Common Sense and Communication

From The Philosopher, Volume CXIII No. 1 Spring 2025

 

Wittgenstein with his friend and mentor Eccles at the Kite-Flying Station in Glossop

Common Sense and Communication: The Legacy of Wittgenstein’s Last Philosophical Puzzle

By Elizabeth Rohwer

Philosophy’s enfant terrible, Ludwig Wittgenstein, left us terse remarks scattered with philosophical thought-experiments, epigrams and inscrutable self-dialogues in his unpublished notes. During his lifetime, he completed only one book, the Tractatus Logico- Philosophicus, which was so unconventional in style and obscure in its content that even his mentors Gottlob Frege and Bertrand Russell could not comprehend it. The young Wittgenstein even famously told his Cambridge examiner, G. E. Moore, with a pat on his shoulder, “Don’t worry, I know, you will never understand it”. Nevertheless, Moore stated in his report: “It is my personal opinion that Mr. Wittgenstein’s thesis is a work of a genius,” and recommended that its author be awarded the Cambridge degree of Doctor of Philosophy.

In the years that followed, Wittgenstein became one of the most influential and commented-upon philosophers, yet the Tractatus, his only book, still lacks a coherent and generally agreed-upon interpretation.

One of the reasons the text is hard to comprehend is that Wittgenstein employs a plethora of technical terms, mathematical formulas, tables, and graphs to present the book’s main point:

“the theory of what can be expressed by propositions — i.e., by language — (and, which comes to the same, what can be thought)...”

(Letter to Russell, August 1919. The German term Wittgenstein uses, rendered here as “expressed”, is gesagt.)

It has often been overlooked that Wittgenstein’s educational background equipped him with a wider range of analytical tools than those available to academic philosophers, many of which he creatively used in his early philosophy.

When he began writing his book, before the outbreak of the First World War, Wittgenstein was only twenty-two years old, trained as an aeronautical engineer. The root of the Tractatus’ unintelligibility is that it relies on a mathematical theory of probability, a theory central to its understanding, that would not fully mature for another century. The correct interpretation of probabilities had grown out of the progress in physics during the latter half of the 19th century, spurred by Ludwig Boltzmann’s new and poorly understood Maximum Entropy Law. As an engineer who himself had designed and patented an advanced turbo-propeller, Wittgenstein would have been familiar with the laws of thermodynamics that were the focus of Boltzmann’s research.

So what are these, and how do they link to more conventional philosophy? Today, we know that the Second Law of Thermodynamics is governed by the same probabilistic principle that surprisingly governs the transfer of information between a speaker and a listener, and also rules the seemingly intelligent logical reasoning of modern Artificial Intelligence (AI) applications. My own research into Wittgenstein leads me towards an understanding of how Boltzmann’s Maximum Entropy Law operates in the context of common-sense logic and language communications that seems to dissolve many, if not all, of Wittgenstein’s philosophical puzzles. Furthermore, examination of the role of entropy in this context is crucial for grasping the consistency of his entire body of work and understanding his thinking.

Wittgenstein’s reflections over the last year and a half of his life are a case in point. On April 27, 1951, just two days before his death from cancer, he was mulling over one of his hallmark philosophical puzzles that showcases the challenges of language communication:

Remark 671. I fly from here to a part of the world where the people have only indefinite information, or none at all, about the possibility of flying. I tell them I have just flown there from.... They ask me if I might be mistaken. They have obviously a false impression of how the thing happens.

Wittgenstein’s private notes from this period were edited and thematically organized by G. E. M. Anscombe and G.H.von Wright in 1969 in a book entitled On Certainty. It explores a topic that was originally raised 25 years earlier by G.E. Moore, who defended the notion of common sense. Wittgenstein re-opens the discussion by examining various aspects of what Moore calls ‘the Airplane Traveller’s Puzzle’, asking how a “reasonable man” endowed with common-sense could be certain about his experiences in the world.

Today, Wittgenstein’s “reasonable man” is an AI model of a linguistic agent able to reason with propositions and communicate through grammatically ordered sequences of words. Today, our matured understanding of probabilities aligns both with the transfer of information between a source (the airplane traveller) and a receiver (the locals), and with the laws of logic underpinning common-sense reasoning (in other words, how the locals learn to extend their incomplete information about the world).

And all these modern achievements result from Boltzmann’s trailblazing use of probabilities and the paradigm shift in physics it created a century and a half ago. The predominant worldview today is probabilistic, recognising that reality is plagued by uncertainty and embracing the role of the linguistic agent in shaping it. By acknowledging the power of language to shape our thoughts, beliefs, and actions, we actively participate in constructing our own realities and influencing the collective understanding of the world. This perspective highlights the dynamic and interactive nature of language in shaping not only individual experiences but also broader societal constructs and paradigms.

