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It's Not Your Fault

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tl;dr - this is a discussion of the philosophy of moral responsibility, a half-serious attempt at a mathematical proof for its rejection, and what living morally means to someone who accepts this

In my mathematics and computer science courses years ago, I loved proofs by induction. A proof by induction is a technique to demonstrate that a proposition holds over a large range of cases by examining a much narrower set of cases that simplifies the problem space. It works like this:

First, you prove that the statement is true for a specific situation, the base case. To take a numerical example, let's consider $n = 1$ and prove that our proposition $P$ holds for $P(1)$.

Next, you assume that the statement is true for a generic situation and prove that this guarantees the statement to be true for a future situation, the induction case. To continue our numerical example, assume that the situation is true for $n = k$ and prove that $P(k) \implies P(k + 1)$.

If you can show that the statement is true for $n = 1$, and that if it's true for $n = k$ then it's also true for $n = k + 1$, then you have proven that the statement is true for all integers $\geq 1$.

Why do I tell you this? Well, in recent discussions as part of an anti-racist activism group I participate in, the conversation focused on the difference between "good" and "bad" people, most of which characterized large swaths of the country in an extremely negative light at a spiritual level.

Given my upbringing in the reddest of states by very religious parental figures and my professional path through the Godless, liberal technocratic metropolis that is Silicon Valley, I consider myself fairly practiced at bridging the political divide and shedding light on both perspectives when called upon to do so. In fact, I do not believe even the worst person you can possibly think of who has committed horrific attrocities is "bad" on a spiritual level.

Which finally brings me to my thesis: there is not, nor has there ever been, nor will there ever be, a single "good" or "bad" person on Earth. Allow me an inductive proof to make my case.

Proposition

Throughout an entire person's life, they are not ultimately responsible for who they are, what they think, what they have accomplished, or how they have wronged others. That is to say, each person is the cummulative result of forces 100% outside of their control, and no individual can be reasonably blamed, in a spiritual or cosmic sense, for their actions.

Let $\Omega(t)$ reflect the person you are at time $t$ since conception in femtoseconds, completely encompassing your physical, biological, mental, emotional, and spiritual state.

Let $\Lambda(p)$ reflect the percentage of $p$ for which you are ultimately accountable.

$\forall t \in N, \Lambda(\Omega(t)) = 0$

Proof

The following proof is somewhat hand wavvy from a mathematical perspective and mostly for fun. Hardcore fans of unassailable logic will be disappointed, but please educate me! If you understand my perspective, allow me to 🤓🔫 you into improving this :)

Axioms

These axioms help us limp through some of the non-mathematical aspects of our proof.

$\Lambda(f(0)) \equiv 0$

Our proposition focuses on whether any self-fault can be found and does not care about any other mathematical relationship between component magnitude. As such, we consider the proportion of fault of a constant with no inputs to be 0 by construction.

$\Lambda(f(p, 0)) \equiv \Lambda(f(p))$

Our proposition focuses on whether any self-fault can be found and does not care about any other mathematical relationship between component magnitude. As such, we are not interested in specific constants or transformations, merely whether a component affects $\Lambda(\Omega(t))$ at all.

$\Lambda(f(p, q)) \equiv \Lambda(p) + \Lambda(q)$

Our proposition focuses on whether any self-fault can be found and does not care about any other mathematical relationship between component magnitude. As such, we consider the proportion of fault of a transformation of inputs to be equivalent to any transformation of the proportion of fault for each input, addition chosen for simplicity.

$\forall c \in N, c * \Lambda(p) \equiv \Lambda(p)$

Our proposition focuses on whether any self-fault can be found and does not care about any other mathematical relationship between component magnitude. As such, we consider a constant multiple of the proportion of fault to be equivalent to simply the proportion of fault.

Base Case

By intuition, the first femtosecond of your existence as a distinct entity from another person cannot possibly be your fault yet. That is to say, the circumstances under which sperm and egg joined could not have been influenced by you prior to your existence.

$\Lambda(\Omega(1)) = 0$

Induction Case

In order to prove our proposition, we must prove the following:

$\Lambda(\Omega(t)) = 0 \implies \Lambda(\Omega(t + 1)) = 0$

If the current time is $t$, the person you are going to be in the immediate future ($\Omega(t+\epsilon)$) is a function of...

