On the Observer and Form

If every form depends on how it was distinguished, it seems natural to add a separate observer to the formalization.

The form $F$ then becomes $F_R$, the distinction $\Delta$ becomes a distinction relative to $R$, and every transition must additionally specify the organization through which it was articulated.

This move appears cautious: the observer is not concealed but explicitly present in every operation. Yet it often adds no new determination to the formalization. It merely reintroduces what is already expressed in the organization of the form itself.

The Reflexor#

Here, $R$ does not necessarily designate a person or a conscious subject.

$R$ is the reflexive organization through which some state of the world becomes available as a determinate form. It may be an organization of perception, measurement, description, or computation—any established mode through which distinctions are retained and connected into a whole.

Let $S$ denote the present organization of the world and $\operatorname{Art}_R$ its articulation through $R$. A form can then be written as

The same aspect of the world, articulated through different reflexive organizations, may produce different forms and open different possible continuations.

But it does not follow that $R$ must be added to every subsequent operation.

The Form Already Bears Its Mode of Articulation#

A formalism does not operate upon $S$ as something given independently of every distinction. It operates upon an already articulated form $F$.

The boundaries, elements, relations, and admissible transformations of this form express the mode through which it was distinguished. The more concretely a form is specified, the more fully the organization through which it was distinguished is expressed in its structure.

This does not mean that the reflexor that produced a form can be fully reconstructed from that form. Different organizations may produce the same form, and much of their internal organization may be irrelevant to the present operation.

The form does not retain $R$ in full, but only the aspect of $R$ that became operative in this particular distinction.

The same applies to a concrete distinction $\Delta$ and transformation $g$. They are not neutral entities to which a viewpoint is subsequently added. Their mode of articulation is already expressed in which relations were distinguished, which continuations became admissible, and which transformation can be applied.

Adding $R$ to every formula therefore often counts the same determination twice: first in the organization of $F$, $\Delta$, and $g$, and then again as a separate external parameter.

When a Separate $R$ Is Not Needed#

At a developed operational level, a possible continuation can be written as

Here, $F$ is the current articulated form, $\Delta$ is a relation distinguished within it, $G_{\Delta}(F)$ is the field of available continuations, $g$ is the selected transformation, and $F'$ is a new articulation of the present state.

No observer is missing from this notation. The operative mode of articulation is already expressed in the concrete organization of its elements.

If a change in $R$ is expected to change the result, it is necessary to identify what relevant difference, not already represented in $F$, $\Delta$, or $g$, produces that change. That difference can then be incorporated into the organization of the corresponding form or introduced as a separate variable.

The claim that “everything depends on the observer” does not by itself require another element in the formalism. Such an element becomes necessary only when differences among reflexive organizations become operative within the problem under consideration.

When the Reflexor Becomes Explicit#

$R$ must be articulated separately when the mode of articulation itself becomes the object of distinction:

• when forms produced by different reflexors are compared;
• when the reflexor changes or reorganizes itself;
• when the limits of the distinctions available to it are investigated;
• when it is necessary to determine what persists across different modes of articulation.

In this case, the reflexor itself becomes a form:

Now $R$ is considered through another operative reflexive organization, $R'$. It no longer functions as the mode of the current distinction but becomes its object.

This does not make the reflexor a separate ontological type. Form and reflexor designate not two classes of entities but two roles within a particular act. Every explicitly represented reflexor is a form, but not every form acts as a reflexor in the relation under consideration.

Why No Infinite Regress Arises#

If $R$ is articulated through $R'$, it may seem that $R'$ must now be made explicit, followed by the organization that distinguishes $R'$, and so on without end.

But a formalization does not attempt to represent all the conditions of its own operation at once. It fixes a relative cut: what acts as a form in the present operation and what acts as the mode of its articulation.

A reflexor can be made an object of distinction, but that distinction is then already made from another position. In a subsequent act, this position may also be articulated as a form. The roles may change, but the current operation does not require a final external observer containing the entire sequence at once.

An infinite regress arises only from the demand that a formalization simultaneously contain a complete account of itself as a condition of its own operation. Such a demand is unnecessary for a particular operational continuation.

The Observer Has Not Been Eliminated#

The absence of a separate $R$ does not mean that the form has become independent of the mode of distinction.

The observer has not been eliminated from the formalization. It is immanently present in the boundaries of the form, the organization of its relations, and the field of continuations it makes available.

An explicit $R$ is not required merely because every form has a perspective. That perspective already participates in its organization.

A separate reflexor is needed when the difference between perspectives itself becomes part of the movement under consideration.