Précis of epistemology/Why is reality intelligible?

Reality is intelligible because it can be explained with observations and principles.

Explanation
Observations show us what is, but they do not tell us why it is so. To satisfy the desire for intelligibility, we do not only want descriptions, we especially want explanations.

What is a good explanation? What does it take for an explanation to enlighten us?

A part can be explained from its place in a whole of which it is a part. We can also explain a whole from its parts. In any case, we have to have a fairly clear view of the totality we are talking about. Fairly clear does not mean always complete, nor always precise down to the smallest detail. We still need to know enough to distinguish the place of the being that is being explained, or those of the beings that constitute the one that is being explained. It is necessary to know fairly well both the peculiarities of the beings studied and the good principles which provide the means of reasoning on these peculiarities.

An event is explained from the conditions which produced it, from the sequence of events of which it is the consequence. Explaining an event means having a fairly clear view of the chain of events of which it is a part.

In general our observations reveal only crumbs of reality. We only lift a tiny corner of the veil, we observe only a tiny part of reality, far too little to pretend we know it well. Our knowledge is too fragmentary to give explanations because we do not know the causes of which our observations are the consequences. This is why fiction sometimes shows the truth better than reality. The author of a fiction can inform us of all the conditions which precede the related events and explain them thus.

We explain events with predictive laws, but these laws too must be explained. We explain particular laws with more general laws and principles by making theories. The explanation of a law places it in a theory that enables us to prove it. It is necessary to have a fairly clear view of the theory, to know its principles and their main consequences.

An explanation of an anticipated event is at the same time a proof of the truth of the anticipation, provided that the premises, the conditions which precede the event and the laws which make it possible to predict it, are true. This is general. A good explanation is a proof of what it explains. Conversely, a good proof must at the same time be an explanation, it must show us why its conclusion is true. In the Socratic definition of knowledge, a true belief accompanied by a reason (Theaetetus 201d, Meno 98a), 'reason' (logos) can also be translated by 'explanation' and by 'justification'. But it comes down to the same thing. Good principles are good both because they explain and justify the conclusions they lead to.

We can explain the same being in various ways. An organ, for example, can be explained with a fairly clear view of its constitution, or with a fairly clear view of its place in the organism of which it is a part, or with a fairly clear view of its place in the systems of the ends pursued by the organism: the explanation by the final cause (Aristotle, Physics, Metaphysics). We can also explain it from its development, with a fairly clear view of all the stages, from the egg, which led to its appearance, or from its evolution with a fairly clear view of its place in the tree of all the lineages that led to its appearance.

We can explain a living species by explaining its physiology, with a fairly clear view of the functioning of all its organs. We can also explain its evolution and development. We can explain its behavior with a fairly clear view of its interactions with its environment.

We can explain a natural substance with a fairly clear view of its constitution. Its properties are explained with a fairly clear view of its interactions with other natural substances. We can also explain how it is produced, giving a fairly clear view of the stages of its production.

The concepts are explained with a fairly clear view of their place in the theories they enable us to formulate. When a concept can be defined from other concepts, it is explained with a definition that situates it in relation to other concepts. When it is a fundamental concept, it is explained with the principles that determine its use.

The concept of explanation is explained by stating the principle that an explanation must give a fairly clear view of the place of the being that is being explained in a totality of which it is a part, or of the places of the parts in the totality that we explain, and show the main applications of this principle. In this way, we situate the concept of explanation in the totality of all concepts, all theories and all sciences.

We explain a principle by giving a fairly clear view of the theories it enables us to found. We have to know its place in the systems of principles and their main applications.

What is a concept?
Observations attribute concepts to observed beings.

Concepts are properties or relations, as soon as they are perceived or thought. Concepts are the properties and relations that we can think. A property, or quality, or trait, is assigned to a single being. A relation is between several beings. When a relation is between two beings, it can be considered as a property of the couple. A relation between three beings is a property of the triplet, and so on for relations between more beings.

Visual perception attributes visual qualities (color, brightness, texture, shape ...) to the objects seen. The same applies to other forms of sensory perception.

When a being is perceived, it is always perceived with qualities or relations. A being without concepts, a kind of thing in itself, to which no concept is attributed, can not be perceived. Beings never come completely naked. They are always dressed with the concepts that perception has given them.

A being is perceived when a detector signals its presence. The detector determines a concept attributed to the object: the quality of being detectable by this detector. A detection automatically attributes to the detected being the quality of being able to be thus detected.

