If you think this essay is too long to read, I recommend you to read 2-5.Money of Intellect. I think it's the most interesting section.

Comparison, why is it considered to be the most primordial phenomenon of intellect? Or what is “comparison” in the first place? How does it relate to “relation?” I need some steps to explain it. In this chapter, I’ll tell them one by one. Before that, I summarize the whole chapter.

To explain the comparison, at first, I’ll discuss three kinds of information which are 1.the definition of information in information theory at “2-1-1.The Definition of Information in Information Theory,” 2. information of sensory organs and 3.information of language at  “2-1-2.Sensory Organs and Language.” As it turns out, information of sensory organs and language have the same relationship which is “selection from possible values” as information in information theory. I consider that relationship to be the fundamental structure of information.

In addition, at “2-1-3.The Undecidability of Solipsism,” I argue the truth value of solipsism which doubts all the information is undecidable, as a result of the fact that our recognition only has information. In short, if one doubts “all the information,” one also has to doubt the information which distinguishes the reality and dreams, so one loses all the information, including the information which certainly indicates the recognition is the reality or not. So, rationally, one cannot distinguish that difference in principle.

I note that I don’t argue that reality doesn’t exist. I just argue if one stands on the premise that doubts all the information, one can neither say reality exists nor does not exist, so, strictly, one cannot refute that solipsism. I’ll explain it later, the awareness of that can have some ethical meanings.

And at “2-2.Comparison, Relation, Knowledge,” I explain the relationship between comparison, relation and knowledge. Comparison is “the state lining up several possibilities and waiting for which one to be selected,” relation is “interlocking of selection,” and about “relation,” when we talk about it in relation to intellect, we can call it “knowledge,” according to the argument 2-1.

At “2-3.The Relativity of the Correctness and Comparison Act,” I argue the following. 1.Judgement of correctness is dependent on the comparison measure which is used for judgment. 2.The object of comparison is relative to the comparator. 3.The difficulty of the comparison act changes depending on the state of knowledge of the person who compares.

At “2-4.The Usability of Information and Theory of Logical Types of Comparison,” I question “What is useful information?” and I argue “comparison” forms hierarchy as sets(classes) and elements(members). And when we move our sight in those hierarchies up and down, we make our recognition abstract or concrete, create theory or pick up individual cases. It’s consistent with the structure of intellect I define at 2-1.

At “2-5.Money of Intellect,” I argue how “unit” is born through the accumulation of relations by a  model process, using the argument of “balance” by Gregory Bateson and “Ontology of money” by Katsuhito Iwai as clues. Moreover I’ll point out that that relationship is common to the argument of “time” by Carlo Rovelli, and the accumulation of relations has a kind of “rationality,” in addition, the theory of idea I take up first may be an adoration for that rationality. 

In the last of this chapter, “2-6.Things We Cannot Compare,” based on the undecidability of solipsism at 2-1-3, I point out a limit of the principle of “comparison” I explained at 2-2. And I’ll show the awareness of that limit is a way to ethics or maturity. I tell it shortly in advance, the aporia of undecidability of solipsism, which we can never solve, shows that we can’t distinguish which “man is the measure of all things” or “all things are the measure of man,” and also shows “all things cannot be reduced to the measure,” I believe.

Humans are born in different places and environments with different bodies, and live different lives and time. There are no uniform people like industrial products—in strict, nor industrial products. All things have different relations to others, lie in different flows of time. But “comparison” compares something by unifying it with abstract identity while removing these differences. The evaluation created by comparison, the world created by it, is not a perfect fair world. 

Humans can never create the perfect fair world, but never live without the violence of comparison. An ethics exists in the attitude of awareness of that aporia and making the world less that violence. And I believe, there’s a moment of maturity, as one of the great awareness of difference between self and others, in the awareness that primarily we can’t compare any person with another person, the awareness that people live in the different flows of time.

It’s the whole picture of this chapter.

2-1.What Information Theory Discovered

Comparison, why is it considered to be the most primordial phenomenon of intellect, or what is “comparison” in the first place? In order to deal with it, first of all, as an act governed by the intellect, I’d like to consider “what is cognising?", "what is knowing?” and “what is information?” Because it is the necessary step to explain “what is relation.”

I think that the act of “cognising” can be defined as having a structure or relationship that is “making a selection(selection can be both singular and plural) from some prepared options or states in any way which are distinguished by difference and identity.” And information is “a matter which makes a selection,” as long as it has the relationship of “ability of making a selection from prepared options,” it can be called “information.”

What I note here is that I have not yet said anything about the correctness of “cognising” and the usefulness of “information.” This is a definition that includes both false “cognising” and meaningless and not useful “information” for the observer. Moreover, I need at least two explanations about the definition itself. I’ll explain the former at 2-1-1, for the latter at 2-1-2.

2-1-1.The Definition of Information in Information Theory

The definition of information above is borrowed from the one of information theory almost  just as it is. In a commentary in The Mathematical Theory of Communication, Warren Weaver explains it as follows:

The information mentioned here is just a mathematical quantity determined only by probability, and does not express the meaning of words. The amount of information is expressed as “the probability that a state occurs out of multiple states” in information theory which is the theory of communication devices. Here, it is considered that the less probability a certain state occurs, the more amount of information, the higher the value of that information is.

However, in my opinion, this concept of “selection,” the relationship or structure of “selection of something from multiple possibilities,”even though does not explain what “meaning” itself is, but it expresses the formal structure that the meaning of language follows — it is the form of forms, so to speak, the king of forms — and the universal structure which is common to all the information. I consider that information theory discovered the universal structure of “information,” at the same time when it had defined the “amount” of information.

I would like to explain the reason why I adopt this definition by taking up some examples of what kind of situation that “not knowing/knowing” is.

For example, if I show the cards drawn with pictures such as some vehicles, foods, animals… to English speakers who do not know the Japanese word for “dog” and ask “Choose the one which pronounces ‘inu(means dog in Japanese)’ in Japanese,” they wouldn’t be able to choose correctly. Or someone who doesn’t know the procedures of the four arithmetic operations may answer “2×2” as “5” instead of “4.” Or people who are familiar with a certain area can choose the exact route to reach the destination, or if they know the existence of map and how to read it, they would be able to select the location on the map, or if people know the cheapest store of the nearby supermarkets, can select that store, or for example, if you know the answer to a four-choice quiz, you can choose the correct option, or if you know what food is healthy and what is not, you can avoid unhealthy foods……

Although there are few examples to give, I think that as a simple definition, the state of “knowing” can be identified as “being able to make the right choice.” In more precise terms, in my view, this is preceded by the qualifier “in comparison,” and the definition is “Having the ability to make the right selection in comparison with the singular or plural measures, system of relations which the one uses,” but since the terms “comparison,” “system of relations,” and “correct” are not defined here, so the detailed explanation will be given later.

Conversely, “not knowing” can be defined as “Not having the ability to make the right choice.”

Those who “know” something can make correct choices, and those who “don’t know” make wrong choices. And information, as a guide to the choice of action, excludes other possibilities and points to multiple or singular options. Though I pigeonhole “correctness” in the previous definition, I hope I show readers that knowing is the ability of selection, and cognising is “making a selection from some prepared options or states which are distinguished by difference and identity,” and information is a matter to make it, or at least, I wish I could show readers that they all are related to “selection.”

Of course, it is possible to make the wrong choice in a hurry even if the one knows the correct choice, and to make the correct choice by accident without knowing it, but if the situation changes, the correct or incorrect choices would be performed. Considering the exception cases, this definition is likely to be about 80% accurate, I guess. I borrowed the definition from the theory of communication engineering, but I think it’s correct in the everyday sense.

There may be some objections to this. The three counter arguments I can come up with so far.

1. With that definition, how can we explain analog information such as the temperature measured by a Galileo thermometer?

2. With that definition, how can we explain the type of knowledge such as explanation by languages?

3. With that definition which can’t explain “meanings,” how can we explain the knowledge?

For (1), I can explain as follows. When the glass ball floating in a Galileo thermometer repeats slight ups and downs due to ambient temperature changes, “a different state” appears in each moment, and each of them is “an option” to be selected. Analog information is difficult to artificially reproduce and maintain the completely “identical” state, but I think it is possible to explain that there is no problem in thinking that each state which slightly changes in every moment can be regarded as “options which are distinguished by difference and identity.”

And I would like to explain(2) and (3)  at 2-1-2.

2-1-2.Sensory Organs and Language

I questioned information in language in the former section, but for the sake of explanation, I would like to first show that information in the sensory organs also matches the above definition of information. For that again I show the definition of information by Gregory Bateson which I quoted at introduction.

As already explained by Bateson, Sensory end organs can be regarded as devices that respond to differences, comparators. He thus defines information as “a difference that makes a difference.” However, Bateson’s definition does not seem to be suitable for expressing “information” which tells “no difference.” I don’t know how Bateson himself was, but at least this definition of him, so to speak, regards only positive “information” as “information.” There is room for improvement. It’s the act of “comparison”—as Bateson had already found it—that detects both information, the information which tells “there’s difference” and the information which tells “there are no differences.” To deal with information, we should take it into consideration, not only reaction to difference, but also no reaction to difference. So I take over the argument by Bateson critically, focusing on comparison.

