Because

  How to Analyze and Evaluate Ordinary Reasoning

  Section 12:  How principles connect reasons to conclusions

 G. Randolph Mayes

 Department of Philosophy

 Sacramento State University

Implication revisited

In section 2 we introduced the concept of logical implication and in section 3 we introduced the concept of practical implication, which is an extension of the concept of logical implication to explanatory and argumentative contexts.  Recall that the definition of practical implication is:

• A set of premises practically implies a conclusions whenever it (1) logically implies the conclusion and (2)  produces the conclusion.

And the definition of logical implication is:

• A set of premises logically implies the conclusion whenever it is impossible for the premises to be true and the conclusion false.  (In other words if whenever the premises are true, the conclusion is also true.)

We said in section 2 that implication is one of the most important concepts in logic.  So perhaps it's mildly surprising that we haven't been making much use of it since then.

Reasons alone don't  imply their conclusions

You may recall that we introduced the concept of practical implication partly to deal with some odd examples of logical implication such as:

• Miguel didn't go to the concert because Miguel didn't go to the concert.

• Lisa does well in logic because she does all the work and gets good grades.

• Jupiter orbits the sun because it is a satellite of the sun.

These are odd because they are logically valid, but profoundly uninformative.  In the first example the 'reason' offered is just the same statement as the conclusion.  In the second and third examples, the 'reasons' are just different ways of stating the conclusion.  So, while these statements do logically imply their conclusions, it's only because they basically are the conclusions.   They do not function as reasons at all because reasons produce their conclusions, and nothing can produce itself.

One of the defining characteristics of a reason, then,  is that it does not, by itself, imply it's conclusion.  A reason can only imply it's conclusion with the help of another kind kind of premise that we call a principle.  

Principles and how they work

In order to understand what a principle is and how it works, it's useful to consider a slightly odd example.

• Butch swears that he's been  faithful to Martha, so I think he's  probably cheating on her.

This is clearly an argument for the conclusion that Butch has been cheating on Martha.  It is a strange argument, though, because the reason given, that Butch swears he's been faithful to Martha, would ordinarily be considered to be evidence that he has been faithful, not that hasn't.

Whenever we are presented with reasoning for a problematic conclusion we find ourselves trying to make sense of the connection.  In this case the job began by noting that the reasoning seems to violate a general principle, namely that if a person swears something to be the case, then it probably is the case. Whenever we are puzzled by the connection between a reason and a conclusion we find ourselves searching for some general principle to make sense of things. This is because principles are what we use to connect reasons to conclusions.

For reasoning purposes, a principle may be understood as a statement with two basic properties.

(1)  Principles are generalizations. 

(2)  Principles are conditional, or "if....then"  statements.

This statement is not a principle: 

• "Butch swears that he is faithful to Martha."

This is just a statement about Butch and his relation to Martha.  T

This statement is a principle

• People swear when they want to be believed by others..

The reason this is a principle is because it is (1) it is a generalization about people and (2)  it can be written as a conditional as follows:

• If a person wants to be believed by another person, then he or she swears to that person.

In order to state principles both precisely and with a minimum of words, we will adopt the convention of using variables (u,v,w,x,y, and z).  to substitute for the pronouns.  So, for example, the principle above can be more compactly expressed as:

• If person x wants to be believed by person y, then x swears to y.

How principles connect reasons to conclusions

Now reconsider the weird example above.  We can now be more precise about what makes it weird:  It is that in order to make sense of what the person is saying we are forced to do so with a weird principle, namely:

•  If someone swears something to be the case, then it is not the case.

The connecting function of the principle can be represented graphically:

In section 12 we developed the concept of an instance.   Although we will not go on to use this  term in connection with principles, it is helpful to observe here that the reason is a specific instance of the antecedent or 'if' clause of the principle.  Also, the conclusion is a specific instance of the consequent or 'then' clause of the principle.  This relationship is possible only because the principle is more general than either the reason and the conclusion. 

Principles as rules

You can think of a principle as a rule.   Rules are just principles that we use to regulate and judge our behavior.  Games have rules; legal systems have rules; societies have rules; languages have rules, logic has rules.  Rules are everywhere.  The Golden Rule, for example, is usually stated as "Do unto others as you would have them do unto you."   This can be written as the principle:

• If person x would have person y treat x in manner z, then x should treat y in manner z.

