The purpose of this essay is to organize various definitions and principles of epistemology. There are 62 sections organized into 7 primary chapters.

This essay was originally compiled in 2018 as a series of blog posts. The text below is the first complete version to be revised and published.

2. Knowledge

2.1 What is epistemology?

Epistemology is the study of knowledge.

Every branch of knowledge relies on epistemology. Everything you accept as true can be analyzed through the lens of epistemology.

2.2 What is knowledge?

Knowledge is a correctly justified true belief.

Establishing knowledge is one of the central goals of intellectual activity. Scientists and philosophers have helped advance the sphere of human knowledge.

According to this definition, knowledge has to be justified. For example, imagine you say, ‘My next coin flip will be heads’. Even if this statement is true, it’s not knowledge because you have no justification to believe it.

Additionally, knowledge must be ‘correctly’ justified. This means correct justification is used rather than faulty justification.

Edmund Gettier claimed the definition ‘justified true belief’ was inadequate to define knowledge. The next paragraph is a Gettier case to demonstrate this problem.

Imagine you observe one sheep standing in a field 100 yards away, but it’s actually a realistic wooden sheep. You believe there’s one living sheep in the field. Since the wooden sheep looks real, it serves as adequate justification. Additionally, this belief is true because there is one living sheep hidden behind a bush next to the wooden sheep. This example shows how ‘justified true belief’ is an incomplete definition of ‘knowledge’.

By adding the word ‘correctly’ to ‘justified true belief’, the Gettier problem is resolved. Your belief that there’s one living sheep in the field is not correctly justified, therefore it’s not knowledge.

2.3 What is justified?

Justified is the attribute of being supported by a good reason.

There is a subjective line between justified and not-justified. I don’t have a strict criteria for what constitutes as a good reason. For example, if you hear loud music playing next door, are you justified to believe they are having a party? Depending on who you ask, the answer could be yes or no. What constitutes as a ‘good reason’ is subjective.

2.4 What is a belief?

A belief is a representation accepted as true.

In our daily lives, we form many beliefs about reality. For example, if you mail a package, you would probably believe the delivery will arrive at the correct destination.

Over the course of a lifetime, a person will accumulate a giant list of beliefs about reality. Many of these beliefs will become forgotten and buried in our subconscious, but as long as they are subconsciously accepted to be true, they qualify as a belief.

2.5 What is a priori, a posteriori, analytic and synthetic?

A priori knowledge is acquired without experience.

A posteriori knowledge is acquired through experience.

Analytic knowledge is the meaning of a concept.

Synthetic knowledge extends beyond the meaning of a concept.

Using these four definitions, we can divide knowledge into four types: a priori analytic, a priori synthetic, a posteriori analytic and a posteriori synthetic.

A priori analytic

A priori analytic is knowledge of the meaning of a concept without experience. A priori analytic knowledge cannot exist, because all meaning retrieval occurs within the bounds of experience. Imagine you ask yourself the meaning of the word ‘fence’. To answer this question, your mind needs to retrieve a mental representation of what ‘fence’ means. This meaning retrieval would be an experience, therefore it wouldn’t be a priori knowledge.

A priori synthetic

A priori synthetic is knowledge that extends beyond the meaning of a concept without experience. A priori synthetic knowledge cannot exist, because all mental activity is an experience.

Mathematical equations cannot be known a priori. For example, take the synthetic equation 76 + 14 = 90. You cannot know if this equation is true or false without mental examination.

A posteriori analytic

A posteriori analytic is knowledge of the meaning of a concept through experience. Consider the meaning of the word ‘rock’. To consider this, a mental representation of the meaning of ‘rock’ needs to be retrieved. This meaning retrieval is an experience, therefore making it a posteriori knowledge.

A posteriori synthetic

A posteriori synthetic is knowledge that extends beyond the meaning of a concept through experience. For example, examine the proposition, ‘There is a bowl in the kitchen’. This proposition is synthetic because the meaning of ‘kitchen’ doesn’t require a bowl. Additionally, this proposition is a posteriori because experience is necessary to determine its accuracy.

3. Language

3.1 What is language?

Language is a system of grammar and words.

Language is one of the most essential tools for communication and the advancement of knowledge. Language helps us express complex and abstract propositions.

3.2 What is a word?

A word is a symbol consisting of letters, phonetic sounds or conventional gestures.

