Philosophy is not a theory but an activity. — Ludwig Wittgenstein
In an era where the mechanical mind converges with the human intellect, the shadows of Ludwig Wittgenstein, a colossus in the realm of philosophy, loom large and enigmatic. Considered one of the paramount thinkers of the 20th century, Wittgenstein’s legacy in analytic philosophy is a tapestry of profound complexity and startling simplicity. Most vividly, he is recalled as a luminary in the philosophy of language, where his thoughts, like streams meandering through a vast and intricate landscape, carved new paths and perspectives.
In the embryonic stage of his philosophical journey, encapsulated within the pages of his seminal work, “Tractatus Logico-Philosophicus”, Wittgenstein wove seven foundational propositions. Starting with the first proposition that “the world is everything that is the case” [1], these propositions, like the threads of a grand tapestry, created a framework that sought to unravel the intricate relationship between the world, human thought, and language. In this treatise, he embarked on a quest to dissect the central quandaries of philosophy, a quest that danced at the edges of logic and the nature of representation, a quest that he believed that once solved, would solve all philosophical problems. Wittgenstein posited that our world is mirrored in our thoughts, and these thoughts are akin to pictures of facts. Sentences are there to depict the world in a pictorial way. Thus our understanding of the world is bounded by our language itself. Through meticulous deductions and logical propositions following the analytic tradition of Bertrand Russell, he constructed a philosophical edifice with a singular ambition — to delineate the limits of the world, thought, and language. It was a venture to segregate sense from nonsense, a journey to understand the boundaries of expression. After all, as he profoundly stated, “what can be shown cannot be said”. and furthermore, “whereof one cannot speak, thereof one must be silent” [2].
Yet, the river of Wittgenstein’s thoughts was destined to meander, and in his later years, as reflected in his book “Philosophical Investigations”, he embarked on a new philosophical voyage that challenged the very edifice he had earlier constructed. Abandoning the notion of “words as pictures”, Wittgenstein introduced the concept of “language games”, which he actually did not give an exact definition (not surprising obviously). This concept, as described by the Stanford Encyclopedia of Philosophy, was “made to do work for a more fluid, more diversified, and more activity-oriented perspective on language” [3]. It marked a paradigm shift from a static view of language to one that is dynamic, contextual, and deeply intertwined with human activity. In this period, Wittgenstein’s focus shifted to the pragmatics of language — the idea that “the meaning of a word lies in its use within the language” [4].
Moreover, Wittgenstein’s later work illuminated the purpose of philosophy itself. In “Philosophical Investigations”, he highlighted the therapeutic, non-dogmatic nature of philosophy, essentially guiding philosophers towards a form of therapeutic inquiry. He suggested that the philosopher’s role was not to dictate truths but to arrange “reminders for a particular purpose” [5]. This perspective opened a new dimension in understanding language and its relationship with our thoughts and the world at large.
2.
As we venture deeper into the labyrinth of artificial intelligence (AI), the prescient ideas of Ludwig Wittgenstein, like ancient runes, reveal themselves in unexpected ways. The advent of technologies such as ChatGPT, generative AI, and multimodal large language models (LLMs) marks a quantum leap in humanity’s journey with natural language. These technologies, once the arcane domain of scholars ensconced in academic ivory towers, now permeate the fabric of everyday life. Researchers, data scientists, software engineers, and even laypersons wield these tools, marveling at their capacity to reshape our interaction with the world. As we stand amidst this digital frenzy, the profound insights of Wittgenstein from a bygone century reverberate with renewed significance.
One of Wittgenstein’s most intriguing inquiries was his exploration of the nature of definitions. Particularly in his later works, he sought to discern between an “essential definition” and an “example definition.” The former, a concept deeply rooted in the scientific and mathematical realms, identifies the necessary and sufficient conditions of a defined entity. It is a definition where the intrinsic nature of a thing is captured succinctly, echoing the Socratic quest for understanding in the Platonic dialogues: “What is it that all and only things of that kind have in common, and in virtue of possessing are things of that kind?” [6] This pursuit of essence, of a sine qua non, not only delineates the boundaries of a concept but also reveals its core, its very being.
Conversely, Wittgenstein introduced the concept of “family resemblance,” a more fuzzy form of definition based on giving examples and similarity. It represents an example definition, where the application of a concept is determined by a resemblance to a family of traits rather than a rigid set of necessary and sufficient conditions. This notion is akin to a tapestry, where each thread contributes to the overall pattern without the necessity for every thread to be present. It acknowledges the open-ended, evolving nature of concepts like justice, love, or abstract ideas, which defy confinement within the rigid bounds of ‘if and only if’ statements in mathematics (or “iff”, for brevity in many mathematics texts). In this view, language becomes a living entity, adapting and evolving, mirroring the ever-changing human experience. Wittgenstein, through discussion over the concept of family resemblance, made us ponder if we are really asking about the impossible? Maybe in our human experience, there is far too much innate uncertainty. The problem is not our language, but an intrinsic ambiguity. Our talk should come first; logic second. Yet we are demanding that logic be served first when we make an exercise of trying to “define” something.