So, I consider when a sensory organ responds to a certain stimulus, it compares stimulus according to a threshold, preparing two possibilities of “reacting/non-reacting”, selects one of them, and generates and passes information to the other organ and nerves. In other words, I regard Bateson’s “difference” as one of these options. So I have been told “possible values” in the former sections, if they are not single but multiple, we can regard them “possible values” even if they are only two.

I consider that the sensory organs in the non-reacting state waiting for the stimulus are “cognising” that “there is no stimulus” in the comparison by its threshold, and by selecting “no-reacting,” it transmits the information “there is no stimulus” to the nerve. Of course, the reverse is transmitting “information” by cognising the “stimulus” by reacting to it.

Bateson may think that the state of “no-reacting” is “nothing is happening” — regardless of whether such a matter is possible in this world — so “information is not being transmitted,” but if we look at the world from the purpose of following the flow of “information,” I think that perspective makes us lose sight of one aspect. Perhaps, the distribution of “information” should not be completely identified with the propagation of physical reactions in all its routes. At least, if we accept the existence of information that something is “not existing,” we should deal with “comparing” as the primordial mechanism of generation of information.

Or, in that case, you may have the question, “Since roadside stones do not always react to the visible light of sunlight, can they be expressed as transmitting the information of “no light” into inside themselves?” But that is wrong. Because roadside stones “always” do not react to visible light within themselves, that is, they do not prepare themselves for the possibility of “reacting,” so information does not exist there. (There may be some aging change due to visible light that I just don’t know. However in that case, there is information on that span of several years, but there’s no short term information which I consider here.)

Thinking this way, you can understand that in sensory organs and nerves, discriminating differences, “selection from prepared states or options which are distinguished by difference and identity” is happening in a chain reaction any time. So the previous definitions include information in sensory organs.

If it is the case with sensory organs, then what about language?

Words (symbols) convey meanings and values, but I would like to think about their forms. For example, Japanese people often have difficulty in pronunciation of “r” and “l.” If a Japanese person intends to say “I eat rice” and another one hears the word “rice” as “lice,” then miscommunication happens. So, at the level of phoneme, if one can’t pronounce correctly — which means one can’t “select” correct phoneme — , transmitting information fails. Thus “selection from prepared states or options which are distinguished by difference and identity” makes phoneme function as information.

And a word appears as a combination of phonemes, but it also should be selected from prepared options. For example, do you understand the word “yutsukinma?” You probably don’t understand it. Because this is the character I just randomly typed. So not prepared words have no meanings and they also have meaning and function as information by “selection from prepared states or options which are distinguished by difference and identity.” Of course, it may have some value even if it has no meaning, but for English speakers, it is also selected, or an option is created within the English phonological value system.

Although there is the case where the receiver can’t discern (select) options yet, the receiver learns something new. It is a case of “learning new matters,” the one is “increasing the options as a recipient (sender).” I’m not quite ready to put “learning” into my own words yet, but I have a hunch that the outlook will probably relate to weaving “relationships.” “Yutsukinma” is also meaningless at first and does not function as semantic information, but by using it repeatedly, one learns that option and the word changes to start functioning as a kind of semantic information.

I also talk about meaning here. I think that the meaning of a word or sentence is something integrated synthesis of countless referentiability to other information that a person has, such information by sensory organ, by memory, by other words, by other sentences…, which is distinguished one by one, but to be quite honest, I don’t know the true nature of the meaning, its whole picture. But at least from the form of the word, we can see that the meaning also follows “selection from prepared states or options which are distinguished by difference and identity.” For example, in my conceivable case, it is inconceivable that “dog” and “cat” show exactly the same meaning in English speakers, other than their usage as proper names. Meaning follows selection of phonemes in most situations.

The fact that the meaning follows the selection cannot be confuted by pointing out that the meaning is influenced by the context, for example. Because the change of meaning by context is just the change of option which is selected. Also, considering the dichotomy “being/not being” I will argue later, I think you will see that the meaning must also follow the information format that I speak of.

Therefore, although there are exceptions due to methods such as double meaning and metaphor, it will still follow “selection from prepared states or options which are distinguished by difference and identity.” Or, double meanings and metaphors are just exceptions in the method of selection, because even with them, we select options from two or more clusters of options at same time, they aren’t different in the point that selection is performed.

Now I proceed further with the propositions (sentences). To think about this, let us look at two propositions.

A. There is a cup on the table
B. There is “Apology of Socrates” on the table.

Unless you are a very peculiar English speaker, you will probably judge that the meanings of propositions A and B are different. This is because, in the place where there was “a cup” in A, there is something different in B, the name of a book, “Apology of Socrates” lies there. So, in many cases in sentences, the “selection” of words changes the overall meaning (or value, if it is a metaphor) of the sentence in which words are included.

And that means “a cup” is selected among the other possibilities as shown in the following image.

When you say ”there is something on the table,” “something” is selected from the prepared words in English, and the information of the entire sentence is fixed.

I learned about this at university as a literary lecture on the value of rhetoric, and I think the book by philosopher of language Nobuo Sato(信夫 佐藤) , “The Rhetorical Sense”(レトリック感覚 Retorikku Kankaku) was presented as a reference at that time. However, I couldn’t find a sentence that could be exemplified from it. My memory is fuzzy, so perhaps it was the content of other literature or the content only of the lecture.

So anyway, it’s the same as each word in the entire sentence: “table,” “on”…. As we saw earlier, if a sentence contains the word that is not prepared for English, such as “yutsukinma,” then the unit “proposition” will not make sense unless it is learned. Therefore, we can confirm that “selection from prepared options” makes the information function as information in the level of sentences as well.

Of course, the grammatical rules are not simple, and the simple examples here cannot tell everything, such as changing the order of words. However, I think it can be confirmed that “selection from prepared options” makes the information function as information.

A sentence has infinite possibilities of meaning depending on the selection and its combination of words. In the words spoken or written, one of those possibilities is selected. As we read and listen to the sentences, we wait for what will be selected, we do not know it till it will have been selected, and we cognise it when it has been selected. And perhaps learning a language means preparing for possibilities inside oneself for receiving and sending sentences.

As I have said above, an objection might be, for example, that “we just say ‘there’s a cup on the table’ and use it without thinking about the other possibilities that have been prepared.” It probably grasps the correctness of one aspect, but the objection might not grasp the correctness of another aspect.

We have to consider, for example, whether the word “being” can be used without the understanding of its precise opposition to “not being.” For example, it is obvious that if the sentence “There ‘is’ a cup on the table” is understood by one as “There is no cup,” or “It is a state that we don’t know whether there is a cup or not,” or “It is a state that superposition of ‘being there’ and ‘not being there,’” or “By that sentence, we express both ‘being there’ and ‘not being there’ as the case may be,” then we will not be able to have precise communication to that one — there might be dispute about state of superposition, here temporarily I talk about only macroscopic topics of daily life.

The word “being” cannot be used unless it is selected in the differentiation, compared with “not bing.” Of course, for philosophers, considering the mystery of the state of “being,” perhaps no one will ever understand “being,” but you can understand that at least, to the degree of routinely acceptable precision, about each word, a language should be used in the situation that users share clusters of distinct options. This is of course the same for the “a cup.” If you misunderstand “Apology of Socrates” as “a cup,” discommunication will occur.

Thus, using language and making sentences always implicitly contains the act of selecting one from possibilities which are compared with. Of course, we are not omniscient beings, so we are making dichotomies with other terms to the level of daily life or academic discovery. If one can recognize the differences and identities of words, make correct selections and write a statement, then it means that one has knowledge, and when another one generates selections of words, and one has received all selection, then one has cognised another one’s sentence. Of course, if one can anticipate another one’s selection, there is no need to receive “all” sentences.

Then, the reason why I write that “it probably grasps the correctness of one aspect” about the objection that we aren’t comparing is “preparing other possibilities, options” costs a lot for daily life communication, and basically, for accurate operations and transmissions of information, avoiding much processing and reducing amount of information are usual practice to secure economy, accuracy and speed —and, they are those of most important functions of works of intellect— much information and processing should be concealed or removed for efficiency. In other words, the one who compares is an entity in the world, always bound by some finiteness.

Increasing the number of prepared options requires a lot of time and energy to examine and resources to prepare them, and furthermore, as a result of examination, the probability of selecting the wrong option increases. It is a risk and a cost in situations where quick decisions are required. So when we rush to conclusions, we often rationally lose sight of “other possibilities.” Taking time to compare and examine is an act of trying to regain them.

The fact that the meanings of words are decided by “selection” out of possible values is not even discovered by me. For example, I don’t know if it can be called Saussure’s work, but in “Course in General Linguistics” it is written as follows.

When a language user says “marchons!(French for “Let’s walk!”)” and another one listens to it, they understand it in comparison to the differences between other possibilities that they have already learned, such as “marche!(French for “Walk!”)” which has different values and nuances. In the similar way at the level of meanings, the words have meaning in the selection from dichotomy and difference between other possibilities, such as mangeons!(French for “Let’s eat!”).

