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No Form Action Theory |
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No Form Action Theory |
https://orcid.org/0009-0005-4318-2670
In the world of language, the core is the use of language. The purpose of using language is for communication between people. This communication between people is not always effective, meaning some people may not express their meanings clearly, and some may not understand others' meanings. The most important reason to consider here is whether people communicate according to certain effective rules. Such rules could be certain habits, tacit understandings, or explicit agreements reached between the communicating parties, which are some customized rules. However, the rules we want are not these; we want a supreme rule that has the highest standard, a rule that any customized rules must also follow. The supreme rule we currently recognize is formal logic.
Formal logic is the fundamental law of human thinking, providing us with tools for reasoning and argumentation. Any philosophical system, if it aims to explain the world, must be built upon the foundation of formal logic. On the other hand, any philosophical system, if it intends to fully explain the world, must adequately explain and integrate formal logic, otherwise such philosophy would be incomplete. Because if it fails to adequately explain formal logic, then formal logic would remain in a position above this philosophy, becoming an a priori, irreducible logical rule. Therefore, this philosophy would have a fundamental flaw in explaining the world, and thus would be unable to fully explain the world. On one hand, we need to use formal logic to study philosophy, and on the other hand, we need to use philosophy to explain formal logic. This seems to lead to a circular argument. On one hand, in philosophy we want to transcend formal logic, but on the other hand, formal logic always accompanies any theory. This seems to suggest that there is no theory that can transcend formal logic to explain formal logic itself.
Traditional philosophical systems often view formal logic as an a priori, self-evident law, without providing a deep explanation or argumentation for it. This has led to a disconnect between formal logic and philosophical systems, where philosophical systems cannot explain their own logical foundations, nor can they provide sufficient basis for the validity of formal logic. Neither Kant nor Hegel could effectively explain formal logic. It seems that no one has yet been able to truly effectively explain and elucidate formal logic. This is because any explanation of formal logic must use the rules and principles of formal logic itself. This again seems to lead to a circular argument: using formal logic to explain itself. Formal logic becomes the ultimate basis for its own legitimacy, unable to be "explained" by any other more fundamental theory. It is precisely this unique self-sufficiency and prerequisite nature that places formal logic in an insurmountable foundational position, upon which any explanation and theoretical construction must be built. Formal logic is in such a situation: it is both an indispensable foundation and difficult to be truly explained and integrated.
Is there a higher basis beyond formal logic? Such a basis would be the standard from which formal logic itself arises. Now let's use the theory of no form action to explain the three basic laws of formal logic. We'll see how formal logic integrates into the theory of no form action to become a unified whole. The theory of no form action itself also uses formal logic; is such an explanation possible? Yes, it is possible, because the theory of no form action can explain itself. The theory of no form action has the ability to integrate itself into itself. The existence of a theory with such capability is not strange, because the entire world itself integrates into itself. This world is a self-organizing, self-evolving system, and its existence and development follow its own laws. This also indicates that formal logic has already touched upon the fundamental nature of this world; it's just a matter of how we find the key to explain it.
Let's first analyze the three basic laws of formal logic: the law of identity, the law of contradiction, and the law of excluded middle. We'll define a few expressions:
A is A (Expression 1-1), A is not A (Expression 1-2); A is B (Expression 2-1), A is not B (Expression 2-2).
Law of Identity: Expression 1-1
Law of Contradiction: Expression 2-1 cannot be both true and false at the same time, Expression 2-2 cannot be both true and false at the same time.
Law of Excluded Middle: Expression 2-1 is either true or false, Expression 2-2 is either true or false.
Let's first look at the law of identity. Expression 1-1 is true, so "A is not A (Expression 1-2)" is false. We are now considering the problem only from the perspective of formal logic. Expression 1-2 is false, but does Expression 2-1 satisfy Expression 1-2? Obviously it does, so Expression 1-2 is false, and eternally false. However, we usually use Expression 2-1 in daily life, for example, "Socrates is a man," where "is" can be interpreted as "belongs to (or is included in)." This means that the "is" in the law of identity and the "is" in Expression 2-1 are different, even if we interpret the "is" in the law of identity as "belongs to," we would still conclude that Expression 1-2 is false. Unless the "is" in Expression 1-1 and the "is" in Expression 2-1 are fundamentally different, meaning they cannot be substituted for each other at all. So how should we explain this? "Socrates is," the "is" in this expression is different again, containing the meaning of "existence."
In other words, the meaning of "is" is diverse, although in practical application, problems generally don't arise, possibly due to the accumulation of experience that helps avoid issues. However, this may lead to obstacles in studying the foundational theory of formal logic, increase the complexity of formal logic, and hinder our clear understanding of formal logic. The question is, although "is" has different meanings, all these types of "is" can have true or false expressions. How do we explain this? I think we need a unified explanation of "is" to avoid such confusion and gain a better understanding of formal logic.