In the age of AI, Wittgenstein’s dichotomy between essential and example definitions finds an enthralling parallel. Large language models (LLMs), in their quest to understand and generate human language, grapple with the very issues Wittgenstein pondered. They must navigate the delicate balance between capturing the essence of language — with its rules and structures — and embracing its fluid, contextual nature. The algorithms that power these AI systems are confronted with the inherent ambiguity and variability of human language, a challenge that echoes Wittgenstein’s observation of the precedence of language over logic. This reflection suggests that in our quest for digital intelligence, we may be demanding an algorithmic precision that language, in its organic essence, may not always be able to provide in the first place
It’s fascinating that as we delve further into the intricacies of artificial intelligence, the concept of family resemblance, as envisaged by Wittgenstein, reveals its profound relevance in the most unexpected of places — within the realm of vector databases. This modern technological marvel stands in stark contrast to traditional tabular databases, such as SQL where a user can query using an exact logical statement written in a particular syntax. Vector databases, with their capacity to store and manipulate data in a multi-dimensional vector space, represent a quantum leap in data processing and storage, particularly suited to the complexities of our increasingly multimodal world.
In the rich world of modern data science, both images and natural language texts are transmuted into vectors. These vectors, much like the brushstrokes of an impressionist painting, capture the essence of the data in a form far removed from the rigid structure of tables and rows. This shift from tabular to vector databases is not merely a technical evolution; it is a philosophical one, resonating deeply with Wittgenstein’s notion of family resemblance. For how does one define, in the traditional sense, a particular document or image within a vast corpus of multimodal data? The challenge is akin to describing a single leaf in an endless forest, where we often run out of words trying to describe what a leaf should look like in essence.
Here, the concept of vector similarity emerges as a modern-day embodiment of family resemblance. When tasked with retrieving a specific picture from a database containing millions, we no longer rely on the precise, logical statements akin to SQL queries. Instead, we engage in a search based on a description that resonates with the characteristics of other images in the database, represented as vectors. This method, though lacking the precision of traditional definitions, captures the essence of Wittgenstein’s insight: sometimes, it is the similarity, the shared traits within a family of data, that defines an entity. It is important to admit that it is far easier to define an object in relation to other objects similar to itself. Many times, it is virtually impossible to exhaustively list out all the properties for a precise, mathematical, traditionally meaningful definition or identification.
Moreover, the capabilities of vector databases extend beyond mere storage and retrieval. The ability to perform arithmetic operations directly on the vectors — addition, subtraction, dot product, and more — imbues these databases with a remarkable efficiency and versatility. In fields like machine learning that involves computer vision problems as well as natural language processing (NLP) tasks, where the identification of similar objects or patterns is crucial, vector databases serve as powerful tools. They enable complex operations to be conducted with a swiftness and precision that echo the very principles of family resemblance in the language of vector calculus.
Thus, in the age of AI, as we harness the power of vector databases, we are inadvertently applying Wittgenstein’s philosophical insights to the digital realm unawares. The concept of family resemblance, once a philosophical musing on the nature of language and definitions, now finds practical application in the way we manage and interpret the vast seas of data. In this, Wittgenstein’s legacy endures, not just as a beacon in the world of philosophy, but as a guiding principle in the ever-evolving landscape of artificial intelligence and data science.
3.
As we navigate through the intricate landscape of AI and machine learning, we find that Ludwig Wittgenstein’s insights illuminate yet another crucial aspect: the burgeoning field of explainable AI. In this realm, where the GPT series and other large language models (LLMs) reign with their jaw-dropping capabilities, new inquiries arise, echoing the age-old philosophical quests for understanding and interpretation.
Explainable AI endeavors to demystify the inner workings of models, much like a traditional statistician would interpret a linear regression model. In simpler models, such as a linear regression with a single variable, interpretability is clear-cut — we can quantify the change in the dependent variable with each unit increase in the independent variable. This clarity of cause and effect, this transparency of operation, is the hallmark of traditional statistical models.
However, the byzantine architecture of deep learning models, such as those transformer models, defies such straightforward interpretation. These models, with their complex neural network structures, are often labeled as ‘black-box’ models. In these enigmatic systems, we see only the inputs and outputs, with the intricate mechanics remaining shrouded in mystery, far from the grasp of our understanding that we so effortlessly apply to simpler parametric models such as a linear or a logistic regression model in which model parameters have an intrinsic meaning, many of which can be explained in a causal way under certain circumstances.
