“Recovery”: let’s do the math

December 26, 2020
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In this essay I make two claims. My two claims will take the form of slightly changed versions of two borrowed sentences. (I will present the original versions of the two borrowed sentences later in the essay).  I simply took the borrowed sentences and changed a few key words.  In my changed version of each sentence, you will see in italics the words I inserted to replace certain words found in the original sentences.

Here are my two claims:

  1. For recovery advocacy, no consistent system of axioms whose theorems can be listed is capable of proving all truths about recovery.
  2. There will always be statements about natural recovery that are true but that are unprovable within the system. And recovery cannot demonstrate its own consistency.

By extension, then, I state that recovery itself is, in a manner of speaking, “false”, or “unprovable” – but useful anyway.

What is interesting is that the program of 12-step recovery is a total system, not just an “outcome”. 

(By “total system” I mean to highlight at least two things.  First, the 12-step version of recovery concerns the whole matter of one’s alignment to one’s self, others, and the world at levels including behavior, thoughts, values, priorities, and personal development over time.  Secondly, not only is 12-step recovery focused on a wide scope of personal change, but it also provides and encourages development of a social structure within which one can undertake and live out the work itself, and one’s recovery.) 

Criticism from Empiricism

Critics of traditional 12-step recovery criticize it on various grounds. Critics often assert that the most compelling arguments against it are those we find under simple scientific scrutiny.

That criticism is traditional.  For thousands of years in the west, tools of verification have included formal logic, math, and structured observation. Later, the scientific method as we know it arose.

As a process, empiricism clears the air of superstition and false beliefs. Periodically, applying processes of logic, observation, or scientific study exposes some “facts” (that have long functioned as “received knowledge”) as actually nothing more or less than simply false. Examples include setting aside the notion of a flat earth, a solar system with the earth at the center, and so on.

On the tree of science1, the study of social systems is held to be the most spongy and most lacking of rigor. Or so it is claimed. After all, the real science inside the study of social groups is psychology.  And of course, for psychology the more pure real science is biology. If one knows everything about biology, one will already have psychology. And for biology we all know the real science is chemistry. But chemistry is nothing more than applied physics; learn physics and you will have the essence of chemistry. Last and best of all is math itself – the pure content that is the essence of physics and core material of the scientific method. Math is most pure.  Or so it is claimed.

For thousands of years in western philosophy it has been set forth that everything that is true: 1) must not be self-contradictory or internally inconsistent and 2) must be provable and subject to proof.

Certainly, math is best and most pure of all.

Math Is Not the Path

But interestingly, math itself is nothing but a model and under proper scrutiny math collapses in violation of itself and of our hopes.  The quotation that follows expounds that fact and lists as numbers 1 and 2 (I added the numbers themselves for clarity) the two borrowed sentences I used to start this essay.

“Gödel’s incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system capable of modelling basic arithmetic. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert’s program to find a complete and consistent set of axioms for all mathematics is impossible.

The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers.

  1. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system.
  2. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.”2

Math collapses as a coherent system under the scrutiny of logic? Is that not a paradox? I thought the presence of a paradox, as 12-step recovery is well known for, was evidence of either illogical statements or false beliefs.

Return to Recovery

Why denigrate either “recovery” or the working a personal 12-step program based on them not being empirically valid? Besides, are there not “other ways of knowing?” And do we not see even math as a system is itself unprovable and incomplete?

The criticism of recovery and of a personal program in the rooms of 12-step recovery on the grounds of math are both in that sense false and, on arrival, in fact – dead – as statements.

A Unified and Inconsistent Model That Works

But rather than study various possible models of recovery, and compare how they compete on mathematical or empirical grounds, can we not turn the lens of observation onto the individual phenomenology of personal recovery?

Doing so would provide (like math itself) a unified and inconsistent model that works, imperfectly accommodating everything that is, including:

  • Recovery-oriented harm reduction3
  • Serial recovery where use of some substances has ended and use of others has not yet4,5
  • Recovery from one substance (like alcohol) while addiction to another (like cigarettes) continues5
  • Recovery during medication maintenance6
  • Recovery starting even at the peak of severity of illness7
  • Abstinence-oriented lifelong 12-step program recovery8
  • Recovery continuing after dropping out of support9,10,11
  • Being in recovery when you say you’re in recovery

A Final Question

Why criticize individuals and individual differences using incoherent models like math to do so, when our whole system is necessarily inconsistent? 

Is it not the case that “one must cultivate one’s own garden?”12,13


1Branches of science

2Incompleteness theorems

3Recovery-oriented harm reduction

4White, W., & Kurtz, E. (2006). The Varieties of Recovery Experience. International Journal of Self Help and Self Care. 3(1-2), 21-61.

5Recovery definition – conceptual boundaries

6White, W., & Coon, B. (2003). Methadone and the Anti-medication Bias in Addiction Treatment. Counselor, 4(5), 58- 63.

7Jellinek, E.M.  (1952).  Phases of Alcohol Addiction.  Quarterly Journal of Studies on Alcohol.  13(4): 673–684.

8 Narcotics Anonymous (2012).  Living Clean: The Journey Continues. Narcotics Anonymous World Services, Inc. 

9White, W. (2016). Enhancing Long-Term Addiction Recovery Outcomes: An interview with Dr. Michael Dennis.

10Disengaged styles of recovery

11Kelly, J. F., Bergman, B., Hoeppner, B. B., Vilsaint, C., & White, W. L. (2017). Prevalence and Pathways of Recovery from Drug and Alcohol Problems in the United States Population: Implications for practice, research, and policy. Drug and Alcohol Dependence, 181, 162–169.


13Why Voltaire Said: You Must Cultivate Your Own Garden


The author thanks Jason Schwartz for comments on a previous version of this writing.

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