1. Who you are right now ($\Omega(t)$), your all-encompassing physical, biological, mental, emotional, and spiritual state.
2. Any decisions you make ($\Delta(t)$), your self-directed trajectory on the many possible paths before you.
3. Environmental conditions you're experiencing ($E(t)$), any audio/visual stimuli, physical atoms around you, other people in your viscinity, etc.
4. Additional external influence that is outside of your control ($G(t)$), call it fate, call it random chance, call it God, call it whatever you want but in this dicussion we will refer to it simply as the G-factor. Some belief systems (nomological determinism) may assert that this term is zero, but we have included it here to ensure broader applicability of the proof.

Formally, we can express this concept with the following expression:

$\Omega(t+\epsilon) = f(\Omega(t), \Delta(t), E(t), G(t))$

For simplicity and in recognition of the fact that the human brain cannot operate at a speed faster than a quantum of time (i.e. we are not in a infinitely diminishing series), we can simplify such expressions into the following:

$\Omega(t+1) = f(\Omega(t), \Delta(t), E(t), G(t))$

At this point, we have the beginnings of a inductive definition of the self, and we can examine each of these components individually.

Past Self ($\Omega(t)$)

This component is our inductive assumption, $\Lambda(\Omega(t)) = 0$. Using this knowledge and our two axioms, we can immediately reduce our original postulation into the below:

\begin{align} \Lambda(\Omega(t+1)) &= \Lambda(\Omega(t)) + \Lambda(\Delta(t)) + \Lambda(E(t)) + \Lambda(G(t)) \\ &= 0 + \Lambda(\Delta(t)) + \Lambda(E(t)) + \Lambda(G(t)) \\ &= \Lambda(\Delta(t)) + \Lambda(E(t)) + \Lambda(G(t)) \end{align}

G-Factor ($G(t)$)

By definition, the G-Factor is additional external influence that is outside of your control. Somewhat trivially then...

$\Lambda(G(t)) = 0$

Thus further reducing our original postulation into the below:

\begin{align} \Lambda(\Omega(t+1)) &= \Lambda(\Delta(t)) + \Lambda(E(t)) + \Lambda(G(t)) \\ &= \Lambda(\Delta(t)) + \Lambda(E(t)) + 0 \\ &= \Lambda(\Delta(t)) + \Lambda(E(t)) \end{align}

Decision-Making ($\Delta(t)$)

The decision you make at time $t$ is a function of...

1. The person you are $\Omega(t)$.
2. Environmental conditions $E(t)$.

We can again include the G-factor for good measure if necessary leading to the following formalization:

\begin{align} \Delta(t) &= f(\Omega(t), E(t), G(t)) \\ \Lambda(\Delta(t)) &= \Lambda(\Omega(t)) + \Lambda(E(t)) + \Lambda(G(t)) \\ &= 0 + \Lambda(E(t)) + 0 \\ &= \Lambda(E(t)) \end{align}

Eliminating our prior zero terms further reduces our original postulation into the below:

\begin{align} \Lambda(\Omega(t+1)) &= \Lambda(\Delta(t)) + \Lambda(E(t)) \\ &= \Lambda(E(t)) + \Lambda(E(t)) \\ &= 2 * \Lambda(E(t)) \\ &= \Lambda(E(t)) \end{align}

Environmental Factors ($E(t)$)

The environmental factors you face at time $t$ are a function of...

1. The environmental factors in the immediate past $E(t - 1)$.
2. The decisions you made in the immediate past that changed the environment $\Delta(t - 1)$.
3. The decisions others made in the immediate past that changed the environment $\Pi(t - 1)$.

We can again include the G-factor for good measure if necessary leading to the following formalization:

$E(t) = f(E(t-1), \Delta(t - 1), \Pi(t - 1), G(t - 1))$

Applying our axioms, prior $\Lambda(p)$ determinations, observations that the actions of others have a $\Lambda(\Pi(n)) = 0$, and conversions of recursive definitions to sums, we can conclude that this term is also $0$.

\begin{align} E(t) &= f(E(t-1), \Delta(t - 1), \Pi(t - 1), G(t - 1)) \\ \Lambda(E(t)) &= \Lambda(E(t-1)) + \Lambda(\Delta(t - 1)) + \Lambda(\Pi(t - 1)) + \Lambda(G(t - 1)) \\ &= \sum_{k=1}^{t - 1} \Lambda(\Delta(k)) + \Lambda(\Pi(k)) + \Lambda(G(k)) \\ &= \sum_{k=1}^{t - 1} \Lambda(\Delta(k)) + 0 + 0 \\ &= \sum_{k=1}^{t - 1} \Lambda(\Delta(k)) \\ &= \sum_{k=1}^{t - 1} \Lambda(E(k)) \\ &= \sum_{k=1}^{t - 1} 0 \\ &= 0 \end{align}

Conclusion

By principle of mathematical induction, the statement is true for all time starting with conception.