It is here, in the dense fog of complexity, that we must recall Wittgenstein’s wisdom. His expansion of the concept of definitions to encompass ‘example definitions’, alongside the more rigorously defined ‘essential definitions’, invites us to rethink our approach to understanding the inner workings of complex models. If we embrace the idea that examples can play a vital role in our comprehension, our perspective widens, allowing a plethora of techniques for interpreting machine learning models to enter the realm of both academic research and practical application.
This philosophical shift is akin to the challenges faced in legal studies when attempting to define abstract concepts, or even concrete concepts like “pornography”. The difficulty lies not in recognizing an example but in crafting a precise definition. Certainly for a judge, it’s very hard to write down a precise definition of a pornography, but if an example were raised, it would be certainly easy to identify what a pornography is and what not. Similarly, in our quest to causally decipher how a machine learning model operates, Wittgenstein’s counsel rings true: “Don’t ask the meaning, ask for the use”. We often seek the comfort of logic first, demanding clarity and precision in explanation, yet in doing so, we may limit the avenues through which we can truly understand these deep learning models. Thus, our logical way of understanding things become a hindrance for our human perception in an overly simplistic way to some extent, blinding us from the true reality and the complexities of an intricate model.
Perhaps, then, we ought to allow these models to demonstrate their capabilities through examples, to reveal their behavior and inner mechanics in a manner more aligned with Wittgenstein’s vision. In this way, we not only broaden our understanding of AI but also honor the intricate relationship between language, logic, and understanding that Wittgenstein so profoundly explored. This approach, one that values utility and example over rigid logic, may well be the key to unlocking the mysteries of these digital intellects, allowing us to traverse the enigmatic landscape of AI with a newfound clarity and appreciation for the subtleties of interpretation.
4.
As we stand at the threshold of an era where artificial intelligence intertwines ever more intricately with the fabric of human existence, the teachings of Ludwig Wittgenstein, that old giant of philosophy, beckon us with renewed urgency. His contributions, a rich set of insights into language, logic, and our perception of the world, cast long shadows across the landscapes of philosophy and technology. In this age of digital proliferation, where the boundaries of what is possible are constantly redefined, we are drawn once more to the timeless wisdom of a historical giant, to rediscover and reinterpret his thoughts in the light of our modern context.
The advancements in AI and technology invite a contemplative return to the philosophical inquiries of the past. It becomes a journey of juxtaposition, where the cutting-edge of scientific endeavor meets the profound depths of philosophical thought. In this convergence, we find ourselves pondering a question of profound significance: How can philosophy, with its rich heritage and deep roots, keep pace with the rapid evolution of science and technology?
Wittgenstein, with his revolutionary ideas on the nature of language and definitions, provides a guiding star in this endeavor. His perspective, one that sees few definitions as precise and essential, challenges our traditional notions of clarity and precision. He suggests that what we often regard as essential definitions might be more suitably expressed as example definitions. In his view, perhaps language is less about the rigidity of logic and more about our perception of objects and facts. It is a tool for us to describe, and moreover, to live. We need language not just for the sake of deduction and induction, but for a type of consensus — a consensus that aids in knowledge discovery and, most importantly, in achieving clarity in a world we cannot always make sense of with our usual sensory perception.
This approach, emphasizing description and consensus over the strict confines of logic, is particularly resonant in the realm of AI. As we strive to understand and harness the capabilities of these digital entities, Wittgenstein’s philosophy invites us to adopt a more fluid, less deterministic view of language and understanding. It prompts us to see AI not just as a triumph of logic and computation but as a complex interplay of perception, description, and interpretation that describe our human life.
In the end, as we stand amidst the marvels and mysteries of this digital age, Wittgenstein’s counsel remains a beacon of humility and wisdom. In the face of all that we cannot explain, all that eludes our grasp in the vast expanse of knowledge, we are reminded of the virtue of silence. It is a silence not born of defeat, but of reverence — a recognition that, in the quest for understanding, there are realms where words fall short, and wonder begins. This, perhaps, is the most enduring lesson we carry forward from Wittgenstein’s legacy: to remain humble in our quest for knowledge, and to embrace the silent awe that comes with standing on the shoulders of giants.
Notes:
[1], [2]: Ludwig Wittgenstein, “Tractatus Logico-Philosophicus”
[3]: https://plato.stanford.edu/entries/wittgenstein/
[4], [5]: Ludwig Wittgenstein, “Philosophical Investigations”
[6]: Plato, “Euthyphro”