Why not interpret the "is" in the law of identity (Expressions 1-1 and 1-2) as manifestation? That is, self-intuitive manifestation (directly manifesting itself, so transparent that it can manifest itself). Isn't the self without indirectness just itself, isn't it identity? From the linguistic form, the two A's in Expression 1-1 look the same, but they are not. For Expression 1-1, the first A is an isolated A, while the second A is a manifested A. For the direct manifestation of the thing A represents itself, it is its own authentic manifestation, and Expression 1-1 as a linguistic expression is the authentic manifestation of A. Such a linguistic expression is also a kind of manifestation, which can be called "true" (manifested truth). This is a state of unconcealment, so truth directly manifests itself. The manifestation of Expression 1-2 is called "false" (manifested falsehood).
However, another question arises: if we interpret the "is" in Expression 1-1 as manifestation, what does "Expression 1-1 is Expression 1-1" mean? Does it conform to Expression 1-1? "Expression 1-1 is Expression 1-1" expresses a kind of manifestation in linguistic expression, meaning that Expression 1-1 expresses the authentic manifestation of A in a linguistic way, and it is itself a kind of manifestation, a manifestation of linguistic expression. Thus, we can express it this way: Expression 1-1 is true (true is also Expression 1-1), or truth is truth. In language, "truth" becomes the highest manifestation, and "truth" as manifestation can only be true; Expression 1-1 can only be expressed as true and nothing else. "Truth" cannot be both true and false. The above explanation applies to "false" as well. In this way, the "is" as non-linguistic manifestation and the "is" as linguistic manifestation in Expression 1-1 are unified. Therefore, the manifested "is" in Expression 1-1 becomes self-consistent. This means that the "is" in Expression 1-1 and the "is" in "Expression 1-1 is true" both mean manifestation, because "Expression 1-1 is true" and "Expression 1-1 is Expression 1-1" mean the same thing.
Only the direct manifestation expression of Expression 1-1 is eternally true. Only the expression of Expression 1-2 is eternally false. In this case, the "is" in Expression 1-1 expresses manifestation, it is a manifested being; while the "is" in Expression 2-1 expresses an "attribute" relationship, it is an isolated relationship, an isolated existence. According to the theory of no form action, they cannot be substituted for each other, but can only be transformed into each other. That is to say, when the second A in Expression 1-1 is replaced with B, the "is (manifested is)" in Expression 1-1 should be interpreted as transforming from manifestation to belonging (isolated is); when B in Expression 2-1 is replaced with A, the "is" in Expression 2-1 should be interpreted as transforming from "belonging" to "manifestation". The current question is how to apply this "is" interpreted as manifestation in the law of identity to Expressions 2-1 and 2-2. Socrates is a man, if this attribute relationship is a fact, then Socrates exists, and for the existence of such a fact, we can define another kind of truth, called "isolated truth". Since existence and manifestation are interconnected at a high level of no form, as long as "Socrates exists" is a fact, then this isolated truth is identical to the manifested truth.
We can rewrite Expression 2-1 as follows: Expression 2-1 can be written as "A is A in set B that contains A (Expression 2-1-1)" ("A is B" can be interpreted as: A manifests according to B, meaning B is the basis for A). For example, "Socrates is a man" can be written as: Socrates is Socrates in the set of humans that includes Socrates. In this way, the "is" still carries the meaning of manifestation, essentially extending "A is A". The added "set B containing A" and "the set of humans containing Socrates" are actually the content of factual empirical judgments (this is an isolated truth), which is incorporated into the law of identity. According to the previous discussion on two types of "truth", this actually combines the two types of "truth". This maintains the law of identity while expressing content. It accommodates both the identity of "A is A" and enriches its connotation, meaning that the individual embodies the whole by manifesting its own properties. Thus, "is" retains the implication of "manifestation", but expands it into a nested manifestation. It integrates individual properties inseparably into the whole, and in turn understands the individual through the whole, forming a unified ontological structure. This illustrates the real meaning of "is".
In Expression 2-1-1, if A is indeed an element of set B, then according to the truth of Expression 1-1, Expression 2-1-1 as an extension of Expression 1-1 is true; according to the falsehood of Expression 1-2, "A is not A in set B that contains A (Expression 2-2-1)" is false. If A is not an element of set B, then in fact, Expression 2-1-1 would become an extension of Expression 1-2, and Expression 2-2-1 would become an extension of Expression 1-1. The same analysis can be applied. Note that the purpose of doing this is for theoretical research in formal logic, not to replace usual expressions. This approach essentially binds the "isolated is" to the "manifested is", thereby unifying these two types of "is". Thus, the law of identity can be expressed as: Expression 1-1; the law of contradiction can be expressed as: Expression 2-1-1 cannot be both true and false at the same time, Expression 2-2-1 cannot be both true and false at the same time; the law of excluded middle can be expressed as: Expression 2-1-1 is either true or false, Expression 2-2-1 is either true or false. In this way, all three basic laws can be explained within the framework of "manifestation".
