Hilary Putnam: From Mathematics to Meaning

Sophi Says Philosobytes Level 3: Discover philosophical principles, some of which are tricky.Introduction

As 20th-century philosophers go, Hilary Putnam holds a special place, not just for the breadth of his work, but for the unique journey of his intellectual evolution. He starts in the realm of mathematics, wades through the murky waters of philosophy of mind, language, and science, and still finds time to profoundly influence theories of truth and realism. This is Putnam, a thinker who wasn’t afraid to challenge his own conclusions, leading to significant shifts in his stance over decades. His intellectual odyssey from a staunch supporter of scientific realism to a more nuanced, pragmatic perspective reads almost like a philosophical thriller. Putnam’s work is a testament to the power of questioning and re-evaluation, making him a figure not just of great academic significance but also a model of intellectual integrity and curiosity. His ability to cross disciplinary borders with ease and his willingness to change his views in light of new arguments and evidence have left an indelible mark on contemporary philosophy. So, buckle up! We’re about to embark on a journey through the complex and compelling landscape of Hilary Putnam’s thought, exploring the depth and diversity of his contributions to modern philosophy.

Image released by Dr. Putnam himself (as copyright holder) under the Creative Commons Attribution ShareAlike 2.5 license, in an email to Wikimedia User:Spangineer.Summary – Philosophies and Ideologies

Hilary Putnam’s philosophical contributions can be categorized into several key areas:

  1. Philosophy of Mathematics: Putnam made significant contributions to the philosophy of mathematics, arguing against traditional Platonism and advocating for a more nuanced understanding of mathematical realism. He explored the implications of mathematical entities’ existence and the nature of mathematical truth.
  2. Philosophy of Mind: Perhaps most famously, Putnam critiqued the prevailing theories of mind, proposing the “functionalist” view. He argued that mental states are defined not by the internal constitution of the individual but by their function in the system of mental states.
  3. Philosophy of Language: In the philosophy of language, Putnam is known for his “meaning just ain’t in the head” stance, which led to the development of the semantic externalism theory. This theory posits that the meanings of words are not determined solely by the mental state of the speaker but also by factors outside the individual.
  4. Philosophy of Science: Putnam’s work in the philosophy of science includes defending scientific realism and later advocating for a form of pragmatic realism. He believed that scientific theories, at their best, aim to describe the world as it truly is, but he also acknowledged the role of human interests and values in shaping scientific inquiry.

These areas, among others, showcase Putnam’s remarkable ability to traverse and contribute to a wide range of philosophical discussions, making him a polymath of philosophy.

Next, we’ll delve deeper into each of these philosophical contributions, starting with his philosophy of mathematics, to provide a clearer understanding of Putnam’s complex and nuanced thought.

Philosophy of Mathematics

Embarking on the journey through Hilary Putnam’s philosophy of mathematics feels akin to exploring a dense, enchanted forest, where each turn unveils a new, unexpected vista. In this realm, Putnam navigated with a rare combination of mathematical rigor and philosophical curiosity, challenging the monolithic structures of mathematical Platonism and venturing into the nuanced landscapes of realism and anti-realism.

At the heart of Putnam’s exploration was the foundational question: In what sense, if any, do mathematical objects exist? Traditional Platonism posits a realm of abstract, immutable mathematical entities, accessible only through the mind’s eye of the mathematician. Putnam, however, was not content with this metaphysical leap. His work in the philosophy of mathematics is a testament to his commitment to a more grounded, albeit no less profound, understanding of mathematical reality.

The Quine-Putnam Indispensability Argument

One of Putnam’s significant contributions to the philosophy of mathematics is his collaboration with Willard Van Orman Quine on the indispensability argument. This argument posits that since mathematical entities are indispensably referenced in our best scientific theories, we must commit to their existence in the same way we commit to the existence of electrons or other theoretical entities in science. Putnam, embracing a form of philosophical naturalism, argued that the empirical success of science indirectly supports the reality of mathematical objects. This stance positioned him as a proponent of mathematical realism, albeit in a form distinct from the traditional Platonist view.

Moving Beyond Platonism

Yet, Putnam’s intellectual journey did not end with the defense of mathematical realism. He was acutely aware of the challenges facing Platonism, particularly the problem of access: how can we, as physical beings, have knowledge of abstract mathematical objects? Putnam’s work in later years showed a shift towards a more nuanced position, incorporating insights from his broader philosophical investigations. He explored various alternatives, including the idea that mathematics is a kind of “make-believe,” akin to the play of fiction, though this does not diminish its objectivity or its indispensability for science.

