This Thanksgiving, I find myself reflecting with gratitude on the education I have received. It’s this education that has provided me with a unique lens through which to view and comprehend the world, equipping me with timeless knowledge that enables me to connect the dots. In this spirit of inquiry, I aim to discuss various aspects of the recent developments at OpenAI.

Unfolding Drama

1. Discussion at APEC CEO Summit: Sam Altman, alongside rivals from Google and Meta Platforms, participated in a panel discussion about the future of AI at the APEC CEO Summit in San Francisco.
2. Internal Concerns at OpenAI: Tensions were growing within OpenAI due to Altman’s approach to safety, commercialization, and his investments in other AI companies.
3. Sudden Board Meeting and Firing: Shortly after the APEC panel, Altman was invited to a surprise video meeting by Ilya Sutskever, where he was informed of his firing by the board. The board constituted: {Helen, Adam, Tasha, Sam, Greg}
4. Public Announcement and Leadership Changes: OpenAI released a statement announcing Altman’s removal, citing issues with his candidness. Mira Murati was appointed as interim CEO.
5. Reaction from Microsoft and Investors: Microsoft, a major investor in OpenAI, and other leaders in the tech industry were caught off guard by the news.
6. Employee and Investor Backlash: OpenAI employees and external supporters expressed shock and disapproval of the board’s decision, leading to resignations and public statements of support for Altman.
7. Attempts to Stabilize the Company: OpenAI’s senior leadership attempted to reassure employees and stakeholders of the company’s stability.
8. Microsoft’s Offer to Altman and Brockman: On Monday, amid the ongoing turmoil at OpenAI and negotiations for Sam Altman’s return, Microsoft CEO Satya Nadella announced that Altman and Greg Brockman would join Microsoft to lead a new advanced AI research team. This announcement indicated that regardless of whether Altman and Brockman returned to their roles at OpenAI, they had the option to take on significant positions at Microsoft, reflecting the tech giant’s confidence in their leadership and expertise in AI.
9. Negotiations for Altman’s Return: Amidst widespread support for Altman, discussions began about the possibility of his return. Major investors and Microsoft played key roles in these negotiations.
10. Board Reorganization: Talks focused on reorganizing the board as a condition for Altman’s return.
11. Employee Ultimatum: Over 700 OpenAI employees signed an open letter threatening to resign unless the board resigned and reinstated Altman.
12. Altman’s Reinstatement: Following intense negotiations and internal pressure, an agreement was reached for Altman to return as CEO of OpenAI. The board was restructured, with Bret Taylor as the new chair.
13. Celebration and Return to Normalcy: Upon Altman’s reinstatement, employees gathered to celebrate, signaling a return to stability and normal operations at OpenAI but with a different set of leaders on the board {Brad, Larry, Adam}. Sam not on the board upon return

OpenAI Entity Structure

While the aforementioned observations detail the events of the past week, they are underpinned by a foundational structure that governs the actions of the various stakeholders involved. Presented here is an analysis of OpenAI’s organizational framework, which, while unconventional, operates entirely within legal parameters.

1. Board of Directors: This group is responsible for making the high-level decisions that guide the nonprofit arm of OpenAI. They have the authority to hire and fire executives, like the CEO, and set the organization’s strategic direction.
2. OpenAI, Inc. (OpenAI Nonprofit): This is the nonprofit entity that operates under section 501(c)(3) of the U.S. tax code. Its goal is to promote and develop friendly AI in a way that benefits humanity as a whole, rather than serving the financial interest of its owners.
3. OpenAI GP LLC: This is the general partnership entity that likely manages the OpenAI Limited Partnership (LP). The GP is responsible for the day-to-day operations and investment decisions of the LP.
4. Holding Company for OpenAI Nonprofit + employees + investors: This entity is a holding company which means it holds the assets (ownership stakes) of other companies. It is owned by the OpenAI nonprofit, employees, and other investors. This is a structure often used to consolidate control over multiple entities and align the interests of various stakeholders.
5. OpenAI Global, LLC (capped profit company): This is the for-profit arm of OpenAI that operates with a “capped profit” structure, meaning there’s a limit to the financial profits investors can receive. Its aim is to fund the mission of the nonprofit through profitable ventures while limiting the influence of profit-maximizing motives.
6. Microsoft: This reflects a significant investment in, and partnership with, OpenAI, providing financial support and potentially influencing its strategic direction.
7. Employees & other investors: These are individuals who have invested in the holding company and may have equity stakes in the success of OpenAI. Their role is typically to contribute to the company’s operations, and they have a vested interest in its success.

