Georg Ivanovas From Autism to Humanism - systems theory in medicine

3. Epistemology

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3.2 Russell, the paradox and the therapy of diseases

Modern epistemology started June 16, 1902. This day Bertrand Russell wrote a letter to Gottlob Frege pointing out that Frege had not solved the ‘liar’s paradox’. The ‘liar’s paradox’ dates back to the Cretan Epimenides saying: “All Cretans are liars” or in a more strict form: “I am lying”. Logicians of all times had been preoccupied with this paradox which is true when it is false and false when it is true.

This paradox is not only a philosophical and mathematical riddle.

In pushing the button of an electric bell the electricity begins to circulate in order to interrupt the circulation, so that electricity can flow again. Clock-genes (chap. 4.7) use exactly the same mechanism. They produce a protein inhibiting the production of this substance. Such negative feedback mechanisms are characteristic for most, if not all processes of the living. That is, the liar’s paradox is a central principle in biology.

Russell did not really solve the paradox. But he made some first steps for a better understanding of the structure of the argument. .

Russell starts from so-called ‘propositions’.

„We mean by ‚proposition’ primarily a form of words which express what is either true or false........’Socrates is a man’ and ‚Socrates is not a man’. …..A ‘propositional function’, in fact, is an expression containing one or more undetermined constituents, such that, when values are assigned to these constituents, the expression becomes a proposition. In other words, it is a function whose values are propositions….’x is human’ is a propositional function; so long as x remains undetermined, it is neither true nor false; but when a value is assigned to x it becomes a true or false proposition……A ‘propositional function,’ in fact, is an expression containing one or more determined constituents, such that, when values are assigned to these constituents, the expression becomes a proposition” (Russell 1930: 155-156).

In other words, we start with premises that lead to an undetermined conclusion, the propositional function. Statements on the basis of this function are propositions which are either true or false.

In medicine, diseases are propositional functions. Diseases are defined in respect to anatomical, physiological and/or biochemical alterations which constitute our premises. That is, we regard it as meaningful to model diseases in this way (chap. 3.4). The next step is that someone might suffer from the disease defined in the premise (e. g. diabetes), thus representing (logically) a proposition (a diabetic). “Terms satisfying ‘φx exists’ means ‘φx is sometimes true” (Russell: 165). Diseases are thus potentialities on a logical curve but do not exist as such.

In a first paper in which I combined Russell’s ideas with clinical practice I questioned some epistemological basics of randomised clinical trails (Ivanovas 2001). This provoked strong reactions. One reader declared the problem to be diagnostic in nature, not logical. He claimed that although the aim might be to treat the disease, very often this is not practical as the disease is unknown. Thus, only symptomatic treatment is available (Pischon 2001).

Similar was the reaction to an article in the BMJ which doubted the diagnosis of anxiety and the strategy of its medical treatment (Shorter/Tyrer 2003). In a letter a reader claimed that mental disorders are precisely diagnosable and that “drugs are used only to treat disease (cause) not symptoms (effect)” (Weeks 2003).

These are issues which only can be tackled with a sound logic as there seems to be some confusion about what is actually treated. Symptoms? Diseases? People? What are the definitions? Can a symptom be treated without treating a disease? Can a disease be treated without treating symptoms?

For understanding and solving formal paradoxes (and other confusing states) Russell and Whitehead developed the ‘theory of classes’ or 'theory of logical types' in their Principia Mathematica (1911-13).

A logical class is formed when a propositional function is sometimes true (Russell: 160). If there is someone suffering from diabetes the class of diabetics would exist.

The core of Russell’s ideas was that statements true for the members of a class (diabetics) are logically different than statements about the class (diabetes). “Statements about functions are functions about functions” (Russell: 186). A paradox arises when statements about a class are used for the members of the class and vice versa (Russell: 136). The theory of classes prohibits in doing so.

This kind of paradox shall be demonstrated with a simple example.

There is the enterprise Ford as the class and the car Ford as a member of the class. Statements about the class (enterprise) are not valid for the member of the class (car) and vice versa. The car can drive with high speed, the enterprise not; the enterprise can be in financial difficulties the car never; if a car is sold the enterprise is not sold and so on. Until here it is obvious. The difficulty (and the paradox) arises if we sell the enterprise. One could argue that selling the enterprise all unsold cars are sold, as well, but stay unsold. Such paradox statements are neither true nor false, they are, according to Russell, just meaningless.

The relation between the diagnosis and the symptom follow the same principles:

  1. A statement about symptoms is no statement about the disease: we might have an unclear situation, in which we cannot be sure whether the symptoms belong to one disease or another.
  2. A statement about a disease is no statement about the symptoms: In appendicitis we might see pain in the lower right quadrant (McBurney), local or general resistance, local or crossed rebound and so on. But nothing of that might be present in this form and nothing proves appendicitis alone.

Of cause there has been much criticism for Russell’s theory of types because it simply prohibited a logical operation. One of the first to contradict Russell was Wittgenstein, when he referred to recursive functions (chap. 4.2) in his argument 5.51 of his Tractus logo-philosophicus. He maintained that a function cannot be its own argument, whereas an operation can take one of its own results as its base (Wittgenstein 1922). Gödel developed his incompleteness theorem (chap. 3.3) by using the statements of the Principia Mathematica recursively and showed that a complete proof is not attainable (Guerrino: 79). Spencer-Brown (who later developed his own recursive formalism) dismissed the basic approach of the Principia Mathematica altogether (Spencer-Brown, 1997: 126).

However, Günther, whose polyvalent logic is quite close to Russell’s ideas, says that all the critics of Russell missed the main semantic question (Günther, 1979: 53) as they are only concerned with syntax. In fact, Russell’s theories were the starting point for a lot of research on semantics (Korzybski, Watzlawick, Bateson).

Russell’s theory of types is rarely used today. Mathematicians and logicians tend to claim that the problem he posed is solved. At most, the theory of types might be helpful to investigate the soundness of arguments, to detect circular reasoning and to avoid that a premise becomes its own proof (Guerrino: 79). But actually Russell’s ideas are still crucial for the understanding of living processes as will be demonstrated later (chap. 6.4). Also the science of emergence (chap. 4.10) deals exactly with the questions Russell posed: How is the relation of parts (for example the genes) and the class (the phenotype or behaviour). How can there be an upward causation (from the elements to the class) or a downward causation (from the class to its elements)? Or are things totally different?

In order to investigate such issues, one has to be aware with which level of abstraction one is dealing. With elements/parts? With classes? With classes of classes? If these categories are not absolutely clear, all reasoning becomes meaningless.

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