“A description of reality is not a property of reality.”
At first glance, this is a careful reminder: the map is not the territory, a text about a thing does not reside inside that thing, and an equation of motion does not move along with the body.
But the phrase is more complex than it appears. It is easy to conflate four distinct levels within it:
- the object;
- a property of the object;
- the subject’s relation to the object;
- the form in which that relation is fixed.
Until these are separated, two opposing misconceptions can be derived from the correct thesis that “description is not identical to reality.” In one, describability is declared unreal simply because it depends on a subject. In the other, a successful description imperceptibly becomes the structure of reality itself.
It is in the second transition that epistemology begins to present itself as ontology.
Four Different Questions in One Phrase
Let there be some $X$, an object, process, or fragment of reality. A subject $S$ distinguishes it through a language or system of notation $L$ and creates a description $D$.
This sequence can be written as follows:
$$
X \longleftrightarrow S \xrightarrow{L} D(X)
$$
Here at least four different questions must be asked:
- What is $X$?
- Can $S$ distinguish and describe $X$ using $L$?
- What is the form $D(X)$ that has been created?
- Which properties of that form may legitimately be attributed to $X$ itself?
The statement “a description is not a property of reality” may mean only that a particular text, diagram, or formula is not an intrinsic property of the thing being described. In that sense, it is true.
But it does not follow that the relation of description does not exist at all, that it is arbitrary, or that describability tells us nothing about reality.
Is Describability a Property?
The answer depends on what is meant by a property.
In the narrow sense, an intrinsic property concerns the structure of the object itself. Its definition does not require the inclusion of a particular observer or another thing.
But relational determinations also exist:
- being north of another city;
- being visible from a particular point;
- being reachable under given conditions;
- being measurable by a particular instrument;
- being known to a particular subject;
- being expressible in a particular language.
“Paris is north of Rome” requires both Paris and Rome to exist. Dependence on two relata does not make the relation fictitious. It merely prevents us from locating the relation entirely “inside” one of them.
Describability is structured in the same way:
$$
\operatorname{Describable}(X,S,L,C)
$$
where $C$ denotes the conditions of description: the accessibility of the object, scale, time, accepted distinctions, and permissible precision.
Therefore, describability cannot be written simply as $P(X)$ without qualification. It arises within the configuration:
$$
X + S + L + C
$$
If the narrow distinction between property and characteristic is used, describability is more precisely called a relational characteristic: it does not “reside within” $X$, but arises through a particular way of relating to it. In broader philosophical terminology, it can be called a relational property of $X$.
The disagreement between these formulations often turns out not to be a dispute about reality, but a dispute about the boundaries of the word “property.” What matters is something else:
Describability need not be an intrinsic property of a thing in order to be a real determination of the relation among the thing, the subject, and the system of description.
Description Is Not Describability
This distinction is more important than the terminological dispute over properties.
Description $D(X)$ is a form already created: a text, image, set of readings, table, equation, or model.
Describability is the possibility, under given conditions, of establishing a relation in which some distinctions of $X$ are fixed using $L$.
What is described, $X$, is that with which this relation is established.
Therefore:
$$
X \neq D(X)
$$
Moreover, the existence of describability does not yet imply the existence of an actual description. Something may be accessible to description even though nobody has described it yet. And the existence of a description means only that some attempt at fixation has already occurred; it does not itself guarantee its completeness, precision, or truth.
We therefore obtain three distinct assertions:
$$
X \text{ admits description under } (S,L,C)
$$
$$
D(X) \text{ has actually been created}
$$
$$
D(X) \text{ is adequate to certain distinctions in } X
$$
None can be substituted for another without justification.
The description itself is, of course, also part of reality: a book exists, a graph has been printed, a formula has been written down, a state of memory has been realized. But a description is real as a description, not as an identical duplicate of what it describes. The existence of a map does not turn the map into the territory.
Formalizability Is Not the Same as a Formula
Suppose the motion of an object has been expressed by a function:
$$
x(t)=f(t)
$$
What exactly has happened?
A subject has chosen a coordinate system, singled out the time parameter, identified position as a significant variable, established a measurement procedure, and discovered a stable correspondence between the resulting values and the function.
This is a powerful cognitive result. But its minimal content is:
Given these distinctions, conditions, and degree of precision, the observed states of the object can be consistently expressed by the function $f$.
Subsequently, stronger formulations begin to appear almost imperceptibly in discourse:
Motion obeys the function.
Then:
The function expresses the law governing motion.
And then:
Motion is by its nature the realization of a mathematical structure.
Thus a ladder of ontological smuggling arises:
$$
\text{can be described}
$$
$$
\Downarrow
$$
$$
\text{can be formalized}
$$
$$
\Downarrow
$$
$$
\text{formalization corresponds to observed relations}
$$
$$
\Downarrow
$$
$$
\text{the object obeys the formalization}
$$
$$
\Downarrow
$$
$$
\text{formalization expresses the nature of the object}
$$
$$
\Downarrow
$$
$$
\text{the object is ontologically a mathematical structure}
$$
The arrows create the impression of an inference, but each conceals an additional premise.
Describability does not imply formalizability: not every distinction can be represented in the chosen formal system.
