Modern society is driven by logic, and logical thinking is required in various aspects. However, many people do not consciously think logically, similar to how they do not consciously think about grammar in everyday conversation.
When people think of logic, they often think of mathematics or sciences like physics. However, logic is not limited to science. Recently, logical thinking has been discussed in various business contexts. But what exactly is logic? Often, there is no fundamental definition. People may feel logical just by mentioning logic, yet claim that AI is not logical.
Many people seem to mistakenly believe that deductive reasoning is the entirety of logic. While deductive reasoning is a representative form of logic, it is not all-encompassing.
Accounting is logic. Therefore, management is an action based on logic. A nation-state is also logic. The constitution is a definition. Existence is the people. A nation-state is justified by procedures. Organizations are also logic. Organizations have their own logic. Without understanding this logic, one cannot control the organization.
Logic is a system or mechanism that, when given any task or proposition, derives some result or conclusion according to certain rules, standards, or algorithms. It is a procedure or path.
Logic itself has no meaning. Logic is a function and does not inherently possess meaning. Logic has certain procedures and rules.
Logic refers to the path or process. It does not necessarily operate on a one-to-one relationship. One-to-many, many-to-many, and many-to-one relationships also exist. A one-to-one relationship is a two-dimensional relationship. However, today, science requires multi-dimensional analysis.
Logic is not a single path.
In modern times, the concepts of logic extend widely even within mathematics, including group theory, sets, functions, mappings, matrices, statistics, probability, and Bayesian methods. Particularly, functions, mappings, and sets are important concepts.
Moreover, the concepts of sets, statistics, and probability algorithms are incorporated into logic. Thus, it has evolved from a single factor to the connection and operation of sets.
Conjunctions also become important.
Each step needs to be verified. The core concept of logic is equality.
What is considered equal determines the direction of logic.
Logic cannot be verified simply by one-to-one correspondence. Logic is a means, a tool, not an end. Logic is a process, a procedure. Logic is composed of settings, order, arrangement, structure, reorganization, and verification. Logic can be said to be an algorithm and a program. Logic presupposes traceability. Without guaranteed traceability, legitimacy is not recognized.
もちろんです。以下が英訳です：
- Logic consists of the whole and its parts (elements).
- The elements that make up the whole are connected to other elements in some way.
- The elements that make up the whole have positions and functions.
- Logic has a structure. Syntax is required.
- Consistency and non-contradiction are required between preceding and succeeding elements.
- Logic has certain rules.
- Logic starts at one point and ends at one point.
- All elements are connected.
- Factors other than the starting and ending points have a sequence.
- Logic itself has no meaning. Logic is a mechanism and a system.
- Logic must be based on definitions.
- Logic is a means and a tool. It is not an end.
- Logic is a process, a procedure, and a protocol.
- Because logic is a process, it is composed of settings, order, arrangements, structure, assembly, reorganization, and verification.
- Logic can be said to be an algorithm and a program.
- Logic presupposes traceability.
- If traceability is not guaranteed, legitimacy is not recognized.
Logic is a procedure. Logic can be regarded as a kind of programming language. Therefore, what makes logic valid is properties and literacy.
What disrupts logic are leaps, deviations, deceptions, substitutions, lies, falsehoods, fallacies, impositions, distortions, prejudices, and preconceptions.
Logic must be based on definitions. Definitions must be based on recognition. Definitions require infallibility. The syntax and language use of definitions must not be contradictory.
Definitions are arbitrary and thus hypotheses.
Definitions are premises. What is the premise? How is it proven? Can it be understood? The issue of understandability. What is believed? What is the basis? This determines what is self-evident.
If the premise changes, the definition also changes. For example, the definition of depreciation expense changes depending on whether management accounting or financial accounting is the premise.
Definitions are determined by premises. Premises are based on recognition.
Facts can only be proven by facts such as experiments and observations, which is positivism. Logic is merely a means and a procedure. Being logically infallible does not prove the validity of definitions or hypotheses. The infallibility of officials. No matter how precise a public works plan is, if the premise is wrong, miscalculation is inevitable. Finances will also collapse.
The basis of logic is the premise. In other words, the validity of logic lies in the validity of the premise. The validity of the premise lies in understandability. The validity of logic is guaranteed by verifying that there are no contradictions in each process.
Logic is an extension of recognition. Validity is guaranteed by placing the basis on recognition. Logic is proven by empirical evidence. Existence, recognition, and logic are unified by sharing a starting point. Faith, philosophy, and science are integrated.
The premise of logic must be a fact. If the premise or initial statement or proposition is wrong, even if it is logically infallible, it will lead to a wrong conclusion precisely because it is logically infallible.
Definitions must be based on facts. Definitions not based on facts separate the external world from the internal world.
Logic not based on facts is delusion. Delusion not based on facts is impossible to prove and cannot be controlled.