Words are portable concepts. For example, think of the word ‘wall’. To establish the word ‘wall’, we can point to multiple examples of a wall and say ‘wall’. After this process, the word ‘wall’ becomes an established tool to convey the concept of a wall.

Another common way to establish a word is to provide a definition. This method is only possible after a large variety of other words have been established.

3.3 What is a name?

A name is a word that designates something.

Words and names have a perfect overlap, but have different meanings. Every word is a name for a concept, and every name is a word. The purpose of a name is designation, while the importance of a word is the collection of letters or phonetic sounds.

For example, when meeting somebody, usually you will provide a name to identify yourself. This is called a ‘name’ rather than a ‘word’ because designation is the purpose.

3.4 What is a symbol?

A symbol is something that represents a concept.

Language is a dynamic system of symbols. Every word and letter is a symbol. Because symbols are relatively easy to arrange and control, language is capable of a vast array of meanings and uses.

3.5 What is a concept?

A concept is a general representation.

Generality is the essential aspect of a concept. For example, the concept of ‘grass’ refers to a wide range of things. It refers to different types of grass and the entirety of what grass stands for. The concept of ‘grass’ is general.

Concepts are representations. For example, the concept ‘fork’ is not an actual fork, but instead it’s a representation of a fork.

3.6 What is a form?

A form is a general representation.

Plato claimed every form we encounter in life has a corresponding transcendental ideal form. For example, if we see a frog, there is also an ideal frog form in transcendental reality.

Additionally, Plato believed the world of transcendental forms is the most true reality. When we recognize a horse, we are remembering the ideal form of a horse. Forms are based on remembering the ideal form.

Conversely, Aristotle claimed forms are created through experience rather than remembering an ideal form. We can learn the dog form by observing multiple examples of dogs. Through experience we can realize the commonality shared by every dog and label this concept.

I agree more with Aristotle on this topic. There’s an unlimited amount of potential forms. For example, we can establish the form of a computer sitting on top of a stack of books and call it ‘A’. It seems unlikely that an ideal form of ‘A’ exists in transcendental reality.

3.7 What is a definition?

A definition is a statement of the meaning of a word.

Most words have multiple meanings. Therefore, most words have multiple definitions. The first step in creating a definition is to figure out which meaning will be targeted.

When making a definition it’s important to include all instances that qualify and exclude all instances that do not qualify. This can be tricky because some words represent complex concepts.

Judging the adequacy of a definition is always subjective to a degree. For example, take my definition of ‘definition’: a statement of the meaning of a word. Imagine I replace the word ‘meaning’ with my definition of ‘meaning’: an underlying representation. The new definition of ‘definition’ would be: a statement of the underlying representation of a word. This new definition is subjectively worse because it’s not clear.

3.8 What is establishment?

Establishment is the process of causing something indefinitely into existence.

Language is formed through establishment rather than usage. For example, imagine a computer creates a million different colors and we want to give a word to each color. We could name every color a separate number. Although we wouldn’t use every color, the meanings would be established. This example shows how usage is unnecessary for a word to have meaning.

Imagine somebody starts using a word in a new way. In this case, usage and establishment occur at the same time, but establishment is more important for creating meaning.

3.9 What is a meaning?

A meaning is an underlying representation.

In terms of language, there are two main types of meaning: literal and implied. The literal meaning refers to the primary meaning of the words. The implied meaning refers to something not explicitly stated. People can say one thing and mean another.

3.10 What is literal?

Literal is according to the primary meaning of language.

Almost every word in the English language has multiple meanings. For example, the word ‘argument’ could mean a verbal disagreement between two people or it could mean a line of reasoning to support a belief. Another example, the word ‘time’ could mean a specific occasion or the entire phenomena of past, present and future.

Even the most basic words have multiple meanings. For example, the word ‘for’ could indicate a length of time or intended ownership. Another example, the word ‘in’ could mean surrounded by something else or refer to a condition. These examples show that being perfectly literal is an elusive task.

3.11 What is a sentence?

A sentence is a unified segment of words that has at least one subject-predicate pair and follows grammatical rules.

The subject of a sentence is the thing being described, while the predicate describes that thing. For example, examine the sentence, ‘Frank went to the beach’. The subject is ‘Frank’ and the predicate is ‘went to the beach’.

3.12 What is grammar?

Grammar is a system of rules for the combination and formation of words.

