Dictionaries, lexicons and glossaries provide information on meanings that are not, most often, statements that conform to the definition of the mathematical definition of finite sets.
1. The definition of the mathematical definition of finite sets can be summed up in three propositions.
A finite set is definable in extension or intention.
An extension definition lists all the objects that are part of the set under consideration.
A definition in intention states a property or properties that all the elements of the set under consideration and they alone possess.
2. It is to be expected that the definitions of economic objects and acts will be for the most part understood.
The statement of a definition in intention can often be intertwined with a partial enumeration. For example, economic wealth is the product of human labor, such as tools, food, and clothing, which is most often exchanged for a quantity of money and for the rest directly among themselves. The partial enumeration could be the beginning of an extended definition if all tools, food, and clothing were traded economically. However, this is not the case because of those that their owners have produced and that they keep to themselves, among other reasons. By this kind of impossibility, in economics the definitions admissible in the logic of finite sets are for the most part comprehensible. This fatality increases the need to bring great care to this discipline beforehand with literary mathematics.
3. Definitions that are admissible in set theory, other observations of reality, and reasoning use semantic conventions.
This is why economic thought is only brought to its highest point of rigour by explicitly mentioning the major naming conventions it uses. The most typical verb clauses in economic theory are reputed to be "all other things being equal" and "sooner or later". In fact, the clause most necessary for the elaboration of genuinely scientific economic theory is: "let us agree to call..." – followed by a word or expression – "the whole..." – followed by an acceptable definition in the logic of finite sets.
4. Despite the propensity for relativism, the principle of the search for truth is simple.
A theory is a series of statements that express a relationship between several terms. In other words, a theory is a series of propositions. A proposition that describes an aspect of reality is true when this description is in accordance with the facts. A theory, however partial, is itself completely true when none of its propositions is contradicted by a true proposition, whether or not the latter is part of the theory presented. Karl Popper included A Supplement to the Critique of Relativism (1961) at the end of The Open Society and Its Enemies13. It reads:
"The main philosophical disease of our time is intellectual relativism and the moral relativism which, at least in part, stems from it. By relativism, or skepticism if one prefers this term, I mean the doctrine according to which any choice between rival theories is arbitrary: either because objective truth does not exist; either because, even if we admit that it exists, there is in any case no theory that is true, or (without being true) closer to the truth than another; or because, in cases where there are two or more theories, there is no way to decide whether one is superior to the other. Some of the arguments advanced in support of relativism flow from the very question, "What is truth?" to which the convinced skeptic is sure there is no answer. But, to this question, one can reply in a simple and reasonable way – which would probably not satisfy our skeptic – that a statement or statement is true if, and only if, it corresponds to the facts14. / What does it mean to "correspond to the facts"? Although a skeptic or relativist may find it as impossible to answer this question as it would the previous one, it is actually as easy and even almost trivial. For example, every judge knows well what a witness means by truth: it is precisely what corresponds to the facts. We must make a clear distinction between knowing what truth means and having a means, a criterion, to decide whether a statement is true or false. Most of us don't know the criteria for determining whether a banknote is genuine or fake. But if we found two notes bearing the same number, we should have good reason to declare that one of them [at least] is false: an assertion which would not be deprived of meaning by the absence of a criterion of authenticity. It is, in my opinion, the requirement of a criterion of truth that has led so many philosophers to believe that it is impossible to answer the question: "What is truth?" But the absence of this criterion does not render the notion of truth meaningless, any more than the absence of a criterion of good health renders the notion of health meaningless. In the absence of any criteria, a sick person may seek to regain his health, and a man who has made a mistake may seek the truth. / One of the direct results of Tarski's work on truth is the logical theorem: there can be no general criterion of truth. This theorem is well-founded, and it is based on the very notion that truth is the correspondence with facts: that is, on a notion for which we have no criteria. The unreasonable requirement of the philosophies of the test, if it had been complied with in this case, would have prevented us ever from arriving at this logical result – which is of great importance. Certainly, there is a kernel of truth in skepticism and relativism, namely that there is – in fact – no general criterion of truth. But we have no right to conclude from this that the choice between rival theories is arbitrary. It simply means that we can make a mistake in this choice: that we are fallible. / ... / It is an illusion to believe in scientific certainty and the absolute authority of science; Science is fallible because it is human. But this does not give reason to skepticism or relativism. We may be mistaken, of course; It does not follow that the choice we make between several theories is [inevitably] arbitrary, that we cannot learn, and get closer to the truth. »
