Neural Logic
In the previous article, I presented the differences between humans and machines and at the same time emphasized logical thinking as a commonality.
But what kind of logic is it? Is it generalizable and unambiguous?
The logic that arises from language models is indeed comparable in many ways to the logic of human thought, especially on an abstract level. The cognitive aspects of thinking, such as reasoning, recognizing patterns, and processing information, are core functions in both human intelligence and artificial intelligence.
It is interesting to note that large language models (LLMs) have made impressive progress and can solve tasks that were once considered the domain of human intelligence. These models are capable of handling complex tasks that require logical reasoning, understanding, and inference.
However, there are also differences. While people are able to integrate non-linguistic aspects such as emotions, intuition, and sensory perceptions into their thinking, language models are limited to working with text and the information it contains. The non-linguistic aspects of human thinking are a challenge for language models, as these dimensions of the human experience are not directly transferable to text form.
Research continues to improve the capabilities of AI systems to bring them even closer to the complexity of human thought. Plausibility and the modelling of subjective knowledge play an important role here.
The difference between pure logic and language logic is a topic that touches on the relationship between language and thought. Pure logic, often referred to simply as “logic,” is the science of correct reasoning. It deals with the principles and criteria of validity of arguments and conclusions, regardless of the language in which they are expressed. It is formal and mathematical, with a focus on structures such as sentences and arguments that can be represented in symbolic form, such as in propositional logic or predicate logic.
Language logic, on the other hand, looks at the logic embedded in natural language. It examines how logical relationships and structures are manifested in language and how linguistic expressions are used to convey logical concepts. Language logic deals with issues of meaning, reference, and truth within language and how these elements are used in logical arguments.
Pure logic provides a toolkit for precise and unambiguous thinking that is applied in many fields, from mathematics to philosophy. Language logic, on the other hand, allows us to navigate the nuances and complexities of natural language when we use logical concepts in everyday discussions and arguments. Both are important for understanding how we think and communicate.
When we talk about logic, which is similar in language models and in the human brain, we are referring to language logic. This form of logic is anchored in natural language and reflects how people use logical concepts in communication. It is contextual and takes into account the meanings and nuances of the language.
Pure logic, on the other hand, is abstract and formal. It is not bound by the specifics of a particular language and focuses on universal principles of reasoning that can be represented in symbolic form. While language models are able to simulate and apply language-based logic, they do not operate at the level of pure logic in the same sense as is the case in mathematics or formal logic.
Thus, in interacting with language models, we experience a form of logic that is very close to language logic, as they are trained to understand and generate language that is logically coherent and meaningful. Pure logic, on the other hand, remains a field that is more likely to be cultivated by experts in the relevant fields such as mathematics, philosophy and logic itself.
Pure logic also plays a role in language models, but in a different form than in human thinking. Language models use principles of pure logic to understand the structure of language and the relationships between words and sentences. These principles help to generate coherent and logically coherent answers.
Pure logic forms the basis for algorithms and models used in natural language processing. It allows language models to recognize patterns and draw conclusions based on the data they have been trained with. For example, language models often use statistical probabilities and mathematical models to determine the most likely continuation of a sentence or the answer to a question.
However, the application of pure logic in language models is not identical with its application in mathematics or formal logic. In language models, pure logic is extended and adapted by the complexity of natural language and its multiple forms of expression. For example, language models have to deal with ambiguity, idioms, metaphors and other linguistic subtleties that do not occur in formal logic.
To sum up, pure logic plays an important role in the functioning of language models, but it is applied in a context shaped by the specifics of natural language.
There are different types of logic that can be applied in different contexts. Formal logic is probably the best known, which deals with the form of arguments and deductive reasoning. It includes, among other things, propositional logic and predicate logic, which work with the help of symbols and formal languages.
In addition to formal logic, there is also informal logic, which deals with arguments in natural language and also includes non-deductive arguments. This type of logic is closer to what could be called “language logic” because it deals with the structure and evaluation of arguments in everyday life.
