Arguments with missing premises (Dr. Van Cleave)

By Matthew Van Cleave

Quite often, an argument will not explicitly state a premise that we can see is needed in order for the argument to be valid.  In such a case, we can supply the premise(s) needed in order so make the argument valid.  Making missing premises explicit is a central part of reconstructing arguments in standard form.  We have already dealt in part with this in the section on paraphrasing, but now that we have introduced the concept of validity, we have a useful tool for knowing when to supply missing premises in our reconstruction of an argument.  In some cases, the missing premise will be fairly obvious, as in the following:

The premise and conclusion of this argument are straightforward:

However, as stated, the argument is invalid.  (Before reading on, see if you can provide a counterexample for this argument.  That is, come up with an imaginary scenario in which the premise is true and yet the conclusion is false.)  Here is just one counterexample (there could be many): Gary is a convicted sex-offender but the country in which he lives does not restrict convicted sex-offenders from working with children.  I don’t know whether there are any such countries, although I suspect there are (and it doesn’t matter for the purpose of validity whether there are or aren’t).  In any case, it seems clear that this argument is relying upon a premise that isn’t explicitly stated.  We can and should state that premise explicitly in our reconstruction of the standard form argument.  But what is the argument’s missing premise?  The obvious one is that no sex-offenders are allowed to work with children, but we could also use a weaker statement like this one:

It should be obvious why this is a “weaker” statement.  It is weaker because it is not so universal in scope, which means that it is easier for the statement to be made true.  By relativizing the statement that sex-offenders are not allowed to work with children to the place where Gary lives, we leave open the possibility that other places in the world don’t have this same restriction.  So even if there are other places in the world where convicted sex-offenders are allowed to work with children, our statements could still be true since in this place (the place where Gary lives) they aren’t.  (For more on strong and weak statements, see section 1.10).  So here is the argument in standard form:

This argument is now valid: there is no way for the conclusion to be false, assuming the truth of the premises.  This was a fairly simple example where the missing premise needed to make the argument valid was relatively easy to see.  As we can see from this example, a missing premise is a premise that the argument needs in order to be as strong as possible.  Typically, this means supplying the statement(s) that are needed to make the argument valid.  But in addition to making the argument valid, we want to make the argument plausible.  This is called “the principle of charity.”  The principle of charity states that when reconstructing an argument, you should try to make that argument (whether inductive or deductive) as strong as possible.   When it comes to supplying missing premises, this means supplying the most plausible premises needed in order to make the argument either valid (for deductive arguments) or inductively strong (for inductive arguments).

Although in the last example figuring out the missing premise was relatively easy to do, it is not always so easy.  Here is an argument whose missing premises are not as easy to determine:

The conclusion of this argument, that the state should not allow gay marriage, is apparently supported by a single premise, which should be recognizable from the occurrence of the premise indicator, “since.”  Thus, our initial reconstruction of the standard form argument looks like this:

1.    Children who are raised by gay couples often have psychological and emotional problems.

2.    Therefore, the state should discourage gay couples from raising children.

However, as it stands, this argument is invalid because it depends on certain missing premises.  The conclusion of this argument is a normative statement—a statement about whether something ought to be true, relative to some standard of evaluation.   Normative statements can be contrasted with descriptive statements, which are simply factual claims about what is true.  For example, “Russia does not allow gay couples to raise children” is a descriptive statement.  That is, it is simply a claim about what is in fact the case in Russia today.  In contrast, “Russia should not allow gay couples to raise children” is a normative statement since it is not a claim about what is true, but what ought to be true, relative to some standard of evaluation (for example, a moral or legal standard).  An important idea within philosophy, which is often traced back to the Scottish philosopher David Hume (1711-1776), is that statements about what ought to be the case (i.e., normative statements) can never be derived from statements about what is the case (i.e., descriptive statements).  This is known within philosophy as the is-ought gap.  The problem with the above argument is that it attempts to infer a normative statement from a purely descriptive statement, violating the is-ought gap.  We can see the problem by constructing a counterexample.  Suppose that in society x it is true that children raised by gay couples have psychological problems.  However, suppose that in that society people do not accept that the state should do what it can to decrease harm to children.  In this case, the conclusion, that the state should discourage gay couples from raising children, does not follow.  Thus, we can see that the argument depends on a missing or assumed premise that is not explicitly stated.  That missing premise must be a normative statement, in order that we can infer the conclusion, which is also a normative statement.  There is an important general lesson here: Many times an argument with a normative conclusion will depend on a normative premise which is not explicitly stated.  The missing normative premise of this particular argument seems to be something like this:

Notice that this is a normative statement, which is indicated by the use of the word “should.”  There are many other words that can be used to capture normative statements such as: good, bad, and ought.  Thus, we can reconstruct the argument, filling in the missing normative premise like this:

However, although the argument is now in better shape, it is still invalid because it is still possible for the premises to be true and yet the conclusion false.  In order to show this, we just have to imagine a scenario in which both the premises are true and yet the conclusion is false.  Here is one counterexample to the argument (there are many).  Suppose that while it is true that children of gay couples often have psychological and emotional problems, the rate of psychological problems in children raised by gay couples is actually lower than in children raised by heterosexual couples.  In this case, even if it were true that the state should always do what it can to decrease harm to children, it does not follow that the state should discourage gay couples from raising children.  In fact, in the scenario I’ve described, just the opposite would seem to follow: the state should discourage heterosexual couples from raising children. 

But even if we suppose that the rate of psychological problems in children of gay couples is higher than in children of heterosexual couples, the conclusion still doesn’t seem to follow.  For example, it could be that the reason that children of gay couples have higher rates of psychological problems is that in a society that is not yet accepting of gay couples, children of gay couples will face more teasing, bullying and general lack of acceptance than children of heterosexual couples.  If this were true, then the harm to these children isn’t so much due to the fact that their parents are gay as it is to the fact that their community does not accept them.  In that case, the state should not necessarily discourage gay couples from raising children.  Here is an analogy: At one point in our country’s history (if not still today) it is plausible that the children of black Americans suffered more psychologically and emotionally than the children of white Americans.  But for the government to discourage black Americans from raising children would have been unjust, since it is likely that if there was a higher incidence of psychological and emotional problems in black Americans, then it was due to unjust and unequal conditions, not to the black parents, per se.  So, to return to our example, the state should only discourage gay couples from raising children if they know that the higher incidence of psychological problems in children of gay couples isn’t the result of any kind of injustice, but is due to the simple fact that the parents are gay. 

Thus, one way of making the argument (at least closer to) valid would be to add the following two missing premises:

So the reconstructed standard form argument would look like this:

In this argument, premises 2-4 are the missing or assumed premises.  Their addition makes the argument much stronger, but making them explicit enables us to clearly see what assumptions the argument relies on in order for the argument to be valid.  This is useful since we can now clearly see which premises of the argument we may challenge as false.  Arguably, premise 4 is false, since the state shouldn’t always do what it can to decrease harm to children.  Rather, it should only do so as long as such an action didn’t violate other rights that the state has to protect or create larger harms elsewhere.

The important lesson from this example is that supplying the missing premises of an argument is not always a simple matter.  In the example above, I have used the principle of charity to supply missing premises.  Mastering this skill is truly an art (rather than a science) since there is never just one correct way of doing it (cf. section 1.5) and because it requires a lot of skilled practice. 

Do Quiz 6b before moving further in the course.