In other words, words transmit information about their meanings and values through continuous “selection” in various layers from “sets of possible words, letters, and phonemes.” Since it’s actions by humans, we may not always use language in complete comparison to all terms under a strict rule. But when we think about it systematically, it can be said that we are comparing various possibilities.

So the meaning of the words exists in “sequence of selections.” Or conversely it also shows that until the “sequences” end, we can’t completely understand “the meaning of something.” This way of thinking is consistent with the way of thinking that “the meaning is integrated synthesis of countless referentiability to other information.” Because synthesis of referentiability to other information is another expression of “sequence of selection(information)” from another point of view in certain situations.

By the way, when we have discussed sensory organs, phonemes, meanings, and sentences, and find the same structure so far, you may feel something strange about this structure itself. For example, we can say that the sky is selected from the “night/day” possibilities, an animal is selected from the “adult/juvenile” possibilities, and some colors are themselves by excluding other colors. It can be said that even the stone on the roadside does not react to light, but the selection is made from the possibility of “angular state / round state without corners.” And, for example, from a stone, it may be possible to read information about the stone’s history up to that point. If we look at the world in that way, isn’t there anything that doesn’t follow this structure? That’s the question.

That’s natural. Because, I believe, ultimately, we can’t distinguish the world composed of information from the world of things-in-themselves, so the world viewed as the physical world, the world of society, and the world of words must all fit into this definition.

2-1-3.The Undecidability of Solipsism

It’s simple when you think about it. When we see, hear, feel, or think about something, the object itself never exists in the sensory organ. It never happens that a small entity is created in your head and reproduces the causal relationship in reality. Others do not exist in our own brain. Therefore, only information exists in the world of our perception. Or we can do this thought experiment. It is a hypothesis that a kind of solipsism is undecidable. 

As a simple model, consider the case of thinking about solipsism while the other is really existing. Here, the brain that is thinking about solipsism follows the procedure of judging whether the information obtained from the input devices, sensory organs is coming from the outside or is occurring inside the brain. The suspicion of solipsism asks whether the input to the input device is caused by someone else, external to the input device or not.

In other words, although what is being asked here is about the outside of the “total of inputs,” judgments about the existence of others cannot be made without information obtained from “inputs.” For this reason, for example, if it verifies whether a certain input A is an input from the outside, to do so, it needs to refer to another input B. However, in that case, it becomes necessary to verify whether the input B itself is an input from the outside. Then it will refer to input C to validate input B. But also input C needs to be verified… This is a never-ending procedure.

Even if it tries self-recognition and identifies the externality from the form of the recognition system of self, it must suspect that the input itself that constitutes the “self-recognition” is a “mere mental phenomenon” that does not perceive the object of itself. Any number of combinations of information constructed from suspected inputs is meaningless. This is because it cannot deny the possibility that the input information itself is a mental phenomenon that does not involve others.

This suspicion has the structure that the evidence proving the externality itself can only come from what is to be proved. Trustworthy logic cannot be constructed because only the entity under suspicion provides the logical means that must be relied upon to make proofs. Or, in other words, as long as the correctness of all information is questioned, a reliable logic cannot be constructed. For this reason, this suspicion cannot be rationally stopped, and solipsism cannot be determined to be false. And even if we can’t deny it’s false, it doesn’t mean we can prove it true. Because we cannot deny the possibility that the suspicion itself is just a delusion that is happening inside of one’s self.

On the other hand, let us consider a case in which solipsism is true. In that case, the previous question is reversed, and the solitary self that exists alone has the suspicion that “Aren’t the others existing?”

In this case, even though “all phenomena” which happen in the world, all the information which the alone self has are the mental phenomena inside the solitary self, but the solitary self suspects that there’s externality, others are existing. Even if all the information is available and the internal semantic content that occurs in the solitary self proves the non-existence of the externality, the suspicion cannot be dispelled. That suspicion questions all the information and existence of external entities that can overturn all the premises of all logic.

There is a perfect match between the suspected object and the logical means of proof, and no credible argument can be produced. Again, a final determination cannot rationally be made. This is also the same as the previous question, and as long as all information is suspected, it is meaningless to combine any number of information that should be suspected.

We cannot rationally persuade against the stance of doubting all information. For this reason, the suspicion that the others exist cannot be stopped. And we cannot deny the possibility that the suspicion that the other exists is just a delusion. There is no way to stop this suspicion with any reasonable solution. Solipsism is therefore undecidable whether it is true or false.

I note that I don’t argue that reality doesn’t exist. I just argue if one stands on the premise that doubts all the information, one can neither say reality exists nor everything is dream, so, strictly, one cannot refute that solipsism. So to speak, our recognition is always suspended in the air, between reality and dream. If not, we never make mistakes. If all reality exists in our recognition from the beginning, we don’t need to put effort into exploring the truth.

If you think in this way, you may find that the physical world, society, words, and all kinds of things must fall under the above definition of information.

Because what these hypotheses point to is that we cannot hear, see, or know what is not information.

At this point, let us suppose that “cognising” and “information” can be defined as “selection from prepared states or options which are distinguished by difference and identity.” I think this structure is so universal that once you start looking at the world from that way of thinking, you’ll be amazed at its obviousness.

It’s all based on my amateur knowledge, so some modifications may be necessary, but let’s move on to “comparison.”

2-2.Comparison, Relation, Knowledge

2-2-1.Comparison

It may be obvious now, “preparing states or options which are distinguished by difference and identity” means lining up several possibilities and waiting for which one to be selected. It is nothing but an act of “comparison.”

And the abstract things that I have called options, states, or possibilities are the ways of dividing the world, which are distinguished by differences and identities prepared by the structures that perform comparison, they can be such as reaction/non-reaction, words or physical states. They are a unit in that relationship, and the collection of those could be called a “comparison measure.” Furthermore, the mechanism of selecting one or more from among the options that which one is selected is unknown can be called “comparator,” and that process can be called comparison act, comparison process.  

However, I can assume the counterargument question against those definitions as follows. That is “this definition cannot express the comparison such as comparative study of cultures which is comparing the properties of multiple objects?” This is certainly true, but such comparisons are never different from having the basic structure of “preparing options.”

So to speak, my definition of information above can be compared to putting a “ruler” to a certain object and measuring it. A measure has a structure in which one is selected from a set of possible values, such as “1 cm, 2 cm, 3 cm”…, or sets which have the feature of setting the differences and the identity of elements simultaneously, is nothing but another name of comparison measure.

The “comparison” in case of “comparing multiple objects” can be expressed as performing comparison by “prepared options,” measures with multiple targets multiple times.

For example, when we say “an adult is bigger than a child,” we use the measure of ”size” to two objects, and when we say “this child is quieter than that child,” we use the measure of “quietness” with two objects, and when we say “this animal is more ferocious than that,” we are putting the same “cluster of options” to two objects.

Or maybe there is a comparison like this. A case where such as we “compare humans and dogs,” which is just lining two objects up. However, in this case, what is said next is that “humans walk on two legs, dogs walk on four legs, and compared to humans, dogs have a superior sense of smell…” and so on, unless in an overly nonsensical way, we put the same or similar measures or measures which we guess to be interrelated and measure the difference and the identity.

Thus, though there are complex cases, fundamentally, we can define comparison as “preparing states or options which are distinguished by difference and identity and waiting for which one to be selected.”

2-2-2.Relation

And if we admit the above definition, we can define the concept of “relation.” So, the thing born among which we measure something lining up multiple comparison measures is the “relation.”

For example, when we consider which of “children” and “adults” is larger, we measure the size of each individual, and select one from the options of relations, such as “children > adults”, “children < adults”, and “children = adults.” Thus when we line up multiple comparison measures and examine things, the new “relation” is recognized between the objects of comparison,whether it has already been named or not.

And we can define “relating” epistemologically, it’s that one selection determines another selection when we line two or more measures up and measure objects. This definition contains both causal and correlative connections, regardless of whether the relation has an order or not.　Because I’m talking about the most fundamental definition of “relation in general” which is not limited by any properties.

And the most basic definition of “relating”(not only epistemologically) which includes causality and correlation, valid both in the cognitive and physical worlds, is that “selection makes selection,” and the definition of “relation” is that “selection makes selection and its way of making.” So, “relation” is “sequence of selection.”*1

*1…You may call this definition “correlation.”  I think it’s proper to call “interlocking of selection” thus. But I can only admit it in the case that it is not contrasted with “causal relation” or “family relationship…,” but it also contains them. To reiterate, what I am describing here is the most basic definition of “relations in general” without specifying any of its properties.

For example, consider  “the parent and child relation.” Though we cannot regard it as a completely universal example, among a family, we generally call the relation between the one who bore the child and the child “the parent and child relation.” “The parent and child relation” is recognized in the selection of two members. For example, that relation is not recognized between a child and another child, and the relation between those two members is called “sisters” or “brothers.” For example, there may be disowning, so when we see the unique relation in the realty, the above case is not completely universal. But generally speaking, when we choose two members from kinship members, “the relation” between them is determined.