This lays the foundation for us to explain the law of contradiction using the law of identity. Expressions 1-1 and 1-2 are clearly contradictory for A. This contradiction arises because in Expression 1-2, a "not" is used to negate Expression 1-1, thus transforming it into Expression 1-2. To change a thing into something maximally different from it, one must negate it, turning it into something that negates it. Therefore, "negating" a thing is the greatest change it can undergo. This "negation" is the expression of motive force in language. It is the motive force in language. Since we have interpreted "is" as manifestation, any change to any concept in the linguistic world is a negation of this concept, so in the linguistic world, there is only "negation" as a motive force. Therefore, contradiction is produced by motive force. It is motive force that produces two mutually negating things. The negation of Expression 1-1 is, under the action of motive force, a transformation of such a linguistic manifestation into opposing contradictory parties (these two mutually negating isolated things are the most distinguishable). This is a united transformation of no form action. Thus, the "is" of motive force is "is not" (therefore, there is also a truth of motive force). In this way, according to the theory of no form action, we have found the "is of manifestation", the "is of isolation", and the "is of motive force".
Regarding "Socrates is", it does not point to any specific object in its expression, or rather, it can point to any object it is capable of pointing to. For example, "Socrates is human", through a process of limit, we can arrive at "Socrates is a being of isolation". Even if we don't know exactly what a certain thing is, we can reach such a conclusion. For instance, dark matter - we only know that dark matter is (exists), but we don't know exactly what it is, and we don't need to know what it specifically is. In any case, it must be something (because we already know it has gravity, at this stage we can at least say it's a thing with gravity). Through the process of limit, we can also say that dark matter is a being of isolation.
Regarding "is" meaning manifestation, this was the original understanding as early as ancient Greece. Heidegger says in "The Principle of Reason": The Greek word εἶναι, which represents the Latin esse and our German auxiliary verb "sein", means: an-wesen [present manifestation]. In the Greek sense, "Sein" means: flashing into concealment and flashing out of concealment, thus flashing, enduring and lingering.[2]
Since we have found three types of "is", are these three types of "is" a no form integrated transformation? This becomes quite clear. If the "is" of manifestation is to transform into the "is" of isolation, it needs the "is" of motive force (that is, the "is" of negation), which is to transform Expression 1-1 into Expression 1-2. The meaning of this transformation is to negate A manifesting itself by itself, and if so, then A must exist in the form of a basis. If the "is" of manifestation is to transform into the "is" of motive force, it needs the "is" of isolation. Obviously, Expression 1-2 is the negation of Expression 1-1, and Expression 1-2 does not manifest itself. If the "is" of motive force is to transform into the "is" of manifestation, it needs the "is" of isolation. By negating Expression 1-2, that is, A manifesting itself by itself, it becomes a direct, open, transparent manifestation, thus becoming the "is" of manifestation; the other three cases of no form transformation are similar to the above. Therefore, the "is of manifestation", "is of isolation" and "is of motive force" are a no form integrated transformation.
For the "is of isolation", based on different characteristics of B in Expression 2-1, it can be divided into three different types of "is of isolation". For example, "That flower is red" can be rewritten as "That flower is a red thing", where A is that flower, and B is a red thing (usually simply said: B is red). This B contains "red" as a manifesting quality, so this "is" is a manifestative "is of isolation". Another example, "The Earth is warmed by the Sun", can be rewritten as "The Earth is a thing warmed by the Sun", where A is the Earth, and B is a thing warmed by the Sun (usually simply said: B is "warmed by the Sun"). This "is" is a motive force "is of isolation". In addition to the previously mentioned "is" with an inclusion relationship, which is an isolative "is of isolation", there are three different types of "is of isolation" according to the different B's. In fact, both the manifestative "is of isolation" and the motive force "is of isolation" can be seen as isolative "is of isolation", and can be extended to Expression 1-1 in the same way as the isolative "is of isolation". For example, it can be extended to: That flower is that flower in the red things that include that flower (or simply put: That flower is that flower which is red).
Since, in language, truth and falsehood are the highest manifestations, we can completely replace A and B in the three basic laws of formal logic with true and false to conduct deductions and derivations between the three basic laws. Then the law of identity becomes: True is true, false is false; the law of contradiction becomes: True is not false, false is not true; the law of excluded middle becomes: It's either true or false. This is the "true-false" version of the three basic laws of formal logic. In fact, the three basic laws are operating on the relationship between A and not-A. That is, a set is divided into A and not-A. The result is that A and not-A are completely independent. The three basic laws together determine this result. Similarly, this applies to true and false, where false is defined as not-true.This is actually transforms the two-dimensional static relationship between A and not-A into a three-dimensional dynamic relationship (the three fundamental laws of formal logic).
