A PHILOSOPHY OF THE FOUR-DIMENSIONAL SPACE-TIME
The Worldview of Relative Simultaneity (MURAYAMA Akira)
CHAPTER II The Problems of Continuity and Contradiction
7. Logic Looks at Time from a Macroscopic Perspective
This chapter examines the relationship between time and logic on the basis of Zeno's paradoxes. In this section, I focus on how logics deal with time.
A logical rule is that if a proposition is true, its contraposition is also true. For instance, if the proposition that "if it is a human, it is an animal" is true, we can say that "if it is not an animal, it is not a human." The proposition obtained by denying the premise and conclusion of the original proposition and replacing them in reverse is called a contraposition. A proposition and its contraposition have the same truth value. This is a basic of logic.
Think about the proposition that if he is not scolded, he does not study. Suppose that the proposition is true. Then, the contraposition is as follows: "If he studies, he is scolded." This must be true, but there is something strange about this.
The fact is that its correct contraposition goes as follows: "If he had studied, he would have been scolded before that." Additionally, the correct contraposition of "if they do not invest, they cannot get money" goes like this: "If they could have gotten money, they would have invested," not "If they can get money, they will invest." Logic does not guarantee that they will invest again.
The point is that logic is established essentially beyond time and can look at events from a macroscopic perspective. The former proposition "if it is a human, it is an animal" is logic relating to inclusive relation and represents consistent relations throughout time. This kind of logic has no problem if it is transformed into its contraposition. However, the latter proposition expresses a causal relationship. That is, it involves the tacit implications that the premise (cause) and conclusion (result) are connected in the context in terms of time. Therefore, you have to carefully consider tense in giving a contraposition against the original proposition expressing causal relationships. Carefully considering tense means freeing yourself from being bound by "now" and placing yourself in a position where you can look at things from a macroscopic perspective at an arbitrary point of time.
That is why logic cannot let itself go as time goes by. Logic needs to place itself outside the flow of time so it can look at space-time from a macroscopic perspective. If you want to examine the logic of causal relationships, you have to place yourself in a position where you can look at the past and future from a macroscopic perspective. With regard to dynamics, if it tries to analyze a moving object by differential and integral calculus, the dynamics have to observe the object's entire process in the way of drawing trajectory of the object (by using functions, for example) instead of seeing the object as it moves. Using the same reasoning in music, if you just sing and play as you feel, you can enjoy being in the flow of time. But once you try to logically examine the structure of music, you need to change the music in the form of a score that is consistent throughout the current of time. A score is a spatial sketch of the time sculpture of music. This is the kind of spatial and solid things that logical thinking examines. We can draw one important thing from this point. In essence, logic perceives things in fixed form and is not appropriate for handling change.
A fundamental factor of logic is concept. The English word concept is derived from the Latin word conceptus, which means "accept and embrace." The German word Begriff is derived from the verb begreifen, which means "get hold of and grasp." These words connote "getting a good grip on something." That is, letting something move as it wants to does not lead to creating a concept. Not letting something move and fixing it leads to creating a concept. If you want to understand an essentially moving thing as a concept, you have no other choice but to place yourself outside time flow and get hold of the thing by looking at time from a macroscopic perspective.(*3)
The questions become why we recognize concepts and engage in logical thinking and if this is it to know truths in the world. We learned to engage for independent purposes only when our culture became mature. We recognized concepts and engaged in logical thinking to live more than anything else. We usually choose more advantageous behaviors after having seen, heard and known phenomena and learned rules from them. This is what animals with ability to learn have universally done in their own way however different their potential is, and human beings with high-level social organization and language ability have remarkably developed this strategy. Concepts and logic are products of these life activities and they do not exist primarily to find truths in the world.
This means that it is significant to formulate rules from past knowledge and recognize the world by putting them to their utmost use. This rule formulation and recognition is inseparable from solidifying things.
Now, think about a simple movement in which an object changes its position. We usually recognize the position of an object to understand our situation. This means the fixation of the object's position. However, a moving object changes its position as time passes. Therefore, we need to think that the object exists at a different position at a different point of time. This is another fixation of the object's position. In accordance with this reasoning, we consider the concept of velocity, or the rate of changes in the object's position per unit time. The velocity is fixed in this context, but we need to employ the concept of acceleration, or the percentage of changes in velocity, to more accurately understand the situation. Acceleration is also fixed in this context. In fact, a movement with equal acceleration occurs only in a limited world. Generally, positions, velocity and acceleration constantly change in the real world. Modern analytical studies simulate ultimate minute structures and have succeeded in recognizing to a certain extent the constantly changing real world by applying a continuous function to their changes, but you should remember that the consideration of those ultimate minute structures is based on fixed conceptual recognition. This is the fate of logical thinking.
Logical thinking will inevitably face contradictions in the twisted real four-dimensional world. For example, an object exists in a position, but not in another position or an object moves at a velocity, but not at another velocity.
The dialectic highlighted from Hegelianism to Marxism should be interpreted as a form of long-running ideological movement, not as an established methodology or logic. That is, I think it meaningful to regard the dialectic as a warning to the gaps with the reality that fixed conceptual recognition and logical thinking can never avoid facing. We tend to force concepts and rules we have recognized without any limitation and condition, but the real four-dimensional world is distorted and complicated-structured. Unless we notice that, we threaten to self-destruct as a result of rigidification, for example, as in the failed trials of socialism.
(*3) Hegelianism considers concepts as moving and developing by themselves, involving special implications. As an antithesis to concepts that solidify things, a unique way of thinking is to regard the concepts themselves as if they were living things that survive throughout, or at least through the history of humankind. In addition, richness in development of content is surprising and attractive to the author. This perspective is based on the worldview that objective spirits exist. I do not take the stance of objective idealism. I look upon concepts as the function of human consciousness as human consciousness is socially organized. I believe that concepts are not capable of moving and developing by themselves but are the results of the self-movement of the world itself and the activities of human beings that recognize such movement. Because Hegel’s stance regards concepts as something that move by themselves, he understands time as negativity (negativität in German). On the contrary, I think these forms of understanding and expressions demonstrate the fateful fixation of concepts that cannot realize self-movement without being continuously triggered by denial and eventually contradictions.