What are the Formal Sciences?

by Dave

Scholars discuss the formal sciences regularly in research, but too few people know the simple meaning of this branch of academia. Explore the fields of study in this subject and find out which disciplines fall under this umbrella. Also, explore why these branches hold great importance to society. What are the Formal Sciences?

What are the Formal Sciences?

The formal sciences can help you classify an otherwise chaotic universe by applying organization and language to complex systems of information. There is so much information in the world, and I would venture to say even just in our daily lives. But how do we organize it and find meaning in science? For example, how am I creating this web page on the internet for you to read it? And how did you find it when there are so many choices? Learning the definition and meaning of the formal sciences provides students with information to master a list of various branches of study in college and independent research.

The formal sciences consist of computer science, mathematics, statistics, and systems science. They provide languages that organize and characterize the systems, allowing us to communicate better with each other and with machines. Such formal languages make it easier to understand and work with complex informationThis clarity is especially true in systems involving math and logic, including computers, statistics, and even linguistics.  

Knowing the formal sciences allows you to list your findings of the world accurately and derive meaning from discoveries. You can then develop inferences about the results, further test them, communicate them to others, or implement them in various fields. For instance, I use them to write web pages and determine factors that attract readers to the pages.

The Meaning of Formal Science

The formal sciences information I provide below will help you further understand the branches and meaning of the field. There are various types and definitions of sciences, and it’s essential to know their differences. Before getting into the areas within this main branch, I first want to emphasize the differences between pure science and formal science.

What is the pure definition and meaning of formal science? In several fields and branches of the formal sciences, students use the phrase often but don’t understand its significance. The simple definition and meaning of the formal sciences is any study that utilizes systems to generate information. There are several lists of examples of formal sciences with many sub-fields coming from mathematics and branches of computer science. Across several areas of study, systems provide a framework for application and utility.

Through study and research

Things like theoretical languages and algorithms emerge through study and research. Once an application proves to be useful, the finding can assist professionals in answering additional questions. This process goes through ebbs and flows, with months at a time lacking any groundbreaking progress. These fields hold a list of goals that expand beyond merely broadening the systems used in study and research.

A straightforward definition is tough to pinpoint across the several branches of formal science. While similarities exist across the long list of fields of study, unique considerations must go into defining how logic emerges and applies to practical application. A helpful way to further explore the meaning of formal science is to contrast the phrase against the study of science as a whole.

Science vs. Formal Science

I would venture to guess that pure science is the most familiar to most readers. It’s what we think of when we think about physics, biology, or chemistry. Pure science encompasses a method of observing and testing the natural world to discover truths about it.

A formal science, on the other hand, lists symbolic systems or those systems founded in logic.   

Unlike natural sciences wherein scholars study things to understand them better, scientists in the formal sciences design systems to categorize understanding, which means that the field does not rely on empirical testing or evidence. Instead, people base this on definitions and axioms that deduce statements. Thus, statements in formal sciences are inherently accurate, also known as being analytic. This truth makes the formal sciences applicable to and useful in all other fields of science.

The formal sciences develop formal languages for logical, mathematical, and theoretical systems. As such, they exhibit key traits as tools that aid other fields of scholarship. Examples include the natural and social sciences through the provision of structure. This structure allows scientists to describe their findings of the world better and develop inferences about them.

What Subjects Do the Formal Sciences Include?

Within this category, I go over several disciplines of formal sciences and their definitions. These include mathematics, theoretical computer science, programming, accounting, and actuarial science. These schools of thought rely on the formation of language and systems to categorize their elements for study.

I split the formal sciences articles, definitions, and other information that is detailed here into four categories. They are computer science, mathematics, statistics and a relatively new area called systems science. There is one common trait joining these categories: Each studies formal language that describes symbolic systems. Math, statistics, general logic, and other similar fields all need such a system for us to work in and understand them. The formal sciences give us those languages, and I believe the formal sciences articles here help you master their meaning and applications in the real world.

What Does a Degree in the Formal Sciences Entail?

If you are thinking about getting a degree in the formal sciences, I think you should know that you will undoubtedly run into very particular classes. Like any degree, you will start with a group of core classes that include various subjects. These will introduce you to the underlying meanings of the larger main branches and definitions in the sciences.

