A User's Guide to Reason/Epistemology

Epistemology is the knowledge about knowledge.

This chapter is the most important in this user's guide to reason, because epistemology is the knowledge that provides the means to observe all knowledge and thus acquire it. The two preceding chapters are preliminaries.

What is knowledge?

A statement is never knowledge if it is false. Knowledge is always a true statement. But a true statement is not always knowledge. What is required for a truth to be known?

Between a statement and its negation, we don't always know which is true. A truth does not always show that it is a truth. But knowledge must always show that it is knowledge. Knowledge that is not accompanied by apparent signs that it is knowledge, that cannot be recognized as knowledge, is not truly knowledge.

A truth stated by chance is not knowledge. If we were to rely solely on chance to know the truth, we would be nothing but misguided souls; we would never truly know the truth, since even if we speak it, we cannot recognize it as truth.

For a truth to be known, it must clearly appear as truth. How can a truth demonstrate that it is truth?

The path that leads to truth must show that it is truth. The method of arriving at a true statement must bear visible marks that it is a sound way to attain truth. Sound methods, sound tools, honesty, and hard work are necessary. The scholar's motto: you will earn truth by the sweat of your brow and bring it forth through pain. Knowledge is truth that is the fruit of good work.

A statement is knowledge if and only if it is the product of a good work of research into the truth.

Even an observation must be the result of careful work to constitute knowledge, because it must be a sound observation. Was I well-positioned to observe? Did I have enough time to observe properly? Was the lighting adequate? Did I truly see what I claim to have seen? Discipline and honesty are essential to being a good observer. That is why it can be called work.

A statement is always equivalent to the observation that it is true. Therefore, a search for truth can always be considered a work of observation. A good observation is the result of good observational work. Therefore:

A statement is knowledge if and only if it is a good observation.

Good work that leads to truth must simultaneously be good proof that it is the truth, because the path leading to knowledge must demonstrate that it is the truth. The process of producing knowledge is therefore always proof that it is the truth. If a scholar has worked well in producing the truth, their work is good proof of their result. Conversely, good proof is always obtained through good work. Therefore:

A statement is knowledge if and only if it is well proven.

Intellectual virtue is the capacity to do good work in the search for truth. An act of intellectual virtue is good work in the search for truth. Therefore:

A statement is knowledge if and only if it is produced by an act of intellectual virtue.

This definition is presented by Zagzebski in Virtues of the Mind (1996).

We make observations using observational devices: our sensory organs and instruments of observation. An observational device is a truth-producing device.

A truth-producing device is the equipment of the worker who must produce the truth. Doing good work in the search for truth always involves using a good truth-producing device.

A truth-producing device can be good without being infallible. It is good if and only if it functions well most of the time, not necessarily always (Goldman 1986). Even if a good truth producer has produced a true statement, this statement is not necessarily knowledge. Due to unknown circumstances, such as a series of offsetting errors, a good truth producer can produce a true statement even if they haven't worked well. In such a case, the resulting statement is not knowledge, but merely a truth obtained by chance. For a statement to be considered knowledge, its truth must result from the error-free work of a good truth producer (Zagzebski 2017). Good work must be error-free to be truly good.

A statement is knowledge if and only if it is produced using a good truth-producing device that functioned without error in producing it.

Knowledge is not always known with certainty. An observation may be good because it is produced by a good observational device that functioned without error in producing it, but the knowledge thus produced is not known with certainty if the observational device is good but not infallible.

Is a low error rate criterion necessary for a truth producer to be considered good? Zagzebski (1996, p. 182) offers the following counterexample. A scientist is very creative and makes a significant contribution to science one time out of twenty, but she makes serious errors the rest of the time. It seems that she is a very good producer of knowledge despite her very high error rate. She may even be one of those who most advance science. But her errors must be corrected to arrive at knowledge. When we have a nineteen out of twenty chance of being wrong, we don't know. To be a good producer of truth, creativity must be accompanied by a method that reduces its error rate.

A theory is an observational device

A line of reasoning is logical if it leads from the premises to the conclusion while respecting the rules of logic. If the premises of a logical argument are true, the conclusion is also true, because the rules of logic always lead from truth to truth. A logical argument is a proof of its conclusion, conditioned by the truth of its premises. Therefore:

A statement is knowledge if it is the conclusion of a logical argument whose premises are already known.

A line of reasoning can enhance our observational abilities: we can reason about observations already made to produce new observations.