Each of these entities in turn could have their own charters, bylaws and operating agreements, which define at some level of abstraction how the handshakes between themselves and other external entities happen.

Formal and Informal Systems

A formal system in the context of mathematics, logic, and computer science, is a set of rules and symbols used to construct a logical framework. The key characteristics of a formal system include:

• Alphabet: A finite set of symbols from which strings (sequences of symbols) can be formed.
• Axioms: A set of initial expressions or statements assumed to be true within the system.
• Rules of Inference: Precise, well-defined rules that specify how to derive new expressions or statements (theorems) from existing ones.
• Syntax: The rules that govern the formation of valid strings of symbols within the system.
• Semantics: The meaning or interpretation of the strings and symbols within the system.

In a formal system, every proof or derivation is a finite sequence of steps, each of which applies a rule of inference to axioms or previously derived theorems/lemma to produce new theorems. These systems form the basis for mathematical logic and theoretical computer science, enabling rigorous and unambiguous reasoning about mathematical and logical propositions. The “axioms” lay the foundational rules and principles from which the entire structure logically follows. They are considered the undisputed truths within the system, intended to guide the interpretation and implementation of the system’s more detailed rules and provisions. Once we have axioms, there exist rules of inference. They form the backbone of deductive reasoning, providing the means to infer new truths from established ones.

1. Modus Ponens: If ‘P implies Q’ (P → Q) and ‘P’ is true, then ‘Q’ must be true.
2. Modus Tollens: If ‘P implies Q’ (P → Q) and ‘Q’ is false, then ‘P’ must also be false.
3. Chain Rule: If ‘P implies Q’ (P → Q) and ‘Q implies R’ (Q → R), then ‘P implies R’ (P → R).
4. Universal Generalization: If a statement is true for all instances that have been observed, it can be generalized to all instances (within the bounds of the logical system).
5. Existential Instantiation: If it is known that ‘there exists an x such that P(x) is true’, then we can infer that ‘P(a)’ is true for some specific instance ‘a’.
6. and few others

While the legal entities are not formal systems in a theoretical sense, they do operate within a framework of laws and regulations that define their creation, governance, operation, and dissolution. In the case of an entity structure like the one used by OpenAI, the “axioms” would be the fundamental agreements and legal structures that define the organization:

1. Corporate Charter: The formal document that establishes a corporation’s existence.
2. Bylaws: The rules governing the operation of the corporation.
3. Operating Agreements: For LLCs, this document outlines the financial and functional decisions of the business, including rules, regulations, and provisions.
4. Partnership Agreements: Documents that set forth the terms of the partnership, such as profit sharing, decision-making processes, and dissolution terms.
5. Investment Agreements: These dictate the terms under which investors contribute to the company and what they receive in return, such as equity shares.
6. Mission Statement: While not a legal document, this is a declaration of the organization’s core purpose and focus, which influences all other agreements and actions.

In both cases, However, just as Gödel identified potential inconsistencies in mathematical systems, one could, in theory, scrutinize these legal and organizational axioms for logical consistency and coherence with their applied outcomes.

Gödel’s Work

Gödel’s work showed that there are intrinsic limitations to what can be known or proven within mathematical systems, highlighting the inherent complexities and mysteries in the foundations of mathematics. The following are his theorems

1. First Incompleteness Theorem: In any consistent, formal axiomatic system that is strong enough to include arithmetic, there exist statements that can be neither proven nor disproven within the system. In other words, there will always be undecidable statements or propositions within such systems.
2. Second Incompleteness Theorem: No consistent formal axiomatic system can prove its own consistency. This implies that if a system is consistent, it cannot be used to prove that it is free from contradictions or inconsistencies.