Causal logic could refer to relevance logic or causal logic, which studies cause-and-effect relationships and their validity in arguments. This type of logic is particularly important in everyday thinking and science, where it is a matter of understanding and explaining causal relationships.
There are also specialized logics such as multivalued logic, which allows more than two truth values, and fuzzy logic, which works with uncertainties and gradual truth values. In addition, there is intuitionist logic, which is based on a philosophical view that rejects the principle of the excluded third party.
In modern logic, non-monotonic logics are also studied, which make it possible to revise conclusions as new information becomes available. This type of logic is particularly relevant in computer science and artificial intelligence.
Each type of logic has its own rules and applications, which can vary depending on the context.
Human thought is often associated with a form of logic known as plausible reasoning. This type of thinking involves the ability to analyze information, identify patterns, hypothesize, and draw conclusions. It’s about modeling subjective knowledge that we find plausible and making decisions based on that assessment. This form of logic is less rigid than formal logic and is more similar to the way people think and make decisions in everyday life.
Language models that mimic human thinking aim to understand and generate natural human language. These models are based on complex algorithms and statistical models that allow them to understand texts, make predictions, and process contextual information. They are able to provide differentiated and contextual answers, making them valuable components of technology and business applications.
Human thinking is characterized by flexible, plausible logic, while language models attempt to replicate this thinking by processing and generating natural language. Large language models such as GPT-4, BERT, or Transformer-based models are examples of such technologies that are used in various fields to simulate human-like communication and problem-solving skills.
Philosophical logic is a complex and profound form of thought that goes beyond the boundaries of formal logic.
Philosophical logic and logic of thought are closely related, as both seek to capture and structure the way we think and understand the world. Philosophical logic often deals with the basic structures of thought and reasoning and tries to organize them into a coherent system. It goes beyond pure formal logic and also takes into account the contents and contexts of thought.
The logic of thought, on the other hand, refers to the actual processes that take place in the human mind when we think, draw conclusions and make decisions. It includes both conscious and unconscious elements and is often less formalized than philosophical logic. The logic of thought also includes emotional and intuitive aspects that are not always present in formal logic.
Philosophers, such as Hegel, have tried to develop systems that reflect and explain the complexity of human thought. Hegel’s dialectic, for example, considers the process of thinking to be dynamic and constantly evolving, which is closer to the real experience of human thought.
The challenge is to find a balance between the precision of formal logic and the diversity and flexibility of the human way of thinking. Philosophical logic that seeks to integrate the logic of thought can lead to a deeper understanding of reasoning and truth while acknowledging the rich complexity of the human mind.
In his early work, the “Tractatus Logico-Philosophicus”, Ludwig Wittgenstein advocated a perspective that can be described as logical-realistic. He argued that the structure of language reflects the structure of reality and that language is limited by its logical form. Wittgenstein coined the famous phrase: “What cannot be spoken of, one must be silent about”, which emphasizes the limits of language and thus of the world we can describe.
In his later works, especially in the “Philosophical Investigations”, Wittgenstein turned away from this early view and developed a more pragmatic approach. He no longer saw the meaning of language in its correspondence with reality, but in its use in a social context — the meaning of a word lies in its use. This later approach had a major influence on the development of ordinary language philosophy and pragmatics, a field of linguistics that deals with the relationship between linguistic expressions and their users.
Language logic is closely linked to ontology, i.e. the study of being and the categories of reality. Language logic often reflects the ontological structure of the world by using subjects, objects, predicates, and properties in a way that corresponds to our understanding of existence and truth.
Language serves as a tool to shape and guide our thoughts. It allows us to think about the world and describe it. In this sense, language logic can be seen as a kind of guide to thinking, as it provides the structures within which we think and communicate.
These different forms of logic are not isolated, they influence and complement each other. Linguistic logic uses the structures of pure logic to construct meaning and truth, while pure logic is often expressed in linguistic terms to communicate its principles and conclusions.
In philosophy and cognitive science, it is often argued that our language and logic not only reflect our worldview, but also shape the way we think and understand the world.
