Omnisyndetics — non-essentialist mathematics, formal foundations, and open research

Omnisyndetic Framework

Non-essentialist mathematics · formal foundations · quantitative tests · open archive.

Can non-essentialist ontology meet physics?

Welcome to Omnisyndetics.

This is an open research programme that explores the question, what can be derived by not taking identity as primitive? And how might that commitment affect derivation, how we describe things and the mathematics we assume available.

Relational quantum mechanics has already opened the door. Physical facts are treated as valid in interaction. So, if physical facts are settled through relation, then one is naturally led to ask what settles the identities involved in those facts. What lets something count as one thing, rather than another, before we have already supplied objects, labels, values, and classifications at the base?

Omnisyndetics means, roughly, all-binding. Omni means all. Syndetic means binding or joining. The word is used because the project studies how identity, value, fundamentality, and classification may be bound through relation, comparison, and resolved participation.
Start with the question → Read Volume I → Open OSF →

The first restriction is severe. Identity is not treated as primitive. Objects, values, labels, and classifications are therefore not allowed to sit at the base as already assumed accessible primitives. They have to become available through the derivation.

Let us take the example of baryons.

To take the non-essentialist claim, that identity is not primitive, one has made an ontological argument, and thus from ontology, the only real test is to see if one can reach fundamentality. Not just qualitatively but quantitatively too. Baryons remain among the most well documented, rigid, and yet historically among the hardest to predict of fundamental structures. Each one as an object holds a large amount of structure that would have to be recovered from a relational description alone. They have charge, mass, family placement, spin-partner structure, radius information, and decay ordering. What happens if we do not assume intrinsic masses? That too would be a primitive identity, a fact before relation that determines the organisation of the spectrum. Can the organisation be recovered by something simpler? Something without such input variables? The question may first seem quixotic, but if the commitment to non-essentialism is possible. Then this is a step we must explore. So, if a non-essentialist ontology is to meet physics, it should do more than describe relation in qualitative terms. It should open a quantitative route.

This introduces a hard austerity to the derivations and practices shown here. Any numeric value that cannot be derived from relation itself would therefore count as a primitive identity. It is thus excluded. This is an experiment in method and austerity.

The first commitment

Think of a coin toss.

Before the result is read, heads and tails remain possible. Once heads is read, tails is excluded. The result becomes readable because its counter has been ruled out.

That exclusion is the first commitment.

Here, we call that commitment contrast. Contrast is the least act by which one outcome can stand apart from what would undo it. A claim can settle only where its counter is excluded. True has to be held apart from false. Presence has to be held apart from absence. Identity has to be held apart from what it is not.

How the programme works

How the programme works

What does a station ask?

The work proceeds by stations.

A station is one step in the derivation. The reader stops there and asks the same questions each time. What has become available? What remains unavailable? What follows from the previous step?

The first stations use first-order logic. The purpose is to make the order of dependence explicit. What can be said before identity is resolved? What requires distinction? What requires comparison? What requires a completed return?

About Why Pre-Dynamics? Volume I Glossary
How the programme works

When is geometry allowed?

The continuation is geometric, but the geometry is synthetic and axiomatic.

That means the construction does not begin with coordinates, fitted measurements, physical labels, or supplied values. It begins with declared relations, boundaries, and construction rules.

So a line, an angle, a closure, a displacement, a ratio, or a boundary can be used only when the derivation has made it available.

That is the discipline of the programme.

Axiomatic geometry Synthetic geometry
How the programme works

What does the route test?

So, the route is simple in discipline, even where the derivation becomes technical.

Withhold primitive identity.

Ask what relation permits.

Derive only what the restriction permits.

Then test whether the recovered organisation can meet physics.

Baryon test Calculator OSF Glossary

What follows from the restriction?

  • Test what becomes available.
  • Derive the structure.
  • Calculate its consequences.
  • Then compare the recovered organisation with physics.

What role does QCD keep?

  • QCD remains the dynamical theory of the strong interaction.
  • Omnisyndetics leaves that role intact.

How much baryon organisation can be recovered?

QCD remains the dynamical theory of the strong interaction. Omnisyndetics leaves that role intact. Omnisyndetics does not replace that role. It asks a classificatory question. Before baryons are named, sorted, assigned masses, placed into flavour families, and described dynamically, what organisation is already recoverable from a stricter relational derivation? So the question becomes, how much baryon organisation can be recovered before baryon identities, masses, flavour labels, empirical constants, or fitted sector parameters are allowed to do the determining work? The answer has to be inspected. It is tested through calculators, source tables, inverse recovery, and interval containment. Follow the stations. Check what enters. Check what is derived. See what organisation is recovered.

Open research materials

OSF archive

The public archive.

Open OSF

Project DOI

The project remains open. The first claim is methodological.

Open DOI

GitHub source

The answer has to be inspected. It is tested through calculators, source tables, inverse recovery, and interval containment.

Open GitHub

Research logs

Follow the stations. Check what enters. Check what is derived. See what organisation is recovered.

Open logs

Library

Long-form materials

Across the site, the work can be followed station by station. The opening question. The first-order derivation. The synthetic axiomatic geometry. The calculators. The baryon audit. The public archive.

Open research

Open research

This is a somewhat unusual niche of exploration, and we welcome you to it nevertheless. The route may look strange from the outside. The discipline is still strict.

Across the site, the work can be followed station by station. The opening question. The first-order derivation. The synthetic axiomatic geometry. The calculators. The baryon audit. The public archive.

The project remains open. The first claim is methodological.

Withhold primitive identity.

Derive what the restriction permits.

Then test the recovered structure against physics.

Follow the stations.

Open OSF Open GitHub Research logs

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