These subjects will be both related and unrelated to the formal sciences. But the most important ones for the formal sciences are math and logic. So if you have the opportunity to select specific classes in these areas, I suggest you do some research by reading science articles to help you choose wisely.

You will then start to take classes that focus more on a specific area of formal sciences with narrow definitions. The formal sciences help to classify information. Because of this, you will need to learn about the information with which you are working. For example, if you focus on accounting or actuarial sciences, expect to take business and finance classes. If you focus on computer science or programming, you will be learning a lot about computers and technology.

Primary Branches of the Formal Sciences

Collecting a comprehensive list of all the formal sciences is challenging. We know the apparent inclusions to the category are mathematics and computer science. Are those the only ones you and I should consider as a portion of this field? No. The vital aspects of formal science to keep in mind are not a mathematical approach to research. The true signifier is systems and the use of logic. Logic is not something that only exists in computer code or mathematical proofs. How can students or interested learners differentiate these branches with such a generic definition yet a vastly diverse list of included fields?

Proofs over observations

A great way to clarify the branches of formal science is to consider anything that involves proof over observations. That would mean that the definition of formal sciences also includes additions to the list like linguistics. The field is non-empirical, just like other entries in the list of the formal sciences. The theoretical nature of an area helps to define what makes up this category of studies. The primary branches of linguistics, computer science, and mathematics may seem different, but all fall under this category.

In several aspects, the branches of formal science often feel neglected by the general public. If you work in these fields, then you keep up with the latest findings and research. Otherwise, the types of the study included in this group seem too complex to translate effectively to mainstream information channels. This fact is one major challenge fields in the formal sciences face in reaching new students and scholars. With this in mind, let’s further explore how these branches of the formal sciences hold importance in our society.

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The Importance of Computer Science in the Formal Sciences

Due to the extraordinary pace at which computers evolve, there are several fields and definitions within this branch of science. In many ways, computers have become a lifeline for formalizing processes used to observe and study all kinds of phenomena.

I indeed rely on them for my work, as do many others. They have also made life in the 20th and 21st centuries much easier. With them, complicated calculations and data tracking can now take place automatically. In this way, computers are an intrinsic part of the study of natural sciences and the field of applied sciences.

However, what goes into making computers and their programs are themselves formal sciences. The formal sciences articles I recommend here will help you understand the meaning of this process. Learning about these processes helps you to get involved in it yourself.

Computer science is a quickly growing field

As it is relatively modern in terms of its development of formal languages and systems, computer science is a quickly growing field. I link to articles on the history of this applied science here to help you get a better idea of the definitions and background. Put simply, the field develops programs that represent how processes and data interact through the use of algorithms. These algorithms are capable of manipulating, storing, and showing digital material. As such, the computations required to develop these algorithms are reliant on computers and computer-based programs.

Degrees, Careers, and More

I want to note that computer science is a readily available field in many nations across hundreds of universities. Additionally, I think you might appreciate that a career in the domain is also quite lucrative. You can take a look at what it’s like to work in the field by reading formal sciences articles on outstanding computer scientists.

You’ll see that all types of industries rely on computers and people who understand how they work. Moreover, numerous sectors are contingent on the use and development of programs to make them more lucrative. I think it is safe to predict the 21st century will see a boom in training computer science professionals.

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Mathematics as a Formal Science

Believed to have emerged in several ancient cultures simultaneously, the study of mathematics is broad and foundational in numerous societies. In short, this formal science devised several formalized languages in systems to identify and utilize patterns that can resolve conjectures.

Through discussion of and discovery within topics and definitions like change, quantity, space, and structure, mathematicians model concrete phenomena meaning that they can offer insight into “why” and “how.” This data also enables predictions about said phenomena, meaning the science highly applicable in other fields like natural science.

In the applied sciences articles I provide here, you will learn about history, such as how calculation, counting, and measurement emerged from contemplative topics in mathematics. In using abstraction and logic, the field provided the foundation for numerous scientific discoveries. I will also cover how mathematics is essential to topics within several other areas, principally engineering, finance, medicine, and the natural and social sciences. For any field using quantifying studies, mathematics is necessary.

