Recently, I have talked with a friend and we talked about the idea of knowledge as I have always been confused about the purpose of discussing it. This is a short note of my current thought about it.[^1]

Let us first start with the classical definition of knowledge: knowledge is justified true belief. Though the immediate alarm would be the word "true", let us first talk about belief.

Knowledge, from this definition, is some kind of belief. There are many different kinds of belief, some are stronger and some are weaker. Here I want to give a more general approach to belief: belief is a thought of taking something as true. It is subjective, as thoughts are subjective, and therefore it is intrinsically irrelevant to "objective truth" (if any) as "objective truth" is objective. Notice that the evaluation of a belief and whether a belief represents reality needs to involve something beyond belief itself, which means this process is extrinsic, i.e., the connection to "objective truth" is extrinsic.

Let us first propose an example belief for our future analysis: "It is raining outside." We will use it throughout the text.

We will postpone the discussion about "truth" (the truth condition). However, there are a few points I want to highlight about the truth condition. First, the use of "truth" here refers to "objective truth," i.e., it is objective. Second, there is a lot of debate on what can be considered as truth, and there is also much debate on whether there is truth. We will stay away from those discussions about the definition and existence of truth for now, which might raise difficulties, as knowledge is usually considered an access to truth, or at least a relationship with the truth. However, we can sidestep these debates because in practice (in real life), we do not have direct access to truth; we have direct access to phenomena, suggesting that knowledge is actually a relation with phenomena, which might imply something about truth (if any). To illustrate this with an example, to verify the belief that "it is raining outside," we need to (and can only) look outside to see if it is indeed raining. However, the only thing we obtain is the phenomenon of potential rain, as we might be deceived by a fancy sprinkler.

We will now talk about "justified" (the justification condition). There could also be debate about the definition of justification, yet we will stay away from those discussions too, but look at how justification works in practice (in a justification that happens in real life). To start a justification, you must have starting points. The starting point must be things we can appeal to without first having to justify our appeal to them during current justification.

One example of a starting point is a phenomenon, as we have it without needing justification, just like in the raining example, we observe that it is raining outside. Besides phenomena, the only possibilities are either justified beliefs, which are already justified from other justifications (i.e., not the current one), or truths, if directly accessible, which need no justification. This covers everything because, besides phenomena, we can either appeal to something inside our mind or something mind-independent. The former are justified beliefs according to its definition in this note, and the latter are truths. This establishes that any starting point of a justification must fall into three categories: justified belief, phenomena, or truth.

We have now illustrated all three components of classical definition of knowledge, and we are ready to explain my take to it.

We will first start from "true." As I have shown, knowledge, as a kind of belief, is intrinsically subjective and irrelevant to truth. Its relation to truth is extrinsic and through phenomena. This therefore implies there is no truth intrinsically in knowledge, nor does knowledge directly connect to truth. In practice, this means we do not and cannot use knowledge against truth directly. In the rain example, to verify "it is raining outside," we can only check our memory of whether it was raining, consult a weather report, or look outside, which are either belief or phenomena, but we can never check it against truth. The truth condition is methodologically impossible. From the perspective of truth, knowledge might happen to agree with it, but as individuals, we cannot access this perspective. The fact that we use the concept of knowledge regardless of these constraints again shows that when we use the word "knowledge," there is nothing about truth in it.

We will now move on to justification. As I have shown, justification must be based on justified belief, phenomena, or truth. For justification based on truth, it is, in practice (in a real justification), just based on phenomena or belief, as I have just shown. If it is based on phenomena, then consider the following example:

1. Alice told Bob, "It is raining outside." Bob recalls that when he came in, it was not raining; therefore, Bob rejected this claim (or Bob justifies the knowledge that "it is not raining outside").

2. Alice told Bob, "It is raining outside." Bob recalled that when he came in, it was not raining, so Bob looked outside. Seeing droplets falling, yet being tricked by the fancy sprinkler, he rejected this claim (or Bob justifies the knowledge that "it is not raining outside").

3. Seeing the droplets falling from outside, Bob did not think of rain at all. His thoughts flowed among the changes of light reflected by the water. He was so sad because his beloved girl, Alice, had just left him. In Bob's mind, he did not realize it was raining at all.

These examples show there is an in-between process that converts phenomena into belief. Indeed, to use a piece of phenomenon, we need not only to access it but also to convert it into thoughts, i.e., digestion. Therefore, in practice, justification based on phenomena is justification based on justified belief.

