Rethinking Logic: A New System of Logic called Inferentialism

In the hushed moments before sunrise at Fogg Dam, where the Northern Territory's ancient monsoon forest meets the Adelaide River floodplain, time seems to pause in the heavy tropical air. This wetland is said to have the highest predator-prey biomass of any ecosystem on Earth, surpassing even Africa's legendary Serengeti Plain. The morning mist clings to your skin, carrying the complex aromatics of the landscape: sweet decay from fallen pandanus fronds, the medicinal tang of paperbarks, and the rich organic perfume of water-soaked earth that speaks to thousands of years of seasonal cycles.

As first light seeps through the sky, the dam's true character reveals itself not as a failed rice project from the 1950s, but as a masterpiece of ecological interconnection. Here, spanning 1,854 hectares, six distinct habitats weave together in an intricate tapestry: monsoon forest transitions to eucalypt woodland, melaleuca groves give way to open scrubland, and finally the floodplain stretches toward open water dotted with lotus lilies and grass islands.

Each Pandanus tree stands as a testament to the web of relationships that defines this place. Their silvery roots probe deep into the black soil, forming underground networks with mycorrhizal fungi that pulse with chemical messages, connecting seemingly separate organisms into one breathing system. This hidden collaboration mirrors the visible interconnection above: rainbow pittas dart through the understory of Workshop Jungle, where they maintain their largest known breeding population, while pied kookaburras and little egrets wade through the shallows.

As dawn properly breaks, the reserve's 233 recorded bird species begin their morning chorus, a symphony that has earned Fogg Dam its reputation as one of Australia's top ten birdwatching sites. But the interconnections run deeper than mere numbers. This is Wulna country, where Traditional Owners have maintained cultural and spiritual connections for countless generations. Their Long-necked turtle-dreaming stories and sacred sites add layers of meaning to every aspect of the landscape.

The water itself tells a story of connection. What began as an irrigation dam for the ambitious Humpty Doo Rice Project has transformed into a crucial freshwater wetland that supports one of nature's most remarkable predator-prey relationships. Here, water pythons - known in Aboriginal mythology as the Rainbow Serpent - engage in the world's only known seasonal migration of its kind, following the movements of dusky rats across the floodplain as the monsoon rains dictate their ancient dance.

From the elevated vantage point of the dam wall, the landscape unfolds like a living manuscript. Lotus lilies spread their leaves across the water's surface, creating platforms for Jesus birds to tiptoe across. In the distance, a jabiru stalks through the shallows with measured grace, its presence part of an unbroken chain of ecological relationships that stretches back through time.

This complex web of life faces modern challenges: invasive weeds like Olive hymenachne threaten to choke the open water, while cane toads have impacted populations of northern quolls and goannas. Yet the reserve persists, protected by a partnership between Wulna Traditional Owners and the Parks & Wildlife Commission, supported by dedicated researchers who have made groundbreaking discoveries about everything from snake behavior to lightning patterns in tropical storms.

Rethinking Frameworks

As we step back from the living laboratory of Fogg Dam, where every element interacts in an intricate dance of mutual dependence, we find ourselves confronting a fundamental question: How do we make sense of such complex, interconnected systems? The web of relationships we observe in nature - from the mycorrhizal networks beneath our feet to the seasonal ballet of pythons and rats - challenges our traditional ways of organizing knowledge and understanding causality.

Just as the boundaries between species blur in Fogg Dam's ecosystem, the rigid structures of human logic and language are beginning to show their limitations. The traditional frameworks we've used to categorise and understand the world - much like the failed rice project that preceded Fogg Dam's current incarnation - sometimes require radical reimagining. This brings us to a fascinating parallel development in the realm of human thought, where a global team of researchers has recently proposed a new system of logic called "inferentialism."

This new logical framework suggests that understanding comes not from rigid categorisation, but from recognising the dynamic relationships between elements. Just as the dam's ecosystem demonstrates that no single species exists in isolation, inferentialism proposes that meaning and reasoning emerge from the connections between ideas rather than from fixed definitions - a perspective that might help us better comprehend complex systems like the one we've just witnessed in Australia's Northern Territory.

Thom Markham, Ph.D. 's recommendation led me to a fascinating article in The Conversation UK about inferentialism, a novel approach to logic. The article suggests this system could revolutionise our understanding of both critical thinking and artificial intelligence. Its researchers argue that as traditional linguistic frameworks begin to falter, we have an opportunity to reconstruct our fundamental grasp of reasoning and meaning-making.

First of all, what is inferentialism?

I had a look at Robert Brandom's book for this answer. It's a dense and challenging read, but its core ideas are elegantly simple. Brandom rejects traditional representationalist accounts of meaning and understanding, instead advocating for inferentialism.