Or it’s the same in the correlation. When a value is interlocking to another, we see the correlation. It can be said of interlocking of “selections” in other words, so we see the relation between the selection of those two members. And if we can see “cause and effect” in it, we regard it as “the causal relation.” Or if we change the selection and new members are not interlocking, we would regard it “unrelated.” Though it is also a higher class “relation.”

If you doubt the above definition of relation, consider any relationship among two or more members on a trial basis. And consider whether the nature of that relation you choose is depending on the selection of two or more members which surround it or not. “The relation,” the nature of it which is formed between one and another, can never be independent of the terms which surround it in principle. ”The relation” exists among “selections.”

And logical thinking can be cited as one way to actively weave such relationships. Thinking logically means selecting the next proposition that is inevitably determined = selected from a certain preceding proposition, such as “If it is x, then it is y”,”If it is not x, then it is not y”… I think you can understand from experience and sense that logical thinking is the act of selecting and deciding on each matter like this.

Between propositions and between reason and conclusions, there is the act of comparison and selection with potential other propositions, and it is an act of building relationships. It may be said that there is no comparison, but if there is no moment of comparison with “other possibilities,” it means that humans never make mistakes in logical thinking. Then matters would be similar to a kind of classical economics world in which selling and buying match anytime, which has no crisis. Or in other words, if there’s no comparison, we don’t need to prove something by logic. Because  if there’s no comparison, then there’s no other possibilities. At that time, we never make mistakes, so there’s no need to prove something. Comparison is the moment of intellect, so it’s also both a moment of true and false.

Furthermore, paradoxically even if a selection does not make a selection, we can find a “relationship” that is one level higher. In other words, when the selection of certain two terms are not interrelated, we find the relation of “no relations” between them. And, the relation itself can be treated as a term. For example, “family” and “community” can be treated as subjects and terms even though they are one relationship. Or, in other words, perhaps the distinction between “relation” and “term” is nothing more than a technical distinction of cognition, the product of manipulation of hierarchy.

I think the same goes for numbers. For example,  consider "5" is written in a formula. Then as long as the calculation order is correct, if 5 changes to (2+3) ,(1+4), (8-3) or (10/2)...,  the result of the calculation is unchanged. A number is a centered representation of the collection of other relations that are equal to it. Otherwise, they cannot be connected by equations. The accumulation of such relationships will be discussed in detail in 2-5.

2-2-3.Knowledge

Furthermore, if we regard 2-2-1 and 2-2-2 as correct, we can explain what “knowledge” is, that is “knowledge” is equal to “relation.”

For example, a part of the knowledge about Soseki Natsume(漱石 夏目:A famous Japanese novelist), the information that “Soseki Natsume published a novel called “Kokoro”(こころ in Japanese:Heart) in 1914” is composed of individual pieces of information, for example, which is no other than “Soseki Natsume”, no other than “1914,” no other than “Kokoro”, and no other than “novel.”… And such information is made by the selection on the lined a number of measures which lies at various classes — phonemes, words, their order, compositions of the meanings and proposition by selection of relationships between words under grammatical rule, the connection between sentences, the information that the word Soseki Natsume points no other than one of animals, a certain human who lived in the past, the information that the word “1914” points no other than age…and this is actually a set of “relations.” Or, in other words, although it is obvious, making sentences is nothing but weaving relations of linguistic information.

And since this is the case with logical thinking, the rules and theories as its higher structure are, needless to say, a set of relations. Therefore, the fact that knowledge is a set of relations does not change even in mathematical operations such as “2 × 2 = 4.” The solution of a computable formula is guided by an algorithm, a “rule.” In general, each rule’s clause is a set of one or more measures and ways of selection, and they discriminate, restrict and select the behavior of their objects. And in mathematics, the rules is a set of ways of ordering how to weave relations between the one who is operating and the symbol which records the operation. And a formula which is the result of a solution by obeying rules expresses the relationship between symbols.

If we use the concept of “relations,” we can define “knowledge” containing both singular matters like history and repeated rules like mathematics which have been solved. In other words, knowledge is the network, the system of relations which is connected selections from comparison at uncountable classes — and works of comparison are maximally concealed, omitted and simplified. Actually, if we define knowledge in this way, we can see that the act of acquiring knowledge consists in following the threads of the relation of matters. This is because when a relation occurs, that is, when “selection makes selection”, it means that information and information are linked, and one information can be used to obtain the next information. It’s nothing but increasing our knowledge.

Thus, “knowledge” is “the networks of relations” weaved on numbers of layers.

2-3.The Relativity of the Correctness and Comparison Act

2-3-1.The Relativity of the Correctness

And now, as a matter born from the result of the comparison, I can talk about the “correctness” that was previously deferred. In my opinion, “correctness” (the fact that a proposition is true) basically means a relationship that a certain option can be matched to or settled into a certain range of singular or plural number of options of knowledge, system of relations which the one who judges of truth or falsity uses. In other words, “correctness” does not exist absolutely, but is called so in comparison with the system of relations. I would like to show some examples to explain it.

2-3-1-1.The Correctness and Comparison

First, I will explain why the correctness is “true in comparison.”

For example, is the proposition “Socrates is human” true? We’d be tempted to answer “true”, but let’s think about it this way. Supposing there is a caricature, which draws the ancient philosopher as a dog or a cat, is it true that “Socrates is human” when referring to this? Or can we be sure that no one names a dog or cat Socrates?

At the very least, in order to protect the truth of the proposition, I think that the term “Socrates” must be limited to the specific Socrates who lived in Greece.

What I mean here is that a proposition always, implicitly or explicitly, performs comparison with the system of relations, measures which the one who judges uses — the system of relations is often “the real world” — and it’s limited “true” as long as with that act of comparison.

You may say since the above example is a proposition to the caricature that is a fiction, and its whole work is false as a proposition, so we don’t need to accept that “true.” However, it is probably not an easy argument to accept. Because, then you will not be able to communicate about literature study or fiction in everyday life. For example, if we accept it, propositions such as “In Soseki Natsume’s ‘Kokoro’ ‘Sensei’ appears” or “Hyperspace flight exists in ‘Star Wars series’” become “false.” I think it’s hard to accept from a daily sense.

This is not an argument that when judging the truth of a proposition, normatively we should consider all other possible worlds and limit the proposition. It clearly goes against the economics of processing information, and the possible world is infinite, it’s impossible. What I mean is that the simplest way to describe what we do in judging truth is that we do comparisons.

As I will touch on later when discussing good and bad, this can generally be said of making a "judgment," unless it is a whim, "correctness" cannot exist out of the ternary relationship between “criterion (comparison measure),” “subject of judgment,” and “object of judgment.” In order to dismiss this as relativism, it must be shown that “judgment” is possible without this ternary relationship. And I guess it’s impossible. Therefore, rather than being a relativist perspective, this simply points out the relativity of the act of “judgment” itself. It is precisely because of this that we are forced to have “thoughts” and understand the important ethics of “dialogue.”

2-3-1-2.The Correctness by Deduction and Conditions

I guess it might be more acceptable, I explain why “to be true” means a relation that a certain option can be matched to or settled into a certain range of singular or plural number of options. For example, Soseki is Soseki Natsume’s pen name, so the proposition “The author of ‘Kokoro’ is Kinnosuke Natsume” is true as an alternative solution of “The author of ‘Kokoro’ is Soseki Natsume.” Answers are not necessarily only one. I think this also means that in some other situations there is a certain degree of acceptable precision in being “true.”

This is related to the fact that we are always comparing systems of relations, for example, it is not necessary to describe the proposition “the principle of effective demand” in economics from the quantum level. Though we are arguing the real world, the reason why we don’t need to argue according to the physics which seems to grasp the real word the most, is because it’s impossible and we don’t need such accuracy with propositions of economics, so it’s permitted due to the problem of accuracy, I think.

Isn’t this strange when you think about it for a moment? —at least I had doubts. Why does the truth have a kind of pluralism, hierarchies with respect to the world? The propositions of economics and the propositions of physics could not transcend each other’s domain without any changes. I think there is no way to explain this, that a certain “trueness of a proposition” which in the system of scholarship is the works of comparison, in which the measure used by the one who judges is allowing for the difference of its domain’s objects to a certain degree. As I have said earlier, such a question would show that the act of comparison has a kind of hierarchy structure, and that the truth, the truth of a proposition exists between a system of relations and propositions which lie at proper classes for each other.

Furthermore, the matter that “the proposition is true” is merely an example of “matching or settling within the range of positions.” For example, the survival of the fittest in the natural environment, the precision machining of objects within tolerance, that a basketball gets into the goal, pointing the location of a target on a map, etc… as one of such many systems and games, there is a game of truth.

And proving or demonstrating something by connecting propositions is to continuously exclude other possibilities and to show the way of relations. It would be the act of creating a system of relations, or, if the solution is a known problem, it is the act of tracing. 

It is similar to creating habits for survival in the natural environment, tracing the evolutionary path of living species, programming for precision machining, aiming the way for the goals by basketball players, predicting the path of the ball to goal, and showing the way to a destination on a map in order.

