The Inductive/Deductive Distinction

As mentioned in the last post ("So What Makes an Argument Good?"), the two main criteria for the success of an argument are that 1. the premises are true and 2. that the truth of the conclusion follows from the premises. However, what does it mean for the truth of the conclusion to "follow from" the premises?

There are two primary ways to think of this 'follow from' relationship:
1. They provide good evidence that the conclusion is true.
2. They prove that the conclusion is true.

The first of these is the goal of what we call inductive reasoning; the second is the goal of deductive reasoning. Whether or not the arguments succeed at these intentions is another story, but those are the goals. Accordingly, here are the definitions that we are using:

• An an inductive argument is one in which the premises are intended to provide good evidence for the truth of the conclusion. 
• A deductive argument is one in which the premises are intended to guarantee the truth of the conclusion. 

Here is an example of each:
Inductive: "Every dog I have ever had likes to eat bread. Therefore your dog probably will like to eat bread as well."
Deductive: "All dogs like to eat bread. Rover is a dog. Therefore, Rover likes to eat bread."

We don't know whether the premises are true in each case, but we do know that if the premises are true in the inductive example, then there is evidence that the conclusion is true. And in the deductive example, we know that if the premises are true, then the conclusion must be true. This leads to another important distinction:

• An inductive argument that succeeds in its intention: one that provides good evidence that the conclusion is true, is called strong. 
• A deductive argument that succeeds in its intention: one whose premises, if true, would guarantee the truth of the conclusion is called valid. 

Inductive strength is a matter of degree; An argument is strong according to the degree to which the premises make the conclusion likely to be true. Deductive validity is not a matter of degree. If there is any possible way that the premises could be true and the conclusion false, then the argument is invalid. 

Here is an example: "I left my key under the welcome mat. My laptop is gone now. Mike was the only one I told about the key. Therefore, Mike must have stolen my laptop."

This argument is invalid for at least a couple of reasons: The laptop could have been misplaced, or someone else might have found the key (even though they weren't told about it). As long as there is any possibility that all of the premises could be true and the conclusion false, we know that the premises don't guarantee the truth of the conclusion, so the argument is invalid.

One more important note: This distinction has nothing to do with whether the premises are actually true. An argument can be strong or valid even with false premises. The distinction above is based on whether the conclusion would be true if the premises were true. This leads to one more important distinction:

• An inductive argument that is strong and has all true premises is called cogent. 
• An argument that is valid and has all true premises is called sound. 

For example, this argument is strong but not cogent: "A random sampling of a million dogs shows that 99% are green. Therefore, most dogs are green."

This argument is not cogent because the premise is false; but it is strong because if it were true, then the conclusion would probably be true as well.

This argument is valid but not sound: "All dogs are green. Rover is a dog. Therefore, Rover is green."

This argument is not sound because the first premise is false. But it is valid because if both premises were true, then the conclusion would have to be true as well.

There will be more about strength and validity in future posts.

So What Makes an Argument Good?

Since we now know what an argument is, the next question is what constitutes a good argument. Since the purpose of an argument is to demonstrate that the conclusion is (likely to be) true, a good argument is one that does so well. An argument, then, is good if it makes its conclusion likely to be true. There are several components to an argument's success in this mission; here are the most important two of them:

1. The premises should be true.
2. The truth of the conclusion should follow from the premises. This means that if the premises are true, then the conclusion will (likely) be true as well.

As we will discuss further in the next post, whether an argument is deductive or inductive depends upon whether we include the parenthetical 'likely' or not. In an deductive argument, the premises are supposed to guarantee the truth of the conclusion by making it impossible that the conclusion could be false if the premises are (such arguments are called 'valid'). In an inductive argument, on the other hand, the premises are just supposed to make it very likely that the conclusion is true (such arguments are called 'strong').

There are actually other criteria that are important for an argument to be good. Here's an important third one:
3. The premises should be acceptable to people to people who don't already agree with the conclusion.

