Handbook of epistemology/What is reason?

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Science of the individual or science of the general?[edit]

Is science more about knowing individuals or concepts?

Science must be the knowledge of the truth about reality. But only individuals are truly real. Concepts are only representations. Science must be the science of individuals to really be science.

Science must be universal knowledge, the same for everyone. Concrete individuals have an ephemeral existence. They come from the dust and become dust again. How could the knowledge of an individual deserve the name of science? How could it be a knowledge that deserves to be shared by all?

A law is always about a domain of ​​individuals. It may not mention any particular individual. Its truth is then general and depends only on the concepts it mentions. It is therefore a knowledge of the universal. It seems that to deserve to be shared by all, science must be the knowledge of the laws, so be a knowledge of the universal. Science is sometimes defined in this way: the universal knowledge of the universal (Aristotle, Posterior Analytics).

Is it necessary to conclude that science knows only concepts and that it ignores individuals?

Knowledge of concepts is not separate from that of individuals since by attributing concepts to individuals, individuals and concepts are known at the same time. An individual is known from the concepts that are attributed to it. But we can also say that a concept is known from the individuals to whom it is attributed.

To know an individual well it is not enough to perceive it, or to know what others have perceived of it, it is also necessary to know how to reason about it, because one can thus deduce what has not yet been perceived. And to reason, one must know laws. Even if one is interested above all in concrete individuals, and not in concepts, one needs concepts and laws, hence the science of the general, to make the science of individuals.

An individual is always known with a constellation of concepts: all the concepts we assign to it. Such a conjunction is generally sufficient to identify it among the other individuals, because it is sufficient to distinguish it from the others, but it does not completely determine its individuality, because it could be equally true of another individual, a kind of twin. An individual is therefore never really known in its individuality, but only as an example of a conceptual possibility.

Some concepts are used to be true of only one individual. They can be named with proper names and are determined by detection systems that identify individuals. But as an individual can always have a twin, these detection systems can not be perfect.

Permanence is the only real criterion for identifying an individual. If we follow the trajectory of a mobile, and if it has not evaporated along the way, we can be pretty sure that the individual at the end is the same as at the beginning. This is how we recognize ourselves as individuals. I know that I am myself and that I will never be another because I am a permanent witness of myself.

Similarity and generality[edit]

Why are there some general truths? Events and individuals are always very different. Why should the same affirmation be true of numerous individual cases? Beings are all different, but they are sometimes very similar. Generalities state what they have in common.

Similarities and concepts[edit]

Two beings are similar when a part of what is true of one is also true of the other. Two beings are different when a part of what is true of one is false of the other.

Assigning a concept to an individual is a way of knowing its similarities and differences. As soon as the same concept is true of several beings they are all alike, and all different from all beings for which the concept is not true.

As we always know by concepts, knowing is always knowing similarities and differences.

When a law is true of many individuals, they are all alike, because they obey the same law, and all different from those who do not obey it. To know the laws, one must know the ways in which beings can be alike. The principles of science always state fundamental similarities between individuals and between systems.

Similarity and typology[edit]

A reasoning by similarity is to say that since a and b are similar, what was said to be true of a must be equally true of b. Used without restriction a reasoning by similarity is usually wrong, because two similar beings are also different, there are true statements about one that are not true about the other. A reasoning by similarity is not logically correct.

To justify a reasoning by similarity, we can use typology. a and b are not only said to be similar, they are said to belong to the same type, and that what has been said about a is true of all instances of this type. Thus we state a general law. Then we can conclude logically that what has been said about a is also true of b.

A common property is shared by all individuals of the same type. If p is a common property of the type t, then the general law 'for all x of type t, x is p' is true.

The use of typologies is fundamental to all sciences. One can think of mathematical structures (as types of mathematical objects), species of elementary particles, atoms and molecules, living species...

Similarity between systems and analogy[edit]

In this section a system is defined by a set of individuals (components, constituents or elements of the system) qualities attributed to these individuals and relations between them.

When we speak of similarity between two individuals, it is meant that part of the qualities which are attributed to one can be attributed to the other. When speaking of similarity between two systems, the statement 'what is true of one is true of the other' can receive a more subtle meaning. It is meant that there is a projection f that replaces individuals x of the first system by individuals f(x) of the second system, so that true statements about the first system are replaced by true ones about the second system. Such a projection is called in mathematics a morphism, or, if it is bijective, an isomorphism, to say that both systems have the same shape or the same structure.