Intuitive Explanation

This has been all very mathy, but perhaps we can approach this a simpler way in a few specific steps.

1. You started as two cells from two other humans. It is pretty clear none of that was your fault.
2. How your cells divided and multiplied from that moment to the next was dependent on...
1. Your DNA from the previous step (your previous self, which you had no control over).
2. The specific chemical composition surrounding your fetus (your environment, again, no control).
3. Any response the cell itself made in response to stimuli (based only on your previous self, which you had no control over).
4. Fate/random chance/divine intervention (the G-factor, again, no control).
3. In the previous step, there was not any individual autonomy introduced that one could reasonably be held responsible for.
4. This process continues exactly as described, in perpetuity, for the rest of your life, and at no point is unique individual autonomy introduced.

Most people do actually have an intuitive sense of this and apply it in their daily lives, to children. This proof is precisely the idea that "oh they don't know any better, they're just a baby" but extrapolated forward in time. Collectively as a society, we tend to stop thinking this to be a reasonable explanation when humans reach adulthood (and we'll examine why that's still valuable in Incentives). But even if we reach a point where "we should've known better," our capacity to know better or not was not of our own making! In many ways, this says "Everything about you is either nature or nuture, but it doesn't matter which one it is because you weren't responsible for either."

Ramifications

This conclusion is fundamentally at odds with many accepted societal norms in a predominantly metaphysical libertarian legal system. We exhault "good" people while criticizing or even imprisoning "bad" people who "deserve it." It can feel deflating and confusing to accept this as your reality, so where does one go from here? What are one's morally responsibilities as a person who acknowledges that they are not ultimately morally responsible for their actions?

Behavior vs. Person

• Just because there aren't good or bad people doesn't mean there aren't good and bad actions.
• Behaviors and outcomes can and should be labeled as desirable or undesirable for society for the creation of Incentives.

Incentives

• Even if no one is spiritually responsible for their actions, incentives (both rewards and consequences) to influence behavior for the benefit of society as a whole are still incredibly valuable.
• We don't want people going around murdering each other for the pleasure of an ice cream cone.
• In fact, examining our model of the self, the way to affect who people become is by changing their environment, carrots and sticks included. Leverage them wherever possible to maximize the quality of $\Omega(t)$ for all.
• Whenever an argument, social policy, or strategy relies on "self-reliance" or "independence," consider what incentives are in the path of participants and how to shape them in the most effective way.

Compassion

• Suffering at the hands of a negative incentive is never "deserved." It is unfortunate collateral damage in the quest for limiting global suffering, nothing more.
• No one, and we really mean no one, "deserves" suffering, torture, or prison time.
• The next time you catch yourself thinking otherwise, have a bit of compassion for the unfortunate human and set of circumstances that led to this result.

Humility

• Benefiting because of a positive incentive is never truly "earned." It is as random as winning the lottery in the quest for improving global quality of life, nothing more.
• No one "deserves" success just like no one "deserves" punishment.
• Every accomplishment you've ever had was exactly 0% of your own making, so get off your high horse there richy.

Religious Heresy

• You simply can't subscribe to a religious philosophy that espouses eternal rewards or punishments based on actions, thoughts, or birthright while on Earth and a merciful, loving deity.
• If nothing is our fault, being rewarded or punished for it for eternity is a spiteful and cruel policy, regardless of the potential societal benefits.

Enjoy the Show

• The plot of a movie was determined long before you sat down to watch it.
• Every page of every book you've ever read was printed long before you turned it.
• Yet you still find yourself rooting for the hero and invested in the outcome, no?
• Don't you want to see yourself be the hero of your own story even if you're not the author?

Find Solace in Failure

Even if you fail to uphold all of these or struggle to understand this at all, remember, it's not your fault :)