Putnam’s Pluralism

In his later years, Putnam embraced a form of pluralism in mathematics. This view acknowledges the existence of multiple, equally valid mathematical frameworks and logics, challenging the idea that there is a single, absolute mathematical truth. Putnam argued that different mathematical systems could be applied to understand the world, and the choice between them could be guided by pragmatic considerations rather than an appeal to a metaphysical mathematical reality. This pluralistic turn reflects Putnam’s broader philosophical evolution, highlighting his belief in the importance of practical consequences and the human context of scientific and mathematical inquiry.

The Legacy of Putnam’s Philosophy of Mathematics

Putnam’s philosophy of mathematics is a microcosm of his broader philosophical project: questioning dogmas, exploring new paths, and always remaining open to revision in light of new arguments and evidence. His work challenges us to reconsider the foundations of mathematics, the nature of mathematical truth, and the role of mathematics in our understanding of the world. By blurring the lines between the abstract and the empirical, Putnam invites us into a philosophical landscape where mathematics is not a realm apart but a vital, interconnected part of our quest to understand reality.

Through his explorations, Putnam has not only enriched the philosophy of mathematics but also provided valuable insights into the nature of human knowledge and the complexities of the world we strive to comprehend. His legacy in the philosophy of mathematics is a beacon for those who seek to navigate the intricate relationship between mathematical thought and the fabric of reality.

Philosophy of Mind

In the vibrant tapestry of Hilary Putnam’s philosophical contributions, his work on the philosophy of mind stands out as particularly influential, challenging traditional views and paving new avenues for understanding the mind’s nature. Putnam’s journey through the landscape of the mind was marked by the development of functionalism, a theory that significantly shifted the discourse in philosophy of mind and cognitive science.

The Birth of Functionalism

At a time when the philosophical battleground was dominated by the duel between materialism and dualism, Putnam introduced a third contender: functionalism. This theory proposes that mental states are not defined by their internal constitution—whether they are made of neurons, silicon chips, or cogs and wheels—but by their functional role in the system of the mind. According to functionalism, what makes something a pain, a belief, or a desire is not what it is made of but how it functions within the organism as a whole, in relation to inputs (stimuli from the environment), other mental states, and outputs (behavioral responses).

Functionalism emerged partly in response to the inadequacies of behaviorism, which reduced mental states to mere behavioral outputs, and mind-brain identity theory, which insisted that each mental state was identical to a specific brain state. Putnam argued that neither perspective could adequately account for the complexity and variability of mental phenomena. By focusing on the functional roles of mental states, functionalism offered a more flexible and potentially universal framework for understanding the mind, one that accommodated different types of physical realizations and opened the door to artificial intelligence.

The Computational Model of Mind

Putnam’s functionalist view dovetailed with the computational theory of mind, which posits that mental processes can be understood as computational processes. This analogy between minds and computers—where mental states are akin to the software running on the hardware of the brain—provided a powerful model for exploring cognitive processes and explaining mental phenomena in terms of information processing and symbolic manipulation.

This computational turn in Putnam’s thought was revolutionary, suggesting that understanding the mind’s structure and function could lead to insights into the nature of cognition, consciousness, and even artificial intelligence. However, Putnam was no uncritical advocate of computationalism; he was aware of its limitations and the challenges of translating computational models into a full understanding of the richness of human thought and experience.

Evolving Views and Lasting Impact

Over the years, Putnam’s views on the philosophy of mind, like many of his philosophical positions, underwent significant evolution. He critically re-examined some of the assumptions underlying functionalism and computationalism, especially as debates about the nature of consciousness, the embodiment of cognition, and the limits of artificial intelligence grew more sophisticated.

Despite these revisions, Putnam’s foundational work in the philosophy of mind has had a lasting impact. Functionalism remains a central pillar in contemporary discussions of mind, influencing debates on the mind-body problem, the feasibility of strong AI, and the nature of mental representation. Putnam’s insistence on the importance of the functional roles of mental states continues to inform and inspire philosophical inquiries, cognitive science research, and interdisciplinary studies across the fields of psychology, neuroscience, and computer science.

In navigating the complex terrain of the philosophy of mind, Putnam offered a vision that was both revolutionary and deeply humanistic, acknowledging the complexity of the mind while striving to understand its workings in a rigorous, scientifically informed manner. His contributions serve as a reminder of the power of philosophical inquiry to illuminate the mysteries of human existence and the potential for interdisciplinary approaches to enrich our understanding of ourselves and the world.