If the truth of the premises is already known, a logical argument is a proof of its conclusion, therefore an observation of the truth of its conclusion.The eyes of the soul, by which it sees and observes things, are nothing other than the proofs. (Spinoza, Ethics, Book V, Prop. 23, Scholium).

A theory is a system of principles. A principle is an axiom or a definition. The theorems of the theory are the logical consequences of the axioms and definitions.

The conclusion of a line of reasoning that respects the rules of logic is always a logical consequence of the premises. Conversely, a logical consequence of premises is always the conclusion of a logical line of reasoning based on those premises, because the rules of logic are sufficient to find all logical consequences. Therefore, a theorem is always the conclusion of a logical line of reasoning based on the axioms and definitions of the theory.

The logical consequences of true statements are always true. Definitions are always true by definition. Theorems are therefore always true if the axioms are true.

A theory can be considered as a device for observing truth. We observe that statements are true by observing that they are theorems, that they are logically proven from axioms and definitions.

A theory is not necessarily a good observational tool because its axioms may be false, or because their truth is unknown. For a theory to be a tool for producing knowledge, it must be founded on good principles whose truth is already known.

Without principles, our natural means of observation would be the only sources of knowledge. Good principles enable us to go much further. Theories enable us to know all possible worlds and the actual world even before it is currently observed; they increase our capacity to observe the actual world; they teach us the ends that are truly worth pursuing and how to acquire knowledge and make good theories.

Good principles are inexhaustible sources of knowledge. They are like engines or rockets, because they give us power and transport us to the highest peaks of knowledge.

Observing knowledge

We acquire knowledge by observing that it is knowledge

If we have a good truth-producing device, if we believe in the truths it produces, and if we don't know that it's a good truth-producing device, do we know or do we not know?

If we believe that well-produced truths are truths without knowing that they were well-produced, we are no different from a credulous person who believes any nonsense spouted by a liar, a swindler, or a charlatan; therefore, we do not know.

When we are given knowledge, we must recognize that it is knowledge in order to appropriate it. If we fail to recognize that what we are given is truly knowledge, then we don't know it is knowledge, and we simply don't know:

To know, one must know that one knows.

This principle excludes unreflective forms of knowledge, when we acquire truths without knowing they are knowledge. But unreflective knowledge is not rational. Reason dictates recognizing knowledge, not receiving it without reflection. In this chapter devoted to reason, knowledge always means rational knowledge.

When we are given knowledge, we must examine the proof of its truth. The work of examining a proof is a search for truth. If it leads to observing that the examined proof is good, then it also leads to the observation that what is thus proven is knowledge. We observe that a statement is knowledge by observing that it is well proven, and this is how we appropriate knowledge. Knowledge is known if and only if it has been properly observed that it is well proven.

When acquiring knowledge independently, one must examine the evidence one provides for oneself. This examination is no different from examining evidence provided by others. Acquiring knowledge always requires observing evidence, both that which is given to us and that which we discover ourselves.

Even when acquiring knowledge taught by others, one acquires it independently, because one must rely on one's own resources to recognize that what is being taught is indeed knowledge.

In mathematics, one can always recognize whether reasoning constitutes good proof because it suffices to verify that the premises are axioms or definitions and that the logical rules have been respected. More generally, a proof that does not clearly demonstrate that it is a proof cannot be a good proof. A theorem does not bear visible marks that it is a theorem, because reading it is not enough to know whether or not it is a consequence of the axioms and definitions. On the other hand, a proof always bears visible marks that it is a proof; it must be recognizable as such.

Good work in producing truth must always bear apparent marks that it is good work. If it cannot be recognized as good work, then it is not good work. Demonstrating that it is good work is part of the work itself. Such work cannot be good without demonstrating it.

Virtue is generally not expected to be conspicuous. Discretion and restraint are generally recommended for those who wish to be virtuous. However, the virtue of producing knowledge is not bound by such an obligation of discretion. On the contrary, it must demonstrate its virtue in order to be a virtue.

To be good proof, proof must be blatant. Reasoning that doesn't demonstrate its soundness is not good reasoning. An observation device cannot be good without demonstrating its soundness. If it cannot be observed that an observation device is sound, then it is not good. Proof that is not recognized as good proof is not good proof.

A statement is known if and only if it is well proven. But a good proof must always demonstrate that it is a good proof. It can always be given and recognized as a good proof. If we don't know how to give good proofs, then we don't know, because we need good proofs to know, and because a good proof can always be given.

To know, we must know how to give good proofs. Now, we teach truth to all minds by giving them good proofs. To know, therefore, we must know how to teach. If we don't know how to teach, we simply don't know.