Amongst philosophers, only Wittgenstein had the necessary technical background to grasp the universality of Boltzmann’s statistical method and re-apply it to the analysis of logic and language in order to build a theory explaining how a thought becomes a proposition. Wittgenstein was not someone to sprinkle his writings with sources or acknowledgements, Yet, writing years later, he acknowledged the physicist’s influence on his philosophy:

I don't believe I have ever invented a line of thinking. I have always taken one over from someone else. I have simply straight away seized on it with enthusiasm for my work of clarification. That is how Boltzmann, Hertz, Schopenhauer, Frege, Russell, Kraus, Loos, Weininger, Spengler, Straffa have influenced me. .... What I invent are new similes.

(Culture and Value, 19, Wittgenstein’s emphasis.)

To elucidate his propositional theory in the Tractatus, Wittgenstein creatively borrowed Boltzmann’s idea that the intangible gas molecules in a container are like the concealed thoughts in our heads, and that the way we communicate our thoughts to each other with strings of words is not always reliable but subject to chance variations.

For example, in a situation where two individuals are discussing a complex philosophical concept, such as the nature of reality, one person may use a specific set of words to convey their thoughts on the subject. However, the other person may interpret those words differently based on their own understanding and experiences. This interpretation can lead to miscommunication or misunderstandings, highlighting the idea that the transmission of thoughts through language is not always precise and can be subject to probabilistic fluctuations.

Wittgenstein’s adoption of the probabilistic worldview ahead of his time is evident from his dedication of the longest section of the Tractatus—section five—to the role of probability in language and logic, a fact that has been largely overlooked. However, this oversight is not surprising as it took physicists over a century to recognize Boltzmann's Maximum Entropy Law as one of the foundational principles of physics.

It wasn’t until 1948, that Claude Shannon discovered that the same law applies to the exchange of information as to that of energy. In the early 21st century, E.T. Jaynes, considered one of the fathers of modern AI, proved that the law also applies to human common-sense reasoning and finalized the development of modern probability theory, a nascent version of which is present in the Tractatus.

Perhaps the greatest controversy surrounding Wittgenstein’s youthful book arises from its relatively obscure mathematical insight that the deterministic laws of classical mechanics, proposed by Newton, can be viewed as special cases of Boltzmann’s Maximum Entropy Principle. This connection sheds light on the fundamental relationship between determinism and statistical mechanics. For example, consider the case of a gas in a container where the behavior of individual gas molecules follows deterministic laws, but collectively, the system obeys statistical principles of entropy maximization as described by Boltzmann's principle. There is a theoretical link between determinism and statistical principles, the latter being more general in scope but lacking in certainty.

By contrast, Aristotelian deductive reasoning offers iron-clad certainty but only within a limited analytical framework, especially when compared to the more general statistical reasoning approach that takes into account the common sense of linguistic agents. This was a topic that Wittgenstein explored in his later years, and his philosophy gains in lucidity when seen as a harbinger of the modern perspective that embraces uncertainty and plausible reasoning.

It is worth noting that interpreting the Tractatus from a probabilistic standpoint would have been impossible just a few decades ago. The emergence of modern AI tools (machine learning, deep learning neural networks, large language models) built upon the foundational discoveries of Shannon and Jaynes makes the project of reevaluating Wittgenstein’s philosophy, starting with revisiting the Tractatus, feasible.

In a letter to his prospective publisher, Ludwig von Ficker, in the autumn of 1919, Wittgenstein described his book as “essentially the presentation of a system”. In the context of the 21st century, its interpretation portrays a system of language communication that is driven by a theory on how the intangible thoughts of intelligent linguistic agents are transformed into sequences of words, serving as vehicles for the exchange of information.

Moreover, Wittgenstein himself has left us another and more revealing clue concerning how to revisit the Tractatus. His solution to the Airplane Traveller’s conundrum — how would “people that have only indefinite information, or none at all, about the possibility of flying” extend the concept to include ‘airplanes flying?’— is: “Describe the actual procedure to them.” Can we not follow the same recipe to improve our understanding of the Tractatus – by describing the actual process of language communication?

And perhaps today, it is not human reasoning but artificial intelligence that has mastered the process and given us the tools to describe it.

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 About the author:

Elizabeth Rohwer was born in Bulgaria, completed part of her Ph.D. in the former Soviet Union, undertook research at the Centre for Speech Technology at the University of Edinburgh in the UK, and served for numerous years as a consultant for telecommunications companies in the US, implementing speech applications. She is keen on elucidating the coherence of the entire body of Wittgenstein’s work, leveraging her professional background as an engineer, and specialist in speech processing.

Address for correspondence: 

Elizabeth Rohwer, erohwer@san.rr.com