In the end, if justification is based on justified belief, then it is just a second order of belief (belief about belief). This raises the question, because if all knowledge is at least justified belief, then some of it must have a circular justification, or it must be grounded in a belief that is unjustified, which, in practice, we would not use as a starting point for justification, as an unjustified belief cannot be used as the starting point for the justification of knowledge. If we do not accept circular justification (if you consider that this should not be used as a justification in real life), then this simply suggests that there is knowledge that cannot be justified; knowledge is just... belief?

This illustrates the confusion I have about the purpose of discussing it, because in practice, what we usually consider is "the teacher told me something...", i.e., it is a belief of the teacher, or "I learned that...", i.e., it is a belief of mine. We also learned that knowledge, as people know it, changes over time (e.g., geocentrism), varies among individuals (e.g., knowledge about the Bible or God), and emerges as humans construct it (e.g., is Los Angeles part of California, what is a violin, and what do we consider as art?). Therefore, it seems to me that, in practice, the only thing that exists is "what each individual believes to be correct" (i.e., belief, or you can define it as subjective knowledge if you want). For example, many people hold "1+1=2" as a belief because they typically do not know how to prove it mathematically (they can consult mathematicians if they want to justify it). This suggests that, in practice, "1+1=2" is purely a belief for them if they do not explicitly justify it, yet they consider it to be knowledge. The idea of "what each individual believes to be correct" is useful because it can be extended to "what most people in a field believe to be correct," which can serve as a definition of knowledge and is sufficiently useful for any situation where you need a definition of knowledge.

This is a short list of a few examples of justification bases. In many frameworks, the categorization is debatable, but they end up within these three points:

• Evidence: phenomena or truth (depending on philosophical position)

• A priori justification: justified belief or truth (sometimes phenomena, depending on philosophical position)

• Innate cognitive structures: manifest only through shaping phenomena we experience, thus phenomenon-based in practice

• Prior justified beliefs: justified belief

• Coherence with belief system: justified belief

• Testimony: phenomena or other's justified belief (known through phenomena)

• Norms or virtues: justified belief or truth (depending on philosophical position)

• Mathematical or logical principles: justified belief or truth (depending on philosophical position)

• Reliable processes: phenomena or truth

The key point is that for each justification basis, we must think about how we access it, instead of what is it. Things that are not accessible cannot be used as a starting point in practical justification. For example, to access intuition, intuition needs to manifest in one of three ways.

One may question the focus on access. However, if we want to discuss something that happened in real life, we must start with what we actually have access to. Something we can not access is irrelevant to us.

If readers are confused about the usage of "phenomena," it refers to what we experience or observe.

A classical question in the definition of knowledge is scientific progress. Clearly, people seem to be looking for a "proof" that science is making progress. First, the idea that science is making progress (e.g., modern medicine is better than witchcraft) is itself a belief. In fact, any idea like "some beliefs are better than others" is a belief. Second, in a particular field, there is usually a "standard," which is essentially a set of beliefs about "which beliefs are better." In modern science, the "standard" is typically that a better belief is one that can be justified by phenomena (using a set of rules of interpretation). This "standard" naturally prioritizes beliefs that are more likely to predict phenomena (i.e., its utility). People who believe in other "standards" that prioritize phenomena in some sense are then likely to hold the belief that "science is making progress." If we wish to live a better life, it seems that we should, in practice, discuss the standards we are actually using and how we want to change them, since what we thought to be better is itself a standard.

To see the method discussed in this note in motion, let us examine how experiments in the field of high energy physics work. As we now commonly consider as knowledge, there are fundamental particles like the Higgs boson, neutrinos, etc. However, these particles are never directly observed; instead, particle interactions produce electromagnetic signals in detectors. These signals are then used through a reconstruction with different physics models, and the "best" model wins as it matches (predicts) the signal pattern. This model is known as the Standard Model, which most physicists now agree on. Readers should be able to map each element of this process to the concepts illustrated in this note.

In mathematics, mathematicians typically do not have access to math as truth directly (if any). Instead, a mathematician (or a student) proves something starting from some starting point, i.e., what is taken to be true, and then works from there by piecing them together using method that is taken to be true. A piece of proof is accepted by another mathematician if it aligns with the standards they hold as beliefs, typically including checking that the starting points, together with the methods, are believed to be acceptable and that it does not contradict a set of other theories that are considered true by this mathematician.

