Developing a Well-Formed Thought life: What Is Logic?

 

 

Logic studies the methods that we use to analyze information and draw valid conclusions. As Norman Geisler and Ronald Brooks put it, “Logic really means putting your thoughts in order.”1 “Logic is the study of right reason or valid inferences and the attending fallacies, formal and informal.”2 “Logic is a way to think so that we can come to correct conclusions by understanding implications and the mistakes people often make in thinking.”3 According to Irving M. Copi and Carl Cohen in their Introduction to Logic, “Logic is the study of the methods and principles used to distinguish correct reasoning from incorrect reasoning.”4

 

The  study of logic incorporates a number of elements. At the most basic level, logic examines propositions, arguments, premises, and conclusions. The focus is the use of right thinking to come to correct conclusions. Logic incorporates the study of proper thinking as well as mistakes in thinking (fallacies). Through processes of deduction and induction, inferences are made with the aim of coming to correct conclusions.

In addition, logic also sharpens the use of our language and allows us to articulate our idea more precisely and cogently to others. Christian’s should be very concerned about precision and clarity in communication. As we desire to glorify God with our minds, we ought to seek to formulate the proper structure of arguments. As such, learning to do so allows us to be more careful, methodical, and systematic in the presentation of the truth of Christianity as well as other true ideas.

Logic is built upon four laws:

1. The law of identity (A is A) – A thing is what it is.  “A Rose is a rose.”

2. The law of excluded middle (either A or non-A) – “Either a rose, or not a rose.”  But not sort of a rose  (Think about being “sort of pregnant.”)

3. The law of non-contradiction (A is not non-A) – “A Rose is not a non-Rose.”  Here we see that there can be no contradiction in the idea and have it be coherent.  (Think of a square circle.)

4. The law of rational inference – (If P, then Q.  And P.  Therefore, Q.)  “If it’s raining outside, then it’s wet.  It is raining outside.  Therefore, it is wet.)

These laws are foundational to all thinking and reason. One cannot object to the laws of logic without employing them in the objection itself. These laws are grounded in the nature of God.  God is the basis of all truth as the basis of ultimate reality.

Sequacious reasoning is the correct flow of thought.  It is developed using essential elements derived from the basics of logic. In general, everything else is built upon these elements.  The first element is the proposition.  A proposition is something that is either true or false. Think of an indicative statement (a statement that something is a certain way).  Such statements may either be affirmed or denied because they are either true or false.  Other utterances such as commands, questions, or exclamations are not true or false and so they are not propositional.

Arguments are tools in logic that allow us to take propositions and put them in an order which allows us to arrive at a conclusion about something.  When you have a number of propositions that lead to a conclusion, you have an argument. The conclusion of an argument is that which follows from the supporting propositions, which are called the premises of the argument. The telltale words for premises are called premise-indicators:  “Since, because, for, as, as shown by, as indicated by, the reason is that” are some premise-indicators.

A conclusion without its supporting premises is not an argument.  The conclusions of arguments can often be recognized by telltale words or phrases. The words that point to the conclusion are called conclusion-indicators.  For example, “Therefore, hence, thus, so, accordingly, in consequence, consequently, as a result, it follows that, we may infer, which shows that” are all words or phrases that often point to the conclusion of an argument.

When identifying arguments, it’s helpful to make the distinction between arguments and explanations for things.  The key here is the intention of the presenter.  Just because we see some indicator words, it doesn’t mean we are reviewing an argument.  An explanation is meant to illuminate or give insight into a state of affairs.  An argument is used to support the truth regarding the facts of a state of affairs.  Skillful thinker must discern the difference between explanations and arguments by looking closely at the context and intention.

Arguments come in two kinds—they are either deductive or inductive. These are important terms to differentiate. When an argument is deductive, it means that the conclusion follows from the premises necessarily and conclusively. When a deductive argument is valid, it means that if the premises are true, the conclusion must be true.  Think about that…

An inductive argument, on the other hand, is not a conclusive argument. When an argument is inductive, it means that that the conclusion may be true to a certain degree of probability.  That probability may be very high, so high in fact that its all but logically impossible for it to be false.  For example, we hold that unicorns do not exist in the actual world.  We know this aposteriori (via inspection), and we could certainly provide a decent argument for it.  Nevertheless, since it is logically possible for God to create a unicorns, the conclusion is sufficient, but not necessary as it is in deductive reasoning.

Copi clarifies:

A deductive argument is one whose conclusion is claimed to follow from its premises with absolute necessity, this necessity not being a matter of degree and not depending in any way on whatever else may be the case. In sharp contrast, an inductive argument is one whose conclusion is claimed to follow from its premises only with probability, this probability being a matter of degree and dependent upon what else may be the case.4

One way to look at this is as follows: in a deductive argument, no amount of additional information can change the conclusion of the argument. In an inductive argument, the conclusion may change when new information is discovered. Deductive arguments are certain, whereas inductive arguments are probable to some degree.
When an argument is structured correctly, it is called a valid argument. When an argument is not correctly structured, it is called invalid. An argument cannot be true or false, only valid or invalid. Truth or falsity only applies to statements or propositions. The conclusion of an argument can be true or false (because the conclusion is a statement), but the argument is only either valid or invalid.

Finally, when an argument is valid, and all of its premises are true, it is called a sound argument. This is the kind of argument the skilled thinker is looking for.

 

More to follow…

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1 Norman Geisler & Ronald Brooks, Come Let Us Reason: An Introduction to Logical Thinking (Grand Rapids, MI: Baker Books, 1990), p. 11.
2 Ibid., p. 12.
3 Ibid.,p. 13.
4 Irving M. Copi & Carl Cohen, Introduction to Logic, 11th Edition (Upper Saddle River, NJ: Pearson Education, 2002), p. 3.
5 Ibid., p. 6.