TSFK: Life, the Universe, and Everything

Chapter 1. Decision and Knowledge

Any decision constitutes a choice between possible actions. A choice is determined by a representation of the current state of a system and of the consequences of the available actions. Therefore, a decision depends on knowledge of the situation itself and of its relationships with other phenomena.

If all relevant relationships between an action and its consequences are known, the choice may be justified. If some of these relationships are unknown, the consequences have to be assumed. The greater the number of relevant unknowns, the greater the uncertainty of the result.

This can be represented as follows: an action (A) has a set of possible consequences (C_1, C_2, …, C_n). With complete knowledge of the system of relationships between (A) and (C_i), the choice is determined by the known consequences. With incomplete knowledge, part of the set of consequences or the relationships to them is unknown, and therefore the decision contains an element of assumption.

Consequently, the degree to which a decision is justified is limited by the degree of knowledge on which it is based. It is impossible to obtain a reliable conclusion about the unknown solely from the known if the necessary relationship between them has not been established.

This does not mean that incomplete knowledge makes a decision impossible. It means that every decision made before the relevant uncertainty has been eliminated contains a probability of error.

The following question arises: is there a limit beyond which uncertainty can in principle be eliminated?

Chapter 2. Finiteness and Infinity of Knowledge

The amount of possible knowledge is determined by the structure of the reality that must be known. If the totality of what exists has a finite structure and a finite number of fundamentally distinguishable states, then an exhaustive description of this totality can, in principle, also be finite.

If reality is infinite, however, this does not imply the impossibility of finite knowledge. An infinite object can be specified by a finite principle that determines its structure at any scale. In such a case, describing the object does not require enumerating an infinite number of states.

Therefore, it is necessary to distinguish between the amount of what is being described and the amount of the principle sufficient to describe it. The infinity of the former does not imply the infinity of the latter.

Thus, there are two fundamental cases.

In the first case, finite knowledge may constitute exhaustive knowledge of a finite reality.

In the second case, finite knowledge may constitute a finite system of principles from which the properties of an infinite reality follow.

Consequently, the question of the finiteness of knowledge cannot be reduced to the question of whether the Universe is finite. In both cases, a state is logically possible in which the unknown ceases to be a fundamental obstacle to inference.

This state will henceforth be called finite knowledge.

Chapter 3. Finite Knowledge

Finite knowledge is a state of knowledge in which there are no fundamentally unknown relationships necessary for obtaining justified conclusions about the reality under consideration.

Finite knowledge does not have to contain a description of every possible event as a separate fact. If all events are determined by a finite system of established principles, knowledge of these principles is sufficient to determine an infinite set of their manifestations.

The meaning of finite knowledge therefore lies not in the maximum quantity of accumulated information, but in the elimination of fundamental uncertainty. As long as there is an unknown relationship capable of changing a conclusion concerning the question under consideration, knowledge cannot be regarded as finite in the relevant sense.

The attainment of finite knowledge means a transition from the necessity of making assumptions to the possibility of deriving conclusions. If all necessary foundations and relationships are known, the unknown ceases to be an independent source of uncertainty.

However, humanity is not in a state of finite knowledge. Therefore, the limit described above has not only theoretical but also practical significance.

Before it is reached, decisions must be made under incomplete knowledge. Therefore, the next task of the theory is to determine a principle of behavior under conditions in which final certainty has not yet been attained.

Chapter 4. The Inevitability of Uncertainty

Finite knowledge has not been reached. Therefore, humanity does not possess sufficient knowledge to draw final conclusions about all relevant relationships within reality.

At the same time, the absence of finite knowledge does not eliminate the necessity of acting. Without action, the existence of the decision-making system itself would be impossible: maintaining a state is also the result of a choice and has consequences.

Thus, before finite knowledge is reached, human behavior has two inevitable features: the necessity of making decisions and the impossibility of determining all their consequences in advance.

Therefore, uncertainty is not a temporary error of an individual decision. Before finite knowledge is reached, it is a fundamental condition of decision-making.

It follows that a rational system must take into account not only the presumed correctness of an action, but also the probability of error. If unknown relationships are capable of changing the outcome, an action should preserve the possibility of correcting the resulting error.

This raises the following question: what property of a decision makes it possible to correct an error after it has been detected?

Chapter 5. The Principle of Reversibility of Consequences

The consequences of actions may be reversible or irreversible.

A reversible consequence permits restoration of the original state or transition to another state without the final loss of the original possibility. An irreversible consequence eliminates such a possibility.

Under incomplete knowledge, it is impossible to guarantee the absence of error. Therefore, the choice of an action must take into account not only the presumed result, but also the consequences of a possible error.