Similarity between two systems can be defined in a way a little more subtle. It allows the projection f to replace not only individuals but also qualities and relations, still so that true statements are replaced by true statements. When similarity is defined in this way, it is commonly said that similar systems are analogous and that the projection f is an analogy.

Symmetries[edit]

For a system to be symmetrical, it must have similar parts. More precisely, a system is symmetrical when there are automorphisms (internal isomorphisms). An automorphism f is a (bijective) function that replaces individuals x of the system by individuals f(x) of the same system, so that true statements are replaced by true statements. When f is an automorphism, x and f(x) are always similar. The automorphisms of a system form a group (in the algebraic sense) called the symmetry group of the system.

The knowledge about an individual of a type can be used to know all individuals of the same type. The knowledge about a system can be used to know all isomorphic or analogous systems. When a system is symmetrical, the knowledge of one of its parts is enough to know all the others. Similarities, types with their common properties, morphisms, analogies and symmetries enable us to generalize our knowledge, thus to know by reasoning more than what we perceive directly.

The principle of equivalence of all observers and the generosity of truth[edit]

« It is not possible that the divinity be envious. »
(Aristotle, Metaphysics, Book A, 983a)

To develop empirical science, we must assume that all experimenters are equivalent in the sense that any observation made by one can be made again by another. Experiments must be reproducible. If an experiment is not so, then it is not well controlled. For experiments to be reproducible, it is necessary in particular that their results do not depend on the place or time. Experimental conditions can be reproduced always and everywhere, and have to lead always to the same result. By postulating the principle of equivalence of observers, we thus assume at the same time that the laws of physics are true always and everywhere. This leads to define the symmetry group of space-time. All points of space-time are necessarily similar. When we know one, we know them all. It is the same for all directions in space and more generally for all frames of reference. There is no center of space-time, no preferred direction in space (isotropy, no up and down) and no absolute state of rest (Galileo-Einstein relativity principle). Like the Knights of the Round Table, but in a much larger space, space-time observers never have a privileged position. The group of symmetries of space-time (Poincaré's group) is a mathematical translation of the principle of equivalence of all observers, just as the group of symmetries of a round table is a mathematical translation of the principle of equivalence of all knights.

The principle of equivalence of all observers is not only a foundation of theoretical physics, of its truth and beauty, it is also fundamental to all sciences, empirical, ethical and abstract, because reason requires that all that is known by one can be known by all others.

When we understand that we are all equally capable of knowing, we understand at the same time the great principles on which we can base all rational knowledge. Everything happens just like if the truth was a generous divinity, which gives wisdom to those who really want to know it. The first truth about truth is precisely that it is generous. It is not jealous, it does not deprive us of the best. It would not be the best if it deprived any of us of the best. Knowing that knowledge can be shared by all, we have the fundamental knowledge which enables us to understand all rational knowledge.

Does Nature really obey laws?[edit]

We believe in the conclusions of our reasonings because we believe in the truth of the laws with which we reason. We believe that we are capable of developing science because we believe in the principle of equivalence of all observers.

It is in the nature of the mind to reason and therefore to postulate laws with which to reason. A mind can not develop its mind without thinking of laws. It seems, then, that the existence of laws results from the nature of the mind. But, in general, matter seems naturally without spirit, why should it obey laws?

To justify our knowledge and the principle of equivalence of all observers, we need to postulate that Nature obeys laws, but is it really a justified belief? Is not it rather taking one's desire for a reality? It may be that all the laws of Nature to which we now believe are all refuted by future observations. And could not Nature be without law?

Matter would not be matter if it did not obey laws. Matter is necessarily detectable, so it must obey laws of detection, which result from fundamental laws of interaction. A matter which obeys no law would not be detectable, and there would be no reason to call it matter. We do not know what it might be, it seems inconceivable.

It is as if matter and spirit had been made for each other, because the nature of matter is to obey laws, and the nature of mind is to know the laws.

Neither matter, nor a fortiori life and consciousness, could exist and develop if Nature did not obey laws. We would not be here to talk about it.

