The Penteract Methodology

In higher geometry, a penteract is a five-dimensional hypercube.
It cannot be drawn, only projected into lower dimensions.
Every projection is necessarily a simplification.
And sometimes, in that simplification, a rupture occurs:
a singularity — a point where internal tension becomes so great
that further simplification would cause the coherence of the whole to collapse.

This is not an error.
It is a structural limit.

The legal penteract model functions in an analogous way.
It is a structured projection of how we analyze law:
in layers of language, context, legal order, subject matter and normative foundation.

But this model also has its breaking point.
A zone where further analysis within a single method no longer clarifies,
but where specialized expertise or higher normative review becomes necessary.

We call that breaking point:

the Heyvaertian singularity.



The penteract model as thinking instrument

The penteract model was developed by Peeters Law as a methodological framework
to structure legal reasoning with maximum precision and awareness.

Each case is approached from five interrelated dimensions:

- language and semantics
- normative context
- competent legal order
- materially applicable law
- underlying principles

Together they form a controlled projection of legal reality.
The model functions as an internal verification instrument,
aimed at avoiding systematic thinking errors
and exposing blind spots.

But every analytical model assumes manageable complexity.
And precisely there, where a case exceeds that limit,
the model itself does not become inadequate —
but collaboration with specialized expertise becomes necessary.



The singularity: when specialization is required

When a case, despite correct positioning within all five dimensions,
continues to encounter fundamental tensions —
conflicting legal systems, normative conflicts, or jurisdictional impasses —
then the Heyvaertian singularity marks the tipping point.

Not as failure,
but as recognition of where further expertise begins.

The singularity indicates that point where:

- a preliminary reference to the Court of Justice becomes necessary;
- constitutional review by the Constitutional Court must be considered;
- collaboration with highly specialized colleagues or academics is required;
- the case calls for escalation to a higher normative level.

This is not an anomaly.
It is recognition of the limits of generalist analysis
and the beginning of specialized coordination.



Not a sixth dimension, but a tipping point

The Heyvaertian singularity is not a sixth dimension of the model.
It is a structural limit in the projection itself.

It becomes visible when:

- multiple legal systems offer irreconcilable solutions;
- normative principles conflict without clear hierarchy;
- no single dimension of analysis can still capture the case without ignoring essential elements;
- the lawyer can no longer reason within a single legal system or method,
 and coordination of multiple expertises becomes necessary.

At that point one leaves the standard model —
not from weakness,
but from professional necessity.



In practice: from analysis to coordination

In our practice, this means that Peeters Law, when the singularity is reached,
shifts from executing lawyer to coordinating lawyer.

For example when:

- a cross-border inheritance case encounters irreconcilable PIL rules from three countries;
- international co-parenting finds no ready-made solution within existing treaties;
- a corporate law dispute requires parallel advice from tax specialists, notaries and foreign lawyers.

In such cases, Peeters Law acts as coordinator of expertise:
bringing together the right specialists,
ensuring coherence between their advice,
and translating complexity into a workable strategy for the client.

This is not a failure of our method.
It is a deliberate choice to seek collaboration
where a single approach would be insufficient.



Why this name?

This singularity bears the name of Alfons Heyvaert
as a reminder of a method of legal thinking
that seeks structure, but can also interrupt itself
when further dissection no longer clarifies.

Heyvaert — professor, lawyer, thinker —
brought legal thinking back to its bone structure.
Not to simplify,
but to make visible where legal institutions
have limits they themselves cannot transcend.

His work — including The Law of Persons and Family Dis(bone)d —
shows how legal categories function
as ordering mechanisms with inherent tensions.

In this approach, law is not a neutral system,
but a structured ordering
that sometimes makes its own limits visible.

Those who look this way do not repeat doctrine.
They interrupt it — temporarily, methodically — to move forward.



A necessary interruption

The penteract model claims no complete truth.
It offers orientation.

But this model must also be able to interrupt itself
when a case calls for more than one method,
more than one legal system,
more than one perspective.

A model that cannot interrupt itself
degenerates into dogma.

The Heyvaertian singularity reminds us of this:

Legal thinking begins anew
where the thinking instrument dares to stop itself
to make room for complementary expertise.



Alfons Heyvaert (1936–2024)

Professor. Lawyer. Thinker. Teacher.

Not the one who taught us
what to think,
but where to begin:
with the question,
with the dissection of structure,
with the recognition of limits.

Recommended source:
Met rede ontleed, de rede ontkleed – Liber Amicorum Alfons Heyvaert,
Antwerp, Intersentia, 2002.

In higher geometry, a penteract is a five‑dimensional hypercube. It cannot be drawn, only projected into lower dimensions. Every projection is necessarily a simplification. And sometimes in that simplification a break occurs: a singularity, a point where the internal tension becomes so great that the coherence of the whole collapses. This is not an error. It is a structural limit.

