Knowledge Requires Certainty?

Rob Bass

Fall, 2000

 

 

Bill has offered an argument that knowledge requires certainty that goes wrong in two ways, first on a logical matter and second, more importantly I suspect, by confusing a logical point with a claim about epistemic status. The argument goes approximately like this:

 

1.     Knowledge requires truth – or if a statement  is known, then it is true.

2.     If a statement is true, then it can’t be false.

3.     If a statement can’t be false, then it is certain.

4.     Therefore, if a statement is known, it is certain.

 

The logical mistake shows up in the passage between line 2 and the conclusion. For line 2 is ambiguous, in ordinary English, between two meanings. On one reading, it is true, but, even granting the truth of lines 1 and 3, line 4 does not follow from it, while on the other, line 4 follows but line 2 is not true. Let’s start with the interpretation on which line 2 is true. That would run something like this:

 

5.     Necessarily, if a statement is true, then it is not false.

 

Or, equivalently,

 

6.     It is impossible for a statement to be true and false.

 

Lines 5 and 6, of course, are both true; however, line 4 does not follow from the conjunction of either of them with lines 1 and 3. I’ll come back to this after looking at the interpretation of line 2 on which it is false. That would run like this:

 

7.     If a statement is true, then, necessarily, it is not false.

 

Or, equivalently,

 

8.     If a statement is true, then it is impossible for it to be false.

 

The difference between the first pair (5 and 6) and the second (7 and 8) is that in the second, with the addition of a premise to the effect that the statement in question is true, the consequent can be detached, while this is not true with the first pair. Let me illustrate in this way:

 

1.     P is true.

2.     If  P is true, then, necessarily, P is not false (corresponding to line 7 above).

3.     Therefore, necessarily, P is not false.

 

That’s a valid argument and a premise having the form of 2 here (and therefore of 7 or 8 above) is plainly the sort of thing needed for Bill’s initial argument to be correct. But compare:

 

1.     P is true.

2.     Necessarily, if P is true, then P is not false (corresponding to line 5 above).

3.     Therefore, necessarily, P is not false.

 

That is not a valid argument because the modal operator, “necessarily,” that line 2 applied only to the whole conditional, “if P is true, then P is not false,” has been applied to the consequent of that conditional, “P is not false,” alone. What really follows from lines 1 and 2 is just

 

4.     P is not false.

 

Putting the matter in terms of the scope of modal operators, like “necessarily,” may seem too abstract to be clear, but it’s easy to illustrate the point. Consider the following:

 

1.     John is a bachelor.

2.     If John is a bachelor, then, it’s impossible for John to be married.

3.     Therefore, it’s impossible for John to be married.

 

That’s a valid argument, but the conclusion is absurd. Even if John is a bachelor, that doesn’t mean that it’s impossible – as a matter of logic! – for him to be married. He may have turned down chances to get married. Since the conclusion follows from the premises and line 1 is stipulated to be true for our purposes here, the mistake must lie in line 2. And, of course it does. The right way to put it is:

 

4.     John is a bachelor.

5.     It’s impossible for John to be a bachelor and married.

 

But all that follows from those two premises is:

 

6.     Therefore, John is not married.

 

If we keep these points in mind and return to Bill’s initial argument, it’s plain that the interpretation he needs for the argument to be valid is the way I first represented it above, with the ambiguous line 2 being understood to mean “If a statement is true, then it is impossible for it to be false”:

 

1.     Knowledge requires truth – or if a statement  is known, then it is true.

2.     If a statement is true, then it can’t be false.

3.     If a statement can’t be false, then it is certain.

4.     Therefore, if a statement is known, it is certain.

 

But the interpretation on which the second premise is true would run like this:

 

5.     Knowledge requires truth – or if a statement  is known, then it is true.

6.     It can’t be that a statement is both true and false.

7.     If a statement can’t be false, then it is certain.

8.     Therefore, if a statement is known, it is certain.

 

But that is not valid. What can validly be inferred from lines 5-7 is:

 

9.     Therefore, if a statement is known, then it is true.

 

– which, since it appeared already in line 5, doesn’t need the help of 6 or 7!

 

 

I indicated at the beginning that there was another, and probably more important, way Bill’s argument went wrong. Thankfully, it can be addressed much more quickly. Also thankfully, seeing that there is a mistake here does not depend on the logical points rehearsed above, so, for the sake of this discussion, we can take his argument at face value.

 

That argument tried to establish a link between the claim that if a statement is true, then it can’t be false and a claim about the certainty of the statement. But he cannot forge the link he wants because the first claim, if it is true at all, is a point of logic, while the second, if true, has to do with the epistemic status of the statement – with whether the person making the statement has lived up to whatever the relevant epistemic standards are for being (not just feeling) certain of it.

 

In other words, since the first claim is, if true, a point of logic, it applies to all true statements, whether known or believed or not. It applies, for example, to one or the other of the following pair:

 

a.      There is an intelligent alien race inhabiting a planet within ten light-years of earth.

b.     There is no intelligent alien race inhabiting a planet within ten light-years of earth.

 

Now, I don’t believe (or disbelieve) either of those, and I don’t suppose anyone here knows which one is true. Nevertheless, one or the other is true, and so, the premise that if a statement is true, then it can’t be false applies to whichever one that is. Obviously, that goes no way to showing that one of those statements is certain in any epistemologically interesting sense.

 

The point can be made in another way by constructing a parallel to Bill’s initial argument, using true belief instead of knowledge:

 

1.     True belief requires truth – or if a statement is truly believed, then it is true.

2.     If a statement is true, then it can’t be false.

3.     If a statement can’t be false, then it is certain.

4.     Therefore, if a statement is truly believed, then it is certain.

 

That argument is exactly as good (or as bad) as Bill’s initial argument, but it’s preposterous that true belief is sufficient for certainty. That’s because, to repeat, the relevant sense of “certainty” is a matter of satisfying epistemic standards; it’s not something that logically follows just from the truth of a statement.

Rob
_____
Rob Bass
rhbass@comcast.net
http://personal.bgsu.edu/~roberth