Definitions of 'weight of argument'
Given two sets of propositions, the set h of premises and the set x of conclusions, an argument xh is according to Keynes a logical relation, knowledge of which permits one to infer x from h with a certain degree of rational belief p that defines the probability of x given h. The epis- temic and pragmatic relevance of an argument depends, in his view, not only from its probability but also from its 'weight' (TP, pp. 72-85, 345-9; GT, pp. 148 and 240). The concept of 'weight of argument' (also called by Keynes 'weight of evidence') has been interpreted in different ways by readers of TP and GT. We find in TP different definitions that at least at first sight do not seem altogether congruent:
1. According to a first definition often repeated in Chapter 6 of TP, titled 'The Weight of Argument', 'one argument has more weight
than another if it is based upon a greater amount of relevant evidence' (TP, p. 84).
- 2. According to an alternative definition that may be found in the same chapter, the weight of argument 'turns upon a balance ... between the absolute amounts of relevant knowledge and of relevant ignorance respectively' (TP, p. 77).
- 3. Finally, in Chapter 26 the weight of argument is defined as 'the degree of completeness of the information upon which a probability is based' (TP, p. 345).
Each of these three definitions aims to measure the degree of knowledge relevant for probability; however, the first measure is presented as absolute, the second measure is relative to relevant knowledge, and the third is relative to complete relevant knowledge. In my opinion, contrary to their initial appearance, the three definitions, correctly understood, are fairly consistent and may be represented by the same analytic measure.
Most interpreters picked up the 'absolute' definition, identifying the weight of argument simply with the amount of relevant knowledge K, perhaps because it appears at the very beginning of the Chapter 6 on the weight of argument and it is frequently referred to, explicitly and implicitly, in TP. Therefore, most interpreters believe that a satisfactory measure of the weight of argument may be given simply by:
In my opinion, however, this measure is inconsistent with Keynes's crucial assertion that additional evidence may increase relevant knowledge without increasing the weight of argument: '[T]he new datum strengthens or weakens the argument, although there is no basis for an estimate how much stronger or weaker the new argument is than the old' (TP, p. 34). This reflection clarifies the rationale of the second definition. Unfortunately, this important clarification may be found not in Chapter 6, on the weight of argument, but in Chapter 3, on the fundamental ideas of TP, before the concept of weight of argument is explicitly introduced, which may explain why Keynes's assertion has been often neglected. We notice that, according to Keynes, new evidence may reduce the weight of argument as it may alert the agent to the fact that the gap between her relevant knowledge and complete relevant knowledge is greater than she previously believed.
Consistently with the preceding considerations and the second definition of weight of argument, Runde (1990) suggests the following measure:
This simple ratio between relevant knowledge and relevant ignorance takes account of the exigency, emphasized by Keynes in his second definition, of duly taking relevant ignorance into account. This measure implies that, unlike in the first definition, the weight of argument increases only if relevant knowledge increases more (decreases less) than relevant ignorance. However, it is not fully satisfactory because it is meaningless when relevant ignorance tends to zero (complete relevant knowledge) as this measure takes values tending towards infinity.
We may overcome these shortcomings by introducing the following measure, which is derived from the third definition:
In this case the weight of argument increases only if relevant ignorance diminishes. This measure has the advantage of being clearly defined even in the extreme case of complete relevant knowledge (V (x/h) = 1). In addition, its range of values from 0 to 1 is consistent with the usual measures of uncertainty, such as probability, and conforms to the range of values that Keynes seems to have in mind (see TP, p. 348).1 Therefore I conclude that the third definition, as expressed in measure (3), is the most general and satisfactory of the three definitions of weight of argument, as it explicitly takes account of the relation between relevant knowledge and both relevant ignorance and complete knowledge. Therefore, in what follows, I will define the weight of argument as in measure (3).