The Global Currency Plot

Logic is the anatomy of thought.
— JOHN LOCKE

Logic is the doctrine of right thinking. It does not tell us what to think, but how to think in order to achieve the right results, arrive at the right conclusions. Logic as a science, traces its roots to the Greek philosopher Aristotle (384–322 BC); he called it “analytics.” According to Aristotle, the most important elements of correct thinking are concepts, judgments, conclusion, and proof.4 The concepts are the basic elements of thinking. They are obtained through definitions: the object to be defined is assigned to a class of objects whose characteristics correspond to those of the object to be defined. Example: A human is a living being. In addition, the definition must indicate how the object—the human—differs from the other objects of the class—the living beings. So, a human is a rational living being. Definitions (in the case of “a human”) must therefore have a common (the living being) and a separating (rational) characteristic (or several).

Concepts are linked to form judgments (or: statements or sentences). Each judgment combines at least two concepts: subject and predicate. The subject is the concept about which something is said, the predicate denotes what is said about the concept. Example: “Gold is yellow.” “Gold” is the subject, “yellow” the predicate. Individual judgments are combined to form conclusions and derive a new judgment from other judgments. A conclusion consists of the preconditions (premises) and the conclusion derived from these.

Aristotle’s syllogism is central. It consists of three elements: there is a (general) major premise (“All men are mortal”) and a (special) minor  premise (“Aristotle is a man”). The conclusion is drawn from these two premises (“Aristotle is mortal”). Conclusions are linked to form evidence. A proof is the logically compelling derivation of a judgment from other judgments by conclusions. However, the judgment that proves another judgment must itself be secured.

If we think through such a chain of evidence, we reach a limit, we come to judgments of the most general character, which in turn can no longer be proven.5 According to Aristotle, the rational human being has the capacity to grasp such general sentences without error. The supreme proposition is the proposition of contradiction: “Something that is cannot simultaneously and in the same regard not be.” Later, three further principles were formulated in philosophy: the proposition of identity (“a equals a”), the proposition of the excluded third (“Between being and non-being of the same object there is no third option”) and the proposition of the sufficient reason (“No fact may be considered correct without there being a sufficient reason for it”).

Since Aristotle, logic has been a central element in gaining and judging knowledge: knowledge gained through experience or insight. If we want to derive knowledge from experience—from observation—this is called induction. However, this raises the induction problem. Example: in the eighteenth century people knew only of the existence of white swans. It was concluded that there were only white swans. But then black swans were discovered in Australia—and the previous assumption turned out to be wrong.

This means no generalizations, no universally valid statements can be derived from individual experiences.6 We cannot accept such an induction conclusion per se as valid and justify it logically. If it were valid per se, then—as far as we assume correct observations—there should never be wrong conclusions. But this is exactly what happens again and again! Moreover, the induction conclusion cannot be justified on the basis of experience. For then one would have to claim that the induction conclusion is valid because so far there have been no observable results that contradicted it. But then we would assume that the induction conclusion is already true, circumvent the problem of justification, and end up with infinite regression.

It should also be noted that a strict distinction must be made between truth and probability. It is often assumed that we approach the truth if there is just a high probability that a particular event will occur. Here we equate the probability w = 1 with truth, the probability w = 0 with falsehood. But (logically) this notion is wrong.

Let us revisit the example of the white swans. Although so far only white swans had been observed (the probability that white swans could be observed was therefore w = 1), it only took one observation of a black swan to unmask as false the inductive conclusion that there were only white swans (so that actually w = 0). We may not deduce truth from a high probability.

Deduction means that we want to gain knowledge by inferring the special from the general: we derive a statement (conclusion) from other propositions (premises), as the following example illustrates:

All swans are white.
This animal is a swan
This animal is white.

“All swans are white” and “this animal is a swan” are the premises, and “this animal is white” is the conclusion. In geometry, for example, theorems (conclusions) are derived from premises. The deductive method guarantees that the conclusions are true if the premises are true. But how do we arrive at true premises? How can premises be recognized as right or wrong?

If it is possible to find a true premise, which furthermore also corresponds to the reality of life, then it is possible in the course of logical deduction to derive from it further true statements about the real world. In this context, the Austrian economist Ludwig von Mises (1881–1973) achieved a successful epistemological breakthrough in the social and economic sciences—which, however, has received far too little attention and appreciation to this day.

Mises convincingly argued that economics is not an empirical science, but that it can only be understood (conceptualized) and practiced without contradiction as an a priori science of action. The starting point underlying Mises’s deliberations—the Archimedean point, so to speak—is the seemingly trivial-sounding sentence “Humans act.” But this sentence has a great significance: it is undeniably (apodictically) true. One cannot negate the sentence “Humans act” without already assuming its validity. The findings that can be derived from this are explained in more detail in the following chapter.

• 4See Hans Joachim Störig, Kleine Weltgeschichte der Philosophie (Frankfurt am Main: S. Fischer Verlag GmbH, 2004), pp. 197 ff.
• 5E.g., W. Stanley Jevons writes, in Elementary Lessons in Logic: Deductive and Inductive (London, 1888), p. 3: “The laws of thought are natural laws with which we have no power to interfere.”
• 6See Hans Poser, Wissenschaftstheorie: Eine philosophische Einführung (Stuttgart: Philipp Reclam jun., 2001), pp. 108–19.