What’s the difference between syntax and grammar? While syntax is concerned with the order of words, grammar has a wider scope that goes beyond syntax. Grammar also includes morphology which involves prefixes, root words and other word variations.

Humans learn language and grammar primarily through imitation. Children are able to notice patterns for how nouns, adjectives and verbs relate to each other.

3.13 What is syntax?

Syntax is a system of rules for the ordering of words.

Syntax is essential for the clarity of language. Without syntax, there would be no rules for how words in a sentence relate to each other.

3.14 What is clear?

Clear is the attribute of being easy to understand.

When I write, I try to be clear. Usually the first draft has many problems. Some sentences might be unnecessary or have misleading words. These flaws detract from having a clear meaning.

Clear writing depends on how well the author can translate a thought into words. This process can be difficult because some thoughts are complicated and nuanced.

3.15 What is subjective?

Subjective is the attribute of being open to interpretation.

Subjective words are essential for describing reality. There are aspects of reality that can only be described using subjective words. By excluding subjective descriptions, one becomes limited in their ability to describe reality.

Subjective statements are capable of being accurate representations. Although we can’t absolutely prove that a subjective description is true, we can have a high degree of certainty in its accuracy.

3.16 What is objective?

Objective is the attribute of not being open to interpretation.

Numbers have an objective meaning. Think of the number 4. To establish the meaning of 4, we can point to groups of 4. The meaning of 4 is an objective concept which is easily differentiated from the meaning of 3.

This idea also applies to mathematical concepts such as squares and circles. We can point to examples of squares and non-squares to establish the objective meaning of a square.

With the exception of mathematics and symbolic logic equations, it’s impossible to make a 100% objective proposition. The most objective-looking statements can always be twisted and purposefully misinterpreted. Below are two examples.

1. ‘My car is in the driveway’. The word ‘in’ could be interpreted as ‘inside’. This could mean the pieces of the car are embedded into the cement of the driveway. That would be ridiculous, but it shows one possible interpretation of the words.

2. ‘Bob has a car’. In this sentence, the words ‘has’ and ‘car’ can be misrepresented. What is the definition of ‘has’? What is the definition of ‘car’? These words have multiple meanings.

Instead of trying to differentiate between objective and subjective propositions, we should accept that propositions exist on a continuum between objective and subjective. For this reason, the word ‘objective’ is subjective.

4. Representation

4.1 What is a representation?

A representation is something that stands for the actual thing.

Earlier in this essay, I said establishing knowledge is one of the central goals of intellectual activity. If establishing knowledge is a central goal, another central goal is to create true physical representations of reality.

This includes all of our models, descriptions, equations and illustrations. For example, the equation E = MC2 is a representation of a real world phenomenon. Another example, the Mona Lisa by Leonardo da Vinci is a representation of Lisa del Giocondo.

4.2 What is a proposition?

A proposition is a representation to be considered.

Not all propositions are beliefs. Sometimes we make propositions for evaluation rather than for asserting an opinion.

4.3 What is a description?

A description is a linguistic representation about something.

Although we often use images to display information, sometimes it’s more effective to use words. This is why we often see descriptions attached to images.

4.4 What is an explanation?

An explanation is a description that makes something clear.

Explanations are useful for understanding the world. Explanations shine light on the mysteries of reality.

There’s no definitive line between what information qualifies as an explanation and what doesn’t. We subjectively determine the most important aspects to include in an explanation. Clarity is the goal. An explanation can be as short as a single sentence.

4.5 What is mathematics?

Mathematics is the study of numbers, lines and shapes.

Mathematics is a catalog of representations. Ranging from physics to economics, many things are accurately described using mathematics. Numbers, equations and unique shapes are indispensable for describing certain aspects of reality.

How does mathematics relate to logic? Logic is the ‘process of forming conclusions using objective reasons or premises’. Logic and mathematics overlap when it comes to solving mathematical equations.

Imagine you want to figure out the length of the long side on a right triangle. You already know the lengths of the two short sides: a = 4 and b = 3. To answer this question, you can use the Pythagorean theorem, a2 + b2 = c2. Now you can solve the equation using logic:

1. a2 + b2 = c2
2. a = 4
3. b = 3
4. Therefore, c = 5

Solving this equation is simultaneously mathematics and logic. There are objective principles that form a conclusion and simultaneously there are numbers, lines and a shape.