For example, the threat of AI not based on facts is a delusion. Delusion leads to conjecture and becomes uncontrollable. Delusions based on rumors, gossip, and falsehoods can sometimes lead to catastrophic situations. The delusion that there is no war or invasion in today’s world. Delusion cannot protect true peace.
Modern logic is algorithms, systems, and programs. Input is verified by output. Also, the validity of input is determined by the input data.
Therefore, logic is verified by initial premises, requirements definition, algorithms, literacy, prompts, data quality and quantity, and data structure.
The typical modern logic is the algorithm and literacy of machine learning.
Logic, when given a task or proposition, produces some result or conclusion according to certain rules, standards, and procedures, but there is no guarantee that it is correct. Whether the result or conclusion is correct must be empirically verified and validated.
The issue of premises. Definitions are arbitrary and not given. The infallibility of logic is effective only with the validity of definitions.
Logic does not exist in isolation. Logic is an open system that does not self-contain. Therefore, proving the infallibility of logic alone is insufficient to prove the validity of the theory. Even if it is proven to be logically correct, it does not guarantee that the answer is correct.
In that sense, AI can be said to be logical but not purely logical. AI can be self-contained.
If logic does not guarantee the validity of conclusions or results, what proves correctness? It is the premise and the result. This point is important.
In other words, the premise clarifies the basis of correctness, and the result verifies it. Logic lies in between.
In that sense, probability and statistics are the most mathematical and fundamental to mathematics. The foundation of logic is databases and knowledge. In other words, it is the scrutiny, structuring, and credibility of information.
Law is also logic. The articles of law must be mutually consistent and coherent. Logic must be mutually non-contradictory and consistent. Therefore, the basis of law, legal sources, and ideological unity are required. Also, the articles must be interconnected. Therefore, the constitution is required and important.
Furthermore, logic is not linear but structural.
What establishes logic are definitions and the procedures based on them. First, definitions. Definitions are arbitrarily set, so the purpose, motivation, and position regarding the problem are important. Procedures are the processes between oneself and the problem, the problem and the result, and the result and oneself. Verification is required at each point of these three aspects: oneself, the target, and the result. First, what purpose, position, and premise one stands on. Next, what materials, resources, and data one is based on. The basis and credibility of those resources, materials, and data. What procedures, processes, paths, and algorithms one is based on. Logic is established by integrating these.
Logic also encompasses the three elements of the recognizing subject, the recognized object, and the standard. Structurally, it consists of position, function, and relationship.
Proof plays an important role in logic. It involves mapping existence, organizing and analyzing it. It is necessary to prove whether the organized and analyzed results are correct. That is logic.
Once an object is recognized, it is classified and organized. Then, laws are discovered, verified, and proven.
There are algebraic and geometric proofs, as well as probabilistic and statistical proofs. In schools, mathematics is often taught as algebra and geometry, with probability and statistics added as an afterthought. This leads to the misconception that proofs in algebra and geometry are everything, and many people believe that deterministic proofs are always correct. However, in the real world, probabilistic and statistical proofs are more common. From the perspective of recognition, probabilistic and statistical proofs are overwhelmingly more common. This is because the task of proving relative and uncertain phenomena is generally more common.
Weather forecasts, stock price predictions, sales forecasts, and election results are typically presented with uncertainties included, rather than as definitive conclusions. Therefore, logic based on probability and statistics becomes important, no less than algebraic and geometric proofs.
Without understanding this point, one cannot grasp the meaning of proof in logic.
The validity of computer systems and logic is verified from three points: the intention, purpose, and credibility and bias of the data input by the person, the computer’s algorithm, and the result (empirical evidence and verification).
Logic is form. Logic is nominal. Logic has no substance. Logic is a framework. Logic is procedure. Logic is an equation.
Standards are logic. Law is logic. Rules are logic.
For example, sports are logic. War is not logic.”
Why is war not logic?
War has no beginning and no end.
There are no rules; it is killing each other.
Therefore, it is not logic.
Do you think God desires to stain the day of worship with blood?
I do not think so. It is people, not God, who do such things in the name of God.
Fear only God. Fear yourself.
People should not expect from God, but should expect from themselves.
If it can be proven that people can be made happy by war, then it should be proven.
Lies and deceit are contrary to logic.
We trust the alarm clock and set it.
This seemingly trivial act is the truth.
People are saved only when they exist.
It is when they are alive.
It is only when they are alive that they can be happy.
People do not live to eat.
They eat to live. This is the correct syntax.
People do not live to earn money.
They earn money to live.
People are kept alive to make others happy.
Work to make your loved ones, your spouse, your children, and your parents happy.
Think about making your friends and comrades happy.
Seek out those who make others happy.
To make yourself happy.
That is what God desires.
People cannot be happy alone.