The legal penteract model functions in an analogous way. It is a structured projection of how we analyse law: in layers of language, context, legal order, subject matter and normative foundation. But even this model has a breaking point. A zone where further analysis no longer clarifies, but rather dissolves. Where dissection no longer yields clarity, but the system itself visibly fails. We call that breaking point the Heyvaertian singularity.

The Penteract model was developed by Peeters Law as a methodological framework to structure legal reasoning with maximum precision and awareness. Each case is approached from five interwoven dimensions:

• language and semantics
• normative context
• competent legal order
• materially applicable law
• underlying principles

Together they form a controlled projection of legal reality. The model serves as an internal testing instrument, aimed at avoiding systematic reasoning errors and uncovering blind spots. But every analytical model presupposes a certain closure. And it is precisely where the model is applied with the greatest coherence that its own limit can become visible.

When a case, despite correct placement within all five dimensions, continues to encounter fundamental friction, asymmetry, moral dissonance or structural exclusion, it is not the model that fails. It is the law itself that reveals a gap.

The Heyvaertian singularity marks exactly that point: a projection zone in which the legal ordering framework undermines itself or proves structurally inadequate. This is not an invitation to further interpretation, but a call for systemic questioning: through a preliminary reference, a constitutional review, or escalation to higher norms of legitimacy. The singularity does not extend thinking. It interrupts it, temporarily but in principle.

The Heyvaertian singularity is not a sixth dimension. It is a fault line in the projection itself. It becomes visible when:

• the normative structure produces exclusion it can no longer correct
• the law protects itself at the expense of justice
• no dimension can capture injustice without minimizing or masking it
• the lawyer can no longer plead within the system, but must confront, suspend or expose the system itself

At that point one leaves the model not out of weakness, but out of necessity.

This singularity bears the name of Alfons Heyvaert not as a tribute, but as a structural reminder. Heyvaert brought legal thought back to its bare structure and stopped there to reveal what the law conceals. Not as theory, but as method. Not out of ethics, but out of dissection. His work, including Het personen‑ en familierecht ont(k)leed, shows how legal institutions operate as mechanisms of ordering, exclusion and reproduction.

In this approach, law is not a neutral system or an objective technique. It is a language. An ordering. A mechanism that translates social relations into norms. Marriage is not a romantic institution, but a distribution of rights and securities. Nationality is not identity, but a legal gateway. The legal subject is not a free individual, but a position within a system that decides who counts, who is heard, and who gains access to rights. One who sees like this does not repeat doctrine. He interrupts it.

In our practice, this approach resonates — carefully, never literally — in every case analysis where legal fiction collides with social reality. For example, when a cross‑border cohabitation agreement formally presumes equality but materially structures dependency in care, labour, property and future prospects. In such moments, Heyvaert’s way of thinking taught us that law must not only be applied, but also seen through.

The Penteract model does not claim to hold truth. It provides orientation. But even this model must be subjected to doubt. A model that cannot interrupt itself becomes doctrine, and then becomes part of the problem.

The Heyvaertian singularity reminds us of that. Legal thought begins where the thinking tool dares to lay itself aside in order to listen to what the structure can no longer express.

Professor. Lawyer. Thinker. Teacher.

He was not the one who taught us what to think, but where to begin: with the question, with discomfort, with the dissection of law.

This text was written in respectful remembrance of Professor Alfons Heyvaert. It is based on public sources and personal recollection, without any claim to completeness or exclusivity. Recommended source: Met rede ontleed, de rede ontkleed – Liber Amicorum Alfons Heyvaert, Gent, Mys & Breesch, 2002. 

The content of this page is a general methodological presentation of the internal approach of Peeters Law.

It shall not be interpreted as an offer within the meaning of Article 5.57 of the Belgian Civil Code,

nor as personalised legal advice.

This text does not constitute a declaration of intent to conclude a contract (Article 5.20 C. civ.),

nor an invitation to negotiate as defined in Article 5.15, §2 C. civ..

No contractual or pre-contractual obligation may arise from the publication, consultation, or interpretation of this material.

The theory of legitimate expectations (Article 5.22 C. civ.) does not apply,

insofar as no reasonable reliance can be based on a public communication that is explicitly characterised as non-binding.

A valid agreement with Peeters Law may only arise through a written, clear, and unequivocal expression of will,

confirmed in physical or digital form.

Unilateral communications by email, implicit conduct, or prior invoicing may never be construed as acceptance

or as the establishment of a mandate without a formal agreement.

Peeters Law expressly disclaims any contractual or pre-contractual liability arising from this publication,

except in cases of fraud or proven gross negligence.