Giving proofs is always inviting a mind to become aware that it is capable of knowing by itself. Proof, if it is truly good, is a universal path, a path that shows all minds how their own resources enable them to reach the truth. Giving proofs is a form of respect for all minds; it is a way of honoring their capacity to know the truth.

Reflective knowledge and self-awareness

Rational knowledge always adheres to the following principle:

A statement is knowledge if and only if the statement that it is knowledge is also knowledge.

Several equivalent formulations of this principle can be given: if we don't know that we know, then we don't know. To know, we must know that we know. A statement is knowledge if and only if it is recognized as knowledge. A statement is knowledge if and only if the observation that it is knowledge is itself knowledge. Proof is good if and only if it has been clearly proved to be good proof.

This principle leads to an infinite regress: to know, one must know that one knows, therefore one must know that one knows that one knows, and so on ad infinitum. It is often believed that this infinite chain of knowledge is a regress that prevents us from always knowing that we know, because it is believed that an infinite number of statements cannot all be known simultaneously by a finite mind. But this is a misunderstanding of the power of a finite mind.

- How do you know that?

- I saw it clearly.

- How do you know that you know because you saw it clearly?

- This is true by definition of a good observation: for any X, if X is a good observation, then X.

- How do you know you saw correctly?

- I am aware that I saw correctly. I observed that I saw correctly.

- Did you observe that you observed correctly that you saw correctly?

- Yes, because self-awareness means that a good observation is simultaneously a good observation that it is a good observation.

Consciousness is always, by its very nature, self-consciousness. If one is conscious, one is conscious of being conscious. The consciousness of being conscious is not a new consciousness added to the first. It is the same consciousness. The consciousness of being conscious is simultaneously the consciousness of which one is conscious. To be conscious of being conscious is nothing more than being conscious; it is simply being conscious. When one is conscious, one is conscious of being conscious and conscious of being conscious of being conscious, because being conscious of being conscious is, in essence, being conscious. Self-consciousness leads to an infinite number of truths: I am conscious, I am conscious of being conscious, I am conscious of being conscious of being conscious, and so on ad infinitum. But all these truths essentially say the same thing, because being conscious of being conscious is nothing more than being conscious.

We can use the following definitions: 'being conscious to the zeroth order' is 'being conscious'. 'Being conscious to order n+1' is 'being conscious of being conscious to order n'. For any natural number n, if I am conscious to order n, then I am conscious to order n+1, because being conscious of being conscious is nothing more than being conscious. Now, I know that I am conscious to order 0. I can therefore prove, with the principle of mathematical induction, that for any natural number n, I am conscious to order n.

An infinite number of statements can all be known simultaneously by a finite mind. A general law is equivalent to an infinite number of statements. Knowing an infinite number of statements is not beyond our reach; it is what we do every day as soon as we state a generality. For example, 'for any natural number n, I am conscious to order n' is a generality, equivalent to an infinite number of statements.

The awareness that one is doing good work in producing truth is part of good work. When good work leads to a truth A, it simultaneously leads to the truth that A was obtained through good work. A good proof of A is simultaneously a good proof that A was well proven. When one acquires knowledge, one also acquires the knowledge that one has acquired knowledge, because one is aware of having worked well.

'A is known to order 0' is by definition equal to 'A is known'. 'A is known to order n+1' is by definition equal to 'that A is known to order n is known'. If A is known to order n, then A is known to order n+1, for any natural number n, because one acquires the knowledge that one has acquired knowledge at the same time as one acquires knowledge. We can therefore prove by induction that if A is known to order 0, then for all natural numbers n, A is known to order n.

When we know that we know A, we know no more than we know when we know that A. Knowing that A and knowing that we know A are essentially the same knowledge. A statement is knowledge if and only if the statement that it is knowledge is also knowledge, because the statement that it is knowledge is not new knowledge but simply the same knowledge.

When we acquire knowledge taught by others, the knowledge is known by others before we acquire it. But if we acquire knowledge on our own, the statement we want to know is not known before we know it and is therefore not knowledge. However, to acquire knowledge, we must observe that it is knowledge. But how can we observe that a statement is knowledge when it is not knowledge before being observed?

Observing knowledge is like magic. We make the observed property appear at the very moment we observe it. Orpheus made Eurydice disappear by observing her. When we acquire knowledge on our own, we do the opposite of Orpheus; we make knowledge appear by observing it. Observing that a statement is knowledge makes the observed property appear because we acquire the knowledge at the same time as we become aware that we have acquired it.

Observing the consistency of observations

An observational device must demonstrate that it is good to be considered a good observation device. It must be clearly observable that it is good.