If some mathematicians have direct access to truth, when they use it in proofs, they must understand truth as a human does, which is then converted into beliefs. On the other hand, as long as not all mathematicians have direct access to truth, knowledge must still be something knowable by those without direct access, reverting to the earlier process unless knowledge is exclusively for those with direct access to truth.

In some rare cases, if truth is directly accessible to certain mathematicians in a way that allows it to be used in a proof, mathematicians who do not (yet) have direct access to this truth must convert it into beliefs when reading the proof, thereby reverting to the earlier process. Otherwise, if the truth in the proof does not require digestion by the reader, this proof would provide direct access to the truth, granting anyone who reads it direct access to truth. If such a proof exists, please share!

If we accept circular justification and all knowledge is justified (i.e., the other option in the main text), then all knowledge that a human knows is grounded on some circularly justified beliefs. This suggests that humans are born with some innate circular justified beliefs so that every other piece of knowledge can have a base, meaning babies have knowledge.

If babies have knowledge, then this knowledge has to be justified, as we are working with the condition that all knowledge is justified. This suggests either justification before-life or maybe some sort of instantaneous simultaneous justification at birth (since you cannot justify them sequentially), like a glitch in video games.

If we have a before-life (and it needs to be a before-life of which we have knowledge), we would still need to justify some knowledge at the birth of the before-life (or change our definition of knowledge to the one in the main text for before-life and change it back for this life), suggesting instantaneous simultaneous justification in before-life. Otherwise, we need to accept an infinite chain of before-life or a chain of circular life (and we cannot discuss how to start the circle of lives) while some knowledge can be preserved in between for both cases. This is a position that most religions or mythologies do not hold, and most concepts of the before-life in those religions typically cannot preserve knowledge.

In summary, if we accept circular justification and all knowledge is justified, then babies have knowledge. And we also need to accept one of the following: some sort of instantaneous simultaneous justification that we do not understand, an infinite chain of before-life, or a chain of circular life, while the latter two preserve knowledge.

Agrippa's Trilemma proposes a third option, known as infinite regress. For those who are confused by this, please note that infinite justification cannot occur in finite real life.

Recently, I have talked with a friend and we talked about the idea of knowledge as I have always been confused about the purpose of discussing it. This is a short note of my current thought about it.[^1]

Let us first start with the classical definition of knowledge: knowledge is justified true belief. Though the immediate alarm would be the word "true", let us first talk about belief.

Knowledge, from this definition, is some kind of belief. There are many different kinds of belief, some are stronger and some are weaker. Here I want to give a more general approach to belief: belief is a thought of taking something as true. It is subjective, as thoughts are subjective, and therefore it is intrinsically irrelevant to "objective truth" (if any) as "objective truth" is objective. Notice that the evaluation of a belief and whether a belief represents reality needs to involve something beyond belief itself, which means this process is extrinsic, i.e., the connection to "objective truth" is extrinsic.

Let us first propose an example belief for our future analysis: "It is raining outside." We will use it throughout the text.

We will postpone the discussion about "truth" (the truth condition). However, there are a few points I want to highlight about the truth condition. First, the use of "truth" here refers to "objective truth," i.e., it is objective. Second, there is a lot of debate on what can be considered as truth, and there is also much debate on whether there is truth. We will stay away from those discussions about the definition and existence of truth for now, which might raise difficulties, as knowledge is usually considered an access to truth, or at least a relationship with the truth. However, we can sidestep these debates because in practice (in real life), we do not have direct access to truth; we have direct access to phenomena, suggesting that knowledge is actually a relation with phenomena, which might imply something about truth (if any). To illustrate this with an example, to verify the belief that "it is raining outside," we need to (and can only) look outside to see if it is indeed raining. However, the only thing we obtain is the phenomenon of potential rain, as we might be deceived by a fancy sprinkler.

We will now talk about "justified" (the justification condition). There could also be debate about the definition of justification, yet we will stay away from those discussions too, but look at how justification works in practice (in a justification that happens in real life). To start a justification, you must have starting points. The starting point must be things we can appeal to without first having to justify our appeal to them during current justification.