Let's examine whether the "true-false" version of the three basic laws of formal logic is equivalent to the non-"true-false" version:
Law of Identity: For Expression 1-1 being true, It is equivalent to 'true is true' is true, because A includes all things, certainly including "true", so "true is true" is true, simplified to true is true. Conversely, if "true is true", Expression 1-1 as true is true; the same conclusion can be reached for Expression 1-2.
Law of Contradiction: If Expression 2-1 cannot be both true and false simultaneously, then, if Expression 2-1 is true, we can derive "true cannot be both true and false simultaneously", which means true is not false; if Expression 2-1 is false, we can derive "false cannot be both false and true simultaneously", which means false is not true. Conversely, if true is not false and false is not true, then Expression 2-1 cannot be both true and false simultaneously, meaning Expression 2-1 could only be both true and false if true and false had an inclusion relationship.
Law of Excluded Middle: Expression 2-1 is either true or false, so regardless of whether Expression 2-1 is true or false, we naturally have that true is either true or false, and false is either true or false. Conversely, if true is either true or false, and false is either true or false, this determines that Expression 2-1 is either true or false.
This way, we have established that the "true-false" version of the three basic laws of formal logic is equivalent to the non-"true-false" version. Note that in the expression "Expression 2-1 is true", Expression 2-1 serves as truth itself (isolated truth), while the "true" in "Expression 2-1 is true" is the manifestation of "truth" itself. This is similar to the earlier interpretation of the two A's in "A is A". The above discussion of equivalence utilizes this point.
Let's examine whether the "true-false" versions of the three basic laws of formal logic can constitute a no form integrated transformation:
Contradiction Law and Identity Law transform into the Law of Excluded Middle: Due to the Contradiction Law "true is not false", and simultaneously the Identity Law "true is true", therefore, true is either not false or true. Similarly, we can derive: false is either not true or false. This is the Law of Excluded Middle. Note that when defining true and false, we seem to be able to state the Law of Excluded Middle, which is indeed the case. However, we cannot state it this way when defining them because we don't yet have the qualification to do so, and the Contradiction Law and Identity Law give the Law of Excluded Middle this qualification. The reason we can state the Law of Excluded Middle when defining them is that we implicitly assume we have the qualification to do so.
Law of Excluded Middle and Identity Law transform into the Contradiction Law: Due to the Law of Excluded Middle "true is either not false or true", and simultaneously the Identity Law "true is true", therefore, true is not false. Similarly, we can derive: false is not true. This is the Contradiction Law.
Contradiction Law and Law of Excluded Middle transform into the Identity Law: Due to the Contradiction Law "true is not false", and simultaneously the Law of Excluded Middle "true is either not false or true", therefore, true is true. Similarly, we can derive: false is false.
Through the previous analysis, we can see that the law of identity is related to manifestation; the law of contradiction is related to motive force; and the law of excluded middle is related to isolation. The three laws of formal logic in their "true-false" version can be transformed into each other, and all are no form united transformations. Therefore, the three basic laws of formal logic in their "true-false" version constitute a no form integrated transformation (note that the integrated transformation here does not need to verify all 6 no form united transformations, only 3 need to be verified). Due to equivalence, the three basic laws of formal logic also constitute a no form integrated transformation. Thus, we can say that the three basic laws of formal logic are in an inseparable relationship of mutual dependence, mutual support, and mutual definition.
Law of Identity (Manifestation): It embodies the identity of a thing with itself, which is the direct presentation of the manifestation action.
Law of Contradiction (Motive Force): It embodies the changes and negations that occur in things under the action of motive force, leading to the generation of contradictions.
Law of Excluded Middle (Isolation): It embodies how things are distinguished into different categories under the action of isolation, being either one thing or another.
From the above discussion, we can see that the three basic laws of formal logic can completely detach from specific things and only deduce the relationship between "true and false". The essence of the three basic laws is the relationship between "true and false". In fact, it is easy to perform no form integrated deduction among the "true-false" versions of the three basic laws. Manifestation ensures the existence of truth, motive force ensures the existence of falsehood, and isolation ensures that there are only truth and falsehood. This is the relationship between the three actions of no form and formal logic. Our simplification of the expression of the three laws of formal logic allows us to study the three basic laws at a higher level of "true and false". By removing some superfluous elements, we can directly operate on "true and false", making our operation of the three laws of formal logic simpler and our understanding of these three laws clearer. This is how we achieve an essential understanding of these three basic laws. True and false reflect Expressions 1-1 and 1-2, thus the three laws of formal logic at this level of true and false reflect the three laws of formal logic at the level of Expressions 1-1 and 1-2 (and their extended Expressions 2-1-1 and 2-2-1).
