Exclusion of Ideologies and Ideology-Theory Mixtures

Positivism requires [39] that a theory does not recommend courses of action, being restricted to describing characteristics of the universe. The characteristics of the universe that are described may include the consequences of particular actions, but the desirability or otherwise of those consequences is a matter for speculation outside of positivist knowledge. In other words, in terms of the definitions being used here (chapter 1,) neither pure ideologies, which consist solely of values, nor ideology-theory mixtures, which include both postulates and values, may enter into positivist knowledge, which includes only pure theories, consisting solely of postulates. An example is [39] that a positivist would not accept the statement ``penicillin should be administered in cases of pneumonia'' into scientific knowledge, requiring it to be separated into the postulate ``penicillin is an effective cure for pneumonia,'' and the value ``it is good to cure the sick,'' and accepting only the former into scientific knowledge.

This third characteristic of positivist knowledge is concerned with values, and excludes them from knowledge. At first glance, it may appear that Bayesian knowledge also concerns itself only with inferences about postulates.

However, there may also be a way of applying the Bayesian inference process to values. In the definitions of ``ideology'' and ``theory'' used in this paper (chapter 1,) there is, deliberately, a striking logical similarity between the descriptive and the prescriptive. It is easy to imagine building theories about the ideology to which a particular person subscribes, then attempting to draw inferences, about the truth of those theories, from that person's observed policies; this is the nature of Patrick and Wallace's [52] Bayesian analysis of theories of the design principles behind stone circles. Having accepted this, it is entirely conceivable that, as Rawls [59] has explained, one could choose one's own ideology, by an inference process, from one's intuitive preferences for particular policies. Feynman [21] hinted at a similar analogy, when he compared the testing and possible rejection of theories in physics with the testing and possible rejection of political parties in democratic government. One could, further, use Bayes' theorem (equation 7) as the inference rule, updating from the prior probability $P(I)$ of choosing a particular ideology $I$, to the posterior probability $P(I\vert y)$, given that one intuitively prefers policy $y$, using the likelihood $P(y\vert I)$ and the marginal likelihood $P(y)$. A Bayesian who is interested in prescriptive ideologies as well as descriptive theories can, therefore, develop knowledge about both by the same methods. However, this will not be the thrust of this paper; where a choice of policy becomes relevant, it will be considered to be made by someone who believes with certainty in a single ideology.