The same detection signal can serve at the same time to represent the detected being and to represent the concept attributed to this being, because the being is identified by its concept. Beings are represented by the concepts which are attributed to them. For example "the tree in the yard" is an expression which uses the concept of being a tree in the yard to represent a tree.

A concept is determined by the set of detection systems that signal the presence of a being by attributing this concept to it. This definition is not just for sensory perception and empirical concepts. It can be generalized because any information processing unit can be considered as a detection system. An information processing unit produces output signals from signals received at the input. An output signal can be considered as a detection signal of the input signals that produced it. In particular, theoretical concepts are determined by their place in a theoretical system defined by principles. Reasoning from the principles makes it possible to attribute the concepts to the beings of the theory. The ability to reason can be considered as a system for detecting theoretical consequences, and therefore as a system for detecting theoretical concepts.

When a concept is defined by a series of conditions, which together are necessary and sufficient to determine it, a system of detection of the presence of the concept is defined at the same time, because the concept defined is detected by detecting the conditions which define it.

When a concept is defined by similarities with one or more examples, detecting the concept consists of detecting similarities and differences.

Even a single being can be identified by a concept, as soon as we are able to perceive it or imagine it as a single being, because to perceive or imagine it requires a system of detection, and because such a system defines a concept. For example I can have the concept of a person who is familiar to me because I can perceive it and distinguish it from all other people.

Iconic representations, such as visual images, and conceptual representations, which can be formulated with words, are sometimes distinguished. But this distinction is not fundamental. A visual image attributes visual qualities to all its points, so it is already conceptual. To perceive is already to conceive. Conversely, a verbal description such as blue-white-red can be considered as an image of the French flag, because the words are aligned like the parts they represent.

Concepts are often conceived as products of language. Concepts are signified by the expressions used to name them, and they are not known until they have a name. According to the accepted meaning in this book, concepts precede language. As soon as a perception system is able to detect objects, it automatically assigns concepts to them. Concepts are widely used by animals, whether or not they use language (Gould & Gould 1994). For example, all animals capable of fear show by their behavior that they are capable of detecting danger. The concept of danger is therefore one of their internal representations.

Should we consider concepts as beings? As parts of reality?

Concepts are present whenever the beings of which they are true are present. The existence of the concept of horse is simply that of all horses. Concepts are manifested and revealed by the existence of the beings of which they are true and they exist at the same time. Concepts really exist, but not in the way of bodies, because they exist in a dispersed way over all the beings of which they are true.

''« Form finds itself identical at the same time in several places. It is as if you spread a veil over several human beings and say, « The veil remains one in its totality, when it is stretched on several things. » (Plato, Parmenides'', 131b)

Individuals and the binding of concepts
Beings, individuals, are identified from the concepts attributed to them. But for that it is necessary to solve the binding problem (Quine 1992). For example, heat and pain can be perceived simultaneously in two very different ways. In the first case, what is hot is what hurts, heat and pain are bound. It is supposed that there is a being which has two properties, to be hot and to hurt. In the second case, what is hot is not what hurts, heat and pain are not bound. It is supposed that there are two beings, one which is hot and does not hurt, the other which hurts and is not hot.

We solve the binding problem when we attribute to the same individual several properties or relations with other individuals.

The whole being of a being is its being in a whole, or its being a whole, or both
Properties and relations are the ways of being of individuals of which they are properties or relations. The being of an individual, that is to say its particular way of being, is determined by all its properties and its relations with other individuals. Its properties and relations make an individual what it is. To know an individual is to know its properties and its relations. But what determines the being of properties and relations? What makes them what they are? Since properties and relations themselves have properties and relations, we might suppose that their being is determined in the same way as the being of individuals, but then we encounter an infinite regression: to know an individual it is necessary to know its properties and its relations, which must be known by their properties and their relations, which in turn must be known by their properties and their relations, and so on to infinity. It seems that by doing so one could never know anything.

A particular being is what it is by virtue of the totality of which it is part. It has its place in a whole. Once its place is determined, all it is is determined. The whole being of a particular being is its being in a whole.

Properties and relations determine the way of being of an individual by determining its place in a whole. But they too are determined by their place in a whole.

All beings in the world, simple or complex individuals, properties and relations all have a place in the world. As soon as these places are determined, the world is determined, and all the beings that it contains too, with their properties and their relations.