5. The selection of scientific ideas is, in the long term, rational.
At the beginning of 2008, Raymond Boudon enriched the encyclopaedic collection Que sais-je? Presses Universitaires de France by Le relativisme16.The observation that there are no general criteria of truth and scientificity is exposed, with a philosophically more prestigious and didactic reference to peddle than the one used by Popper in the excerpt quoted above. Boudon does so in a passage16 deserves to be quoted here in full (the footnotes are additions for the purposes of the present quotation, the underlining is by the author cited):
"Two main arguments can be made against cognitive relativism17.
"1 / As Kuhn indicates20, the selection of scientific ideas reveals the action of irrational factors in the short term. This does not exclude that, in the long term, this selection will be rational. Lavoisier is objectively right against Priestley, even if the discussion of Priestley's theory of phlogiston20shows that the positions taken by the scientists involved in the debate were often inspired by irrational motivations. It is therefore only if the distinction between the short and the long term is neglected that the principle of the excluded third can be applied20 and declared that since the discussion between scientists is not exclusively rational, the selection of scientific ideas must be regarded as irrational. But, once this distinction is taken into account, the question of whether discussions between scholars are rational or not is disqualified by its very formulation.
"2/ The same applies to the conclusions that have been drawn from the powerlessness of the philosophy of science to determine the criteria for demarcating science and non-science. We have never been able to identify the criteria in question. But one can apply to scientificity a decisive remark of Kant's on truth21; it is not because there are no general criteria of truth that it does not exist. To seek the general criteria of truth, he ironically, is to seek to milk a goat. However, truth is not an illusion.
"Kant means that there is no finite set of criteria that can be applied in the manner of a checklist to determine whether a theory is true. On the other hand, in many cases one can decide with certainty in favor of one theory against another. This is what the history of science teaches us. We can accept the theory proposed by Torricelli and Pascal of the physical phenomenon that was to give rise to the barometer and reject the theories of Aristotelian inspiration because the first better accounts for the phenomena observed and does not introduce the idea that nature abhors a vacuum. In other cases, other criteria will make it possible to decide between competing theories. Thus, the criteria that make it possible to choose between the theories explaining the extinction of the dinosaurs are partly different from those that make it possible to decide between the theories of Priestley and Lavoisier. It is precisely because it is possible to determine on the basis of solid reasons whether one should prefer one theory to another that some theories irreversibly disappear in favor of theories deemed preferable in the light of well-defined criteria that vary from one case to another.
"Kant's remark on truth can be applied to scientificity. There are no more general criteria of scientificity than of truth. As soon as theories can give rise to comparisons leading to an indisputable arbitration, they give the impression of being scientific. But it is difficult to go beyond in terms of precision. There are no general criteria for scientificity, but scientificity exists. ».
6. What is true for truth and scientificity is valid for objectivity.
The most damaging consequence of the negation of the possibility for knowledge to access reality is to eliminate from the field of consciousness the cultivation of the virtues of objectivity. This regression is aggravated by the undue attribution, but as a rule in subjective political economy, of an economic exchange value to knowledge in itself, in other words to knowledge in itself (more on this subject in the next chapter).