Inferentialism Explained

Brandom explains inferentialism as follows: "The idea of privileging inference over reference in the order of semantic explanation" is introduced early in the book. Instead of viewing meaning as primarily a relation between words and the things they represent (reference), Brandom argues that meaning is primarily constituted by the role concepts play in reasoning and inference. This means understanding a concept involves understanding its inferential relations—how it can be used as a premise or conclusion in arguments. As he states, "The overall topic is the nature of the conceptual as such." It's not about what concepts refer to but what one does with them in the inferential practices of a community.

He further elaborates on the implications of this in the book: "The view expounded in these pages is a kind of conceptual pragmatism (broadly, a form of functionalism) in this sense. It offers an account of knowing (or believing, or saying) that such and such is the case in terms of knowing how (being able) to do something." This pragmatist approach highlights the social nature of meaning—that to grasp a concept is to understand its use within a community of speakers who engage in reasoned discourse.

TL;DR

Brandom develops his inferentialist position through detailed engagement with a number of philosophical issues, including:

The Nature of Conceptual Content: He argues that conceptual content is not a matter of representing facts in the world, but of participating in inferential practices.

The Expressive Role of Language: He emphasises that the meaning of expressions is not just what they represent, but also what they express—namely, commitments and entitlements.

The Social Dimension of Meaning: Meaning is not an individual possession but arises from the shared practices of a community.

The Relationship Between Mind and Language: Our cognitive capacities are inextricably linked to the public, social practices of language use.

Practical Reasoning: Brandom uses inferentialism to shed light on practical reasoning and its relationship to action.

Overall Significance:

Articulating Reasons is a challenging but ultimately rewarding exploration of the nature of meaning, understanding, and rationality. By shifting the focus from representation to inference, Brandom offers a powerful alternative to traditional approaches and makes significant contributions to the philosophy of language, mind, and action. It's a cornerstone of contemporary pragmatism and continues to be widely discussed and debated within the philosophical community.

Bridging Traditional and Modern Views of Logical Understanding

Aristotle's Square of Opposition: The Traditional Framework

The Square of Opposition caught my attention during my research on the Internet Encyclopedia of Philosophy . This geometric framework - devised by Aristotle - has shaped logical thinking for over two millennia. Like an ancient Greek compass still guiding modern logical navigation, the Square helps us chart the subtle connections between categorical propositions - statements that make claims about how different groups or categories relate to each other. When we want to understand the logical relationships between claims like "All dogs are mammals" versus "No dogs are mammals" or "Some dogs are mammals" versus "Some dogs are not mammals," this enduring tool remains as relevant today as it was in classical times.

The framework is structured around four fundamental types of categorical statements, each representing a distinct logical form:

1. Universal Affirmative (A statements): "All S are P" Example: "All humans are mortal" This type makes claims about entire categories without exception
2. Universal Negative (E statements): "No S are P" Example: "No cats are fish" This type completely denies any connection between categories
3. Particular Affirmative (I statements): "Some S are P" Example: "Some birds are predators" This type makes claims about at least one member of a category
4. Particular Negative (O statements): "Some S are not P" Example: "Some students are not athletes" This type denies a connection for at least one member of a category

These categorical relationships establish several precise logical connections that form the foundation of deductive reasoning:

• Contradictory propositions must have opposite truth-values When one statement is true, its contradictory must be false For example, "All cats are mammals" and "Some cats are not mammals" cannot be simultaneously true or false
• Contrary propositions cannot both be true simultaneously Though they can both be false For example, "All roses are red" and "No roses are red" cannot both be true, but both could be false since some roses might be red while others are not

This framework continues to be valuable in modern logic, providing a structured way to analyse arguments and understand the relationships between different types of claims.

Think of it like a game of organising statements about groups of things. I don't want to lose you, so let's use a fun example with dogs:

"ALL" statements (A statements):

• Like saying "ALL dogs are animals"
• It means every single dog, no exceptions!
• Think of it like putting ALL your toys in one box

"NO" statements (E statements):

• Like saying "NO dogs are cats"
• This means not a single dog can be a cat, ever
• Think of it like having two completely separate boxes that can't mix

"SOME" statements (I statements):

• Like saying "SOME dogs are brown"
• Just means at least one dog is brown
• Think of it like having a few marbles in a big bag of different colored marbles

"SOME ARE NOT" statements (O statements):

• Like saying "SOME dogs are not brown"
• Just means at least one dog isn't brown
• Think of it like saying "not all your crayons are the same color"

Now, here's the cool part about how these statements relate to each other:

Opposites (Contradictory):

• If "ALL dogs are brown" is true, then "SOME dogs are not brown" must be false
• Just like if you say "the light is on," it can't also be off at the same time!