The part of mathematics that is not logic, has to do with numbers, shapes and lines in themselves. For example, think about the mathematical concept of a square. A square in itself is not a process of forming a conclusion. Therefore, shapes in themselves are not logic. The same can be said for lines and numbers.

To show how logic can stand on its own separate from mathematics, observe this logical argument:

1. All humans are mortal
2. Socrates is a human
3. Therefore, Socrates is mortal

This logical argument is not mathematics because there are no numbers, lines or shapes being referred to.

4.6 What is a number?

A number is a word that represents a quantity of units.

Imagine language without numbers. To describe an amount, you would have to use words like ‘few’, ‘some’ and ‘many’. Depending on the context, this might be unclear and problematic. Numbers allow us to describe quantities with precision and clarity.

4.7 What is exact?

Exact is the attribute of being precisely accurate.

Exact shapes do not exist in physical reality. Imagine a circle drawn by a computer printer with extreme precision on a piece of paper. This circle would not be an exact circle because there would be ink molecules slightly out of place.

5. Reason

5.1 What is reason?

Reason is the process of forming conclusions using explicit justifications or premises.

Whenever we use explicit reasons to form a belief, we are performing reason. Reason is the evaluation of reasons to make a conclusion. Reason can be contrasted with intuition which is based on unclear justifications.

Science relies on reason. Science is a ‘method of establishing knowledge through controlled experiments’. To construct a controlled experiment, scientists need to consider the potential confounding variables. They need to have solid reasons for why an experiment is adequate for testing a theory.

A reason is something intended to support the accuracy of a proposition.

Reasons play a central role in epistemology. Whenever we form a belief, it’s usually based on reasons, conscious or unconscious. The purpose of a reason is to reinforce or strengthen a proposition.

A reason is something that causes something else.

Everything is caused by a reason or multiple reasons. For example, the reason that the Moon orbits around Earth is the Earth’s mass has a gravitational pull on the Moon.

What’s the difference between an explanation and a reason? An explanation is based on language, while a reason doesn’t need to be stated in language. A reason always exists before it’s put into words.

5.2 Belief analysis

Belief analysis is a list of rules for displaying the structure of a belief. There are 6 rules listed below.

1. State the belief using a single sentence at the top of the page
2. List reasons to support the belief (no more than 5 reasons)
3. State each reason with a short sentence
4. After each reason, list sub-reasons to support that reason (quotes or original writing)
5. No more than 3 sub-reasons per reason
6. Each sub-reason is no longer than 3 sentences

By clearly stating reasons and pieces of evidence, it becomes easier to identify flaws in a belief. We can discover some reasons are problematic or have a weak connection to the proposition. This method can help opposing sides in an argument understand each other with greater clarity.

Belief analysis combines objective and subjective reasons into a coherent whole. When faced with a complicated real world question, there’s never an easy formula to provide a solution. Instead we must weigh competing reasons and use our best judgment.

5.3 What is evidence?

Evidence is information that is relevant for determining the truth.

Evidence is essential for all knowledge. It would be impossible to form a justified belief without relevant information. Evidence is the traction that allows a person to learn about reality.

5.4 What is proof?

Proof is evidence that establishes near absolute certainty.

There is not a clear line between proof and non-proof. For example, imagine you see a person driving a public transit bus. Is this proof that the person is employed as a bus driver?

In my opinion, this observation is proof. Somebody else might disagree and require a higher level of evidence. Every situation is different and proof is a subjective concept.

5.5 What is a fact?

A fact is something known with certainty.

According to the first definition, a ‘fact’ is something known with certainty, but does not require absolute certainty. For example, if you see a book on the windowsill, the book being on the windowsill is a ‘fact’. The only chance that the book isn’t there would be if it’s a hallucination. But in practical reality, we regard this observation as a ‘fact’.

A fact is something known with absolute certainty.

According to the second definition, anything that could be a hallucination or a dream is not a fact. For example, is it a fact that you’re reading this sentence? No, because there’s a chance you’re actually asleep in a dream or you’re a brain in a vat experiencing a simulation.

Imagine you’re actually a brain in a vat. What knowledge is still true in this hypothetical? Although this is not an exhaustive list, I can think of seven propositions that are true in this hypothetical:

• I exist
• Consciousness exists
• Experience exists
• A sense exists
• A perception exists
• Reality exists
• Time exists

These seven propositions are necessary for any hallucination to happen. Even the most elaborate hallucination could not negate any of these propositions. These seven propositions are absolute facts.