To clearly observe that an observational device is good, a second observational device is needed. This second observational device must also be good. Therefore, a third observational device is required, capable of observing that the second device is good, and so on ad infinitum. To observe the quality of our observations, we need high-quality observations. However, it then seems that the process of observing good observations cannot even begin.

The same observation can be obtained by numerous observational devices. If we have observed that many independent observational devices mostly yield the same result, there is a very small chance that this consistency results from the operation of faulty devices; therefore, we can conclude that all devices are good. This leads to a criterion for observing good observational devices:

An observational device is good if it is part of a set of independent devices that always or most of the time produce the same result.

Independent observational devices can observe the consistency of the results obtained by other independent observational devices. The consistency of observations of the consistency of observations can therefore be observed. If the observations of the consistency of observations are not consistent, then the observations whose consistency is observed are also not consistent. Therefore, if some observations are consistent, then the observations of their consistency are also consistent. The criterion of the consistency of independent observations is a criterion for observing good observations. It is self-justifying because it shows that it leads to good observations of good observations.

Theories are observational devices, but the criterion of the consistency of independent observations cannot be used to identify good theories because they are not independent devices. When two theories lead to the same theorems, they are not independent theories, but rather different formulations of the same theory. To recognize good theories, another criterion is used: they must be based on good principles.

We recognize good principles by their fruits

« You will recognize them by their fruits. » (Matthew, 7:20)

« We shall see such demonstrations, which do not produce as great a certainty as those of geometry, and which even differ greatly from it, since instead the geometers prove their propositions by certain and incontestable principles, here the principles are verified by the conclusions drawn from them; the nature of these things not suffering that it be done otherwise. It is possible, however, to arrive at a degree of verisimilitude, which is often not much less than complete evidence, when things, which have been proved by these supposed principles, are perfectly connected with the phenomena which experience has pointed out, especially when there are many, and even more so when we form and anticipate new phenomena, which must follow from the hypotheses which are employed, and which we find that in this the effect corresponds to our expectation. If all these proofs of plausibility are found in what I have proposed to treat, as they seem to me to be, it must be a great confirmation of the success of my research, and it is hardly possible that things are not nearly as I represent them. » (Christian Huyghens, Treatise on light, p.2)

For a theory to be a good truth-producing device, it must be founded on good principles whose truth is already known. A good truth-producing device must demonstrate its own goodness. Therefore, we must recognize good principles and their truth. How do we observe that a principle is true and good?

Principles are starting points for reasoning. They are like teachers who teach us their logical consequences, because we can learn them through reasoning. We recognize good teachers by the quality of their teaching. We expect principles to impart good knowledge that helps us adapt to reality, think well, and live well.

Good principles are recognized by their fruits.

In the natural sciences, theories bear fruit when they prove and explain observations of natural phenomena. We must prove that past observations were expected to produce the observed results and that future observations will produce the observed results, thus predicting the outcomes of our observations. These proofs are simultaneously explanations of the observed phenomena because they provide the conditions that explain their existence.

The truth of the consequences of a principle or a system of principles does not prove the truth of the principles themselves. From B and If A then B', one cannot deduce A. But if the principles regularly lead to good observations, there is little chance that all these truths were obtained by chance, and it is reasonable to admit that the principles are also true.

A mathematical theory is similar to the theory of a game. The rules of a game are true by definition of the game. They are axioms of the game theory. Experience with the game confirms the theory but cannot refute it. If, while playing a game, we make observations that contradict the theory, it necessarily means that the rules of the game have not been followed, because the theory is true by definition of the game. When there is a contradiction between theory and experience, it is the experience that is refuted by the theory, and not the other way around. The same applies to logical and mathematical truths. If the experience of calculation or reasoning contradicts the theoretical truth, it means that a calculation error or a reasoning error has occurred. Logical and mathematical principles are confirmed by the experiences of calculation and reasoning, but they cannot be refuted by them. The experience of calculation can be refuted by the theory if a calculation error has occurred, but the theory of calculation cannot be refuted by experience.

Logic is the theory of the relation of logical consequence. It is like a device for observing all logical consequences. The logical rules that determine fundamental logical consequences are axioms of logic. As the theory of logical consequences, logic is simultaneously the theory of all theories, because the theorems of a theory are always the logical consequences of its axioms and definitions. Logical principles bear fruit whenever they help us reason well and find the theorems of good theories.

