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Short history of Logic

If we take Logic to be the activity of drawing inferences (conclusions) from a body of information, then no doubt humans have been using logic for as long as they have been thinking, or at least consciously thinking. The first Neanderthal to formulate the thought "All members of the Cave-Bear clan are our enemies" along with "Thag is a member of the Cave-Bear clan" very likely put the 2 and the 2 together and reached the conclusion "Thag is our enemy". Nor is there any particular reason to suppose that the logic of these primitives was primitive logic-- that is, they probably drew logically correct conclusions from their data about as often as folks do nowadays (i.e. maybe 62.3% of the time). (Besides, chances are that natural selection quickly weeded out the Neanderthals who tended to draw the conclusion "Thag is our friend" from the above data!)

On the other hand, if we take Logic to be the analysis of concepts involved in making inferences, and the identification of standards and patterns of correct inference, Logic can be traced only back to the days of Aristotle (350 years B.C. or so), with some parallel development in early Hindu writings. It's not clear that this increase in logical self-consciousness improved the accuracy of reasoning processes for humankind in general, but knowing what Aristotle knew about logic can definitely help you be a better reasoner.

Around the end of the 19th century, Logic received renewed interest (and an emphasis on symbolic representation), from mathematicians in search of a fundamental connection between logical and mathematical reasoning. Development of, and reaction to, this line of inquiry led to two divergent lines of emphasis in the study of logic, which you may have heard of:

Symbolic (or Formal) Logic vs Informal Logic (or Critical Thinking).

In a typical symbolic logic course, emphasis is placed on the precise symbolic representation of logical concepts, the study of the abstract relationships between these concepts, and the systematization of these relationships.

In an "informal logic" or Critical Thinking course, such as ours here at Longview, the focus is instead on the application of logical concepts to the analysis of everyday reasoning and problem-solving. Elements of symbolic logic will frequently be involved, but only to the extent that it contributes to this practical objective.

Notice that neither of these directions of emphasis really concern themselves much with how people actually think, or what you might call a psychology of thought. Informal Logic begins with the perception that people don't actually reason all that well, but jumps from there to the matter of doing something about it. Symbolic Logic begins with the perception of what constitutes good reasoning at a rudimentary level, and goes on from there to investigate good reasoning at higher and higher levels of sophistication.

What is the point of studying Critical Thinking?

Fundamentally, Critical Thinking or Informal Logic deals with the use of reason in the pursuit of truth. While there is serious doubt about the power of reason to discover any "new" truth, the "rules" of logic concern the ways truth can be preserved as we make inferences -- one or more statements to support or justify another statement. Taken this way, there is no great "mystery" to the concepts of Logic. At the very core of logic is the idea that certain "patterns of inference" - i.e. models for combining statements that support with those which are supposedly supported ­ will, if the supporting statements are true, guarantee the truth of the statement supported by them. In studying logic, we identify, study, and apply these patterns or principles of logical reasoning and express them in some general way - a way which is independent of the subject being reasoned about.

So, if we are interested in knowing the truth, then the answer is obvious: logical reasoning extends our grasp of the truth, from the information we have to what can be inferred from that information.

But why should we be interested in the truth? On the one hand, much of who we are, of the people we have become (and are yet to become) is due to our ideas and beliefs. And what we do and how we react to any situation is also determined by the background of beliefs and ideas we bring to it. Without getting too philosophical here, what sort of life would you consider more worthwhile-- one based on truth, or one based on lies and groundless illusions?

If we believed only what popped into our heads, perhaps we could count on its being true. [Could we? And what should we do when then the opposite idea pops into our head-- give up the earlier one, or keep 'em both?]. But often the source of our beliefs is other people - parents, pals, preachers, pundits, politicians, and others. Who we are, and how we spend our life's energies, is based to a large extent on what we picked up from others. But (in case you never noticed) they don't all give us the same message-- so who are we to believe? Could a liar ever blunder onto the truth? Could a decent person ever make a mistake? Which statement is it more rational to accept-- one unsupported by any reasons, one supported by bad reasons, or one supported by good reasons?

If we are to be in control of our own beliefs, and to somehow gain an understanding of the truth, then we must know what good reasoning is, and be aware of the ways in which our reasoning (and that of others) can go astray.

The main areas which are covered in our own Critical Thinking course are:

  1. The vocabulary of logic and arguments - the basic concepts
  2. The logical form (structure) of good and bad arguments
  3. The types of (informal) incorrect reasoning (fallacies)
  4. New ways to look at language as proposing new theories of how words are to be used.
  5. The usual sources of our information and the most common ways we are led astray by them.

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. 

Last Modified: 9/22/11