Philosophy of Language

 Hilary Putnam’s adventures in the philosophy of language are akin to navigating a labyrinthine library, where each corridor opens onto new perspectives on meaning, reference, and the intricacies of human communication. In this domain, Putnam’s most enduring and transformative contribution is perhaps his theory of semantic externalism, a stance that radically shifted how philosophers and linguists think about the origins and nature of meaning.

Semantic Externalism: A Bold Leap

Putnam’s foray into the philosophy of language led him to challenge the then-prevailing notion that the meanings of words and the mental states of individuals are inseparably linked—that meaning, in essence, “lives” solely in the head. With his famous thought experiment involving “Twin Earth,” Putnam demonstrated that two individuals could be in identical psychological states, yet the words they use might refer to different things based on the external context. For example, the substance referred to as “water” on Earth (H₂O) might have a different chemical composition on Twin Earth, despite the inhabitants of both planets having the same mental content when they use the term “water.”

This groundbreaking idea, that the meaning of words is not determined solely by the mental state of the speaker but also by factors outside the individual, laid the foundation for semantic externalism. It suggests that our linguistic practices and the environment play a crucial role in shaping the meanings of words, thereby broadening the scope of how meaning is understood and how language relates to the world.

The Division of Linguistic Labor

Another significant aspect of Putnam’s philosophy of language is the concept of the division of linguistic labor. Putnam posited that not all members of a linguistic community need to have a thorough understanding of the meanings of all terms they use. Instead, there is a “division of labor,” where specialized knowledge is held by subsets of the community (e.g., scientists, craftsmen), who define the standards for the use of certain terms. This notion further illustrates how meaning is socially constructed and dependent on networks of knowledge and practice beyond the individual.

The Impact on Philosophy and Beyond

Putnam’s ideas in the philosophy of language have far-reaching implications, influencing not just philosophical theories of meaning and reference but also the study of linguistics, cognitive science, and social epistemology. By linking the meaning of words to external reality and the social context, Putnam provided a robust framework for understanding how language captures the world, how individuals communicate about shared and differing experiences, and how knowledge is constructed and transmitted within communities.

Moreover, Putnam’s work challenges us to reconsider the relationship between language and thought, suggesting that understanding the world through language involves a complex interplay between our mental representations and the external, communal, and material conditions in which those representations are formed and used. His theories invite ongoing exploration into the nature of meaning, the dynamics of communication, and the ways in which our languages shape—and are shaped by—the realities we inhabit.

In navigating the shifting sands of the philosophy of language, Hilary Putnam left a legacy of bold questioning and profound insights that continue to influence and inspire. His work invites us to look beyond the confines of our own minds, to the broader social and material contexts that give our words weight and our worlds meaning.

Philosophy of Science

Hilary Putnam’s philosophical quest did not shy away from the intricate and often contentious terrain of the philosophy of science. With a knack for navigating complex ideas and a penchant for challenging conventional wisdom, Putnam made substantial contributions that spurred debates, evolutions, and revolutions in thinking about science, its methods, and its claims to truth.

Realism, Anti-Realism, and Pragmatic Pluralism

A central theme in Putnam’s exploration of the philosophy of science is the debate between realism and anti-realism. Scientific realism posits that the theories and models of science aim to accurately describe the world, including its unobservable aspects. Anti-realism, on the other hand, suggests that scientific theories are mere tools for organizing observations and predicting phenomena, without necessarily providing true descriptions of the world.

Putnam initially championed a robust form of scientific realism, arguing that the success of science in explaining and predicting phenomena provides good reason to believe that scientific theories accurately reflect the underlying structure of the world. He saw scientific theories as striving to map the furniture of the universe, believing in the correspondence between the entities posited by science (like electrons or black holes) and reality.

However, Putnam’s position evolved over time, influenced by his broader philosophical reflections, including his insights into the philosophy of language and mind. He began to question the strict dichotomy between realism and anti-realism, advocating instead for a more nuanced, pragmatic approach. This pragmatic turn led him to propose a form of internal realism, later renamed “pragmatic pluralism,” which posits that truth and reality are not absolute but are constructed within the frameworks of our various scientific and everyday discourses.

The Model-Theoretic Argument

One of Putnam’s most provocative contributions to the philosophy of science is the model-theoretic argument, which challenges the notion of a single, objective reality that science progressively uncovers. This argument suggests that for any given set of empirical data, there can be multiple, equally valid theoretical models that account for that data. Hence, the idea of a one-to-one correspondence between scientific language and the world is untenable. This argument was part of Putnam’s broader critique of metaphysical realism and served to underscore his commitment to a more pragmatic understanding of truth and reference in science.