Mathematics is the science of everything that is logically possible. A mathematical theory is a device for observing logically possible worlds. Mathematics is like a polycosmoscope, an instrument for observing all logically possible universes. Mathematical principles bear fruit whenever they give us sound knowledge of what is logically possible, including the actual world, because what is actual is possible.

We observe the truth of logical and mathematical principles by observing that they are true by definition. From a purely theoretical, logical, or mathematical standpoint, everything is true by definition. Definitions are true by definition of the concepts they define. Axioms are true by definition of fundamental concepts because they are the fundamental laws that determine the proper use of those concepts. Truths about logically possible worlds are true by definition of those worlds because they are logical consequences of those definitions.

Ethics is knowledge about good and evil. Ethical principles bear fruit when they show us how to think well, act well, and live well. They define ideals. They are true by definition of an ideal because they are part of the definition of that ideal. But ethics is not a purely theoretical knowledge, because we learn through experience whether an ideal is good or not.

Epistemology is knowledge about knowledge. It is fundamentally ethical knowledge, because its principles define an ideal of rational knowledge. Epistemological principles bear fruit whenever they show us how to observe good knowledge and thus acquire it. They are true by definition of the ideal of knowledge. But we learn through experience that this ideal makes us capable of acquiring all knowledge.

The principle that good principles are recognized by their fruits is a criterion for observing good principles. It bears fruit whenever it helps us recognize good principles. When applied to itself, it therefore leads to the observation that it is itself a good principle.

We recognize knowledge based on the good principles with which it is produced. We recognize good principles based on the knowledge that can be produced with them. This approach is circular. To recognize good principles, one must recognize knowledge, and to recognize knowledge, one must recognize good principles. But good principles are not the only source of knowledge. A theory is not only justified by the principles on which it is based, it is also justified by the observations of all the phenomena it explains.

The best way to think is to place one truth before another and start again. This is the Cartesian ideal of knowledge. We must begin with already known truths and move from truth to truth while respecting the rules of logical reasoning. Logical rules guarantee that we always move from one truth to another. But to proceed in this way, we must know that our premises, the observations and principles we place at the beginning of our reasoning, are true. However, we do not always know from the outset whether our principles are good. Since good principles are recognized by their fruits, we must wait until the work is finished to recognize that they are truly good. At the beginning, they are only hypothetical. The recognition of good principles is not instantaneous; it results from a long process, because we must allow time for principles to reveal their truth to us.

The theory of all knowledge

Epistemology is knowledge about knowledge. It is a theory of all knowledge.

A theory of knowledge must be a device for observing knowledge. Now, knowledge is always obtained with a good observational device. Epistemology must therefore be a good device for observing all good observational devices.

The principle of observing good principles is that we recognize them by their fruits. The principle of observing good observations of phenomena is that the coherence of independent observations demonstrates that they are good observations. These two principles provide the means to properly observe all good observational devices. They thus make epistemology what it should be: a good device for observing all good observational devices.

Knowledge about knowledge is a necessary condition for knowledge, because we acquire knowledge by observing that it is knowledge.

Epistemology provides everyone with the means to properly observe and acquire all knowledge. It is like a sun for all minds. It enlightens all the truths accessible to us. It reveals all knowledge. It shows in full light all that can be known.

"How can an activity for which we cannot give a reason be considered reliable knowledge?" (Plato, The Symposium, 202a)

Knowledge about knowledge provides the means to reason about all proofs. This is why a good proof, even if it is not a reasoning, can always be presented in the form of a good reasoning. If it is truly a good proof, there must be a good reasoning that proves it is a good proof. We can then complete it to make it a reasoning that proves the same conclusion: let P be a good proof of A without being a reasoning. For any X and any Y, if X is a good proof of Y, then Y. Therefore, if P is a good proof of A, then A. But P is a good proof of A. Therefore A.

Knowledge about all knowledge resembles self-consciousness because it is knowledge of itself. One cannot be conscious without being self-conscious. Similarly, knowledge about all knowledge cannot exist without being knowledge of itself, because it must be knowledge. Epistemology recognizes itself. It provides the means to observe that it is knowledge at the same time as it provides the means to observe all knowledge. Good principles for observing knowledge provide the means to observe all knowledge, including itself.

The existence of good knowledge about knowledge, capable of recognizing itself, explains why one can acquire knowledge at the same time as observing that it is knowledge. Let T be a good observational device for knowledge, capable of observing that it is itself a good observational device. We acquire knowledge K by observing K with T. Now, T is capable of recognizing itself. Therefore, K is observed with T if and only if that K is observed with T is observed with T. When we observe K with T, we simultaneously know that 'K is observed with T' is observed with T. So, when we know K, we simultaneously know that we know K.