(Note: If we use the symbolic logic of formal logic to represent the three basic laws of formal logic, we can also prove that the three laws can be transformed into each other. Law of Identity: P implies P (equivalent to ~P ⅴ P), Law of Contradiction: P · ~P, Law of Excluded Middle: P ⅴ ~P. Thus, the Law of Identity and the Law of Excluded Middle mean the same thing, and adding a negation in front of P · ~P in the Law of Contradiction will turn it into P ⅴ ~P of the Law of Excluded Middle. However, this only shows that they can indeed be transformed into each other. This purely symbolic level of transformation cannot fully reveal the deep meaning of these three laws in logical reasoning and philosophical understanding. This transformation loses the original meaning. Therefore, this is a deficiency of symbolic logic.)
The law of contradiction can be interpreted as: The manifestation of the same thing cannot be both identical and non-identical simultaneously. Otherwise, it cannot be called identity, and identity would not exist. The manifestation of the same thing can only present identity; it cannot simultaneously present both identity and the negation of identity. Therefore, the cause of contradiction is the destruction of the identity of things. Identity, as a foundation, is the prerequisite for the being of things. Once this identity is destroyed, the self-expression of things will show contradictory duality. This self-division constitutes the most essential contradiction, marking the beginning of the movement and change of things. The law of excluded middle can be interpreted as: The manifestation of the same thing must be either identical or non-identical. Of course, explaining expressions 2-1-1 and 2-2-1 also explains the simplified versions of expressions 2-1 and 2-2. This, in turn, explains the three basic laws of traditional formal logic.
Because identity is a characteristic of manifestation, denying the identity of manifestation is actually denying manifestation itself. To deny manifestation means "a thing does not manifest". If "a thing does not manifest", it has no identity, which means that denying identity is equivalent to denying manifestation. Therefore, the law of contradiction can also be interpreted as: a thing cannot both manifest and not manifest simultaneously. What brings about the law of contradiction? If a thing does not manifest, it will necessarily be concealed, meaning it will become a motive force or an isolated thing. In this way, the either-or nature of the law of contradiction becomes an either-or relationship among manifestation, motive force, and isolation. The either-or nature of these three is produced by isolation; isolation is meant to separate independent, distinguishable things that are either-or in nature. This is the true reason for the emergence of the law of contradiction. When interpreting the law of contradiction in this way, we are actually trying to derive the characteristics of the law of contradiction from the identity of manifestation, while using the characteristics of isolation. This is, in fact, a no form united transformation. This explains the law of contradiction at a level higher than formal logic.
The traditional view holds that deriving one law of formal logic from another is meaningless because any such derivation already employs the basic laws of formal logic. Moreover, Heidegger explains that, strictly speaking, these principles of thought cannot be proven. In fact, any proof is already a thought activity, and thus any proof already conforms to these laws of thought[1]. This viewpoint is incorrect as it overlooks the intrinsic connections between the basic laws of formal logic. Even so, it cannot be denied that the basic laws of formal logic can find their own origins. They all stem from the identity of manifestation, which in turn comes from the identity of no form. The key is that the derivation and transformation between them is a no form integrated transformation. The three basic laws of formal logic are all laws concerning the manifestation, motive force, and isolation of things. When elevated to the theory of no form action, these laws have intrinsic connections and can be transformed into one another. Such derivation and transformation conform to the laws of the theory of no form action and can be explained by it.
Through the derivation and transformation between the three laws of formal logic, we recognize that their root source is the identity of no form. The integrated transformation among the three laws of formal logic demonstrates that although they are separate, they are essentially unified. Their separation is due to the isolation action (distinguishability), their unity is because of the manifestation action (identity), and their integrated transformation is due to the motive force action (changeability). Only by rising to this height can we break free from the cognitive shackles we impose on ourselves, thereby recognizing the essence of things. Such a derivation process is not a circular argument. Whether it is a circular argument only holds true when reasoning using formal logic within the realm where formal logic can be applied. The domain of formal logic refers to the realm of pure isolation (or motive force) action. For language, this is a realm composed of concepts that are isolated (or dynamic) in meaning. Reasoning between such individual concepts cannot be circular argumentation. Because such argumentation is merely self-defining, equivalent to manifesting nothing, and is not an integrated transformation under the identity of no form. Formal logic seeks grounds in isolation action or causes in motive force action. The no form integrated transformation embodies the identity of no form. Their functions are different, and their judgment criteria are also different.
The derivation of mutual transformations between the three basic laws of formal logic is actually a no form integrated transformation. This type of transformation does not exist in formal logic; it is a different kind of logic that transcends formal logic. It is because the three basic laws respectively belong to different no form actions that we can use no form integrated transformation to explain them. Any single one of the three basic laws cannot reveal the essence of formal logic; in dynamic thinking, they are an indivisible unity. This also embodies the significance of the three no form actions. We cannot clearly explain each basic law individually; it is only meaningful to explain the three basic laws together from the perspective of the three no form actions. According to the above interpretation of the three basic laws of formal logic, the law of excluded middle cannot be negated because, as one of them, it is indispensable; the three laws are an inseparable unity. Without the law of excluded middle, the law of identity and the law of contradiction would not be explained. Negating the law of excluded middle is equivalent to negating the law of identity and the law of contradiction.