This third criterion is essential if our argument is to be considered persuasive or convincing. Arguments that violate it are said to beg the question. Frequently, it is this third criterion that is the hardest to get right (and on very controversial topics it can be nearly impossible).

We'll talk more about each of these in future posts. Stay tuned!

What is an Argument?

In logic we talk about arguments. We don't mean arguments in the sense of a fight. We mean a piece of reasoning. Think of an argument as an isolated molecule of reasoning: We have narrowed reasoning down into its smallest possible size: An individual unit of reasoning.

So what is an argument? It is a series of sentences, called premises, that are intended to support the truth of another sentence, called a conclusion. To make things super clear, we like to put arguments into standard form, in which we list the premises above the conclusion. Here's an example:

Argument in Standard Form:

Premise 1: Socrates is a man.

Premise 2: All men are mortal.

Conclusion: Therefore, Socrates is mortal.

In case you were wondering whether Socrates was going to die, this argument would strongly support that conclusion.

Here is a funny video that jokes about the two conflicting interpretations of what an argument is (see if you can find the real definition in there):

The Meaning and Origin of the Word "Logic"

The word "logic" comes from the ancient Greek word "logos," which is rich with meaning. It can mean "word," "reason," "discourse," "account," and "study" (among other possible interpretations).

We see it show up frequently at the end of the names of academic subjects as "ology." In such cases, it is generally translated as "the study of." So that Anthropology is the study of humanity, geology, the study of the earth, biology the study of life, etc.

Since logic is the study of reasoning, it can properly be referred to as "logology." I personally like to see the word "logic" as an abbreviation of "logology," the study of study, or reasoning about reasoning.

Optional, but perhaps interesting to many readers: One of the gospels in the New Testament begins "In the beginning was the word ..." (John 1:1). Since the new testament is from the Greek, this 'word' is "logos." Thus, in the beginning was logos, which can be then understood in other ways, including "In the beginning was the discussion" or "In the beginning was the reasoning," continuing, "and the reasoning/discussion/study was with god, and the reasoning/discussion/study was god."

This is also interesting in light of the ancient philosopher Heraclitus, who saw logos as almost deific: It is the ordering principle of the world (Graham, n.d.). Since we know from scientists from Newton on that the universe does seem to have a rational order to it, it would appear that there may be something to Heraclitus's view that there is a logos, a set of rational or unifying principles behind all that we see. It is up to philosophers (in the general sense that includes science) to discover what those principles are.

Reference: 

Graham, D. W. (n.d.). Heraclitus (fl. c. 500 B.C.). Internet Encyclopedia of Philosophy. Retrieved October 27, 2016 from http://www.iep.utm.edu/heraclit/

What is Logic?

Though you can find many definitions of any word, the definition we will use of "Logic" is the study of reasoning. Logic investigates what makes some patterns of reasoning good and others bad. Since the goal of reasoning is to discover truth (and correct action), good reasoning is reasoning that is more likely to lead us to truth (and correct action), and bad reasoning is reasoning that is likely to lead us to error.

We can study logic in many different ways: Formal and informal, theoretical and applied. Very roughly speaking, critical thinking is applied informal logic ... we use it to learn how to reason better in real life. 

Formal logic involves the study of abstract reasoning patterns whose validity is independent of the particular subject matter. It's abstract rigor and symbolic precision even provide the basis for mathematics and computer science. 

Future posts will delve into each of these branches of logic in much more depth. 

Welcome!

Welcome! The purpose of this blog is to promote critical thinking, both in the abstract (the study of logic) and in life (including applications to specific issues).

The author of this blog is Dr. Christopher Foster, assistant professor of philosophy and course lead for PHI103: Informal Logic at Ashford University. It is my hope that this blog serves as a helpful resource, both for my students and for anyone else who should happen to come by.

-Chris Foster
October 2016