That principles justify themselves is not sufficient to prove that they are good, because bad principles can lead to the bad observation that they are themselves good principles. But the principles of knowledge observation are not their ultimate justification. They are justified by all the knowledge they provide the means to acquire.

Good principles define an ideal of knowledge. They are true of this ideal by definition of the ideal. But this truth by definition does not prove that the ideal is good. We prove that an ideal is good by realizing it. The experience of acquiring knowledge is the realization of the ideal of knowledge and the ultimate proof that it is a good ideal defined by sound principles.

Knowledge is always justified by other knowledge. The ultimate justification of knowledge is always its integration into the domain of all knowledge.

The coherence between observations, between principles, and between principles and observations is the ultimate justification of knowledge. The unity of all knowledge reveals that it is knowledge. The coherence of all truths reveals that they are all truths.

Knowledge is a good for other knowledge when it helps it to be known. If they are knowledge, the premises of sound reasoning are goods for the conclusion. A good principle is a good for all its consequences. These, in turn, are goods for the good principle because they help to observe that it is a good principle. All knowledge is united by common principles, which are goods for all knowledge and for which all knowledge is a good. Therefore, all knowledge is a good for one another. There is a universal unity of all knowledge.

That the coherence of all knowledge is its ultimate justification is not a reason to deny the existence of fundamental principles. Concepts are always determined by the laws of their attribution. These laws of the proper use of concepts are fundamental principles. They are true by definition of the concepts they determine, but they are not the ultimate justifications of knowledge, because it is necessary to show that these truths by definition lead to the acquisition of good knowledge.

The universality of good principles

“Only that which is finally perfectly determined is at once exoteric, conceivable, capable of being learned, and possessable by all. The intelligible form of science is the path to it that is open and offered to all and made the same for all, and arriving through the understanding at reasonable knowledge is the just requirement of the consciousness who comes to join science." (Hegel, Phenomenology of Spirit, Preface, p. XV)

As soon as good principles are recognized, they are adopted by all those who understand that they make them more competent, stronger, and more lucid. If they are truly good, truly useful, they naturally impose themselves on all those whom they serve. By inventing or developing good theories with good principles, one can make oneself useful to all minds. The fruits of reason are universal. Good observations, good principles, and good reasoning are always beneficial to all minds. If one mind can reap the fruits of good principles, then all minds can reap the same fruits. When we seek good principles, we seek a good for all minds; we put into practice the great principle of ethics: that the good of one mind is to live for the good of all minds. Reason is a good for all minds. If we defend, teach, or exemplify reason, we do good for all minds.

The great principles reveal to us the power of reason. They give all minds the means to acquire all knowledge, to understand all minds, and to reveal all the benefits of reason. By learning what the great principles teach us, we learn at the same time that we can think for the good of all minds. Being good to all minds is not an unattainable ideal. It is the reality of rational thought.

That the good of a mind lies in living for the good of all minds leads to a criterion for recognizing all forms of knowledge, because a science cannot be a science without being a good for all minds. Knowing that rational knowledge must be a good for all minds, we possess the fundamental knowledge that provides the means to recognize all forms of knowledge.

That reason is a good for all minds has as its consequence the universality of criticism. When one claims to offer knowledge, all objections must be welcomed. A mind is always entitled to share its dissatisfaction, because everyone is a criterion for recognizing good knowledge, because good knowledge must help everyone to think well and to live well in order to be truly good. A claim to science that does not offer its hospitality to all criticism denies science and reason. No science without the freedom to criticize. This is one of the most fundamental rules of the development of science.

For knowledge to be shared, it must draw solely from common resources, accessible to all. One might think this is a very restrictive limit, that by depriving ourselves of private resources, we simultaneously deprive ourselves of the best knowledge, but the exact opposite is true. Our intelligence is most powerful precisely when it is limited to common resources. It is by helping one another that we best discover the power of our intelligence, that we develop the best knowledge, and that we keep reason alive.

What is an explanation?

Causes and laws

When we know something is, we don't just want to know that it is; we also want to know why it is. But is there a why? Why would there be a why? And why would we want to know it?

A set of atomic truths completely determines a universe, a world, a totality, but it doesn't tell the whole truth about that world. Even if we knew all the atomic truths of the Universe, we wouldn't know it very well, because a set of atomic truths is like disintegrated knowledge, reduced to its simplest elements. We want more and better than this fragmented knowledge, devoid of rhyme or reason.

To say why is to say the causes.