Can't Both Be True (Contrary):

• "ALL dogs are brown" and "NO dogs are brown" can't both be true
• Think of it like this: your ice cream can't be completely chocolate and completely vanilla at the same time

Modern Interpretations of Aristotelian Logic

Modern logicians have challenged aspects of this traditional framework. As the website notes, "modern logicians dismiss the traditional square as inadequate, claiming that Aristotle made a mistake or overlooked relevant issues" (Section 7). However, this criticism may misunderstand Aristotle's broader project, as "Aristotle is involved in a specialised project. He elaborates an alternative logic, specifically adapted to the problems he is trying to solve" (Section 7).

The Nature of Logical Understanding

Aristotle's view of knowledge acquisition was more nuanced than often portrayed. The Encylopedia explains that "Aristotle posits a sequence of steps in mental development: sense perception produces memory which (in combination with intuition) produces human experience (empeiria), which produces art and science" (Section 13). Furthermore, "Aristotle does not believe that all reasoning deals with words. (Moral decision-making is, for Aristotle, a form of reasoning that can occur without words)" (Section 3).

Form and Content in Logic

A key distinction between Aristotelian and modern approaches lies in their treatment of form versus content. As the website explains, "Some modern logicians might define logic as that philosophical inquiry which considers the form not the content of propositions. Aristotle's logic is unapologetically metaphysical. We cannot properly understand what Aristotle is about by separating form from content" (Section 8).

The Role of Intuition and Reason

Aristotle recognised multiple paths to understanding. The Encylopedia notes that "The distinction Aristotle draws between discursive knowledge (that is, knowledge through argument) and non-discursive knowledge (that is, knowledge through nous) is similar to the medieval distinction between ratio (argument) and intellectus (direct intellection)" (Section 13). This suggests a more comprehensive view of logical understanding than purely formal approaches. For Aristotle, logic was intimately connected to scientific knowledge. "Aristotle wants to construct a logic that provides a working language for rigorous science as he understands it" (Section 12). This approach sees "science as a search for essential definitions" where "the closer a proposition is to the metaphysical structure of the world, the more it counts as knowledge" (Section 3).

This historical analysis reveals that the apparent tension between traditional and modern approaches to logic might be better understood as reflecting different aspects of human reasoning rather than competing frameworks. Aristotle's system acknowledged both formal logical relationships and the broader context of human understanding, suggesting that effective reasoning requires multiple complementary approaches rather than adherence to a single method.

This more nuanced understanding shows how "Aristotle is too keen a biologist not to recognise that there are accidents and monstrosities in the world, but the existence of these individual imperfections does not change the deep nature of things" (Section 8), suggesting a philosophy that recognised both the need for systematic organisation and the complexity of real-world understanding.

TL;DR

Modern vs. Ancient Views

Modern logicians think Aristotle's logic system has flaws

But some say these critics might be missing the point - Aristotle was trying to solve specific problems of his time

How Aristotle Thought We Learn

He believed learning happens in steps:

First we sense things

Then we remember them

This creates experience

Finally, we develop art and science

He thought we could reason without using words (like when making moral decisions)

Different Approaches to Logic

Modern logicians focus on the structure of arguments, ignoring the content

Aristotle believed you couldn't separate how an argument is structured from what it's about

He wanted logic that could help with real scientific understanding

Different Ways of Understanding

Aristotle recognised two main ways to understand things:

Through step-by-step reasoning (like solving a math problem)

Through direct understanding (like instantly recognising a friend's face)

The Bigger Picture

Aristotle knew the world wasn't perfect - things don't always follow rules

But he believed there were still deep patterns and structures we could understand

His approach tried to balance systematic thinking with real-world complexity

The main takeaway is that while modern thinkers might criticise Aristotle's logic as too simple, they might be missing that he was trying to create a practical system that worked for both formal reasoning and real-world understanding.

Learning in Action: The Web of Meaning

As we contemplate Fogg Dam's intricate tapestry of life, where every species, every interaction, and every seasonal change forms part of an indivisible whole, we find ourselves confronting the limitations of traditional categorical thinking. The very act of trying to separate this ecosystem into discrete components – to draw clear lines between predator and prey, between water and land, between cultural and natural heritage – reveals the inadequacy of our conventional analytical frameworks.

Indeed, the failure of the original Humpty Doo Rice Project might be seen as a perfect metaphor for the shortcomings of rigid, categorical thinking. Where agricultural planners saw simply "land" and "water" to be manipulated, they missed the complex web of relationships that actually defined the landscape. The subsequent transformation of Fogg Dam into a thriving wetland ecosystem demonstrates the power of embracing interconnection over isolation, of understanding systems through their relationships rather than their boundaries.

