Main Thesis
Eliminating infinities from a theory is often not a “discovery about reality,” but a way of preserving a preferred form of description (closure, finiteness, mathematical smoothness).
1) What Is Called “Ideology” Here
- If infinity is removed in order to preserve the integrity of a model, that is already a normative choice.
- The requirement that “everything must be finite and convergent” is a property not of the world but of the selected system of description.
2) Where Substitution Arises
The implicit rule: “A good theory should not yield infinities.”
The problem is that this is:
– not an observation,
– not an experiment,
– not a measurement,
but a norm imposed on a model. Then, instead of changing the method of distinction, constructions are often added to maintain the former framework.
3) Why This Resembles Ideology
Structurally, all the elements are present:
– foundation: “reality must be smooth and finite”;
– framework of admissibility: infinity = bad, convergence = good;
– defense of the system: infinity is declared a “model error”;
– restoration of integrity: compensating constructions are introduced (renormalization, strings, extra dimensions).
4) An Important Clarification in Favor of Physicists
The practical motive is real:
– with ∞, one cannot obtain a numerical prediction;
– without a number, there is no testability;
– without testability, a theory does not function as an instrument.
Their logic is instrumental: infinity must be removed in order to calculate and compare with experiment.
5) A Step Beyond Instrumental Logic
- Usefulness ≠ truth.
- The criterion of “computational convenience” can itself distort the picture of reality.
6) Through the Lens of “Distinction”
If the method of distinction is primary, infinity is not a “bad result,” but an indicator of the limit of the current form of description.
In other words, it is a boundary of the model, not necessarily a “malfunction of reality.”
7) What “Eliminating Infinity” Then Looks Like
Often it is an attempt to preserve the old system of distinctions rather than acknowledge its limitations.
8) Uncompromising Formulation
Infinities are points of rupture between reality and the chosen form.
Two paths:
1. radically change the form of description;
2. “stitch up” the rupture, preserving the old form.
In modern physics, the second path more often dominates.
9) Anti-Dogmatic Balance
One must not fall into the mirror-image dogma that “infinity = good.”
More precisely:
– neither finiteness nor infinity is, in itself, a criterion of truth;
– these are characteristics of a particular method of description.
10) Conclusion
A strong principle:
if a theory changes not because of new observations about reality,
but in order to preserve its own closure,
it shifts toward ideology.
This applies not only to physics, but also to economics, law, and other systems.
The Next Radical Question
And what if reality is fundamentally under no obligation to be:
– closed,
– finite,
– completely self-consistent within a single universal scheme?
Then the project of a “unified theory of everything” becomes problematic as a universal claim.