"Knowledge of the why, that is, of the cause" (Aristotle, Metaphysics A, 981a 30)

"Those who teach are those who, on each subject, state the causes." (ibid., 982a 30)

How do we know the causes? Are there truly causes to be known?

If X is a cause of Y, the statement that X is always a cause of Y is always a law. To know the causes, one must know the laws. An explanation is always reasoning based on laws. Therefore, we need to know the laws to provide the explanations that constitute good knowledge.

Causes have causes. Should we fear an infinite regress when we seek causes?

Explaining necessity or possibility does not lead to an infinite regress, because we stop at fundamental laws, from which we explain all others. With fundamental laws, we can explain all possibilities and all necessities, because they determine everything that is possible and everything that is necessary.

Fundamental laws are the reasons for the existence of everything that exists, even fundamental laws themselves. We explain fundamental laws based on other fundamental laws, and based on themselves.

To explain the current world, we must first explain why it is possible, by showing that it is permitted by the laws of Nature. But this is not sufficient, because the current world is contingent. The laws of Nature are not enough to determine it. They do not preclude it from being other than what it is.

We explain a contingency in the same way we explain a necessity, by seeking conditions of which it is a necessary consequence. However, not all conditions can be necessary, because a necessary consequence of necessary conditions is itself necessary. At least one of the conditions must be contingent. We always explain contingencies in terms of other contingencies. When we explain contingencies, there is therefore necessarily an infinite regress in the search for causes. Laws explain fate, the necessary chain of contingencies, from the night to the end of time.

Reason: proof or explanation?

"He said that true opinion accompanied by reason (logos) is knowledge, while that which is devoid of reason is outside of knowledge; and that of which there is no reason is unknowable—this is the word he coined—while that which has reason is knowable." (Plato, Theaetetus 201d)

In Plato's definition of knowledge logos can be translated as reason, explanation, justification, or proof.

A good proof can also be a good explanation, because it provides reasons for what is. We understand a theorem when we know its proof. The proof is also an explanation because it provides the conditions that explain the truth of the theorem.

A good explanation can also be a good proof if it provides sufficient conditions to prove what it explains. But proof and explanation are oriented differently. Proof seeks certainty, as far as possible, while an explanation seeks clarity by giving us the reasons for what is. A good explanation should enlighten us, and sometimes it illuminates us.

Good proof may not be a good explanation if it proves the truth of what is without giving the fundamental reasons why it is what it is. A good explanation may not be good proof if it gives the main reasons for what is, without giving sufficient reasons to prove that it is.

The explanation of all explanations

“The eternal mystery of the world is its comprehensibility.” (Albert Einstein, Physics and Reality, 1936)

Understanding is always understanding explanations. Conversely, an explanation must enlighten us, therefore help us to understand.

If there were no laws, there would be no truth to attributions, and therefore no concepts. If there were no concepts, there would be no being, because to exist, one must have properties and relations. Therefore, if there were no laws, there would be no being.

There are always explanations for everything, because there is no being without laws. The fact that there is no being without law is a law that explains the existence of all explanations for all beings. Therefore, we can explain and understand why being can always be explained and understood.

Illumination through imagination

"I understand a being if I know how to create it" (Fred Dretske, lecture at the Lyon library)

The author of a work of fiction is like a demiurge, a creator of worlds. They give being through words. They give life to their characters by saying that they exist and what they are.

To understand a material being, one must know what it is made of. One can create it in the imagination if one knows the nature of its constituent parts and their relative positions, like an engineer or an architect drawing up the plans for a building. One can deduce the laws of motion of the system from the laws of motion of its constituent parts. If one knows the laws of motion of a being, one can imagine all its possible movements, as if one were a creator of all the possible worlds in which it can exist.

We can explain all the beings in the Universe and the Universe itself if we are capable of creating them in our imagination, that is, of making models.

We understand a concept when we know how to apply it to all possible beings for whom it is true. Knowledge of laws provides the means to observe the presence of the concept in the current world and in all possible worlds. It's like having created, in our imagination, a detector of the concept.

Knowledge of laws empowers the imagination. When we know the laws, we can imagine all possible worlds as if we were their creator.

We explain a law by showing that it is a consequence of more fundamental laws. It's like imagining ourselves as a legislator who justifies all laws based on the most fundamental ones. To imagine ourselves as legislators, we must know the laws of legislation, the laws of laws. When we know the laws of laws, we are like a legislator and a creator of all possible worlds.