If the self didn’t exist, there would be nobody to view the hallucination. If consciousness didn’t exist, the hallucination wouldn’t have been seen. If experience didn’t exist, the hallucination wouldn’t have been endured. If a sense didn’t exist, there would be no way to access data about the hallucination. If a perception didn’t exist, the hallucination wouldn’t have been perceived. If reality didn’t exist, there would be nothing. If time didn’t exist, there would be no seconds to experience the hallucination.

Mathematical equations are not absolute facts. For example, take the equation 8 + 6 = 14. To demonstrate the accuracy of this equation, you could take eight bananas, add six bananas and then count the total. If you counted the same amount thousands of times, there’s a chance you miscounted every time. Even if you used a calculator, the calculator could have malfunctioned.

Logical conclusions are not absolute facts. Here is an example:

1. Every Y is Z
2. Alice is a Y
3. Therefore, Alice is Z

The conclusion is not an absolute fact. Imagine you read the first premise and memorize it. Then you read the second premise while retaining a memory of the first premise. When you try to combine both premises, you might accidentally warp the memory of either premise leading to a mistake. Even if you perform this task hundreds of times, there’s a chance the same mistake occurred every time.

5.6 What is an axiom?

An axiom is a principle believed to be certain.

Axioms can be used to build an unshakable foundation upon which a person can think about something. By making the axioms clear, a person may improve their ability to determine truth beyond the axioms.

5.7 What is science?

Science is a method of establishing knowledge through controlled experiments.

According to the first definition, there’s not a strict boundary between science and non-science. We can never be absolutely certain that every confounding variable has been controlled in an experiment. There’s always a chance that an unseen variable could affect the experiment.

Is economics a science? It depends on the specific study. Quasi-experimental analyses look at real world economic events which resemble controlled experiments. It’s debatable whether or not these studies qualify as science.

Science is the study of any subject related to physics, chemistry or biology.

According to the second definition, if you are studying something that involves physics, chemistry or biology, you are studying science. This definition corresponds to science class in K-12 education.

5.8 What is an experiment?

An experiment is an event that potentially tests a hypothesis.

I divide experiments into two types: natural and artificial. A natural experiment is a real-world event, while an artificial experiment is a man-made procedure.

Natural experiments are questionable because there are usually many confounding factors. For example, the economic impact of the American Recovery and Reinvestment Act of 2009 is not a clear experiment. There were many other variables affecting the economy at the time making it difficult to isolate the impact of the stimulus package.

With artificial experiments it’s easier to isolate the impact of a treatment. For example, imagine you have two identical groups and implement a different treatment to each group. Since both groups are theoretically identical, any difference in the results can be assumed to be caused by the treatment.

5.9 What is logic?

Logic is the process of forming conclusions using objective reasons or premises.

We subconsciously use logic all the time. Here is a basic logical argument:

1. All locked doors cannot be opened
2. B is a locked door
3. Therefore, B cannot be opened

As we gain experience and learn about reality, we collect an extensive list of beliefs. Using logic, this list of beliefs helps us deduce facts and make decisions. The three-line logical form (i.e. the syllogism) is so ubiquitous we are largely unaware of it.

5.10 What is intuition?

Intuition is the process of forming beliefs based on unclear reasons.

Intuition comes from the subconscious mind. Sometimes we don’t know why we believe something. These beliefs are usually based on a feeling rather than explicit reasons.

5.11 What is memory?

Memory is the faculty that enables an entity to store and retrieve information and data.

Memory and the subconscious are opposite sides on a continuum. Memory is established information while the subconscious is non-established information. There is not a strict line dividing memory and the subconscious.

As time passes, knowledge about past events becomes less clear and we might remember fewer details. This transition is gradual and there’s not a clear moment when a piece of information becomes subconscious.

We store information in two main ways: in the mind and in written form. Using the mind (via memory), we can store and access a large amount of information. Similar to taking an object off a shelf, we can look into the mind and grab a piece of information.

The other method of storing information is to write it down in physical reality. This includes books, pictures, handwritten notes and computer files.

5.12 What is statistics?

Statistics is the study of analyzing numerical data.

Statistics can be useful for testing hypotheses and discovering probabilities. Often in statistics, a researcher will study data from a representative sample to infer conclusions about the whole population. It’s important to have an accurate representative sample because some samples can misrepresent the overall population.