To be is to be a whole or to be in a whole. If a being is in a whole, its being is determined by its place in the whole. If a being is a whole, its being is determined when all the places of the beings which constitute it are determined. A being can be at once a whole and in a larger whole. Such a being is determined both by its internal structure, that is, by the arrangement of its constituents, and by its place in the larger whole. It is the same thing to say that it is determined by the place of all its constituents in the larger whole.

To be is to be a part or a whole, and most often both. The being of a part is determined by its place in the whole. The being of a whole is determined by the being of all its parts.

The holistic principle, that the whole being of a being is its being in the whole, or structuralist, to be an object is to be a place in a structure, is of universal application (Dieterle 1994). It explains both the being of natural beings and the being of mathematical beings.

The nature of matter and the truth of perception
When we perceive an object with our senses we think we know it well. For example, if we see that the wall is yellow, we naturally believe it is really yellow. But is it not a mistake? All we know is that our eyes give us a sensation of yellow. Yellow seems to be on the wall but is truly in our eyes. It could even be that the wall does not exist, that we only have the illusion of a yellow wall. Should we conclude that we will never know the outside world, that we can only know our sensations and ourselves, that perception is always introspective?

The nature of matter is to interact with matter. The properties of a piece of matter (elementary particle, atom, molecule, solid, liquid or gaseous material ...) are always determined by its ways of interacting with other pieces of matter. Matter always does that, interact with matter, and nothing else. There is nothing more to know about matter than its interactions. When we know how material beings interact with each other, we know everything that is to be known about them.

We are sensitive to a being when it acts on our senses. Our sense organs are specialized to undergo the action of external objects. They are not sufficient to know all material beings and their interactions, but they still bring a lot of very useful informations. Observation and measurement instruments, and all detection systems that we can build, are like sensory prostheses. They extend the scope of perception. They enable us to know material beings which the senses are not directly sensitive to. They reveal other forms of action and sensitivity.

Matter can always be detected because its nature is to interact. As soon as it acts on another piece of matter, the latter is a detector. Our senses, complemented by all conceivable detection systems, enable us in principle to know all material beings and all their properties. Nothing can remain hidden. Everything can be perceived, because the nature of matter is to be perceptible (Dugnolle 2017).

The wall is really yellow simply because it is able to excite the sensation of yellow on our eyes, or on any other detector sensitive to yellow light. More generally, all the qualities and all the relations that determine the existence of a material being are detectable by other material beings. We do not have to fear that perceptions maliciously deprive us of what it seems to give us, true representations of perceived beings.

When a being is perceived, or detected, it establishes a relation with the being who perceives or detects it. As the being of a being is determined by all its relations with other beings, being perceived or detected is part of the being of a being. Perception reveals the truth of beings because it reveals their place in the whole.

But this argument in favor of the truth of perceptions seems to prove far too much, since it suggests that all perceptions should be true. If the quality detected is still the quality of being so detectable, it follows that any detection is true, since what is detected is necessarily detectable. How can false perceptions then exist?

The possibility of falsity comes from the existence of a standard of truth. If a measuring instrument has not been correctly calibrated, it provides a false result. The result is false only with reference to the measurement standard. The same goes for perception. They can only be false if there is a standard that determines what should be perceived. In the absence of norms, they are always true, because they always reveal the effect of the object on our senses. Even a false perception reveals a truth about the object, because it is true that it can be so perceived.

Logically possible worlds
A logically possible world is a set of atomic statements (Keisler 1977). A statement is atomic when it asserts a fundamental property of an individual or a fundamental relation between several individuals.

For example, the set of following statements defines the world, or structure, of natural numbers: 1 follows 0, 2 follows 1, 3 follows 2 ... It must be understood that this set contains all the atomic truths formed with the names of the natural numbers and the relation of succession. An atomic statement that is not in this set is therefore false.

The structure of natural numbers thus defined is a logically possible world. In a general way, any set of atomic statements defines a logically possible world, or model, or structure. All the atomic statements in the set are true of the world which they define together, by construction.

The set of atomic truths that defines a world completely determines the individuals it contains, their properties and their relations. Each individual, each fundamental property or relation is determined by its place in the set of atomic truths. 0 is nothing other than the natural number which follows no natural number and which is followed by 1, 1 is nothing other than the number following 0 and which is followed by 2 ... The relation of succession is nothing other than the relation that links at once 1 to 0, 2 to 1, 3 to 2 ... The being of natural numbers and of their relation of succession is completely determined by the totality of the atomic truths about them (Dedekind 1888).