Knowledge can be more or less well known

Several reasons contribute to the degree to which knowledge is known:

• A truth-producing device can be more or less good.
• We can be know more or less well that a truth-producing device is good.
• We sometimes need the testimony of others to know something.
• Knowledge can be more or less well explained.
• The production of knowledge can be more or less well explained.
• We can know more or less well what knowledge is.

The error rate of a truth-producing device can be more or less small. The smaller it is, the better the device and the better the truths it produces are known.

The smallness of the error rate of a truth-producing device can be more or less well known. The better we know that the error rate is small, the better the knowledge is known.

We can acquire knowledge through testimony if we know the witness is reliable. A witness can be more or less reliable. We can be more or less certain that they are reliable. Knowledge is best understood when acquired independently, without relying on the testimony of others.

A low error rate is necessary for a truth producer to be considered good. Is it sufficient?

Imagine an oracle that always tells the truth. It answers yes-or-no questions and is never wrong within its area of ​​expertise, but it never proves or explains anything. We know from experience that it is never wrong, but we don't know why. It seems like a miracle. Is it enough to consult such an oracle to know?

If we have verified that the oracle is almost never wrong, then it is a reliable witness, and the answers it provides can be considered knowledge. But this knowledge is not well known because it is not explained, and because the production of knowledge is also not explained.

Knowledge is better known the better it is explained, and the better the production of knowledge is explained.

We have sensory organs and a brain with which we make true observations. But one must be knowledgeable to know that sensory perception produces truth. If we believe that our perceptions produce truth without knowing it, do we possess knowledge?

To know, one must know that one knows. Without knowledge about knowledge, one cannot know that one knows, and therefore one cannot know. But a little knowledge about knowledge can suffice for knowing: if I believe I know because I saw clearly, then I know, and I know that I know, because my ability to recognize that I saw clearly, that good conditions for observation were met, is a good device for observing knowledge, even if it is not infallible.

The better we know what knowledge is, the better we know what we know.

Knowing without being certain that we know

We can know without being certain of what we know, because our methods of acquiring knowledge are not always infallible, even if they are good methods. A truth-producing device can be good without being infallible.

If we are not certain of what we know, we are also not certain that we know it. Therefore, we can know without being certain that we know. We can know without being certain that we know what we know without being certain of it.

One cannot know without knowing that one knows, but one can know without being certain that one knows.

Certainty gives a feeling of power, as if we needed no one but ourselves to know, as if we needed no God to be powerful.

Certainty leads to intolerance. If I had a good, universal device for observing knowledge with a guarantee of certainty, then I could exclude anything that doesn't pass my knowledge observation test. Any candidate for knowledge that I don't recognize would be automatically excluded.

A community of independent truth producers, equipped to recognize good principles and methods of observation, constitutes a universal device for observing knowledge, but it does not lead to certainty and intolerance. On the contrary, it imposes the law of hospitality: we do not know in advance all the good principles and methods of observation, nor can we know them. Science is necessarily unpredictable. We cannot know in advance what it will become or how we will recognize it. Our principles for observing knowledge are universal, but generally, they do not provide quick and certain answers. Principles, hypotheses, theories, and even methods of observation must be given time to bear their potential fruit. Faced with a new hypothesis, we have a duty to welcome it. A candidate for knowledge is not excluded; they are invited to present their evidence. Certainty and intolerance lead to ignorance because they prevent us from properly observing knowledge. Without a spirit of hospitality, willing to let all forms of truth come to us, and to give them the means to reveal all they can, we are incapable of recognizing knowledge, and therefore incapable of knowing.

Internalism and externalism

Knowledge is internalist if and only if we are aware of all the conditions that make it knowledge.

Knowledge is externalist if and only if it is not internalist.

Internalist knowledge is always certain and reflective, because all the conditions that make it knowledge are known with certainty.

Reflective knowledge is not always internalist. If it is uncertain, the absence of error during its acquisition is a condition that makes it knowledge of which we are not conscious. Reflective knowledge is externalist when we know that we know without being certain that we know.

Purely theoretical, logical, or mathematical knowledge is internalist because its truth does not depend on external conditions but only on conditions that we give to ourselves.

Empirical knowledge is externalist because its truth depends on external conditions of which we are not always conscious.

References

Goldman, Alvin, Epistemology and Cognition (1986), Knowledge in a social world (1999)

Plantinga, Alvin, Warrant and proper function (1993)

Zagzebski, Linda, Virtues of the mind, an inquiry into the nature of virtue and the ethical foundations of knowledge (1996), The lesson of Gettier (in Borges, Rodrigo, de Almeida, Claudio and Klein, Peter D., Explaining knowledge: new essays on the Gettier problem (2017)