Truth and falsehood are distinctions within the space of meaning. A form in itself is not divided into true and false: the question of truth arises in the relation between what is asserted and reality. Therefore, an operation performed on forms cannot, by itself, establish the truth of a statement. Let us examine what happens when the result of such an operation is taken as a measure of alternatives concerning truth.
Normalization of Forms
Here, normalization means assigning equal weight to each element of a selected list of propositions. The rule operates on the form of the list: it does not examine what each proposition corresponds to. Its result depends, among other things, on which elements have been chosen to count as separate.
Suppose the snow under consideration is white. Take two statements:
- A: “The snow is white.”
- B: “The snow is not white.”
If we normalize these two elements, each receives a weight of 1/2. Now expand B into one million statements about particular colors other than white, and assign equal weight to each element of the new list. With one element A and one million elements within B, the formal weight of A becomes 1/(1 000 001), while the combined weight of B becomes 1 000 000/(1 000 001).
The color of the snow has not changed. What has changed is the unit of counting and the granularity with which the alternatives are divided. Further distinctions between shades can reduce A’s share yet again without adding any grounds for considering the snow not white.
Equality of Elements and Weight of Categories
At the first step, A and B functioned as two categories. At the second, the single element A is compared with a multitude of elements within B. Assigning equal weight to the terminal elements gives the categories different aggregate weights. Thus, formal equality of elements does not ensure equal treatment of categories when one is broken down in greater detail than the other.
This example does not establish a general law according to which truth can always be expressed in only one way while falsehood can be expressed in many. It shows how the result depends on the chosen partition. Under the stated conditions, enumerating false alternatives in greater detail increases their aggregate formal weight. Calling this quantity the probability that those alternatives are true would introduce an assumption that the enumeration itself does not provide.
The statement “The snow is not white” and a million specifications of possible colors do not constitute a million independent pieces of evidence against the whiteness of the snow. The number of propositions concerns the organization of forms; evidence concerns what allows us to judge reality.
The Limit of the Inference
If a procedure for discovering truth treats the number of equally weighted forms as the weight of an alternative concerning truth, its result can be altered merely by subdividing the list. In this sense, normalization can reduce the relative weight of a true statement and increase the aggregate weight of false alternatives. It does not increase falsehood itself or change reality.
If grounds for a statement already exist, merely adding unsupported alternatives does not eliminate those grounds. To judge truth, one must examine the grounds for statements rather than derive their strength from the number of available forms.
The case in which a multitude of conceivable scenarios is set against a statement about an action that actually occurred is examined separately in “Possibility and Action”. The fragmentation of other people’s explanations of an intention and their adoption by the subject are examined in “Self-Knowledge and the Fragmentation of Others’ Opinions”.