The Golden Rule is not only a rule for regulating our behavior, it is also a rule that informs our inferences.  In fact, it is only because it informs our inferences that we can use it to judge our behavior.  If someone were to reasons as follows:

• Butch should be honest with Martha because Butch would want Martha to be honest with her.

you would grasp this reasoning immediately because you know the Golden Rule, and you at least intuitively grasp  that it applies to the case at hand.  If you were to make your grasp of this reasoning explicit, you would reconstruct it as follows.

Logical implication and the interpretation of reasoning

You will recall from our discussion of instances that people often do not state their reasons, but rather give several instances from which the implicit reasons can be inferred.  The same is true of principles.  People state their principles even more rarely than they state their reasons. However, people do sometimes state their principles.  For example:

• Barb shouldn't lie to Martha because Martha is his wife and one should always be honest with ones spouse.

Here the statement that one should always be honest with ones spouse is not an additional reason, but an explicitly stated principle tying the reason and conclusion together.

When people do not state their principles, it can become our job to figure out what they are.  This can be a pretty thankless job, partly because the people who are dong the reasoning do not themselves know what their principles are. 

The basic rule for interpreting reasoning, what we will later call the Principle of Charity, is a kind of Golden Rule for reasoning:  

• Always interpret another person's reasoning so that it makes as much sense as possible. 

It is easy to simply misinterpret what people are saying and then reject it because the interpretation makes no sense. (This is what we will later call the Straw Man fallacy.)  But for logical purposes, this is not a constructive thing to do.  Now, part of what it means to interpret a person's reasoning so that it makes sense is  this: 

• Always attribute principles that result in logically valid rationales.

You will notice that in all of the examples above, the reason and principle together logically imply the conclusion. ( So all our talk of the connecting function of principles is really just another way of talking about logical implication or validity.)

Interestingly, this policy means that we will very rarely criticize a person's reasoning as invalid.  It would be tempting to say that the weird example we started with

• Butch swears up and down he is faithful to Martha, so that means he is probably cheating on her.

is an instance of invalid reasoning.  But it is only invalid in the sense that any reasoning that does not explicitly state its principles is invalid.  When it is our job to attribute a principle, then it is our job to attribute a principle that makes the reasoning valid.  Of course, as you'll recall, the principle we had to attribute to make the reasoning valid ended up being a principle that we don't accept.  So if we were to criticize the reasoning, we would not say that it is invalid.  We would say that the only way to make it valid is to connect it with a very weird (what we will ultimately call a weak or unreliable) principle.

It is important to realize that divining, attributing, and criticizing principles in this way is something that you have been exposed to since childhood.  For example, most of us have been on the receiving end  of a conversations like this before:

• Mom:  Why did you spit on Grandma?

• You:  Janie told me to.

• Mom:  And would you push Grandma off a cliff if Janie told you to?  How would you like it if someone did that to you?

Notice that what Mom has just done is called you out on the  principle of your reasoning.  The principle she has implicitly identified is:

• If person x tells y to perform action z, then y should perform z.

Mom has pointed out that in order to see your reasoning as valid, she has to attribute something like this principle to it.  Her rhetorical question amounts to pointing out that this is a very stupid principle to live by.  Then she finishes up by reminding you what principle you are expected to live by, namely the Golden Rule.

Representing principles

Now that we know how principles connect reasons to conclusions, let's be clear about how we are going to include principles in our rationales.  We will no longer draw arrows connecting the reason and the conclusion to the principle as above.  Rather, we will simply draw arrows between the reason and the conclusion, and label the arrow with a P_n, where n is a number like P₁, P₂, P₃, etc.  Numbering the principles allows us to identify reasons simply by reference to the corresponding principles, so we can pretty much drop the policy of writing R₁, R₂, R_3,. etc., under the reason boxes.  The principles themselves we will write in a box below the corresponding rationale.

Here is an example of a rationale in this revised format.

• Even though the evidence is strong that the U.S. is in a recession, economic pundits like chairman of the Federal Reserve Board Ben Bernanke are reluctant to say so.  This is partly because it would be an admission of failure.  The they think that recessions are avoidable by proper government management of taxes, interest rates, and government spending.  It's also because the use of the word 'recession' itself can help to bring about a recession, because it causes investors to panic and pull their money out of the market.