From the above, we can see that although the world of language is a "pure" world of isolation, it is necessary to use words to simulate manifestation and motive force in this world. Otherwise, this language world as a system cannot operate and cannot demonstrate its functions. This also indicates that the identity of the three no form actions is indispensable. Any system needs to revolve around the identity of no form actions to function.
For the statement "A is B", if the connotation of B is greater than the connotation of A, then the "is" in this statement means "belongs to". Through continuous tracing in a limit approach, we can finally determine that A is a being of isolation. That is, it reaches the being of isolation. For "A is A", it is impossible to reach such a being of isolation. Therefore, we can only interpret this statement as the being of manifestation.
Previously, we used the theory of no form action to explain the syllogism of formal logic. In this way, we have used the theory of no form action to explain the most fundamental content of formal logic. Language, like concrete things, is also a concrete thing. It's just that it can describe concrete things (including descriptions of itself). The truth of concrete things is one kind of truth, and the truth of language is another kind of truth. Since the world of language is a "pure" world of isolation, its truth has its own characteristics. The truth of language (which is the isolated truth of a pure world of isolation) is directly manifested by the law of identity "A is A". The truth of other things, however, is manifested in other ways (several cases have been mentioned before).
According to the previous explanation, the truth of language comes from the no form identity of "A is A". Based on this identity, we used the theory of no form action to derive the three basic laws of formal logic that can undergo no form integrated transformation under the no form identity. In other words, this no form identity has been transformed into the three concrete, operable basic laws of formal logic. Therefore, the truth of concrete language is, conversely, guaranteed by the three basic laws of formal logic (or directly said to be guaranteed by formal logic). Beyond this, language itself does not guarantee any truth outside of language. Other truths are guaranteed by other means. For example, the truth of Socrates himself as a person (the truth of direct manifestation) is acquired by humans through some form of collection and transformed into our language as "Socrates exists". Language itself does not guarantee the truth or falsity of this statement's content. The truth or falsity of this statement's content is not within the category that formal logic can guarantee. Therefore, this is the essence of formal logic: formal logic is the law that guarantees the truth of language itself.
However, the world of language is a "pure" world of isolation. For other isolated worlds, because they inevitably also have the identity of "A is A", they must also conform to formal logic (but their "truth" may not necessarily be governed by formal logic, because the truth of other worlds may be governed by other aspects. This governance of truth does not have to violate the truth of formal logic). For some impure isolated worlds in their isolated aspects, or for the isolated aspects of other types of worlds, they all must conform to formal logic. In this way, we have found the legitimacy of formal logic's authoritative governance in the aspect of isolation. This also determines the reasonable position of language in explaining this world, because it is a "pure" world of isolation, and therefore can effectively explain this world in terms of isolation.
According to the above analysis, in the world of language we have divided "is" into three types: the "is" of isolation, the "is" of motive force, and the "is" of manifestation. We see that these three types of "is" are fused and bound together with the three basic laws of formal logic. This illustrates the relationship between "is" and formal logic. This actually also means that "is" is bound together with the identity of no form. Why can "is" be bound together with the identity of no form? In fact, no matter what kind of "is" it is, it must be reduced to no form, and no form is absolute identity, so "is" is bound together with the identity of no form.
However, if we want to analyze this "is" more deeply, it requires some mental effort. For the statement "A is B (expression 2-1)", we can view it as a simplification of expression 2-1-1. Thus, according to expression 2-1-1, we can see that the purpose of expression 2-1 is to express A using B (as distinct from "A is A"), which is to manifest A in an isolating way. For A as an isolation to manifest as B, its motive force comes from human thought (this is why we always feel that "is" has a kind of motive force, but in fact it's not that "is" has motive force, but that human thought has motive force behind it), as humans want to manifest this A. This is a no form united transformation. Therefore, this "is" is a no form manifestation action. Previously, using the method of limits, we arrived at the concept of "being", which according to its path trajectory is a being of isolation. This "is" indeed seems very similar to being, but it is indeed different. This "is" requires to be different from all forms, because it needs to manifest all forms, so this difference can only require "is" to be no form. But through the manifestation action of "is", through the method of limits, we can reach the concept of "being". This connects "is" with being. It seems that manifestation can be transformed (or transitioned) into being through some method. "Is" is the manifestation of the language world, a kind of manifestation of isolation.