More generally, a mathematical being is a structure or a place in a structure (Shapiro 1997, 2000). A structure is a logically possible world. When it is a place in a structure, the whole being of a mathematical being is its being in the whole, the structure. A mathematical being can be both a structure and a place in a larger structure.

We can reason about the world as if it were a big book. To reason about beings is always to reason about what we say about them. All truths are determined from elementary and fundamental truths, all atomic truths about all beings. All these truths together are like the big book of the world. All that is can always be said, because words and expressions can name all concepts, all that can be perceived, all that appears.

A remark on logical possibility: David Lewis fears that there could be a circularity in the definition of the concept of logical possibility, because a logically possible world is such that it is impossible that its definition implies a contradiction (Lewis 1986). By defining a logically possible world as a set of atomic statements, this problem of circularity is avoided. The definition of a logically possible world cannot imply contradiction because atomic statements never contain negation. If there is no negation, there cannot be any contradiction.

A remark on the principle of compositionality - the meaning of a compound expression is determined by the meanings of the component expressions: this principle is not compulsory. We can choose a compound expression to name a concept which is determined independently of the component expressions, because it is convenient. In the present case, the concept of a logically possible world is not defined on the basis of the concepts of world and logical possibility but on the basis of the concept of a set of atomic statements. On the other hand, the concept of logical possibility can be defined from the concept of a logically possible world: a statement is logically possible when it is true in at least one logically possible world. From there we can define the concept of logical necessity: a statement is logically necessary when its negation is not logically possible, and the concept of logical consequence: B is a logical consequence of A when the conjunction of A and the negation of B is not logically possible. We can also define logical necessity and consequence directly: a statement is logically necessary when it is true in all logically possible worlds, B is a logical consequence of A when it is true in all logically possible worlds where A is true. The definition of a logically possible world by a set of atomic statements is therefore the foundation of all logic.

Nothing new under the sun
The light that comes from distant stars is the same as that of the Sun, or the light we produce on Earth. It always behaves the same way. ''« There is nothing new under the Sun. »'' (Ecclesiastes) The laws of optics are among the best known and they are always verified, often with excellent precision. Throughout the Universe light is always the same and always obeys the same laws.

Light reveals the properties of matter. A natural substance can always be identified by spectroscopy, the analysis of the light absorbed or emitted. We can know the chemical composition of distant stars by analyzing their light. Light reveals that matter is always the same everywhere in the Universe.

A natural substance is pure if it is made of identical molecules or atoms. Natural substances always behave in the same way as soon as they are pure. Pure water always has the properties of pure water. It always obeys the same laws. For it too, there is nothing new under the Sun. More generally, elementary particles, atoms and molecules of the same species are all identical and obey the same laws.

All the points of space are identical. When we know one, we know them all. The same is true for points in space-time.

All natural numbers are obtained by adding units that are all identical to each other. We know the constitution of all natural numbers, however large they are, simply by knowing the one. Likewise the elementary constituents of all material beings are identical when they are of the same species. By knowing a small number of elementary species, we know at the same time the constitution of all material systems, even very vast and very complex.

All sciences place beings in fundamental categories. Beings of the same category have common properties and obey the same laws. But apart from fundamental physics, beings of the same category are not identical. Beings of the same category can be very similar to each other, but also very different. Each being can have properties that distinguish it from all others.

Each number is unique but they all obey the same laws of calculation. When beings are all different, they can also be very similar by obeying the same laws.

When beings are similar, it suffices to know only one to acquire knowledge about all the others. In this way, we can know very vast totalities: all material beings, all minds, all space and all spaces, all theories, all that is naturally possible, or logically possible ...

When we know a law, we know at the same time all similar beings that obey this law. It is like knowing a myriad of beings at the same time. In this way, we can know very vast totalities: all material beings, all minds, all space and all spaces, all theories, all that is naturally possible, or logically possible ...

The appearance of a unique being is a novelty. So there is still sometimes something new under the Sun. But it is never completely new. Laws, common properties, categories are not new.

We always make theories by applying principles, generalities, to beings of the same category. If the beings of the same category do not have common properties or do not obey the same laws, we cannot make a theory. That there is nothing new under the Sun, apart from some individual variations, is a necessary condition for the intelligibility of reality. Reality is intelligible when we know the theories which explain it, when we know the principles which remain true always and everywhere.

