it HAS a truth value. For example, you don't know, and neither do we, whether the statement "There is a 10.756 kilogram rock on the dark side of the moon" is true or false, but we all know that either there is such a rock (in which case the statement has truth-value T) or there's not (and the truth-value would be F).

When you really get sophisticated you can do like the big guys do and bring in truth-values like M (for maybe) or U (for Unknown) or S (for Sorta). But for now, do we need to make it any more complicated?

Some types of sentences which are NOT statements are:

a) Questions, like "Will you still love me tomorrow?"
b) Commands, like "Shut up and go away!"
c) Sheer expressions of emotion, like "Hot Diggity-Dog!"

Statement is an easy and straight-forward concept. Where things get a tad tricky is when it comes to making, or expressing statements. The obvious, practical, and straight-forward way of expressing a statement is just to say it. Someone who says, "The moon is 150 miles above the earth," is expressing the statement:

The moon is 150 miles above the earth.

Someone taking the opposite view of the matter could just say,"The moon is not 150 miles above the earth," which expresses very well the statement

The moon is not 150 miles above the earth.

Probably, though, that won't be what they'll say, since it's so obvious, practical, straightforward, and boring. They'll say,

a) "150 miles above the earth? Where did you go to grade school?"
b) "150 miles, my aunt's feather!"
c) "Riiight, it's 150 miles from the earth to the moon, and the Pope is a Jehovah's Witness!"

All of these responses, in this context, express the statement

"The moon is not 150 miles above the earth."

Statements are one thing, how people go about expressing them is another. In determining what viewpoint a person is taking, or what they are saying in defense of that viewpoint, one of the fundamental steps is to determine what statements their actual words express. There are no rules for this basic translation process. You just have to rely on what you know about the language, and the speech customs of its speakers.

So, to summarize:

a. questions, commands, sentences which refer to a probability of an event, statements about fictional characters are not statements.
b. a statement is a sentence or a part of a sentence which is true or false (it has a truth value).
c. Truth of a statement can be established by:

personal experience,
internal consistency, and
consistency with the body of established fact (things we know are true already).

Beyond Simple Statements, we will also have to consider compound statements; will be of four main types, which correspond to the four main types of logical connectives-

1. Conjunctions- (A and B) - for statement to be true both A and B must be true, if either of them is false, statement is false.

2. Disjunctions- (A or B) - for statement to be true only one of the component simple statements need be true.

3. Negations- (NOT A) - in this type of statement the simple statement is modified so that the truth value is reversed.

4. Conditionals- (IF A, THEN B) - in this statement, the first part is identified as the antecedent, and the second part as the consequent. For this statement to be true, the condition expressed for the truth of B must not be compromised. The only case when this happens is when A is true and Bis false.

It is possible to represent the truth values of each of these statements with what is called a 'truth table'. Each kind of statement will have its own truth table which will represent all of the possible combinations of truth and falsity for the simple statements and the resulting truth or falsity of the compound statement of which they are a part.

Copyright © 1996
Critical Thinking Across the Curriculum Project
Longview Community College , Lee's Summit, Missouri - U.S.A.
One of the Metropolitan Community Colleges
An Equal Opportunity/Affirmative Action Employer

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Inquiries to: michael.connelly@mcckc.edu
Last modified: 03/02/04