Now, for someone who wants to describe the universe using symbols.

Let's say I describe some phenomena up-to some approximation. I use some symbols to do this. For example consider the ideal gas equation. I have density, pressure and temperature. These are my macroscopic variables. What does density mean: well it means number of particles in a volume. I zoom in, further, a particle is an excitation in a field and so on ... Now, at some point one wonders if the "zooming in" ever ends? Since which each zoom in there seems to be different set of symbols for that description and then one worries about infinite regress.

So far there seems to be 2 obvious options:

  1. There is an infinite regress of symbols.
  2. There is a fundamental description beyond which no more symbols are required.

But I think with the rise of Quantum Field theory there is a third option on the table.

  1. If your theory is renormalizable then, whatever the ultimate description of reality is, it is irrelevant to the phenomena you are describing. A simple example is described here in classical mechanics where the shape of the potential doesn't really matter as long as it is "extremely steep."


What is this third position known as in philosophy? And where can I read more on this?


2 Answers 2


This is more of a meta-physics question than a philosophy question. Regardless I hope to shed some light for the uninitiated. One immediate note is that density is the total mass within a given volume, while the specific definition you use is "number of particles in a volume" which is called the number-density. In PV=nRT, n is the number density, while another common form is PV=N k_b T where N is the total number of atoms. Please see the Wikipedia page for more info.

First of all the Ideal Gas Law can be described many ways. Fundamentally the ideal gas law is a matter of experiment and is an approximation to the actual ways in which real gasses behave. In a simple sentence, it is the limiting behavior that any theory of physics should approach under certain conditions, such as 'normal' densities and pressures.

Secondly, in quantum mechanics, which is the predecessor to quantum field theory and which shares much of the same mathematical structures, particles are automatically expressed as a combination of infinite states. There is much similarity in this to the statement 'an infinite regress of symbols' in that this is literally an infinite linear combination of eigenstates and their associated probability (more accurately complex coefficients) where each state takes a singular symbol and has definite properties such as expected position, momentum, and energy.

There are generalizations that are more broadly applicable, such as the theories of statistical mechanics or N-body models of particle interactions of the same QFT you mention.

There is no theory in which 'symbols' are no longer needed since the symbols themselves are just substitutes for entire volumes of text and needlessly wordy explanation and solution. Further to attempt find a theory without the use of symbols would be to abandon the centuries of mathematical development and would be fruitless. Even if a theory could be reasonably described, any predictions obtained would either be wrong or approximately identical to predictions from symbol containing theories (mathematical theories). Where there is unsettled theory, the world is your oyster. But for that which is very well physically understood what ever theory you make must make approximately identical results.

The best place to begin learning physics is with typical undergraduate books, recommendations for which can be found in abundance with google.

  • 1
    Metaphysics IS part of Philosophy, so the question is in the right place.
    – RodolfoAP
    Jan 19, 2023 at 6:42
  • 1
    I meant more in the sense that I wasn't going to avoid jargon since this question was closer to physics, not that metaphysics isn't a branch of philosophy.
    – Gerald
    Jan 19, 2023 at 12:56

This is not a direct answer, but the question seems viced of certain fallacies. This is a comment intended to clarify the view.

Knowledge is a map of the terrain, not the terrain itself. Knowledge can be described as a system of concepts (system = set of interrelated parts). Concepts do not depend on symbols: the ratio of the radio and the perimeter is the concept, pi is the symbol. Of course that pi becomes a concept, but in order to understand nature, symbols are not required. They are only required for communication (which includes formalization, that is, writing).

So, you can't make a one-to-one association between terrain facts and symbols or concepts. The map (knowledge) is just an abstraction of the terrain.

However, your problems is not the symbols that are associated with physical systems. Of course, if there's no limit on dividing parts into smaller parts (molecules, atoms, quarks...), then, there's no limit for the amount of symbols. Your problem is the content of knowledge, and the association of it with symbols, which is far from being a precise representation of the terrain.

But that's how our mind works: that's called systemic thinking. We don't learn all about any thing. We just make an abstraction, a concept of it. Which can contingently be associated with a symbol. The act of dividing a thing is not necessary. You know what a radio is, how it is used, and that's enough. You don't understand at all the hugely complex dance of electrons that occur inside the circuits when you listen a song on it.

Google for "moon icon". That's a symbol. Look at the moon: that's the object it signals. Now, think on the concepts you relate to the moon. They are far from being a precise knowledge.

Symbols are intended to abstract objects, not make them more complex; symbols don't necessarily depend on other symbols (no need for infinite regress of symbols).

So, the three proposed options are not the problem. The problem is the method of perception of the terrain (we want to describe the full terrain from the top to the smallest possible part? That is simply impossible, you don't need to consider what symbols you need to represent something that you can't represent).

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