This shift in perspective – from viewing the world as a collection of discrete categories to seeing it as a network of meaningful relationships – brings us to a fascinating parallel development in the realm of human thought, where researchers are proposing new ways to understand how we make sense of the world around us. Just as ecologists have learned to study Fogg Dam through its interconnections, philosophers and logicians are beginning to reimagine how human understanding itself emerges not from rigid categorisation, but from the rich web of relationships between ideas.

"Rather than assuming abstract categories of objects floating around the universe, we recognise that understanding is given by a rich web of relationship between elements of our language."

Consider how you would explain what a "vixen" is to a curious child. The traditional logic would say you're identifying whether something fits in the category "vixen." But as the article points out, you'd more likely say, "a vixen is a female fox." You're not pointing to an abstract category - you're showing connections between ideas.

This shift from categories to connections has profound implications. It's like the difference between looking at a pressed flower in a book versus observing a living ecosystem. The pressed flower might help you categorise, but it's the living ecosystem that shows you how everything works together.

The Power of Context

Think of meaning like a constellation in the night sky. The stars don't exist in isolation - they gain meaning through their relationships with other stars, through the patterns we recognise. Similarly, words and concepts gain their meaning through their connections and how they're used in different contexts.

As noted in the article, this becomes particularly relevant when dealing with complex contemporary issues like gender identity. Instead of getting stuck in debates about abstract categories, inferentialism asks us to consider what we can infer from statements and how these inferences might differ based on context and perspective.

From Theory to Practice

The practical implications are substantial. As the article explains, "By leveraging inferentialism, we may be able to give them [AI systems] some understanding of the words they are using." This could help prevent AI "hallucinations" - those moments when AI generates plausible-sounding but logically inconsistent statements.

Chain of Thought

The progression from traditional logic to inferentialism follows a natural chain of reasoning:

1. Traditional logic assumes meaning comes from categorisation
2. This view fails to capture how we actually understand and use language
3. Inferentialism suggests meaning comes from connections and relationships
4. This better reflects how we naturally think and learn
5. The implications extend to how we teach, learn, and develop AI systems

Inferentialism is Cross-Disciplinary

The beauty of inferentialism lies in its cross-disciplinary nature. It draws from philosophy, cognitive science, computer science, and linguistics. This convergence of disciplines suggests a deeper truth: understanding itself is inherently interconnected, just like the subjects we study.

Inferentialism represents a shift from reductionist thinking (breaking things down into categories) to systems thinking (understanding things through their relationships). This mirrors other paradigm shifts in science, from ecology to quantum physics, where we've discovered that relationships and connections are often more fundamental than individual elements.

What Does This Mean for Education?

The implications for education are profound. If meaning comes from connections rather than categories, we should:

• Focus on helping students build rich networks of understanding
• Emphasise relationships between concepts rather than isolated facts
• Encourage exploration of how ideas connect across disciplines
• Develop critical thinking skills through understanding contextual relationships

24-Hour Takeaway

Start thinking in terms of connections rather than categories. When learning or teaching something new, focus on how it relates to what you already know rather than trying to fit it into rigid boxes.

Metacognitive Thoughts For Further Exploration

1. Network Mapping Project Prompt: "Analyse the connections between five key concepts in your subject area. Create a visual map showing how they relate to each other and to broader themes."
2. Context Exploration Prompt: "Take a controversial term or concept and explore how its meaning changes in different contexts. What can we infer about it in each situation?"
3. Cross-Disciplinary Connections Prompt: "Choose a concept from one discipline and explore its relationships to concepts in three other disciplines. How do these connections enrich your understanding?"
4. Critical Thinking Exercise Prompt: "Analyse a recent news article using inferentialist principles. What relationships and connections are assumed or implied?"
5. AI Understanding Project Prompt: "Compare how a large language model and a human explain the same concept. What does this reveal about meaning and understanding?"

Wrapping Up: The Living Web of Knowledge

As we conclude, let's return to our Fogg Dam metaphor. Just as fogg dam is SO much more than a collection of individual trees and wildlife, knowledge is more than a collection of categorised facts. It's a living, breathing web of relationships, constantly growing and evolving.

Inferentialism is a recognition of how understanding actually emerges from the rich network of connections that make up our thoughts and language.

I wonder..

How might viewing human knowledge as an ecosystem rather than a collection of categories change the way we approach complex modern challenges like climate change, artificial intelligence development, or cultural understanding? Consider how the lessons from Fogg Dam's transformation from a failed rice project to a thriving interconnected wetland might inform this perspective.

Phil