One example of a starting point is a phenomenon, as we have it without needing justification, just like in the raining example, we observe that it is raining outside. Besides phenomena, the only possibilities are either justified beliefs, which are already justified from other justifications (i.e., not the current one), or truths, if directly accessible, which need no justification. This covers everything because, besides phenomena, we can either appeal to something inside our mind or something mind-independent. The former are justified beliefs according to its definition in this note, and the latter are truths. This establishes that any starting point of a justification must fall into three categories: justified belief, phenomena, or truth.

We have now illustrated all three components of classical definition of knowledge, and we are ready to explain my take to it.

We will first start from "true." As I have shown, knowledge, as a kind of belief, is intrinsically subjective and irrelevant to truth. Its relation to truth is extrinsic and through phenomena. This therefore implies there is no truth intrinsically in knowledge, nor does knowledge directly connect to truth. In practice, this means we do not and cannot use knowledge against truth directly. In the rain example, to verify "it is raining outside," we can only check our memory of whether it was raining, consult a weather report, or look outside, which are either belief or phenomena, but we can never check it against truth. The truth condition is methodologically impossible. From the perspective of truth, knowledge might happen to agree with it, but as individuals, we cannot access this perspective. The fact that we use the concept of knowledge regardless of these constraints again shows that when we use the word "knowledge," there is nothing about truth in it.

We will now move on to justification. As I have shown, justification must be based on justified belief, phenomena, or truth. For justification based on truth, it is, in practice (in a real justification), just based on phenomena or belief, as I have just shown. If it is based on phenomena, then consider the following example:

1. Alice told Bob, "It is raining outside." Bob recalls that when he came in, it was not raining; therefore, Bob rejected this claim (or Bob justifies the knowledge that "it is not raining outside").

2. Alice told Bob, "It is raining outside." Bob recalled that when he came in, it was not raining, so Bob looked outside. Seeing droplets falling, yet being tricked by the fancy sprinkler, he rejected this claim (or Bob justifies the knowledge that "it is not raining outside").

3. Seeing the droplets falling from outside, Bob did not think of rain at all. His thoughts flowed among the changes of light reflected by the water. He was so sad because his beloved girl, Alice, had just left him. In Bob's mind, he did not realize it was raining at all.

These examples show there is an in-between process that converts phenomena into belief. Indeed, to use a piece of phenomenon, we need not only to access it but also to convert it into thoughts, i.e., digestion. Therefore, in practice, justification based on phenomena is justification based on justified belief.

In the end, if justification is based on justified belief, then it is just a second order of belief (belief about belief). This raises the question, because if all knowledge is at least justified belief, then some of it must have a circular justification, or it must be grounded in a belief that is unjustified, which, in practice, we would not use as a starting point for justification, as an unjustified belief cannot be used as the starting point for the justification of knowledge. If we do not accept circular justification (if you consider that this should not be used as a justification in real life), then this simply suggests that there is knowledge that cannot be justified; knowledge is just... belief?

This illustrates the confusion I have about the purpose of discussing it, because in practice, what we usually consider is "the teacher told me something...", i.e., it is a belief of the teacher, or "I learned that...", i.e., it is a belief of mine. We also learned that knowledge, as people know it, changes over time (e.g., geocentrism), varies among individuals (e.g., knowledge about the Bible or God), and emerges as humans construct it (e.g., is Los Angeles part of California, what is a violin, and what do we consider as art?). Therefore, it seems to me that, in practice, the only thing that exists is "what each individual believes to be correct" (i.e., belief, or you can define it as subjective knowledge if you want). For example, many people hold "1+1=2" as a belief because they typically do not know how to prove it mathematically (they can consult mathematicians if they want to justify it). This suggests that, in practice, "1+1=2" is purely a belief for them if they do not explicitly justify it, yet they consider it to be knowledge. The idea of "what each individual believes to be correct" is useful because it can be extended to "what most people in a field believe to be correct," which can serve as a definition of knowledge and is sufficiently useful for any situation where you need a definition of knowledge.

This is a short list of a few examples of justification bases. In many frameworks, the categorization is debatable, but they end up within these three points:

• Evidence: phenomena or truth (depending on philosophical position)

• A priori justification: justified belief or truth (sometimes phenomena, depending on philosophical position)

• Innate cognitive structures: manifest only through shaping phenomena we experience, thus phenomenon-based in practice

• Prior justified beliefs: justified belief

• Coherence with belief system: justified belief

• Testimony: phenomena or other's justified belief (known through phenomena)

• Norms or virtues: justified belief or truth (depending on philosophical position)

• Mathematical or logical principles: justified belief or truth (depending on philosophical position)

• Reliable processes: phenomena or truth

The key point is that for each justification basis, we must think about how we access it, instead of what is it. Things that are not accessible cannot be used as a starting point in practical justification. For example, to access intuition, intuition needs to manifest in one of three ways.

