Logic of probabilistic language 1

Probabilistic language logic in medicine

Every scientific idea (whether in medicine, architecture, engineering, chemistry, or any other subject), when put into practice, is subject to small errors and uncertainties. Mathematics - through probability theory and statistical inference - helps to precisely control and thereby contain these uncertainties. It always has to be considered that in all practical cases "the outcomes also depend on many other factors external to the theory", whether they be initial and environmental conditions, experimental errors, or something else.

All the uncertainties about these factors make the theory–observation relationship a probabilistic one. In the medical approach, there are two types of uncertainty that weigh the most on diagnoses: subjective uncertainty and casuality.

It becomes essential, therefore, in this scenario to distinguish between these two uncertainties and to show that the concept of probability has different meanings in these two contexts.

We will try to expose these concepts by linking each crucial step to the clinical approach that has been reported in the previous chapters and in particular the approach in the dental and neurological context in contending for the primacy of the diagnosis for our dear Mary Poppins.

Subjective uncertainty and casuality

Let us imagine asking Mary Poppins which of the two medical colleagues — the dentist or the neurologist — is right.

The question would create a kind of agitation based on inner uncertainty; therefore, the notions of certainty and uncertainty refer to subjective epistemic states of human beings and not to states of the external world, because there is no certainty or uncertainty in that world. In this sense, as we have mentioned, there are an inner world and a world outside ourselves that both do not respond to canons of uncertainty, yet of probability.

Mary Poppins may be subjectively certain or uncertain as to whether she is suffering from TMDs or a neuropathic or neuromuscular form of OP: this because "uncertainty" is a subjective, epistemic state below the threshold of knowledge and belief; hence the term.

Subjective uncertainty

Without a doubt the term ‘subjective’ scares many, especially those who intend to practice science by pursuing the healthy ideal of ‘objectivity’, as this term is perceived by common sense. It is, therefore, appropriate to make some clarifications on the use of this term in this context:

• ‘Subjective’ indicates that the probability assessment depends on the information status of the individual who performs it.

• ‘Subjective’ does not mean arbitrary.

The so-called ‘objectivity’, as perceived by those outside scientific research, is defined when a community of rational beings shares the same state of information. But even in this case, one should speak more properly of ‘intersubjectivity’ (i.e. the sharing, by a group, of subjective opinions).

In clinical cases — precisely because patients rarely possess advanced notions of medicine — subjective uncertainty must be considered. Living with uncertainty requires us to use a probabilistic approach.

Casuality

The casuality indicates the lack of a certain connection between cause and effect. The uncertainty of a close union between the source and the phenomenon is among the most adverse problems in determining a diagnosis.

In a clinical case a phenomenon $A(x)$ (such as for example a malocclusion, a crossbite, an openbite, etc ...) is randomly associated with another phenomenon $B(x)$ (such as TMJ bone degeneration); when there are exceptions for which the logical proposition $A(x)\rightarrow B(x)$ it's not always true (but it is most of the time), we will say that the relation $A(x)\rightarrow B(x)$ is not always true but it is probable.

«We are moving from a deterministic condition to a stochastic one.»

Subjective and objective probability

In this chapter, some topics already treated in the fantastic book by Kazem Sadegh-Zadeh, who tackles the problem of the logic of medical language, are taken up again and we reshape their content by referring them to our clinical case of Mary Poppins, to keep our understanding closer to dental contexts.

Random and subjectively uncertain events are said to be probable; consequently, casuality and uncertainty are treated as qualitative, comparative or quantitative probabilities.

To clarify this concept, let us go back to the example of Mary Poppins. A doctor, having heard her symptoms will be able to say that:

1. Mary Poppins is probably suffering from TMDs (qualitative term).
2. Mary Poppins is more likely to have TMDs than neuropathic OP (comparative term: number of diagnosed cases of TMDs versus _nOP.
3. The probability that Mary Poppins has TMDs is 0.15 (quantitative term, relative to the population).

Subjective probability

In a context of human subjective uncertainty, the probabilistic, qualitative, comparative and/or quantitative data can be interpreted as a measure of subjective uncertainty by the clinician, in order to make the 'states of conviction' numerically representable.

For example, saying that "the probability that Mary Poppins is affected by TMDs is 0.15 of the cases" is the same as saying "in the measure of 15%, I believe that Mary Poppins is affected by TMDs"; which means that the degree of conviction is the degree of subjective probability.

Objective probability

On the other hand, events and random processes cannot be described by deterministic processes in the form 'if A then B'. Statistics are used to quantify the frequency of association between A and B and to represent the relationships between them as a degree of probability that introduces the degree of objective probability.

In the wake of the growing probabilization of uncertainty and randomness in medicine since the eighteenth century, the term "probability" has become a respected element of medical language, methodology and epistemology.

Unfortunately, the two types of probability, the subjective probability and the objective one, are not accurately differentiated in medicine, and the same happens in other disciplines too. The fundamental fact remains that the most important meaning that probability theory has generated in medicine, particularly in the concepts of probability in aetiology, epidemiology, diagnostics and therapy, is its contribution to our understanding and representation of biological casuality.