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

To justify our knowledge, 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 spirit 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, as long as it is not refuted.

Naturally possible worlds
Observations reveal beings only through what they are or have been. Imagination and thought enable us to go further because they reveal what they could be, what is naturally possible.

Naturally possible worlds are logically possible worlds such that the laws of Nature are true about them.

A theory of Nature states fundamental laws, its axioms, and makes it possible to define properties or relations from the fundamental ones. If the theory is true, all theorems of the theory, the logical consequences of axioms and definitions, are laws of Nature.

The logically possible worlds where a theory is true are generally called models of the theory or of its axioms. A naturally possible world is a model of a theory of Nature. Here we must distinguish two meanings of the concept of truth. The truth of axioms for a model is a formal or mathematical truth. It results from the definition of the model. But when one says of a theory of Nature that it is true, one wants to say more than its formal truth for a logically possible world, one wants the theory to be true about beings that really exist, one wants that the truth of the theory be physical or realist. Naturally possible worlds are the models of a theory of Nature provided that the theory is true in the realist sense.

If the laws of Nature are formulated with a system of differential equations, the naturally possible worlds are the solutions of the system.

We explain what is present, real, actual by showing that it is naturally possible. We explain the movements of the planets for example by showing that they are solutions of the differential equations of Newtonian physics.

The space of naturally possible worlds is much larger than the real world, but in a way knowing it is easier, because we only need to know the laws. To know the actual world, one needs moreover to be informed about the possibilities that have been realized.

The fundamental properties and relations of a theory of Nature are completely determined by their place in the set of naturally possible worlds, which is itself determined by the system of fundamental laws of Nature postulated by the theory. More generally, all natural properties and relations are determined by their place in the system of the laws of Nature, because the whole being of natural properties and relations is their being in the totality of naturally possible worlds.

The power of natural properties
''I suggest that anything has real being that is so constituted as to possess any sort of power either to affect anything else or to be affected, in however small a degree, by the most insignificant agent, though it be only once. I am proposing as a mark to distinguish real things that they are nothing but power.''

(Plato, The Sophist or About Being, 247d–e)

The fundamental laws of matter are laws of interaction. If a species of matter did not interact with the rest of matter, it could not be detected, and therefore it could not be recognized as matter. All material beings interact with other material beings. All the matter we can detect, that is, all the matter in our Universe, is necessarily part of an interconnected network of interactions of which we are also part.

The power of a being, its capacity to intervene in natural arrangements, the effect it has on other beings, is determined by the laws of interaction between beings. The laws of interaction attribute the same power to beings that have the same natural properties. The power of a being depends only on its natural properties. Any other being with the same properties naturally has the same power.

When we know what a being is made of, we can deduce its effects on all other beings, provided we know the laws of Nature. What it is made of says what it does.

A natural property can itself be considered a power. It must be understood that it contributes to the power of the beings of which it is a property. If two natural properties always have exactly the same natural effects, if they can not be distinguished as natural powers, then they are necessarily the same property, because a natural property is determined by its place in the system of the laws of Nature. It can also be said that a natural property is determined by its place in the system of causal relations (Shoemaker 1980, Bird 2007), because the latter is itself determined by the laws of Nature.

Since geometric relations are natural properties, they too are powers. This consequence of the theory is sometimes regarded as an objection to it, because geometrical relations seem inert and incapable of acting. It is to forget that proximity is essential to the exercise of a power. Distance is a power because it is part of the exercise conditions of the various powers. To protect oneself from danger, it is often enough to move away. Distance has the power to protect us.

The totality of all beings
The most fundamental explanations relate to the vastest totalities: all material beings, all spirits, all principles, all concepts, all theories.

When we say of a spirit that he must use good principles to live for the good of all the spirits, we explain his place in relation to all the spirits and to all the principles, we locate him in the totality of all beings and thus we answer very fundamental questions about his being.

As concepts and theories are always determined with principles, the totality of all beings rests on three fundamental categories: material beings, spirits and principles.

Metaphysical principles are the most fundamental principles, those which help us to understand the totality of all beings. As soon as a science sets out very fundamental principles, it contributes to metaphysics. Ethics, epistemology, logic, physics, psychology are all metaphysical disciplines, as soon as they give very fundamental principles. Metaphysics can be considered the most fundamental part of all the sciences put together. It gives us principles with which to reason about the place of each being in the totality of all beings. For example, material beings obey laws they do not choose, while spirits can be formed by obeying laws they choose.