One may question the focus on access. However, if we want to discuss something that happened in real life, we must start with what we actually have access to. Something we can not access is irrelevant to us.

If readers are confused about the usage of "phenomena," it refers to what we experience or observe.

A classical question in the definition of knowledge is scientific progress. Clearly, people seem to be looking for a "proof" that science is making progress. First, the idea that science is making progress (e.g., modern medicine is better than witchcraft) is itself a belief. In fact, any idea like "some beliefs are better than others" is a belief. Second, in a particular field, there is usually a "standard," which is essentially a set of beliefs about "which beliefs are better." In modern science, the "standard" is typically that a better belief is one that can be justified by phenomena (using a set of rules of interpretation). This "standard" naturally prioritizes beliefs that are more likely to predict phenomena (i.e., its utility). People who believe in other "standards" that prioritize phenomena in some sense are then likely to hold the belief that "science is making progress." If we wish to live a better life, it seems that we should, in practice, discuss the standards we are actually using and how we want to change them, since what we thought to be better is itself a standard.

To see the method discussed in this note in motion, let us examine how experiments in the field of high energy physics work. As we now commonly consider as knowledge, there are fundamental particles like the Higgs boson, neutrinos, etc. However, these particles are never directly observed; instead, particle interactions produce electromagnetic signals in detectors. These signals are then used through a reconstruction with different physics models, and the "best" model wins as it matches (predicts) the signal pattern. This model is known as the Standard Model, which most physicists now agree on. Readers should be able to map each element of this process to the concepts illustrated in this note.

In mathematics, mathematicians typically do not have access to math as truth directly (if any). Instead, a mathematician (or a student) proves something starting from some starting point, i.e., what is taken to be true, and then works from there by piecing them together using method that is taken to be true. A piece of proof is accepted by another mathematician if it aligns with the standards they hold as beliefs, typically including checking that the starting points, together with the methods, are believed to be acceptable and that it does not contradict a set of other theories that are considered true by this mathematician.

If some mathematicians have direct access to truth, when they use it in proofs, they must understand truth as a human does, which is then converted into beliefs. On the other hand, as long as not all mathematicians have direct access to truth, knowledge must still be something knowable by those without direct access, reverting to the earlier process unless knowledge is exclusively for those with direct access to truth.

In some rare cases, if truth is directly accessible to certain mathematicians in a way that allows it to be used in a proof, mathematicians who do not (yet) have direct access to this truth must convert it into beliefs when reading the proof, thereby reverting to the earlier process. Otherwise, if the truth in the proof does not require digestion by the reader, this proof would provide direct access to the truth, granting anyone who reads it direct access to truth. If such a proof exists, please share!

If we accept circular justification and all knowledge is justified (i.e., the other option in the main text), then all knowledge that a human knows is grounded on some circularly justified beliefs. This suggests that humans are born with some innate circular justified beliefs so that every other piece of knowledge can have a base, meaning babies have knowledge.

If babies have knowledge, then this knowledge has to be justified, as we are working with the condition that all knowledge is justified. This suggests either justification before-life or maybe some sort of instantaneous simultaneous justification at birth (since you cannot justify them sequentially), like a glitch in video games.

If we have a before-life (and it needs to be a before-life of which we have knowledge), we would still need to justify some knowledge at the birth of the before-life (or change our definition of knowledge to the one in the main text for before-life and change it back for this life), suggesting instantaneous simultaneous justification in before-life. Otherwise, we need to accept an infinite chain of before-life or a chain of circular life (and we cannot discuss how to start the circle of lives) while some knowledge can be preserved in between for both cases. This is a position that most religions or mythologies do not hold, and most concepts of the before-life in those religions typically cannot preserve knowledge.

In summary, if we accept circular justification and all knowledge is justified, then babies have knowledge. And we also need to accept one of the following: some sort of instantaneous simultaneous justification that we do not understand, an infinite chain of before-life, or a chain of circular life, while the latter two preserve knowledge.

Agrippa's Trilemma proposes a third option, known as infinite regress. For those who are confused by this, please note that infinite justification cannot occur in finite real life.