We do not have to expect from our experiences that they definitely prove that Nature obeys laws, which they can not do, since any law verified today could be refuted tomorrow, but only that they would help to find the laws of Nature. We know beforehand that Nature obeys laws but we do not know which ones. Since Nature does not seem to be mischievous, but rather generous, it seems that honest work and well-controlled experiments are enough to find and prove the laws to which it obeys. If a law is verified by a well-controlled experiment, or if it is a logical consequence of already well-established premises, it can be regarded as proven, until proven otherwise.

Where is the grain to grind?[edit]

Reason is to develop universal knowledge in common, honestly seeking truths and evidence, respecting the principle of equivalence of all observers, and more generally by voluntarily submitting to all the rules of critical thinking.

Critical discipline enables us to develop reason by putting theories to the test. It is like a mill, intended to give good flour, good knowledge, from the theories we give it. But where does one find the grain to grind? Where do the theories that we submit to criticism come from?

There is no need to look very far: everything that goes through our minds and everything we say, common-sense thoughts, or contrary to common-sense, trivial or original intuitions, even dreams and delusions, because they make us think and speak. Any thought is a candidate for critical review, but of course we do not want anything. We look for thoughts that help us develop good knowledge, or make us hope that they can help us.

When we search for knowledge, we sometimes feel as if we are lost in a forest in search of a treasure whose location we do not know, and there is enough to despair. It would take a miracle to find it. But it is an illusion, because the location of the treasure is known in advance. It can only be in ourselves. When we seek knowledge, we seek ourselves because we seek knowledge that makes us competent. There is no other place to look. Where could knowledge be if it was not already potentially in ourselves?

Good knowledge is the knowledge that makes us competent[edit]

How do we recognize good knowledge? It is the knowledge that makes us competent. There is no more fundamental criterion. Good knowledge is by definition the knowledge that makes us competent.

I am for myself the fundamental criterion of recognition of good knowledge, since I recognize it by recognizing my competence. But this autonomy is rational only if it is united. Good knowledge is not only the knowledge that makes me competent, it is above all the knowledge that makes us competent. Knowledge must be shared to be rational. When I acquire knowledge, I must acquire at the same time the capacity to teach it, otherwise my knowledge is not rational. To develop reason, we must work together. Isolated individual knowledge is not enough to make reason.

I am the source, the middle and the end of reason. Not me as different from all others but as similar to all others. All I, all who can think that they are, who can say "I", are the sources, the middle and the ends of reason, the sources because reason is born of our thoughts, the middle because it develops when we work for it, the ends because it is there so that we can accomplish ourselves.

One can reason about reason as if it were the wisdom of a person and attribute to it a will because one can attribute to it ends. Ethics teaches us what deserves to be pursued and thus gives us the means to fulfill ourselves. That we pursue the ends that reason prescribes for us may just be considered as an end of reason. Everything happens as if reason was a good authority that shows us the right paths.

Knowing that a mind must work for the mind is not enough to decide the particular ends we give ourselves. This is expected of a good authority. If it deprived us of our freedom, it would not be a good authority. Rational ethical knowledge is not a totalitarian enterprise that decides for us what we need to do. It is the exact opposite since it asks us to decide freely and intelligently. One can even say that it is a condition of true freedom, because one makes a bad use of one's freedom if one does not use it for good. The more we know the good, the better we can do it and live like a really free spirit.

The unity of reason[edit]

For knowledge to be shared, it must draw only on common resources, accessible to all. One might think that it is a very restrictive limit, that by depriving oneself of private resources, one also deprives oneself of the best of knowledge, but the exact opposite is true. Our intelligences are the most powerful just when they are limited to common resources. It is by helping each other that we discover best the power of our intelligences, that we develop the best knowledge and that we make reason live.

Despite their diversity, all knowledge manifests the unity of reason. The great principles of logic and critical discipline are the same for all. Such unity is essential to the development of science. All that is understood by some must be understood by all the others, otherwise it is not reason. From this point of view it can be said that all sciences speak with one voice and that all human beings contribute to the development of common knowledge.

The unity of reason does not exclude diversity; on the contrary, it encourages it. The great logical principles, for example, never forbid us to study theories. On the contrary, they always give us the means to study all theories as soon as they are properly formulated.