I’ll show some examples of those correctness.

2-3-1-3.The Correctness of Deduction

When one states something, one proves the relationship of the terms at the lower level elements by the relationship of a certain high-level class of abstraction, the definition of the set, the condition and its relation to other terms. In other words, one proves something by pointing out the existence of relationships that the definition of the set of superclasses, the relationship between the condition and its relation to other terms contain each element at the level of the demonstrating. This may be just a paraphrasing of simply proving by means of rules and necessary conditions, but being within the scope of this superordinate set and conditions, I regard that as “correctness.” I think it’s easier to understand if you look at the following syllogism.

Socrates is human
Humans die
Socrates dies

This translates into the following.

“Socrates” is an element that satisfies the conditions for the set “human”
Elements that meet the conditions for the set “human” must meet the conditions for the other term “die”
The element “Socrates” satisfies the condition of the term “die”

The “correctness” of a certain reference depends on the “correctness” of this superordinate class. The reason why I use both the expressions “set” and “satisfy the condition” is because the number of “elements” can be either one or more.

And what does it mean to be within an option or set or to match a condition? People would distinguish the difference and identity between what the conditions indicate, the definition of the set and the object of judgment. When they are the same, they are said to match the conditions or be within the set, and when there is a difference, they are said to not match or do not fit. 

Examining whether conditions match or differ and whether they are elements of a set is an act of comparison that simultaneously identifies the differences and sameness between the object and the set or condition as norm. How this is done depends on the particular comparator. For example, if you are using a ruler, you would look at the position of 1cm, 1.1cm, 1.2cm, etc. where the end of the measurement object is the same, and if it is a verbal question, you would check whether the object fits the definition of the word or not. 

2-3-1-4.The Correctness of Induction

Induction gathers the terms at the level of the elements, abstracts the terms and relationships with a certain identity, determines the terms and relationships at the level of the set, and makes this a new rule. “Correctness” in induction is this “identity.” This is because the “identity” guarantees that the induction is a normal induction.

Thinking in this way, the simple correctness of 2-3-1-2 and other correctness basically consist of whether or not a set contains elements, and how they are combined in many layers.

From this perspective, the concept of correctness is consistent with discussions of comparison measure, and we can see how it relates to sets, elements, differences, and identities. Or, if we look at things formally, we only have sets and elements. This is equivalent to saying that our recognition is only composed of comparison measures. However, as will be discussed later, this poses certain ethical problems.

2-3-2.The Relativity of the Comparison Act

Here, I will discuss the relativity of the act of comparison itself. The definition of comparison, “preparing states or options which are distinguished by difference and identity” contains vague and extremely mundane language. What does it mean to be “preparing?”

This abstract word has two problems: (1) the diversity and relativity of the act of "comparison" and (2) the infinite freedom of thinking possibility with language and the finiteness of the object of measurement itself. I would like to explain from (1).

2-3-2-1.The Relativity of Comparable Object

There’s some exceptions, but basically the comparison act has limits about its object because of the physical properties of the comparator and comparison is performed relatively. What does it mean?

For example, can we feel light with our ears? Or can we hear sounds with our eyes? Can we taste food with our index finger? Can a weathervane measure the temperature, can a thermometer measure earthquake intensity…you would understand what I mean. A comparator can measure only proper objects. This is the relativity of comparable objects.

Of course, if some kind of mechanical device is used, it is possible to convert them in some way, such as visualizing the wavelength of sound, so that infrared rays can be visualized, but once the wavelength of sound is converted, it becomes vision. Seeing and hearing are still different, even if they can be translated. Their possible states, that is, options are all prepared in different ways.

So, the method and object of comparison are basically unique to each comparator, and when talking about “comparison” in general, we can only settle for an abstract way of talking that does not rely on specific substances or rules. Thus we can’t avoid the abstract word “prepare” in the definition.

However, as far as I know, at least two comparators violate the constraint that “the measuring object is limited.” They are language and money. These measures don’t need the identity derived from the physical properties of things, and can measure the difference and the identity of all objects of comparison only by the identity of “comparing by them.” When their works are viewed as a cycle, they are expressed as “baseless.”*2

*2…Here, I refer to “Ontology of Money” by a Japanese economist “Katsuhito Iwai.” At 2-5, I briefly explain his work.

By way of caution, I don’t think money can solve everything. Ultimately, if there is an agreement of the people who evaluate, the price can be set regardless of the possibility or impossibility of the exchange. In the past, even humans themselves were commodities, and in principle it is permissible to put a value on all things. Regardless of whether they are wrong or right.

The peculiarity of the object of the comparator shows that “difference” and “identity” are recognized in a relation like circulation. In other words, the difference between certain objects is “not known unless compared,” but since comparison means “preparing states or options which are distinguished by difference and identity,” so “difference” and “identity” are detected in the case that the possibility of detection is in advance prepared.

This is, for example, one reason why the whiteness of multiple types of snow cannot be distinguished by ordinary Japanese people, and that ultraviolet rays cannot be perceived as visible light by humans. Or it means, at a certain class, that we can explain things like “mutually understandable/not mutually understandable” between different cultures as whether they are sharing their measures to a certain degree, or in another class, it shows from an epistemological standpoint that human’s perception is limited to the limits of comparators that humans can use.

Despite these limitations, the reason why human beings have been able to advance science so far may be because we have been able to invent and combine a wide variety of comparators by leveraging the substances that exist in the world, and we can use languages and symbols that can be used without physical limits. Language and symbols can set up virtual possibilities — distinguished options — that can even compare technically and physically incomparable things, speculative hypotheses thus set up, and then we follow them by developing technology, or vice versa, or repeat them in a cycle.

2-3-2-2.The Relativity of Information in Knowledge(Linguistic Information)

Next, about (2). About “preparing possibilities and options”, what we must consider is the duality of the prepared options when thinking about them in language. I mean the value of information for an individual is different between the state of ignorance (a state in which one cannot recall appropriate options) and the state of having knowledge (a state in which one can recall appropriate options). I guess, perhaps this is related to the concept of relative entropy.

 I would like to explain what it means, starting with the human imagination.

When people use language, imagination is not regulated by the laws of physics, so we have freedom of preparing and selecting whatever possibilities, even if they are fantastic. For example, when you make a sentence “birds fly with wings,” instead of “birds” you can say “people fly with wings,” “stones fly with wings,” “glass and houses fly with wings,” “freedom and future fly with wings,” “Light, umbrella, and electricity fly and fall fly with wings.”etc… Oddly enough, our imagination is as infinite as our thoughts go, so the possibilities prepared by language follow it.

Although it is quite strange from the point of view of information theory, if we disregard the context of real life, common sense, rules and physical limitations that we have as knowledge, the amount of information in the conversation by meaning of language is infinite. This is the source of creativity and error at the same time, and one of the qualities of freedom that humans have uniquely over other animals. With this freedom, the possibilities that one can prepare when using language are potentially limitless.

However, the reality is different. The possibilities that things can have in reality are limited. This is where the duality of “prepared options” occurs.

For example, there are no possible “positions” other than on the straight line of the trajectory for a ball rolling straight on a flat surface with no obstacles. A measuring object is limited to possibilities that it physically takes. Or, in the formula “y = 2x” in mathematics, the possible values of “y” are limited. But in human imagination, the ball can fly or any character can be written in “y.” That is the duality.

Here, when we refer to a physical phenomenon, perhaps a kind of epistemological problem arises, such as whether humans can really know “actual possibilities” and how to distinguish them from imaginary ones.

Thus, when selecting something, for an ignorant person —a person who is unable to imagine the next possible options according to the system of relations— the number of prepared options becomes infinite, for a person who has knowledge can predict appropriate options and restrict them.

This duality must be taken into account when thinking about “prepared options” in language. This is because it is one of the activities of intellect to reduce the options to be prepared from infinity and optimize them. Or conversely, art is an attempt to expand its possibilities to infinity or to unknown worlds.

2-4.The Usability of Information and Theory of Logical Types of Comparison

Having said this so far, I would like to write down my thoughts on what is meant by the "usefulness" of the information that I mentioned at the beginning —although that is an incorrect expression. Also, as has been mentioned several times in the discussion above, I show comparison forms a kind of hierarchical structure when we look at the phenomenon of comparison from the definition of information defined in 2-1. And I show moving up and down in these layers is one of the most important works of intellect.

2-4-1.The Usability of Information

When thinking about useful information, the question: what is “usefulness?” must be asked in the first place. In my view, usefulness is not something that absolutely “exists.” For example, comparing a hammer to a banana, thinking of a question: which one is more useful for hammering nails? This would be a “hammer.” But when thinking of another question:which one is more useful for quickly quenching hunger?, then, it is clear that “banana” wins. Usefulness is always limitedly called so by its relation to other things, surrounding things.