Divisions of Math

Of note, this field contains two critical areas of study: applied and pure mathematics. Applied math is more recent in its evolution as an application of mathematical principles. Statistics and game theory are examples of this category.

Pure mathematics, on the other hand, engages simply in performing math to further the discipline. Those who participate in this field simply wish to discover more about math concepts themselves without necessarily feeling complied to use it elsewhere. If applied mathematics is more your speed, I recommend checking out articles in the applied sciences category. Additional readings may interest you as well in the formal sciences.

Using the Formal Science of Math in the Field

While mathematics is a type of formal science in its own right, its subtopics contain various meanings, definitions, and applications. They create symbolic systems relying on the language of math, at least initially, to explain other phenomena. Particularly within economics, finance, business, and insurance, math plays a significant role in developing different topics.

The most fundamental formal science, math, plays a crucial role in giving meaning to all of the others listed here. It has been around for millennia in many cultures, modern and ancient. Some of the math we use today comes from these ancient cultures. But much of the math we used today have come from excellent refinement over time, especially in the past few centuries.

Math gives us various formal languages and definitions in the sciences that help us identify and use patterns. The language it uses contains numbers and symbols. These numbers and symbols allow for representing abstract concepts and logic itself. But getting to such abstract ideas can be tough if you don’t understand the language. Like any language, it can be tough to learn and require a substantial time commitment. But the formal sciences materials and articles I recommend here are designed to help students struggling with the sometimes complicated concepts. They focus on some tricky areas and reinforce the ideas with practice problems, diagrams, and examples.

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When you have an abundant source of data and information in science, it can be hard to determine the meaning of it all. Statistics helps collect, organize, analyze, interpret, and present data such that you can understand how it all works together. Managing these tasks might involve taking millions of data points and plotting them on a graph to see the pattern they create. Or it might mean applying mathematical functions to the data points to show properties such as average, median, deviation, or other relationships.

In terms of utility, statistics is applicable in uncovering meaning in all of the main branches of science. Any area that works with large amounts of data will benefit from statistical analysis as well as mathematical models.

Statistical Methods

In terms of data analysis, there are two main definitions for methods used in this sub-branch of the formal sciences. The first is descriptive statistics, and the second is inferential statistics. The former has to do with summarizing data using indexes. The latter, on the other hand, uses data that may have substantial influence from random variation.

In the science of descriptive statistics, the goal is to summarize data to make the meaning more clear. Such summarization might include data about a sample such as the overall size, subgroup sample sizes, demographics, and proportions with specific characteristics such as age, gender, or religion in a sample of people. The handiest measures for these types of descriptions are measures of variability and central tendency. These include the mean, median, mode, standard deviation, minimums, maximums, and skewness.

In inferential statistics, there is less emphasis on summarizing the sample and more on learning about the population from which the data comes. For example, if you already have a distribution of probability, then you can use this method to infer the underlying causes. This method involves some assumptions in the form of various statistical models. Selecting which of them you should use will depend on the particular situation.

Applications of Statistics

While theoretical statistics look at the underlying logical arguments and justification of statistical inference, applied statistics look at what statistics can do for you in the real world. You can find many articles on definitions and how the field applies in other areas and main branches of science.

Some of the most vital areas are in computers and programming, such as data mining and machine learning. Statistics are also useful in a wide range of academic disciplines where they give meaning to the mountains of data in social sciences. All of these areas can help experts in different fields to continue research, validate findings, make reliable business decisions, and further public initiatives.

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Systems Science

When you take a look at everything around you, I want you to try to think of it as a group of systems. By that, I mean that you should attempt to see how the different parts work together in individual groups.

This mode of thinking is accessible in modern problem-solving, particularly in all main branches of the sciences. After all, the modern world is continuously becoming denser with increasingly complex and interlinked parts. The internet, globalization, world trade, and quickly developing technology all push this field to the forefront.

System sciences involve recognizing and studying the systems that surround us. These systems include nature, society, technology, and even systematic areas within our brains and minds.