Formalizability does not imply empirical adequacy: a consistent formula may also be constructed for a process that does not exist.
Empirical adequacy does not imply completeness: a model may describe one range perfectly and cease to work beyond it.
Agreement with all available observations does not imply ontological identity: the success of all tests performed does not yet prove that form and reality have the same mode of existence.
Each subsequent stage may be a separate hypothesis. None is automatically contained in the preceding one.
Where Appropriation Occurs
Formalization in itself appropriates nothing. It is necessary where distinctions must be made precise, reproducible, and testable. The error begins with reverse projection.
First, the subject distinguishes a certain structure in reality:
$$
X \xrightarrow{S,L,C} D(X)
$$
Then the subject investigates the resulting form and discovers properties $P$ within it:
$$
P(D(X))
$$
Afterward, the temptation arises to read the result in the opposite direction:
$$
P(D(X)) \Rightarrow P(X)
$$
But this implication is not a general rule.
A model may be continuous, infinitely precise, deterministic, linear, symmetrical, or computationally reversible. It does not yet follow that the modeled process possesses the same properties in the same sense. Some properties may have arisen from the chosen coordinate system, idealization, method of discretization, language, or computational requirements.
For such a transfer to be justified, a bridge is necessary: a separate hypothesis explaining why the particular property of the form corresponds to a determination of the modeled object, together with a test of the domain in which this correspondence holds.
Schematically:
$$
P(D) + B(D,X,C) + V(C) \Longrightarrow P^{*}(X,C)
$$
where $B$ is the justification of the connection between the model and the object, $V$ is verification, and $P^{*}$ is no longer a property mechanically copied from the model but a carefully formulated assertion about the object under the specified conditions.
It is precisely the bridge, the conditions, and the verification that usually disappear from the everyday formulation “science has shown that reality is structured this way.”
The Map-and-Territory Trap
The statement “a description of reality is not a property of reality” is often used against confusing the map with the territory. It is useful in this capacity because it establishes a boundary:
$$
\text{reality} \neq \text{description of reality}
$$
But the boundary that has been recognized must also be preserved once the description has proved successful.
One cannot first assert that the description does not belong to what it describes and then, without an additional argument, declare the mathematical properties of the description to be properties of the world itself. If the map is not the territory, then even an exceptionally accurate map remains a form of relation to the territory.
Its success may indicate that:
- the distinction was not arbitrary;
- there is a stability in reality that sustains the correspondence;
- the chosen form captures some structure of relations;
- the model permits reliable action within a particular domain.
But it does not prove that:
- no other adequate distinctions exist;
- the model fixes every significant aspect of the object;
- the boundaries of language coincide with the boundaries of reality;
- what is described is exhausted by the description;
- the mode of existence of the formula coincides with that of the process.
A successful map is not accidental, but neither is it total.
Two Symmetrical Errors
Separating form and reality does not require treating description as an arbitrary invention.
The first error is naive projection:
If a model is successful, reality literally is what is written in the model.
The second is radical disconnection:
If a description is created by a subject, it says nothing about reality.
Both positions destroy the relation. The first dissolves the object into the form; the second encloses the form within the subject.
But description does not arise solely through the subject’s activity. Reality constrains possible descriptions: some predictions come true and others do not; some distinctions are reproducible and others fall apart; some forms enable action and others lead to error.
Therefore, the adequacy of a description belongs neither to the form in itself nor to the object in itself. It characterizes the stability of the relation:
$$
X \longleftrightarrow D(X)
$$
under given conditions and for a given task.
Description does not copy reality in its entirety, but neither does it hang in a void. It fixes what proved accessible through a specific way of distinguishing.
What a Successful Description Actually Proves
The success of a description proves less than ontological formalism would like, but more than radical relativism permits.
It shows that a stable relation has been established among subject, form, and reality. This relation may be repeatable, practically effective, and capable of withstanding testing. The broader the domain of testing, the stronger the grounds for saying that the form captures a real structure.
But even maximal practical success does not eliminate the distinction between levels:
Form may be adequate to reality without becoming reality.
A property of a model may indicate a property of what is modeled, but it is not transferred to it without justification.
Describability may be real without being an intrinsic property of the thing described.
This allows realism and critical distance to be preserved simultaneously: we can recognize that we are dealing with reality without declaring our particular way of accessing it to be its definitive structure.
Where Epistemology Turns into Ontology
A subject encounters reality, distinguishes a certain structure within it, and fixes this distinction in a form. If the form proves stable, a temptation arises to project backward: to declare the properties of the form to be properties of reality itself.
But the success of a description proves, above all, the existence of a stable relation of describability. It does not yet prove that what is described is exhausted by the description.
Therefore, the correct conclusion is more modest:
$$
\text{reality admits this form of description}
$$
rather than:
$$
\text{reality by its very nature is this form}
$$
Between these assertions lies the entire distance between a method of cognition and ontology.
The preceding question is examined in “Form as a Condition of Description”. Related texts: “Summary: Description, Perception, and Distinction”, “Properties and Characteristics”, “What Is a Model and Where Does Substitution Occur?”, “No Form Exhausts Reality”.