7. In economics, too, the claim of pure description is fallacious.
In Relativism , two pages of which have just been quoted, Raymond Boudon, at the beginning of his third chapter, entitled Explaining Beliefs, asks the question: "Should we accept on the other hand the opposition often proclaimed between normative knowledge and descriptive knowledge?" At least in economic theory, the descriptive is very often, if not always, normative, positive or negative. In any case, to describe is in itself to recommend seeing things in this way and, in economic affairs, to administer them according to what is held, explicitly or implicitly, to be normal and abnormal. To devote economic theory — economic science, the foundation of political economy — to description in the first place in order to ensure its scientificity? It is in reality impossible to stick to it, while pretending to do so is necessary to pass off prejudices as explanations and the particular as general, while giving the impression of sticking to impartial considerations.
8. Pseudo-definition is essential to give in to one's partialities.
The use of acceptable definitions in finite set logic is necessary for economic theory for the same reasons as in other disciplines. The neglect of these reasons is particularly tempting, however, when it comes to economics. This negligence is, in fact, essential to give in to one's partialities when they are closely involved in what I am or believe to be on a daily basis. This is why overcoming them is always difficult and often impossible. Economic subjectivism, in its individualist and collectivist declinations, needs pseudo-definitions to appear rational.
9. Pseudo-definitions are the basis for petitions of principle.
The pseudo-definition favors the petītiō principiī, i.e. the reasoning that holds as true what is to be demonstrated22. The effort to pay attention to the facts required by definition, in the sense of this concept in mathematical logic, opens the way to demonstration, whereas the petītiō principiī obstructs this path. Let's take an example. I hold it to be true that the law of supply and demand mainly governs the formation of all prices. I derive curves and equations from it, and other kinds of considerations, and then I say to myself that it is "therefore" quite true, although I have not demonstrated it, that the law of supply and demand mainly governs the formation of all prices. The avoidance of this petītiō principiī comes of itself as soon as the attention has been sufficiently sharpened by the effort of true definitions. The understanding then lets slip that: 1) "mainly" does not mean "complementarily"; 2) it is all the prices and not a part of them that are in question. This "mainly" and "all" are not in line with the facts.
10. In other words, an agricultural commodity whose price falls when its supply exceeds its demand and rises when it does not.
Noting this in no way prevents us from asking: what determines the objective exchange value of this commodity when there is neither an excess nor an insufficiency of its supply over its demand?24 The same question is formulated in another way: what does the objective exchange value represent at which there is possibly an underbidding or overbidding? The answer to this question completes the avoidance of the petītiō principiī of the law of supply and demand which is supposed to govern mainly the formation of all prices. A theorization by means of pseudo-definitions, petitions of principle and abuses by excluded third parties24reinforces prejudices which in turn facilitate its accreditation. Claims about what economic theory cannot have in common with the "hard sciences" are inadmissible in the light of what these sciences admit is methodologically more elementary: knowing what exactly is at stake.
11. The mathematics of economics is first and foremost literary.
In economics in particular, concepts without equations from a doctor of physics are better than all the equations that one wants to deal with notions. The definition of the definition is a mathematical instrument logically indispensable for the proper use of the rest of the range of mathematical tools, including, in the first place, the rule of three. The choice of words and the assembly of sentences is a mathematical exercise, in which one strives for the maximum accuracy and completeness in the observation of which one is capable, as well as for the minimum of non-contradictions, petitions of principle and other sophisms. To devote oneself to it as an author and reader is to do literary mathematics. Arithmetic, algebra and geometry are, among other things, part of mechanical mathematics. In this matter, doing literary mathematics is essential so that the complementary use of mechanical mathematical instruments participates in the exact resolution of objective problems. Failure to push this effort far enough opens the door to more corruption than could be avoided. Much of the mechanical mathematics in economic research will only become progress after a significant amount of literary mathematics. Not only scientific but also social progress: literary mathematics, once established and more didactically exposed, falls under common sense, while mechanical mathematics falls under the meaning of only the minority of its followers. If the geometric rigour of authoritative economic discourses had progressed significantly, for example since the 1850s or 1950s, the economic pathology would have been greatly reduced, in an almost mathematical way.