Another issue is the relationship between correlation and causation. Just because two variables are correlated doesn’t mean one variable causes the other. In order to draw the conclusion that one variable causes the other, further research might be needed such as analyzing confounding variables or examining the causal mechanism.

5.13 What is analysis?

Analysis is a detailed examination of something.

Analysis is not limited to a single method or set of rules. There are many different ways a person can perform a detailed examination. Analysis may include writing down observations, performing experiments, evaluating statistical data, thinking about various pieces of evidence, looking at graphs or determining the significance of something.

5.14 What is a conclusion?

A conclusion is a representation reached after thinking.

Often in life we are confused about certain things. In my experience, I will ruminate through related thoughts and try to reach a stable conclusion.

This process is similar to pouring dirt into a glass of water, stirring the contents and waiting for the substance to settle. Once the substance has settled to an equilibrium, the conclusion has been reached. I normally appreciate the conclusion because my thoughts have become united into a coherent whole.

7. Phenomena

7.1 What is a phenomenon?

A phenomenon is something that can be perceived.

Every detail of experience is a phenomenon. This includes every event, attribute, object, piece of information, thought and anything else that can be observed.

What’s the difference between a phenomenon and a perception? A phenomenon is the thing being sensed, while a perception is the experience. Imagine somebody watches a tree fall over. The phenomenon is the tree falling, while the perception is the sense datum occurring in the mind of the viewer.

7.2 What is phenomenology?

Phenomenology is the study of immediate perception.

Phenomenology is one of the most interesting things to study. Take one of your senses and examine the sense itself. You can do this for any sense: vision, hearing, touch, taste, smell, thought, etc. Observe the intricacies of the sense, especially the small details you never notice.

7.3 What is experience?

Experience is the totality of past and present sense data.

Experience is the only thing we know in life. It’s impossible to perceive anything without it being an experience. Even our thoughts are experiences.

7.4 What is a perception?

A perception is a conscious sense datum.

In everyday life, we are exposed to a large amount of sense data. Not every piece of sense data receives conscious attention. We are unaware of most data we encounter. The moment that a datum captures our attention, it becomes a perception.

7.5 What is a sense?

A sense is a faculty that retrieves data.

Senses are the only way we learn about reality. Everything we know was originally received through a sense. This includes sensing our thoughts and feelings.

Unconscious machines can also have senses. For example, some light bulbs have motion sensors that turn on the light bulb when somebody enters the room.

7.6 What is data?

Data is rudimentary information.

Data is the root source of all knowledge. Everything we experience is data received through a sense. Data is the most basic material we use to construct beliefs.

7.7 What is information?

Information is something that educates.

Information must have the ability to teach something. Imagine you see a kiosk with some language and maps displayed. This is information because you can learn something from the kiosk.

Information is not always true. As long as the material has the potential to teach something, it qualifies as information.

7.8 What is a detail?

A detail is information about something.

What’s the difference between a detail and a piece of information? These words have a perfect overlap but they have different emphases. The emphasis of a detail is its relation to a subject, while the emphasis of information is education. Every detail is a piece of information; every piece of information is a detail.

7.9 What is a pattern?

A pattern is something that recurs consistently.

Reality is full of patterns. Some patterns are observed while others are unnoticed. We automatically search for consistencies to help us understand reality.

7.10 What is a cause?

A cause is something that gives rise to something else.

Causation is observable. Causation is a relationship between two separate phenomena where one phenomenon gives rise to the other.

Causation is also subjective. There’s not a clear line between a cause and a non-cause. For example, imagine a pineapple sitting on a table. What caused the pineapple to be sitting there? I’m using the pineapple to create a painting. Why? I’m in a painting contest. Why? My teacher encouraged me to join. This process can turn into a never ending list of causes. For this reason, it’s subjective whether or not something is a cause.

7.11 What is an attribute?

An attribute is an identifiable part of something.

Anything that can be noticed as being part of something is an attribute. Imagine making a list of attributes about a tractor. You might include the horsepower or exterior color. These are both attributes because they are identifiable.

7.12 What is a quality?

A quality is a non-numerical attribute.

Although many qualities can be measured numerically, qualities themselves are not numerical. For example, the quality ‘fast’ can be stated in miles per hour, but the word ‘fast’ is meaningful without a number. We can observe something is fast without attaching a numerical value to this attribute.