From the above analysis, we can see that the three basic laws of formal logic all originate from identity, while contradiction comes from the destruction of identity, and the law of excluded middle requires that identity must have a clear distinguishable (isolated nature) state, any proposition must have a definite truth value. The three basic laws are the highest standards of the language world, and also the laws that the world of isolation must obey and cannot violate; in the emotional world, there will also be a highest standard, which will certainly come from identity, this standard is harmony, corresponding to the harmonious unity between different emotions and psychological states, and the destruction of identity is conflict; in the world of sensations, there will also be a highest standard, which will certainly come from identity as well, this standard is beauty, and the destruction of identity is ugliness, while the completion and repair of incomplete identity produces beauty; beauty originates from a kind of identity, which is the state of things being perfect and self-sufficient. When this identity is destroyed, it produces a state of ugliness. By repairing and sublimating this destroyed identity, the form of beauty's existence is rebuilt. In summary, beauty is our consciousness acquiring identity. This is the essence of beauty. In fact, the completion and repair of identity is the acquisition of identity. Beauty refers to the nature of things having perfect and self-sufficient qualities, giving people a sense of pleasure and enjoyment. There are many ways to acquire identity, for example, the harmony of music is the identity of motive force, which is the beauty of music; in painting, the use of contrast and light and shadow can produce a strong visual effect. This visual effect is the unity of opposites of identity.
For example, clearly expressing certain things will produce beauty. Before an object is clearly expressed, it is in a concealed state, and this concealed state is a state lacking identity. When we remove this concealment and reveal a kind of unconcealed state, we achieve a kind of identity. At this point, beauty is produced. This is especially true in literature, for instance in poetry. Poetry aims to clearly express a certain direct understanding or feeling. If a poem lacks this clarity, it has no artistic value. The fact that poets in ancient Greece liked to write philosophical poems is evidence of this. Because philosophy is a discipline that pursues the clearest concepts, writing philosophical poetry can more clearly express one's understanding and feelings.
We always feel uneasy about contradictory thoughts and seek reasonable non-contradiction. If "non-contradiction" were not a form of beauty, why would we pursue it? Non-contradiction is a kind of identity. From this perspective, whether it's the harmonious melody in music, the contrast and balance in painting, or our pursuit of non-contradictory thoughts and ideas, all are processes of capturing and realizing identity through different artistic or cognitive methods, thereby bringing about the experience of beauty. In this sense, beauty can be understood as the acquisition of identity by consciousness, an affirmation of the complete and self-consistent nature of things.
Formal logic, seemingly unrelated to beauty, through the discussion of normative laws such as the law of identity, the law of contradiction, and the law of excluded middle, and through layer upon layer of logical deduction, has surprisingly led us to the concept of beauty, bringing us closer to the poetic and mysterious realm of aesthetics. The secret lies in the impossible. Formal logic and aesthetics, two worlds that seem entirely different, but through meticulous conceptual connections, we discover hidden correspondences and associations between them. Although formal logic and aesthetics appear to belong to different domains of knowledge on the surface, when we delve deeper, we find that they are both built on an understanding of the core concept of "identity". Therefore, when we face a difficult problem that cannot be solved in thought, it is a correct path to use "beauty" as a guide for thinking to solve the problem.
The same is true for harmony. Beauty, harmony, and truth are all interconnected at this high level of no form identity. In other words, artistic beauty, emotional harmony, and logical reasoning are also interconnected at a high level and have intrinsic connections. Therefore, our human pursuit of these three aspects is equally important, without distinction of high or low, and without opposition. Since they have intrinsic connections, they can also promote each other.
Kant, in his studies around 1790, said: "The understanding can only demonstrate its power in judgments, which is nothing but the unity of consciousness in the relation of general concepts..." (Progress..., Freund edition, p. 97). Where some relation is represented, there must be some unity that maintains this relation being represented, this unity is realized through the relation, so what is realized in judgment must have some characteristic of unity. Aristotle had already expressed exactly the same view (On the Soul, Γ6, 430a, p. 27 ff): in judgment, multiple representations are always already gathered into some unity.[3]
Kant made this clear in the title of the important Section 19, which reads: "The logical form of all judgments consists in the objective unity of the apperception of the concepts contained therein."[4]
Both Aristotle and Kant recognized the unity of concepts in judgment, but Kant did not clarify what this unity means. In fact, the unity Kant spoke of is to be unified at a higher level. Through the previous analysis, this higher level is "A is A" and its extended identity. The identity of formal logic ultimately needs to rise to the identity of manifestation in human consciousness, because it is human thinking, it is human manifesting.
In short, no form and its three actions have "descended" into this isolated world of language in an isolated manner. Therefore, our rational understanding of no form must necessarily be linguistic and isolated, and we express no form in a way that conforms to formal logic. The three basic laws of formal logic are the isolation of the laws of no form action, they are the "incarnation" of the laws of no form action in the isolated world of language. Our explanation of formal logic using the theory of no form action above is actually using formal logic to explain formal logic itself. This is also the theory of no form action explaining itself in the isolated world of language in the manner of formal logic, while the theory of no form action is self-explanatory. This statement is not contradictory. In other words, this self-explanation of formal logic is the isolated version of the self-explanation of the theory of no form action.