And then let’s move on to the next question, why is “hammering nails” useful? Let’s think. Because the usefulness of “a hammer,” at least as far as we have seen, must depend on the usefulness of “hammering nails.” The answer to this would be, for example, “Because we can fix wood to wood.” Then why is it useful to “fix wood?” Then, the answer would be for example ”Because we can build a house by doing so.” And why is it useful to “build a house?”, then the answer would be “Because we can live there avoiding rains and winds…,” if we automatically continue to ask, we would reach the question:“Why is living a life useful?” which is a question that we can’t answer quickly, or we should avoid the act of asking itself about it.

Now, with all that I have said so far, I would like to show that basically the usefulness of something comes from its use in the next tool or function that contains or uses it, furthermore the usefulness of them has the structure that continues to depend on the next, the next next… tool or function.

So, for example, a “banana” that can’t be used in nailing and fixing wood, cannot be included in the relationship between the usefulness of building a house — I wonder if it may be different if a banana is frozen or used as carpenter’s food. It cannot be used in any of the previous scenes. Or, for example, it’s impossible or hard to find the usefulness for things such as radioactive waste that has no other tools or functions to use and has no choice but to bury it in the ground, or such as people’s “purpose of life” that we should avoid treating as a tool or function.

In other words, usefulness is a “relationship” which exists as the circulation circuit of functioning linkage of various tools and functions, and that relationship and circuit exist in reality as only one, or would be one of numberless possibilities. And, for better or for worse, individuals who are outside the circulation of usefulness may feel the joy of freedom or the depression and anxiety of being excluded from the functioning linkages of the ecosystem, and it can be said that in the society that generates large amounts of waste and cannot reuse them, the circulation is broken.

Now then, what is useful information? It is primarily information that can be used in a “comparator”, “act of comparison”, which is a function that processes information. Of course, information will also be used for certain tools. Therefore, information that is “useful” or “meaningful” is nothing but the information that “can be passed to the next comparator, tool, or function and used by them.” The usefulness of information is found in the circuits which various “comparators” and “act of comparison” form, and it’s in their relation to other tools, functions, and people, underpinned by its circulation.

For example, in the formula “y = 3x”, when you substitute a value for x to find y, x is “waiting for one value out of the possible values,” so in the sense defined here, it performs the act of comparison. And since it “outputs a result selected from the possible values of y” by that substitution, it can be regarded as a comparator.

Then, is there any meaning in substituting the information “I have US citizenship” for this x? Of course, this information has no meaning or utility in “y=3x.” However, the information “I have US citizenship” will be processed as useful in the immigration process at the airport — an act of comparing decides whether to permit or not one to enter the country based on passport information. With the information “x=3” it is reversed.

So, in fact, the phrase “useful information “ erroneously ascribes to things the attributes of their external relations. Usefulness is not a term of belonging to something, but it’s a term of a relation to something else — and perhaps most adjective-noun conjugations do so. For example, even the nonsensical word I made earlier, “yutsukinma,” demonstrated its usefulness as an explanation.

I note that though I’ve said the above, I don’t praise “usefulness” without limitations. But generally speaking, if something has no usefulness, it’s a needless game for life, or if someone got attached to usefulness too much, it would be a pain.

The usefulness of the information I described here is another way of saying that the object of comparison is unique to each comparator. And from this, humans, whose language does not have a specific object of comparison, have the freedom to verbalize all kinds of information and disembeds‎ it from relationships, and can find usefulness in a wide variety of ways. And we often lose sight of what it was in the first place, forget that it is something which can only be found in relations.

This is perhaps the kind of logic that can be said of relations in general, which is, in other words, the denial of Plato’s theory of ideas, that ideas such as “truth,” ”goodness,” “beauty”… do not exist “in themselves” but rather they are always called so in relation to one term with another in the form of circulation.  Such matters can be generalized.

2-4-2.Logical Types of Comparison

So far, though I have often said that, the act of comparison forms hierarchies. Because I don’t know a good other way to express them, I call them hierarchies of comparison, but they are not top down like a tree or pyramid. Rather hierarchies “exist” nowhere. They do not “exist,” but every time we perform an act of comparison, or every time we define a set, in Russell and Bateson's terms, its class and members, we are simultaneously establishing it implicitly. Sets I refer to are not something that exists in themselves. Rather, I mean the act of “regarding something as the same” or “distinguishing the difference of something.”

For example, consider a class(set) called “Chair.” It will form a tier with many elements — chairs as individual objects — bound together by the identity of the definition of “Chair.” When a person is asked to give a chair and picks up one as a member of the word “chair” or an individual object, there exists a relationship of “selecting one from prepared options.” In other words, there is always one piece of information when going down the logical hierarchy.

Or consider this example. When people were shown cards with various pictures on them and were told, “Choose the one which pronounces ‘inu(means dog in Japanese)’ in Japanese,” people choose a member(element) from a class, “the set of cards with various pictures.”

In other words, “answering questions,” one of the activities of intellect, is no other than selecting an element, a member, so “the answer” from the class which still has unknown, “the set of possibilities or options which people consider as can be an answer.” If I express it like this, you will understand how important it is to “select a member from a class,” that is to move up and down the hierarchy of comparison. Or, selection from a measure corresponds to going down the hierarchy of comparison and making an expression of the object of comparison more detailed and specific. In the field of information theory, this would be equivalent to receiving information.

And vice versa must also be considered. To move up the hierarchy of comparison, to retroact to the options of options. For example, it means collecting elements, members to create a new set, class, which is nothing but “abstraction” and “generalization.” Or, in an analogy on another level, it corresponds to the act of constructing a theory that expresses various phenomena on a single measure. In the field of information theory, this can be compared to the act of creating a “receiver” itself.

Also, about the act of “knowing” or “understanding,” hierarchies of comparison means that we call by those names the relationships between appropriate hierarchies to each other. This is easy to understand, considering that I said earlier that there is no need to describe the propositions of economics from the quantum level.

Although both are representations of the world, it is not necessary to “know” quantum-level behavior in order to “know” the economics proposition. Although there is no clear standard for “knowing,” we vaguely share some kinds of scope about hierarchy such as “to a certain degree, if one can make selections for questions, we judge one to know or understand something.” In other words, “knowing” means being able to make selections in a relationship between appropriate hierarchies, in that scope.

And this is related to two philosophical questions with different meanings. One is the question of whether a computer “understands.”

For example, an expert system can answer the questioner’s question, but does the machine really understand the knowledge? Regarding this question, I think that the hierarchical nature of comparison can bring about one view. So, the system “knows” the relationships up to a certain superficial level, but deepening the question beyond a certain level, it “does not know.” Or, a parrot that shouts “Good Morning” certainly “knows” the greeting at the level of phonological pronunciation, but does not “know” at the level of its communicative meaning. There is a hierarchy problem here. And, I note that fundamentally the relationship between economic propositions and quantum behavior is no exception.

If we want to draw a line between humans, parrots, and machines, we unconsciously have the scope of “knowing,” and the desire to give human privilege, I think. But they are the same as a matter of hierarchy. Despite “understanding” up to a certain degree of hierarchy, the reason we can communicate is that next receiving comparators and functions use that hierarchy’s “understanding,” and we can pass the second “understanding” which is generated there to another comparator and functions, and we can pass the third “understanding” which is generated there to another…as long as its circulation continue, we can use our “understanding.”

Our “knowing” about many matters is in a very crude accuracy or short-sighted framework, and even if we do not “know” the behavior of the quantum or the system of the whole world, we can live by exchanging the wisdom unconsciously inheriting customs “know.” And if we cannot save our own living environment in this destination of the international society, or if we bring about a nuclear war, then from the point of view of the long survival of human beings, “knowing” by the “customs” of the past “primitive” society could be superior to “knowing” by present civilized society.

Such a matter, a kind of vanity of “knowing” just expresses a simple fact that is “the object of cognition does not exist within cognition itself,” “thing points to and thing is pointed to are different”  in other ways. I said so in the section of the undecidability of solipsism, there’s no entity in recognition. At most, there are only models. If we admit this premise, ”separation of thing points to and thing is pointed,” in principle, our recognition is no other than regular “interlocking” between “the media or symbol used in recognition” and “the object of recognition.” As long as the “interlocking” is shared, we can communicate the information of recognition of objects by words or symbols, economically omitting reference to the extremely complex process through organisms or measuring instruments.

In the above, I'm saying “knowing” is “relation=interlocking of selection” from another point of view. The definition of knowledge derived from the definition of information is still consistent here. It can be said that “We only have relations,” as the rephrase of ”We only have sets and elements” and “We only have comparison measure.” And there, the problem of ethics will appear again.

And another problem with the scope of the hierarchy of “knowing” relates, for example, to the Socratic question and answer. Socrates, speaking of his own ignorance, made the other person aware of the ignorance of the good through dialogue. Socrates was unusually obsessed with the scope of “knowing.” His drastic examination has the true value of philosophy. Therefore, examining beyond the scope of this “knowing” is an act that is very closely related to philosophy, and it may be said that examining is philosophy itself.

Having said this so far, I think you can understand how important this hierarchy of comparison is.