Legacy and Influence

Putnam’s work in the philosophy of science has had a lasting impact, not only in fostering a more nuanced debate between realism and anti-realism but also in influencing how we understand the nature of scientific inquiry, the role of values in science, and the relationship between scientific theories and the world they seek to describe. His pragmatic pluralism, in particular, offers a compelling framework for understanding the dynamic and context-dependent nature of scientific knowledge, encouraging a more open-minded and flexible approach to scientific theory evaluation and acceptance.

Through his contributions to the philosophy of science, Hilary Putnam invites us to reconsider the aims, methods, and achievements of scientific practice. He challenges us to view science not as a monolithic quest for absolute truths but as a rich tapestry of human endeavor, woven from diverse theoretical perspectives, methodologies, and practical considerations. In doing so, Putnam’s work continues to inspire philosophers, scientists, and anyone intrigued by the quest to understand the complex relationship between our scientific theories and the multifaceted world they aim to capture.


Navigating the philosophical landscapes carved out by Hilary Putnam, we’ve journeyed through the realms of mathematics, mind, language, and science, each path revealing new insights into the nature of reality, truth, and understanding. “Hilary Putnam: From Mathematics to Meaning” has been an odyssey, exploring the evolution of one of the most influential philosophers of the 20th century, whose work spans an astonishing breadth of subjects and disciplines.

Putnam’s intellectual legacy is one of profound curiosity, rigorous thought, and a willingness to challenge and revise his own views. From the foundations of mathematics to the intricacies of language, the complexities of the human mind, and the pursuit of scientific truth, Putnam’s contributions are unified by an overarching commitment to seeking understanding in a complex and often ambiguous world. His work exemplifies the power of philosophical inquiry to illuminate not just the abstract realms of thought but the concrete realities of our lived experience.

Importance and Wider Significance

Putnam’s philosophical explorations have left an indelible mark on numerous fields. In philosophy of mind, his functionalism paved the way for new approaches to understanding consciousness and cognition, influencing both philosophical thought and cognitive science. His work on the philosophy of language, particularly his arguments for semantic externalism, revolutionized understandings of meaning and reference, impacting linguistics, psychology, and artificial intelligence research.

In the philosophy of science, Putnam’s pragmatic pluralism offers a nuanced perspective on the nature of scientific inquiry, challenging researchers and philosophers alike to consider the roles of context, values, and pragmatism in the pursuit of knowledge. Across all these domains, Putnam’s willingness to revise his positions in light of new arguments and evidence serves as a model for intellectual integrity and openness.

A Continuing Journey

As we reflect on Putnam’s contributions, it’s clear that his work is not just a collection of philosophical positions but a call to engage with the world thoughtfully and critically. Putnam’s journey reminds us that philosophy, at its best, is not about providing final answers but about deepening our questions, challenging our assumptions, and exploring the many dimensions of human understanding.

In “Hilary Putnam: From Mathematics to Meaning,” we’ve only scratched the surface of Putnam’s rich philosophical legacy. His work continues to inspire new generations of thinkers to explore the depths of philosophical inquiry, ensuring that Putnam’s journey through the landscapes of thought will continue to resonate and inspire.

Whether you’re a seasoned philosopher or a curious newcomer to the world of philosophical exploration, the works of Hilary Putnam offer a treasure trove of insights, challenges, and opportunities for discovery. As we close this chapter on Putnam’s philosophy, we’re reminded that the journey of understanding is never truly complete. In the spirit of Putnam’s own intellectual odyssey, let us continue to question, explore, and marvel at the complex tapestry of the world around us.

See also: Reductionism and Non-Reductionism

Reading List
  1. “Reason, Truth and History” by Hilary Putnam
  2. “The Collapse of the Fact/Value Dichotomy and Other Essays by Hilary Putnam
  3. “Representation and Reality by Hilary Putnam
  4. “Philosophy of Mathematics: Selected Readings edited by Paul Benacerraf and Hilary Putnam
  5. “Mind, Language and Reality. Philosophical Papers, Volume 2” by Hilary Putnam

Clicking a links from the reading list helps us. As an Amazon Associate we earn from qualifying purchases. The links below will take you to Amazon where, if you make a purchase, we earn a small commission, which helps us out enormously – so thank you if you do.

Online Resources
Share this chat

Leave a Comment