While exchange rates behave as logical processes in themselves, separately they are the result of an illogical system (process).
By: Miguel Alejandro Hayes
The most important contributions to mathematics and the most important advances in modern logic are found in set and function theories .
Its use offers an organized view of almost any process (if it’s organized), including the Cuban monetary system. For example, the relationship between sets allows for the explanation of processes and the modeling of these processes, that is, the translation of them into mathematical functions.
The rule states that each element of set A corresponds to a single element of set B, although one element of set B may correspond to several elements of set A, always within a certain theoretical framework (rationality) that gives meaning (logic) to the relationship. Example:
When this rule is met, the existence of logical processes is verified, that is, continuity in the behavior of one variable explained (causally) by another. Such conditions allow these processes to be rationally susceptible to refinement or optimization through tools such as differential calculus.
Then, if we were to apply the Cuban exchange rate multiplicity relationship to the prism of set theory, with the aim of having a logical approximation to what the possible process could represent, we would have the following:
On the left, the two Cuban currencies; on the right, the corresponding exchange rates. As can be seen, the relationship between a currency and its assigned exchange rates breaks the rules of set relations. We are therefore faced with the result of an irrational model, one that cannot be rationalized, lacking a coherent structure, discontinuous—in other words, illogical in itself. If the monetary model is illogical in itself, it will not be logical for the Cuban economy.
Let’s look closely (all the logical information available is in this diagram).
Let’s try to make each element of the set A correspond to a single element of the set B. How can we achieve this?
The first option would be to delete the lines and leave only one for each element of set A. However, the diagram doesn’t provide any logical criteria for rationalizing the removal of lines from within. For all intents and purposes, all lines are equal.
Any criterion responds to information and rationales not generated within the model. The line chosen to be placed at each point in A is not based on a rationalization of the model; it could be based on empathy, superstition, tradition, or some external calculation, but never something derived from the internal logic of the diagram. Therefore, adjusting it has no solution in itself.
On the other hand, rectifying the existing diagram would be equivalent to accepting the results (the relationships) of the theoretical framework that generated it. But when it comes to rationalizable structures and processes, such a practice makes no sense.
The diagram reflects the results of an (i)logical model. Using a criterion outside the (i)rationality of the diagram as a solution (eliminating lines) does not escape remaining within the framework of that irrationality, since it accepts, as a logical starting point, terms resulting from an (i)logical model. It is remaining within the same limits.
Therefore, the most coherent thing would be to simply throw away this diagram (of course, the real relationship that is represented as well) and make a new one: one that from the beginning generates a single correspondence to each element of the set A. Make a logical diagram.
Let’s look at it mathematically now, starting from the following graph:
As can be seen, the result is not a function, that is, a logical process, but rather a set of scattered points for each value of CUC. From the perspective of differential calculus, since the relationship lacks continuity and stability, it has no logic and cannot be optimized. You cannot optimize (find the best location within the process itself) something that lacks a coherent, continuous, and stable order. You cannot derive logic from something that lacks logic.
However, the very behavior of the exchange rates separately, which, as can be seen in the following diagram, do function as logical processes in themselves, creates the illusion that leads people to try to study the relationship between both currencies as if they were also logical processes.
And while exchange rates behave as logical processes in themselves, separately, they are the result of an illogical system (process), which becomes evident when looking for and graphing the relationship between the different exchange rates. Therefore, seeking a foundation based on these is trying to link things that have no link at all.
In short, working with current exchange rates and seeking an optimal relationship between them is, from a logical standpoint, working with the results of an illogical model and trying to make it logical.
On the other hand, the search for a new exchange rate would also be a move within the price system, and therefore within the current monetary system; it is seeking order within the framework of a model without logic. It is accepting erroneous premises. No illogical system generates a logical model for itself by applying a logical model as a formula, just as the defined as a multiplier of the indefinite produces the indefinite.
The transfer from multiplicity to a single rate, within the same monetary system, would imply maintaining the previous distortions, which, to be sure, leaves it unclear where they might appear in terms of resulting prices.
The solution, from a logical point of view, is none other than to generate (and everything that would entail) a new price system (as the foundation of the monetary system), that is, to reset the current monetary system.
Even if, from a practical (historical) perspective, a single rate is necessary as a solution, this could only be (from a monetary perspective) an inevitable step toward pursuing a new monetary system (a new price system) as the ultimate goal. Therefore, unification would only make sense if it generates an effect on the economy that would serve as the basis for generating such a change in the price system, driving favorable (expansionary and linked) changes in business cycles.
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