2-5.Money of Intellect—about Set Rationality

Up to here, I have been using the term “comparison measure” in a special definition that does not generally apply, meaning “a set of possible values.” In this paper, I will continue to use the term in this sense in the next chapters, but here I will discuss the comparison measure in its original meaning, the comparison measure as socially acceptable weights and measures. For convenience and distinction, here comparison measures in their original meaning are expressed as <comparison measure> and <unit>.

The reason why I’m having that discussion is because the socially accepted <comparison measure> has extremely significant properties when thinking about “intellect.” Here, I will critically examine Gregory Bateson's argument with reference to Katsuhito Iwai's “Ontology of Money,” and demonstrate that it brings about a certain kind of rationality. Furthermore, this argument has a similar relationship to Carlo Rovelli's explanation of time, and the theory of ideas can be considered to lie on an extension of that rationality.

The discussion in this section doesn’t show the actual generation process of <comparison measure>. I note that I just show it is more rational to recognize something by using it than recognizing “relations” which are not centralized.  

2-5-1.The Birth of <Comparison Measure>

For discussing <comparison measure>, I'll refer to Katsuhito Iwai's ”Ontology of Money.” It can be said that money is one of the most commonly used <comparison measures>. What Katsuhito Iwai describes in his “Ontology of Money” by modeling emergence of money has a relationship that can be extended not only to money but also to the birth of <comparison measures> in general.

The summary in “Ontology of Money” by Katsuhito Iwai is as follows.

Unlike mere commodities, money has privileged exchangeability with various other commodities such as linen, outerwear, tea, coffee…… and so on. And as long as money has such exchangeability, it can be the money that sustains the market economy.

Because the reason why the one pass the money as “money” to others is that the one believes money have the exchangeability to other’s commodities, on the other hand, the reason why others receive the money as “money” is they believe that they can exchange it for another one’s commodities, and the reason why another one receive the money as “money” is the one believes that other people exchange it to their commodities…… it continues forever. So for example, if hyperinflation arises, and money changes into mere paper, a piece of metal or electronic information, money loses its own being as “money.”

Thus, Katsuhito Iwai concludes that the reason why money is “money” is that it is treated as “money” by all the people who use it, and the being of money is structured by this baseless circular reasoning.

One of the reasons why money which has privileged exchangeability emerges is because the barter economy is quite inefficient. If money does not exist, exchange—the coincidence of values of things which people who exchange evaluate—become difficult.

To explain it, I show a very simple allegory.

Assume the world is without money, and a person who has only vegetables in a farming village wants fish. But another person who has fish wants a shirt which is an industrial product. In that case, to achieve the exchange, they need mediation by a person who has a shirt and wants vegetables.

In reality, there are not so many cases in which the coincidence of exchangeable things which various consumers and producers have. If money does not exist, we need so many such miracle mediations for the exchange of everything. 

Money was born to avoid this kind of inefficiency. Although this is not the actual birth process, the above can be considered as a model to explain its rationality. This is the outline of “Ontology of Money.”*3

*3…”Ontology of Money” is not translated to English. If you want to learn more, I recommend reading “The Capital” Vol.1 by Karl Marx. Katsuhito Iwai is a Keynsian, but in “Ontology of Money,” he examined “The Capital” in detail and discovered the ontological structure of money. He critically used the formal structure of Marx’s argument and removed labor value theory from it. The labor value theory is denied but, Marx's work would help you to understand my argument. Alternatively, in order to read ”Ontology of Money,” you can learn Japanese!!

The exchange of the barter economy has no centralized measure. So, the exchange of things to things has much inefficiency. The birth of money, the centralized measure changes the situation and makes the economy efficient.

And this kind of logic can be extended to <comparison measure> in general. What do I mean? To explain it , let's take a look at Bateson's argument in “ANGELS FEAR.” He says the following.

This Bateson’s argument has extremely important implications for the act of “comparison” that I have been discussing so far. According to him, there is an important difference between “comparing” and “measuring.” To close this gap, Bateson says, “a further addition to the balance” is needed.
Then, what is “a further addition to the balance” Bateson mentioned? I believe that is the following.

To explore “a further addition to the balance,” what he calls the difference between measuring ratios and detecting subtractive differences, we have to consider “What is the situation that we already know the weight of one of the items to be compared?” 

So, assuming that we use only the balance to determine the measuring unit, think about what is necessary for that. To do that, it would be necessary to prepare a certain thing to be standard weight, weigh it against other things many times, and prepare a large number of balanced ones. Thus, assembling one or more of the “initial weights and their balance” and comparing something with those, we can distinguish how many of the “initial weights” the other objects weigh. In other words, a <unit> and a <measure> as its set is born.

What this means is that what is necessary for “measuring’’ is “continuing to compare a single or a plurality of something which is identical enough to use as a unit.” That changes and elevates class, “comparing” to “measuring.” As a result, the differential relationships between various individual objects are centered on the differences in one <unit>.

And it’s the situation that we already “know(define)” the weight of one of the items to be compared. After all, the thing which we use to “measure” another thing as a <unit> tells nothing about itself. I think it’s fundamentally the same as when we consider the whole of recognition. As I have said that because if “thing points to and thing is pointed to are separated,” it’s no other than a “relation,” “interlocking of something to other.” 

Why is this related to Katsuhito Iwai's “Ontology of Money”? This is because the formation process of <unit> has the same logical structure to the generation of money. This is not surprising considering that the latter is one of the former. Furthermore, the three functions of money, “unit,” “exchange,” and “store,” are originally the essence of the function of complete information, and money is a special element of the set of information.

A comparison of “Ontology of Money” and <comparison measure> is as follows. The state of “comparing ratio” in Bateson's words is a state where we compare individual objects to individual objects, in which there is no central unit, it’s the state of barter economy. And as the process continues, when the stable weight is found, then it can be compared with the state in which the money is born. 

However, the reader of “Ontology of Money” might argue that such a comparison contradicts the baselessness of money. In contrast to the baselessness of money, <comparison measure> has a physical basis. That may be true, but when I compared the circular reasoning in “Ontology of Money,” I had a different idea.

Comparing “Ontology of money” with “comparison measure,” I thought it means that these circulation would rather express the structure of a certain type of “act of reasoning” itself. “Reasons” that are given by intelligences aren’t just mere preparations for linear demonstration such as syllogisms, having a bird’s view, they are parts of the cybernetic loop of intellectual cyclical activities. Therefore, it has a high affinity with the circular reasoning of “Ontology of money.”

In other words, “measure” is based on each “identity of different objects of measuring,” and “differences of identical objects of measuring” are measured on the basis of “measure.” 

<Comparison measures> and <unit> appear to exist in themselves when used, but they are never grounded in isolation from the environment of the real world, but are supported by their functional relationships.

The above discussion applies to various <comparison measures>. For example, I think Carlo Rovelli pointed out the same relationship to what I have said above about time.

What he is saying is not that "time exists" and it is flowing to everyone, but that we call all "changes" in this world "time."

This means that even the observer himself is a part of “time itself” and can only be understood by comparing something with something else – in a similar way to circular reasoning. Time t in classical mechanics is not an “existing entity” but temporarily created by centralizing a change as standard of all other changes.

I believe that here, exactly the same work that Katsuhito Iwai has done to Marx's theory of form of value –removing the “entity” of value which is “labor power"– has been done to classical physics.

While Katsuhito Iwai worked towards solving the mysteries of money from barter exchange, Carlo Rovelli's work is the opposite, moving away from the time of classical mechanics and towards the elucidation of microscopic time by loop quantum gravity theory. Even so, Katsuhito Iwai's argument and Carlo Rovelli's argument may seem to be different, but they are essentially the same, and are discussions about the birth of <unit>, <comparison measure>, the dissolution of the entity.

In other words, they are talking about how things that appear to be  “entities”' are created along with relational theory, and how things that appear to be “entities” are nothing more than an accumulation of relations.

I cannot say for sure that the loop quantum gravity theory is correct, as it may change with future developments, but I think this kind of argument has some validity.

It is no wonder that time has a similar relationship to money. Time is one of the <comparison measures> that people have no choice but to measure whether they like it or not.

You would clearly understand that the transition from “barter economy” to “the birth of money,” from “comparing” to “measuring” as described above involves the development of a certain kind of rationality. It is efficient rather than treating individual objects with individual objects, defining a centralized and privileged individual object, the <unit>. When we “compare” the privileged individual object with other individual objects, we can “understand” various things as long as that <unit> is shared.

The importance of this rationality can be easily understood by considering that we measure distance without any <unit>. It is easy to understand how life would be inconvenient if we were asked to communicate the length of something without a <unit> such as “1 cm.” In such a world, to express distance, you have to say things like, “From my house to yours, it is 100 burdock, 200 eggplants, 300 tomatoes, and 250 apples.” Accurately, even you can't say it's 100 burdock, because if you compare the same thing, it becomes a <unit>.

Of course, centralization of <unit> is an ongoing process. It is possible that we have various trial and error and twists and turns to reach a more stable identical <unit>, such as those exemplified by money, and that is an ongoing phenomenon.

In this way, the <unit> or money treats other individual objects, various commodities which have various differences in a unified way by comparing self and makes others comparable things. The world of cognition essentially changes depending on whether the centralized object exists or not.