"You shall love your neighbor as yourself" (Leviticus 19:18) is not only a religious principle, it is also a rationalist principle, because the sciences and reason can develop only through mutual help and cooperation. If human beings do not want to help each other, reason can not be among them.

We are the sources, the middle and the ends of reason, the sources because reason is born of our thoughts, the medium because it develops when we work for it, the ends because it is there so that we can accomplish ourselves.

Is reason only a human invention?[edit]

To know that reason exists, we need to make it exist, by sharing it among us. In this sense, we do it. It would not be here if we did not work to make it live among us. But the belief that reason is our invention is wrong, because we do not decide what it is, we can not make that it is what it is not, or that it is not what it is. When we work we discover it. Everything happens as if reason had always been there forever, and we are the last to learn it.

The conditions for the appearance of reason are general: beings who speak, that is to say that they voluntarily emit signals to influence the imagination and the will of their peers, and who want to find together truths and proofs, respecting the principle of equivalence of observers and all rules of critical thinking. These conditions do not depend specifically on our humanity on Earth. Other living beings, on other planets, in other times, or in other universes, could also develop the same reason, because its conditions of appearance are universal.

What can we hope?[edit]

Before looking, we usually have to look for what to look for, to choose for ourselves the problems we will be working on. But we do not really know what to look for when looking for what to look for. We want interesting problems, promising topics, we dream of making major discoveries, to advance knowledge and reason. But the conditions of the problem are not well determined. What are we looking for when we are trying to advance reason? And how can we look for it if we do not know what we are looking for?

Reason makes us capable, but of what? What can we achieve with the skills we develop rationally? What can we hope?

If the list of problems that we can solve rationally was known in advance, we would know what to hope. But precisely, it is not known in advance. We do not know the range of skills that reason can give us.

We want to satisfy a desire for intelligibility. We want to understand. We want explanations. We do not know where this leads us, but it is not necessary to know it to be driven by this desire. We may want without knowing very well what we want, just looking for satisfaction. We are guided by ideas even if we do not know what they are.

As we do not know what reason makes us capable of, we can place our hopes very high, that the kingdom of reason come, that its will be done in earth, as it is in heaven, that the ephemeral present be the splendor of eternal truth, or very low, reason will never be more than a poor consolation in a valley of tears.

The development of reason is the story of a perpetually renewed astonishment. The sciences have exceeded our expectations. Nature has revealed many more secrets than we could dream. It is no longer possible to be skeptical. The power of science has become indisputable.

To know what reason makes us capable of, the best way, and the only way, is to try. If we do not try we have no chance to see what works. That's why we have to hope. We sin more often by lack of hope than by excess.

The proof of Anselm[edit]

We do not know very well what God is, but we know we can not give him any blemishes. If he had an imperfection he would not be God. He brings together in him all the perfections. His wisdom is perfect. He always chooses the best possible. His power is not limited by any opponent. It is the same for all the qualities that one can think of attributing to him. He is always the best, or the sum of all perfections.

A fictitious being is suffering from an imperfection, precisely because it is only fictitious, that it is nothing more than a product of the imagination. Since God has all the perfections in him, he can not be fictitious, hence he exists.

Such is the argument (Anselm of Aosta 1078) of Saint Anselm, Archbishop of Canterbury, to prove the existence of God.

Anselm is sometimes accused of committing a fault of logic, especially since Kant (1781). But if we understand it well, the proof of Anselm is quite logical and rational.

For a rationalist free thinker, the initial affirmation, that no fault can be attributed to God, is simply a hypothesis with which one can reason, as with any hypothesis. Nothing prevents us from making assumptions and seeing, by reasoning, whether they can teach us anything.

Anselm's argument proves with impeccable, perfectly rigorous logic that to think of a fictitious God is like thinking of a square circle. We reason badly about God, about being flawless, if we conceive it only as a product of our imagination. A faultless being can not be purely imaginary, because being only imaginary is a defect. Logic, our natural faculty of reasoning, is enough to prove it.

Like all mathematical proofs, Anselm's proof reveals a tautological truth. The conclusion, that God exists, is already asserted in the premise, since it makes the assumption that there exists a being without defect. But this tautological character does not invalidate the proof, on the contrary. All reasonings reveal tautological truths unless they commit logical errors.