Because there are systems within systems, this way of thinking allows you to narrow down on both small and large groups. You might look at the order of workers within a company or the more extensive system of the company as a whole. Furthermore, the company is part of an even more extensive network of the national and global economy.

As this area of science only came into being in the mid-twentieth century, it is still in the process of finding an inner meaning and sorting out definitions. Like other sciences, finding meaning and definition still hinges on distinguishing between three main parts of the field. These three segments are the domain of inquiry, the body of knowledge, and the method.


There are several frameworks and definitions for different approaches centering around the various purposes and meanings of systems science. For example, the theory of analysis considers how the field can analyze the structure, arrangement, and interactions of a system.

Design in the area, on the other hand, focuses on creating the structure and interactions that lead to the most effective outcome. The field of dynamics then takes a look at how complex interactions behave and change over time.

Theories from other parts of mathematics also come into play in many of those within systems science. Some important ones include chaos theory and control theory.


While the idea behind systems science is to observe systems, the application of the field is to enhance human-made systems. One of the most compelling examples for almost any company out there these days is that of information technology (IT), making it a great place to end up in this field. Within IT, you can become an expert in any number of vital areas. Positions might include data analyst, data scientist, IT consultant, software engineer, or cybersecurity analyst.

Because the applications in IT often concern computers, you will likely benefit significantly from courses or even a degree in computers. I recommend considering programs centering on programming, computer science, and mathematics.

Further Reading

You can find both articles and even books that delve further into the definition and meaning of this area of science in the modern world. Areas in which you might find this study most useful are other formal sciences such as information theory, cybernetics, and linguistics. But it also has applications in the other two main branches of natural and social sciences. For example, systems biology, ecology, engineering, and psychology are prominent fields.

Frequency Asked Questions About the Formal Sciences

Curious and eager to explore the list of uses and applications of formal science? Read these essential topics across all branches of the field.

What subjects do the formal sciences include?

The formal sciences help us work with and understand complex information, especially in systems that involve mathematics and logic. Thus, formal sciences are most important in areas that apply math and reasoning, including computers, statistics, and even linguistics. The main areas are computer science, mathematics, statistics, and systems science.

What does a degree in the formal sciences entail?

A base in math and logic is essential for a degree in the field of formal sciences. Core classes will center on math and logic, while other courses will narrow in on specific subtopics within these or related fields. These topics will then extend into higher levels and start relating to other areas of application, such as business, finance, and technology.

What difference is there between formal science and science?

Pure science is a method of studying and understanding the world around us. It builds knowledge through testing phenomena. Formal science, on the other hand, is a way of organizing and understanding systems of knowledge and information. It uses patterns and languages to characterize data in fields like mathematics, statistics, and computer science.

What jobs can you get using a degree in formal science?

Because managing large amounts of information is a big part of the modern world, formal scientists are in high demand. Popular jobs include accountant, actuarial scientist, mathematician, professor, programmer, and computer scientist. Many of these jobs are particularly important for the current and future information economy that focuses less on physical human labor.


I am sure it’s now clear that the formals sciences form a cornerstone of quantitative science. They are a unique way of applying math and logic to a wide variety of critical modern fields like computer science, business, and more.

The formal sciences information, articles, and books that I provided in this article aim to help you get involved in these topics in the way that’s best for you. The online format allows easy access anytime, anywhere. And I am sure the practice problems and examples found in many of the books will enable you to put your brains to the test, but at your pace.

If you’re unsure where to begin, I suggest starting with something small. Read one of the linked articles here, or even watch a summary video on YouTube. Then you can decide if you want to go deeper with a book or even an academic course.

Exploring More Topics in Formal Science and Academics

The critical element of growth for any field of study is to expand who can learn about your subject. In many ways, technology increases our ability to reach new sources of information. I believe more opportunities for education exist now than ever before in history. That fact is due to online resources becoming more accessible and affordable. Not only do costs seem to trend down, but I think many independent learners want to explore subjects in their own time. Many who have jobs cannot attend college. Even those in college regularly search for new ways to supplement their academic work.

What list can you come up with of every significant branch in the formal sciences? 

How can formal sciences begin to expand their research to the general public?