2-5-2.Set Rationality

If we abstract and define the essence of this rationality, it can be reduced to the following two points.

1. The circulation of the system itself is sustained through continuing being verified and used by many people and elements.

2. The system communicates, exchanges, expresses, or transforms many other elements in a centralized and unitaried way and procedure.

With only these two conditions, we can find the formal analogues to the circular reasoning of “Ontology of Money.” I think there are many things that fit this definition. I show those below.

1. The problem of universals

“Universals” and “individuals,” comparing the former as “money,” the latter as “commodities,” the concept of “universals” makes sense as long as “universals” can be exchanged for “commodities.” Furthermore the living circular reasoning may be realized in the dichotomy “abstract/concrete.”

2. The Internet as an information exchange system for computers

Although there are various protocols, the Internet, in which communications arise by enumerating binary differences in the physical layer, can be said to be “money” that exchanges various information as “commodities” processed by servers and client PCs. Or you may think binary differences in the physical layer are “money,” and the Internet is rather a “market.” However, looking only at the abstract logical structure, I think that the whole Internet and the information processed by terminals correspond to “money” and “commodities.” Binary differences may be in this relationship for information processed on individual computer applications on the more fundamental layer rather than the Internet.

3. Platformers as unitary systems that subsume diversity

Furthermore, although they are systems in the higher layers of the Internet, Facebook, Amazon, and Google are all unitary systems that subsume diversity, for each, platform of people, platform of things, and platform of information. And as a result, they are imitating the structure of “money,” I wonder. These platforms are sustained by the network effect of being used by a large number of people, and as long as the effect continues, they can sustain.

Although the subject providing these services is a private company, the platform has a public nature similar to money. This is similar to a situation where the set itself becomes an element of the set. I think because of this kind of situation, the debate over regulation of platforms becomes so confusing.

4. Various phenomena and a theory

A theory explains the mechanism of a number of phenomena by their identity, however a theory can be a valid theory because of the existence of numerous phenomena that prove it. I think this is common to all disciplines, whether it is “social phenomenon/sociological theory”, “physical phenomenon/physical theory”, or “psychological phenomenon/psychological theory”…… Therefore, it can be generalized to more abstract levels, such as the relationship of “inductive/deductive” or “rule/cases.”

5. Languages, symbols

This has already been pointed out by Katsuhito Iwai, but I have my own interpretation. So I will deal with them again. Language makes the recipient of it refer and select certain information from various information which humans have, such as language itself, the five senses, memory…and so on. Language is the “money” of “information=commodities” for humans.

6. Market

I think that the market is indispensable for the construction of “Ontology of money” itself, and this is exactly the analogue of the Form of Money. A market is born when diverse buyers and sellers come together, growing markets attract more merchants, and disappear when they all have gone away.

7. A set and elements

A set selects elements by its definition, and when elements assemble, a set is born. An empty set is also a set formed by the fact that it has “no elements” — because if it has elements, it’s not an empty set — , which is also born from the contents of the set, and its definition also selects “no elements.” In other words, they are called “class” and “member” by Bertrand Russell and Bateson.

As far as I know now, the above has the same logical structure as the structure of money. If the hypothesis that a set and elements are analogue of circular reasoning of “Ontology of money” is correct, due to its high level abstraction, they can be treated as the center, “money” of these structures with circular reasoning logic. So, I name this rationality “set rationality.”

2-5-3.The Dream of Theory of Idea

By reaching this point, I can explain without contradiction the conflict between Bateson's definition of information and Plato's theory of ideas, as mentioned in the introduction.

So, Bateson's definition of "information" referred to the most primitive "intellect," the lowest level of "relations," whereas "absolute intellect" in Plato's theory of ideas referred to the abstract “intellect,” the accumulation of relations which is highly developed to even reaching theory or <comparison measure>.

Ideas, which are flawless and perfect prototypes of things that exist in this world, correspond to the “universals” in the problem of universals, and “intellect” which is absolutely correct and infallible, corresponds to “theories” that predict the world. I think we can think of it that way.

However, as mentioned earlier, “set rationality” can only be located within the environment of the real world and its relationship. If that seeks for right things to this world. “Set rationality” appears to be absolute. But rather it is the opposite. The absolute is an accumulation of many relations, the more it is supported by more relations, the stronger it becomes.

Therefore, I believe that the theory of the idea that seeks absolute knowledge was a dream that Plato, who lost Socrates, had in “set rationality.” And I am sure that the dreams and passion for seeking such things are still passed down to those who pursue theoretical knowledge.

2-6.Things We Cannot Compare

Finally, I will discuss the ethics and maturity issues surrounding “comparison.” As I said earlier, in a sense, we only have “sets and elements,” only “comparison measures,” and only “relations.”

To put it bluntly, there’s almost no meaning in pointing out that something is a measure or a relation despite its appearance. Those of us who have language and relate to the world through information can use everything as a measure of comparison, whether it is useful or not.

For example, if an adjective and a noun are combined to express a situation, the noun is already a measure of comparison — as the identical thing to compare other possibility of description of situation, that is, difference, or if we regard adjective as the identical thing, then we select one noun from other numberless possibilities of nouns which can be described by the adjective. 

As we saw earlier, this applies to verbs, and as well as other parts of a sentence. They specify the relationship between each piece of information in a way that excludes others, and produce terms.

The above is just an example of how everything is a “comparison measure.” However, there are big intellectual, ethical, and maturity-related problems in making an absolute determination that “there are only relations” and “there are only comparison measures.”

A “comparison measure” fundamentally follows the logic of the comparator, the receiver of information. A comparator, a comparison measure, produces information by eliminating information that it cannot process. Although the information produced in this way reconstructs reality, to live in that world is equivalent to losing reality as it is, the world itself. The attitude regarding “there is only a comparison measure” basically views the world of information as absolute, and it is an attitude that risks losing the reality that we cannot yet know.

In particular, the “comparison measure” created by language can be set arbitrarily. Generally speaking, those who live according to a “comparison measure” created in a way that denies reality are doomed because of the incompatibility between their own nature and reality. So, I think it is extremely necessary for human life to somehow correct such “comparison measures” against reality.

However, there are some complications with this. Ecosystems and human societies produce comparison measures in themselves, and are also sets of comparison measures that interact with each other. Such conformity within society and conformity to reality itself and nature are not the same. Conformity in Nature does not necessarily mean social success. The pursuit of social success can lead to failure in nature. Adaptation to social reality cannot be equated with adaptation to reality in nature.

In addition, if the undecidability of solipsism is correct, it would indicate the following aporia. In principle, we cannot declare that the totality of our recognition is reality or a dream. Any position asserting either is intellectually dishonest. It rejects both the position that the world of one's own information (comparison measure) is reality itself, and the position that all information in this world (comparison measure) is unreliable. In other words, it shows that it is impossible to distinguish whether the "comparison measure" is on the side of humans (is everything a dream shown by the comparison measure) or on the side of the world (is the comparison measure reality itself) .

Therefore, from the above, we can conclude that the boundaries between “all things are the measure of man” and “man is the measure of all things” is ambiguous, and yet both cannot be asserted, so “all things cannot be reduced to the comparison measure.” All things can be compared, and all things cannot be compared.

The situation in which the possibility and impossibility of comparisons are actually established—the situation in which we are in the world of information—are directly connected to ethical issues.

Thinking that the world of comparison measures is the whole world is equivalent to thinking that the relationship between oneself and something is the whole world. At that time, people literally become self-centered and lose sight of the existence of others who are related to something different from themselves. On the other hand, when one considers the world of comparison measures to be a dream, one loses all reality and the existence of others. Relationships with others are formed in the middle between them.

However, in reality, absolute trust and distrust in “comparison measures” are not good for us to simply dismiss both sides. When making judgments based on strictly logical thinking, you cannot use anything other than  “comparison measures” as a standard, and the absolute distrust of comparison measures, which I will discuss later in this paper, also has some kind of religious and psychological significance. We need to deal with matters at the appropriate time, with the appropriate attitude and with the appropriate “comparison measures.” It is also the “comparison measures” that determines “what is appropriate,” and we determine it both in accordance with and against the actual environment and the flow of time. Thus, people exercise their freedom and move forward.

Or,humans are born in different places and environments with different bodies, and live different lives and time. There are no uniform people like industrial products—in strict, nor industrial products. All things have different relations to others, lie in different flows of time. But “comparison” compares something by unifying it with abstract identity while removing these differences. The evaluation created by comparison, the world created by it, is not a completely fair world. 

Humans can never create the perfect fair world, but never live without the violence of comparison. An ethics exists in the attitude of awareness of that aporia and making the world less that violence. And I believe, there’s a moment of maturity, as one of the great awareness of difference between self and others, in the awareness that primarily we can’t compare any person with another person, in the awareness that “I cannot compare self with someone,” in the awareness that people live in the different flows of time. In the place we are flowing, between the things we can compare and cannot compare.

Next Chapter : 3.The Form of the World, the Forms in the World, the Form “Good” and “Bad” Weave