12. The proper use of the rule of three is not as simple as it seems.
The rule of three is widely used in economics, as in the work of the engineer, the cook and the doctor, among many others. In Le relativisme, a work cited above, Raymond Boudon helps us to realize that there is every reason to expect that this use lends itself to established consensuses on misconceptions.
"In a famous experiment, J. Tooby and L. Cosmides25asked doctors the following question: 'A disease has a prevalence rate of 1/1,000. There is a test to detect its presence. This test has a 5% false positive rate. An individual is subjected to this test. The result is positive. What is the probability that the individual is actually affected?" / The question elicited false and yet widely shared answers. A majority of doctors believe that, under the conditions described, the subject who tests positive has a 95% chance of actually being affected by the disease. If we average the doctors' responses, the subject who tests positive is assigned a 56% chance of being sick. As for the correct answer..., it is given by just under one in five doctors, exactly 18%. / … The prevalence rate being 1/1,000, per 100,000 people there are an average of 100 sick and 99,900 healthy subjects... However, these 99,900 non-sick people have a 5 out of 100 chance of being declared positive. Hence it follows that there are a little less than 5,000 "false positives" among the 100,000 people. Thus, the probability of being sick when you are positive is 100 / (5,000 + 100), i.e. a little less than 2%. »
In economics, there are many comparisons of percentages that do not have the same base 100; the proportions in relation to aggregates that make it possible to reduce or increase them; correlations that give the impression of cause-and-effect relationships that do not exist or that include a decisive intermediary that is not reported; distribution problems deemed to have no objective solution when they have one. The adage is well known: you can make numbers say anything, sometimes including the truth; to numbers and equations, as well as to econometric models. One of the keys to more relevant political economy, and therefore to economic policies that are themselves more relevant, is of course to pay more critical attention to what is most commonly said on the one hand, and the most cleverly on the other.
13. Scientific law is rigorous.
I have the right to say, if I am convinced, that this phenomenon, whatever its nature, participates in the configuration of economic activities or results from it. On the other hand, I never have the scientific right to affirm that this phenomenon is inherent in all or part of these activities without demonstrating it in one way or another. There is no economic science epistemologically worthy of the name unless it is bound to respect this discipline for all that it admits of principality. A particularly important application of this rule is this: no one has ever demonstrated, and never will demonstrate, that the inclination to maximize profit is inherent in the commercial enterprise. Whether skilfully articulated or spontaneous, a theorization of economics that is based on the affirmation of this inclination is not scientific on this key point. If we add to this the fact that definitions, in the sense of this concept in the logic of finite sets, are only found in a residual way, or even are not found at all for all that is accepted as principal, then there is no doubt that this theorization is fundamentally unscientific.
14. An economic theory is established as rationally as possible by being formally made up of propositions that are not only explicitly stated but also stated before their argument.
The key observations, the articulation of which constitutes a theory, are made by dint of looking with one's own eyes and through reading, of thinking pencil in hand, of losing one's way until one finds landmarks lost to sight. For each of these observations, there is no other way of methodically putting it to the test of reason than to formulate it as concisely and precisely as one is capable of in order to verify its admissibility several times by the argumentation that authorizes it.
Of the "rational selection of ideas", Raymond Boudon notes that it "unfolds... necessarily slowly for an essential reason, namely that the criticism of an idea has little effectiveness in itself as soon as it comes up against 'opinion' and 'social power'."26 Once again, we can illustrate Tocqueville's analysis with an example that came after him in order to underline the importance of his thought for the intelligence of our societies: that of the countless critical essays, from Viktor Kravchenko to Alexander Solzhenitsyn, which denounced the Soviet system, its efficiency and its cruelty. They only shook the non-believers: those who were not convinced that the communist system was a real alternative to the liberal system, both viable and preferable to the latter.