Friday, February 15, 2013

Deductive Vs. Inductive Reasoning

The spring semester has brought with it new challenges for us writing center consultants. Aside from trying to stay healthy during a merciless flu season, many of us are moving to the classroom as teaching apprentices. A couple weeks ago, I discovered, during two separate conversations with two different colleagues, that they would soon be giving a lecture explaining the difference between deductive and inductive reasoning.  

After discussing with each colleague his/her teaching strategy, I asked myself how I might distinguish deductive reasoning from inductive reasoning, then I asked myself how I might give this information to a freshman composition student. This blog post will be the abbreviated version of my cerebral labors. 

Let me begin by asking you a question: What can you conclude from the following two premises?
1. All men are mortal.
2. Socrates is a man. 

I would imagine many of you have seen these two premises before. Lots of introductory philosophy or critical reasoning books include this example to illustrate the features of a valid chain of deductive reasoning.

Now if we assume that (1) and (2) are true, we can conclude--conclude without any doubt, without any qualification the following:

3. Socrates is mortal. 

Part of what makes deductive reasoning distinct from inductive reasoning is that first premise. How many men does it say are mortal? All of them. And given the fact that (1) and (2) are related to each other in a specific linguistic way, and given the fact that we are assuming both to be true, the conclusion is guaranteed to be true. In other words, if (1) and (2) are true, then it is impossible for (3) to be false. In a world full of doubt and uncertainty, a sound deductive argument is a bastion of knowledge. 

Other kinds of deductive reasoning move from some universal statement to a particular one. The valid forms of such reasoning chains would be called syllogisms.   

Here is another example:
4. No book on my shelf has a pinstriped cover.
5. Catch-22 is a book on my shelf.

6. Catch-22 does not have a pinstriped cover. 

(6) is entailed by (4) and (5).  Part of what makes this chain of reasoning deductive is the content of (4).  How many books on my shelf have a pinstriped cover? That's right, none of them.  To show how (1) and (4) effect the nature of the reasoning chain lets slight modify these two examples. 

1* 99 percent of men are mortal.
2* Socrates is a man.

Now if we assume that both 1* and 2* are true, what can we conclude? Or maybe the better question is to ask, what can't we conclude?  

Because 1* is probabilistic, because it leaves that 1%  of men floating around who could be immortal, even if both 1* and 2* are true, we would not be able to conclude, for certain, that "Socrates is mortal."  

Instead, what we could cogently conclude would be something like, "It is very very probable that Socrates is mortal." Or maybe, to express the same basic idea in a different way, we could conclude, "Any rational person would believe that Socrates is, in fact, mortal."   Even if both 1* and 2* are true, the conclusion "Socrates is mortal" might still be false, thus this chain of reasoning would not be deductive. 

Let's look at our second modified argument:

4*Out of 250 books on my shelf 249 do not have a pinstriped cover. 
5*Catch-22 is a book on my shelf. 

4* gives information about the number of books on my shelf--I have 250 books on my shelf. 

4* also gives information about a characteristic that 249 of the books do not possess--a pinstriped cover.  

But even if 4* and 5* are true, it is still possible that 6* "Catch-22 does not have a pinstriped cover" is false. Maybe it's the one book that actually has a pinstriped cover. For those of you who believe that you've seen the cover of Catch-22 and know that it doesn't have a pinstriped cover, my edition is very special. So special, in fact, there is only one in existence. Since it's so special, I've never shown it to anyone, thus no one, at least no one who hasn't had some supernatural assistance, could possibly know about the features of its cover.     

Just like in the other example, most of us would believe, given the truth of 4* and 5*  that Catch-22 does not have a pinstriped cover" is true, but since the truth of the premises do not guarantee the truth of the conclusion, it would be an inductive chain of reasoning, not a deductive one. 

To sum up some of what I've tried to illustrate with the above examples, a chain of deductive reasoning includes a couple of key features that are distinct from a chain of inductive reasoning. The first one is that, in a deductive chain of reasoning, if the premises are true, then the conclusion must also be true. A chain of inductive reasoning does not, even if its premises are true, entail the conclusion. The second one is that all the valid syllogistic forms (all of which contain a universal modifier like All or No) use a deductive chain of reasoning to draw their conclusions. 

If you see a valid argument that contains only premises that itself includes either the term All or No, without some qualifying distinction, (For example, in the following proposition: All the penguins that have ever been seen by human beings..., the part in bold print qualifies the All), then it will be using a deductive chain of reasoning.  

On the other hand, an inductive  chain of reasoning will base its premises on a series of observations that will always fall short of universality. It's for this reason that, powerful as it may be, the scientific method only generates conclusions through a chain of reasoning that is inductive. Because a set of data collected by human observation will always be qualified by the natural limitations of either human faculties or the instruments we create, the conclusions generated by the scientific method are always inductive. 

Induction and deduction are both essential ways of reasoning.  In all honesty, we would be lost without either one.  

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