The proof of Anselm is not enough to convince a skeptic. It only shows that one can reason correctly about a being without flaws, and that it must be more than a fiction to be truly flawless. But this is not enough to prove that this flawless being is not a fiction, since one can reason correctly on fiction.

That we can reason correctly about a being without defect is the important point. Natural light is enough to know the best. It is as if God had given us the faculty of reasoning and the idea of ​​a flawless being so that we could know him. A skeptic can always answer that such knowledge is hypothetical, what it is, but that does not prevent us from developing it. If it is really a good knowledge, we only have to discover by reasoning all that it can teach us to realize it. Good knowledge bears fruit.

Anselm proves the existence of God from the idea of a flawless being, but to say that God exists is only to know very little of Him. The premise, that God is without blemish, the best, the sum of all perfections, is much more important than the conclusion, that He exists, because it is much richer in consequences, because it teaches us everything we need to know about God.

There are many ways to exist. When one affirms the existence of God, one does not speak of any way of existing, one wants to say above all that he exists as Creator, that he has proven his existence by creating the Universe, that Creation is the revelation of his truth. The existence of God is Creation, it is the matter and the light in which we live.

Since God is the best, he has the best existence. To be the best and not to give us the benefits of it is weakness or selfishness and so can not be the best. God created the world because he is generous. He would not be the best without this generosity.

Anselm is the saint of rationalist thinkers (Descartes, Spinoza, Leibniz, Hegel ... but not Kant, because he had illusions about reason) and of all believers, Christians or not, who believe that science is a gift from God.

The affirmation that God is the sum of all perfections is an open hypothesis. It alone is very indeterminate. It invites us to reason. We must complete it by affirming what are the perfections we can attribute to God. When we say that he is the best we do not know in advance what it is to be the best, we have to learn it.

Rational theology is the rational knowledge of God. But how can God be known rationally? From his work, including reason. All creation, without exception, can be interpreted as the word of God. Everything speaks, everything says the word of God. In giving creation, God gave his word and the beings able to hear it. Reason is the knowledge and the wisdom that he makes us share.

Epidemics, famine, misery, torture, massacres and all the horrors, are part of the creation. If God is the best, why does he allow all the horrors to exist? Is the existence of evil not a proof that all the discourses on divine perfections are vain and foolish? (Voltaire 1759)

We can not always reason about divine perfections as on human perfections (Spinoza 1677). For a human being, letting evil exist in one's home is surely not perfection. But transposing this reasoning to the Universe and its creator does not seem legitimate. We do not know what could be a universe that would not allow evil to exist, because it would deprive us of our freedom, and because the deprivation of freedom is an evil. But above all we are not in a position to judge what God should have done and what he did not do. To believe that we can know better than God what he should have done is vain and foolish. Obviously we can not teach him what it is to be the best, he is the one who teaches it to us.

From the point of view of some atheists (not all) the term rational theology is contradictory, like a square circle. They do not make the difference between religion and superstition and consider that religious beliefs are just fantasies. The development of science and reason is supposed to open our eyes and rid us of these vain illusions. But this alleged opposition between reason and religions is contradicted by the history of the development of knowledge. Many scientists have advanced science by seeking to know God from his work. And the very existence of reason, of our capacity to develop it, can be interpreted as a proof of divine generosity. Atheists or believers, we do not know in advance what reason is, we discover it every day, and we must learn it. Atheists are not the only ones to oppose unreason, believers too. And one does not have to be an atheist to be a scientist. If atheism leads to ignoring all that religions teach about reason, it becomes blinding.


- Oh, you do not know that God exists?

- I never saw it. Why would I believe he exists?

- We can not see him. To recognize him in his creation, one must know him by thought. If you seek him in your mind, and if you want to find him, you will find him. He never abandons anyone, especially not those who seek him.


« No man has seen God at any time. If we love one another, God dwells in us, and his love is perfected in us. Hereby know we that we dwell in him, and he in us, because he has given us of his Spirit. » (1 John 4: 12-13)


The wedding ring between God and life (Genesis 9, 8-17):

Double rainbow.jpg


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