Let's look at "negation" again. The negation of expression 1-1 is a negation of the manifestational "is", which is a negation of manifestation. Negating "A is A" is a complete negation, a negation of identity, meaning A no longer manifests itself, thus producing a contradiction and completely moving towards the opposite of A. This is a strong negation. The negation of expression 2-1 is a negation of the isolational "is", which is a negation of isolation. "A is not B" doesn't necessarily produce a contradiction; the result of this negation could be: A is C. Therefore, this isolational negation is not a complete negation. This is a weak negation. Thus, in the isolated world of language, not all "negations" are the same.
Since the motive force in the isolated world of language has negativity, it can be inferred that the motive force in other isolated worlds also has negativity. For example, in the macroscopic isolated world, an action force will produce a reaction force. These two forces have negativity. While the negativity in the language world comes from the destruction of identity, the reason why an action force produces a reaction force is also due to the destruction of identity. This is using the laws of the language world to explain physical phenomena in the macroscopic world. This is not surprising, because we are using language to describe this world, and language is able to describe this world, so these two worlds must have commonalities.
Previously, it was explained that when a force pushes an object, to manifest change, it must be isolated into opposing action and reaction forces. This is a no form united transformation.
Modern physics uses the principle of momentum conservation to explain action and reaction forces. The principle of momentum conservation is a fundamental physical principle stating that in a closed system, the total momentum (the product of an object's mass and velocity) remains constant. When one object exerts a force on another, this force changes the momentum of the other object. However, due to momentum conservation, the object exerting the force must lose an equal amount of momentum, which produces a reaction force. Therefore, the existence of action and reaction forces is a direct result of the principle of momentum conservation. All interactions between objects obey the law of momentum conservation. If one object exerts an external force on another object, according to momentum conservation, the object exerting the force will lose momentum equal to the magnitude of the external force. The object receiving the force gains an equal amount of momentum. This demonstrates that force has reciprocity.
However, this explanation does not truly explain action and reaction forces, because in the quantum world, which also follows the principle of momentum conservation, there are no action and reaction forces as we see in our macroscopic world. In other words, using only the principle of momentum conservation to explain the generation of action and reaction forces is insufficient. It does not find the root cause of the generation of reaction forces. In fact, an explanation from the theory of no form action is also needed: when one object exerts a force on another object, it disrupts momentum conservation, which is actually breaking the identity of the isolated world. Breaking the identity of the isolated world produces a completely negative force, and this completely negative force is the reaction force. Therefore, in the macroscopic world, every action force produces a reaction force.
Using the no form action theory to explain Russell's paradox: Although methods like restricting sets, such as the axiom of regularity in ZF set theory, can effectively avoid Russell's paradox, there is indeed a lack of satisfactory deep explanation for why these restrictions work and what Russell's paradox really means. A set cannot contain itself, which is derived from the Axiom of Regularity (also known as the Foundation Axiom) in ZF set theory. The Axiom of Regularity states that for any non-empty set A, there exists an element x in A such that x and A have no elements in common, i.e., x ∩ A = ∅. Intuitively, this means that no set can have itself as an element, because if a set contained itself, according to the Axiom of Regularity, this set would not be able to find such an element that satisfies the condition. Therefore, within the framework of ZF set theory, a set containing itself is excluded, which avoids paradoxes in set theory. I interpret the "is" in "A is A" as a manifestation action, and the "is" in "A is B" as an isolation action. They are different no form actions. This is actually saying that when a set A belongs to itself, "belongs to" should be transformed into a "manifestation action". Therefore, a set cannot contain itself. This is consistent with the requirements of the axiom of regularity. Interpreting the "is" in "A is A" as a manifestation action comes from the identity of no form. Thus, the generation of Russell's paradox is a violation of the identity of no form, which is the fundamental reason for the emergence of Russell's paradox. The interpretation of the axiom of regularity demonstrates how the "inclusion" relationship (isolation action) transforms into a manifestation action. This transformation actually connects the no form action theory, formal logic, and set theory. This is because they undergo the same transformation.
References
[1]Heidegger. Identity and Difference, translated by Sun Zhouxing, Chen Xiaowen, and Yu Mingfeng, Commercial Press, 2011, p. 120-121.
[2]Heidegger. The Principle of Reason, translated by Zhang Ke, Commercial Press, 2016, p. 226.
[3]Heidegger. The Question Concerning the Thing, translated by Zhao Weiguo, Shanghai Translation Publishing House, 2010, p. 140-141.
[4]Heidegger. The Question Concerning the Thing, translated by Zhao Weiguo, Shanghai Translation Publishing House, 2010, p. 144.