[Note for bibliographic reference: Melberg, Hans O. (1997), More on internal and
external negation, http://www.oocities.org/hmelberg/papers/970419.htm]
More on internal and external negation
by Hans O. Melberg
Here is the general pattern of a common inference: If A is not true, B must be true!
For example, B is not a Christian, so he must be an atheist. As I tried to explain last
week, this kind of inference is false. The basic problem is that there are often more than
two alternatives. Or, in abstract terms, when A is not true, this does not necessarily
imply that B is true, since there is also a third alternative - C - which may be true.
Again, to be concrete, when a person is not religious, he need not be an atheist, since he
might instead describe himself as an agnostic. Last week I considered only three
alternatives: Christians, atheists and agnostics. I now want to add a fourth category: the
Satanists.
Assume you live in a community of mainly Christians. You are then told that your
neighbour is not a Christian. Ignoring, for the moment, the option that he might be a
Muslim or of some other faith, you have three options:
1. To believe he is an agnostic
2. To believe that he is an atheist
3. To believe that he is a Satanist
The first point is thus to recognize that there are more than two alternatives (Christians
vs. Not Christians).
The choice between the three alternatives depends on how you define the opposite of
"I believe in God." To create the opposite of a statement, we simply insert a
"not" in the sentence. If you go infer from the statement "Your neighbour
is not a Christian" that "He is a Satanist" then you are inserting the
"not" right before God. Thus the opposite of "I believe in God"
becomes "I believe in not-God." The two other alternatives are, as described
last week and ignoring grammatical rules, "Not I believe in God" (agnostic) and
"I [do] not believe in God" (atheist). Thus, the negation of "I believe in
God" depends on the position in which you insert the "not" in the sentence
"I believe in God." [Note, this is not entirely accurate, see Jon Elster's Political
Psychology , p. 73ff, for a more accurate description.]
Once again, the question is: So what? Do these examples have some real life
significance? Last week I mentioned the implications for the design and inferences drawn
from a questionnaire. I also mentioned how a lack of awareness of these problems might
make people draw false inferences - in short, to arrive at false beliefs. (Even if they
appear to be based on statistics). Lastly I mentioned how these problems might make the
average a bad statistical descriptor of a population. Now, I want to add a few more
reflections on the significance of the problem.
One potentially significant implication, could be for the practice of
psychology/psychiatry - both in terms of explaining the behaviour of people, and in
creating therapeutic treatments [I owe the inspiration for this idea to Jon Elster]. A
person who consistently ignores the fact that statements have many possible negations,
might behave in a very paranoid fashion. For example, everybody who is not his friend,
becomes his enemy (i.e. there are no neutrals). In this case we can explain paranoia by
our theory of negation (in terms of where he inserts the "not"), and we might
try to create a treatment based on this realization. I suspect the solution is a bit more
complicated than simply proving to the man that there are more than one possible negation,
yet I believe a possible treatment could be based on the idea that the man must come to
realize/experience that neutrality (or indifference) is a possible attitude toward him.
Jon Elster also presents another potentially significant implication: To explain the
actions of a regime. For example, Zinoviev - according to Elster - describes the Soviet
society as one in which the core irrationality is the confusion between internal and
external negation, and the impotence that follows from the ensuing contradictions. (The
reader is referred to Elster's book Political Psychology for a more detailed
description).
In conclusion, I do not know if I am much closer to a real understanding of all the
implications of the logic of negation. I will however, close this chapter for now, untill
a reader or a book give me some inspirational input.
[Note for bibliographic reference: Melberg, Hans O. (1997), More on internal and
external negation, http://www.oocities.org/hmelberg/papers/970419.htm]