There are different views on the relationship between language, logic, and ontology, which is viewed differently by different philosophical traditions.
In the tradition of analytic philosophy, especially among philosophers such as Gottlob Frege, logic is seen as a tool that is independent of ontology. Logic provides a structure for thinking about concepts and objects without committing to a particular ontology.
The philosophy of language examines how language influences our perception of the world and how logical structures in language shape our communication and thinking. There is a view that language influences ontology by prescribing the categories through which we understand the world.
Pragmatists such as Charles Sanders Peirce consider the importance of concepts in terms of their practical implications and benefits. In this sense, the relationship between language, logic, and ontology is dynamic and contextual.
Phenomenologists such as Edmund Husserl and Martin Heidegger see language as an expression of human experience. Ontology here is closely linked to the way we experience and describe the world, and logic is a means of structuring these experiences.
Jacques Derrida and Michel Foucault argue that language and texts have no fixed meanings and that the relationship between signs and signified is unstable. This has implications for ontology, as they question the possibility of a fixed reality.
These different views show that the relationship between language, logic, and ontology is a complex and controversial issue that depends on many factors, including the philosophical perspective, the historical period, and individual interpretation.
The idea that language logic and pure logic are ultimately expressions of neuronal structures and processes finds support in cognitive science and neurophilosophy. These disciplines explore how cognitive processes such as thinking, language, and reasoning are anchored in the brain’s neural networks.
The neuronal constitution of humans — i.e. the specific way our brains are structured and function — enables us to develop and use complex logical and linguistic systems. These systems are not only tools for communicating or thinking about the world, but also reflections of the cognitive abilities made possible by our biological makeup.
Understanding the neurobiological foundations of logic and language can help us dig deeper into the essence of human thinking and how our mental abilities are connected to the physical reality of our brain. It can also shed light on the limits of what we can recognize and understand, based on the limitations that our neural architecture imposes on us.
In this sense, it could be argued that all human constructs — be they language, logic, or culture — are ultimately manifestations of the unique way our brains process and interpret information. This view emphasizes the importance of biology in our understanding of human nature and our intellectual abilities.
Orthogonality — or the logic of the environment — plays a crucial role in the development of our cognitive abilities. Our brain has evolved to respond to the challenges and realities of our environment. This adaptation has led to the fact that our cognitive processes, including our logic, are closely linked to the structure and laws of the environment.
Neurological adaptation to the environment means that our perception, thinking, and decision-making are shaped by interaction with the environment. This includes not only the physical environment, but also the social and cultural contexts in which we live. The way we solve problems, draw conclusions, and communicate reflects the complexity of these interactions.
In this sense, the logic that our brain uses can be considered a product of ecological rationality, which states that our cognitive abilities are optimized for the specific environments in which they have evolved. Our brains are wired to recognize patterns and make predictions that are beneficial for survival and reproduction in our environment.
The realization that our logic and cognition are influenced by the environment has important implications for understanding human behavior and thinking. It helps us understand why certain ways of thinking and logics may be differently effective in different environments, and why what is considered rational in one context may not be true in another. This perspective also opens up new ways to think about the development of artificial intelligence and other cognitive technologies that are better adapted to the complexity of the human environment.
A “superlogic” could be understood as an abstraction that summarizes everyday logics and creates metastructures that serve as orientation for them.
“General pure logic” refers to the formal systems we use in mathematics and philosophy.
The “everyday logic” or “language logic” is the logic we use in daily life to communicate and make decisions.
This division helps us understand the different levels at which logic operates. It also shows how logic is both a tool for structuring our thinking and a means of navigating our environment. The ability to switch between these different levels of logic and apply them appropriately is an essential part of human intelligence and adaptability.
The language we use significantly structures and shapes our perception and interpretation of reality. According to the Sapir-Whorf hypothesis, our mother tongue forces us to perceive certain aspects of the world and block out others.
The logic of the thinking of machine and man is a mixture of the three logics mentioned above.