The story of Gödel’s Citizenship

Kurt Gödel purportedly discovered an inconsistency in the U.S. Constitution occurred when Gödel was preparing for his U.S. citizenship exam. Gödel, an Austrian-born logician and mathematician who had fled Europe during World War II, had settled in Princeton, New Jersey, and was applying for naturalization. His profound understanding of logic and systems naturally led him to scrutinize the principles of the U.S. Constitution while studying for his citizenship test.

According to accounts from his colleagues, such as the mathematician Oskar Morgenstern who accompanied Gödel to his citizenship hearing, Gödel mentioned to Morgenstern that while studying the Constitution, he had found a logical contradiction that could potentially allow a dictatorship to emerge within the legal framework of the Constitution.

On the day of the examination, Morgenstern and Albert Einstein, who was also present, feared Gödel might actually bring up his discovery during the citizenship exam. The story goes that during the hearing, the judge asked Gödel if he thought a dictatorship like the one in Germany could happen in the U.S., and Gödel started to explain his discovery of a loophole that could allow for such an event. However, the judge, noticing where the conversation was heading and not wanting to delve into theoretical discussions, deftly interrupted Gödel and moved the conversation along, averting any detailed exposition on the matter.

In the context of Gödel’s work and his views on the U.S. Constitution, “axioms” refer to:

1. The Preamble: This sets the stage for the Constitution’s purpose and introduces the guiding principles of justice, peace, defense, welfare, liberty, and prosperity.
2. The Articles: These establish the structure of the federal government, its powers, and the relationship between the states and the federal entity.
3. The Amendments: Including the Bill of Rights and subsequent amendments, these are the changes and clarifications to the Constitution that have been ratified over time.
4. The Federal Structure: The division of power between the executive, legislative, and judicial branches, known as the system of checks and balances.
5. Rule of Law: The principle that the law applies to everyone, including those who govern.
6. Popular Sovereignty: The idea that the authority of the government is created and sustained by the consent of its people.

In the context of a legal framework like the U.S. Constitution, the “rules of inference” are not as formally defined as in mathematical logic, but the reasoning process is somewhat analogous. Legal rules of inference include principles of statutory interpretation, precedent (stare decisis), and the application of legal doctrines that guide how the Constitution and laws are to be understood and applied. This involves:

• Literal Rule: Taking the plain, ordinary meaning of the text as the basis for interpretation.
• Golden Rule: Modifying the literal meaning to avoid an absurd result.
• Mischief Rule: Considering what “mischief” the statute was intended to prevent.
• Precedent and Stare Decisis: Following previous court decisions to ensure consistency.
• Proportionality: Ensuring that legal consequences are proportionate to the relevant actions or issues.

In conclusion, while entities like OpenAI and constitutions like that of the United States are not formal systems in the mathematical sense, the principles of axiomatic thinking are still deeply relevant to them. Gödel’s Incompleteness Theorems, though primarily concerned with mathematical logic, offer a potent analogy for understanding these structures. They suggest that any system, no matter how robustly designed, might harbor inherent limitations or unexpected pathways. Gödel’s analysis of the U.S. Constitution, where he speculated about a loophole that could theoretically lead to a dictatorship, is a case in point. It illustrates how even the most meticulously crafted systems can contain unforeseen consequences or vulnerabilities.

In the context of OpenAI, particularly with the advent of advanced AI models like GPT-4 and the anticipated GPT-5, this analogy takes a significance. These AI systems, embedded within complex organizational and legal structures, have far-reaching impacts on humanity. Their governance and decision-making processes, though not strictly axiomatic systems, are subject to similar principles of foundational assumptions, rule-based inferences, and the potential for unexpected outcomes.

Therefore, it is necessary to engage in careful deliberation and debate regarding the decentralized (or less centralized) governance and decision-making surrounding entities like OpenAI. This discussion is not just a matter of legal and organizational necessity but also a fundamental requirement to anticipate, understand, and mitigate the profound implications these powerful AI systems have on society. As we embark on this era of unprecedented technological advancement, we must apply the lessons from axiomatic systems and Gödel’s insights to ensure that these AI entities operate in a manner that is ethical, transparent, and ultimately beneficial to all of humanity.