The Triadic of Reason…
Part 1: Semiotics, Metaphysics and Logic - Abduction, Induction and Deduction – Meaning, Being and Thought
“You should carefully study the Art of Reasoning, as it is what most people are very deficient in, and I know few things more disagreeable than to argue, or even converse with a man who has no idea of inductive and deductive philosophy”…
– William John Wills
“Abduction is the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea; for induction does nothing but determine a value and deduction merely evolves the necessary consequences of a pure hypothesis”…
– Charles Sanders Peirce
“But man has such a predilection for systems and abstract deductions that he is ready to distort the truth intentionally, he is ready to deny the evidence of his senses only to justify his logic”…
– Fyodor Dostoyevsky
The nature of reason continues to be at the centre of the unfinished Enlightenment Project.
An intellectual and cultural movement that emerged in Europe during the 17th and 18th centuries characterised by a focus on reason, empirical observation, and the pursuit of knowledge as a means to improve society, politics, and human well-being.
A Primacy of Human Consciousness and Human capacity to embrace critical thinking and cognitive processes to reveal new knowledge, challenge existing beliefs & habits (orthodoxies, dogma, ideologies) and support human agency in navigating and shaping (Hegel’s Second Nature) an emergent complex World.
A recognition of reason’s central role throughout the rich history of Western Philosophy in providing conceptual clarity, supporting our problem-solving capacity, and ultimately ensuring a sense of coherence — comprehensibility, manageability and meaningfulness.
“That which is apprehended by intelligence and reason is always in the same state, but that which is conceived by opinion with the help of sensation and without reason is always in a process of becoming and perishing and never really is”…
— Plato
The mental foundations of our ongoing exploration of fundamental questions about our physical World (e.g. scientific inquiry ) and our metaphysical World (e.g. study of thought, study of being, ethics, theology).
Questions that go to the very core of the nature of reality, our place in the World and the eternal nature of the Human Condition.
Through logic (study of thought) reason provides us with the capacity to engage in a common semiotic dialogue and communicate understanding, knowledge and meaning.
“Logic and mathematics are nothing but specialised linguistic structures”…
— Jean Piaget
According to Immanuel Kant, reason provides us with the capacity to metaphysically transcend our sensory experience (phenomena) and seek universals and truths (noumena) by revealing the cognitive structures of our thoughts.
“the law of reason to seek unity is necessary, since without it we would have no reason, and without that, no coherent use of the understanding, and, lacking that, no sufficient mark of empirical truth”…
— Immanuel Kant
For over two millennia, reason has been a guiding force that has empowered humanity to explore the depths of human thought and understanding.
The emergence of Deductive Reasoning – Aristotle’s Logical System of Thought ( Term Logic – Aristotelian Logic )
Logic ( Study of Thought) – First Order Categories of Abstraction – Dyadic Relationships of Meaning ( Subject and Predicate) – Types of Propositions ( Relationships between Categories) – the Abstraction of Truth Claims about the World – Modalities – Syllogisms —Deductive Method
“Reason is a light that God has kindled in the soul”…
– Aristotle
In Aristotle’s seminal work The Organon — a collection of six treatises that Aristotle composed on logic and human thought — he attempts to bring coherence by systematising the rules of valid reasoning.
“Bad reasoning, as well as good reasoning, is possible; and this fact is the foundation of the practical side of logic”…
– Charles Sanders Peirce
In particular, two treatises — Categories and Prior Analytics — are central to understanding his contributions to term logic and deductive reasoning:
- Categories: In this work, Aristotle explores the fundamental notions of category and predicates. He delves into how things can be classified and how language expresses these classifications. Aristotle outlines ten first-order categories of things that can exist in the World (substance, quantity, quality, relation, place, time, position, state, action, and affection) that form the categorical elements of his logical system; and
- Prior Analytics: This treatise focuses on deductive reasoning. It introduces Aristotle’s concept of syllogism, a structured linguistic argument composed of premises that lead to a conclusion. Aristotle analyses the different forms of syllogisms and provides rules for valid inference.
These two treatises and other works in The Organon collectively form the foundations of Aristotle’s logical system.
They established many core concepts and methods that have shaped Western philosophy, logic (study of thought), scientific inquiry, mathematics, and human progress for over two thousand years.
Aristotle’s ideas when combined led to groundbreaking contributions in domains such as metaphysics, science, deductive reasoning, term logic, and linguistics.
His system of thought was largely comprised of the following foundational ideas that provided the conceptual building blocks:
- First-Order Categories: Aristotle categorised entities based on their fundamental characteristics, organising them into first-order categories such as substance, quantity, quality, relation, place, time, etc. This provided a systematic framework for understanding the nature of things that could exist in the World;
- Subject and Predicate: Aristotle recognised that linguistic statements can be deconstructed into a subject (the entity being described) and a predicate (the attribute or action ascribed to the subject). This dyadic semiotic distinction formed the basis for his analysis of language and reasoning.
- Types of Propositions: Aristotle identified four basic types of categorical propositions based on their quantity (universal or particular) and quality (affirmative or negative) – Universal Affirmative (All S is P) – Universal Negative (No S is P) – Particular Affirmative (Some S is P) – Particular Negative (Some S is not P) – These propositions were essential for making truth claims about the World (known knowns, known unknowns, unknown knowns, and unknown unknowns).
- Truth claims about the World: By combining subject-predicate linguistic structures with categorical propositions, Aristotle could make various types of abstract truth claims about the World. For example, he could assert universal truths (e.g. All humans are mortal) or particular truths (e.g. Some mammals are aquatic).
- Necessity, Possibility, and Impossibility: Aristotle introduced the modal concepts of necessity (what must be the case), possibility (what could be the case), and impossibility (what cannot be the case). Modal logic allowed Aristotle to go beyond simple assertions of existence or non-existence. He could now make more nuanced claims about the necessity or possibility of certain states of affairs and even predictions about the future. An example of necessity: all bachelors are unmarried. An example of possibility: it is possible that it will rain tomorrow. An example of impossibility: it is impossible for a square to have five sides. Aristotle’s syllogistic reasoning, at the core of his deductive method, could incorporate these modalities.
- Deductive Reasoning and Syllogism: Aristotle’s term logic and syllogistic reasoning relied on his understanding of subject-predicate linguistic relationships. Syllogisms — structured arguments composed of premises leading to a conclusion — formed the core of his deductive method. In Aristotle’s work The Organon he laid the foundation for what we now recognise as term logic. Aristotle’s term logic was based on the analysis of categorical propositions, which are statements that assert or deny a relationship between categories. For example, by combining two related linguistic categorical propositions that are considered true — Socrates is Man, All Men are Human — a further linguistic categorical proposition truth claim could be deduced — Socrates is Human.
- Metaphysics: Through the development of a logical system of thought Aristotle was able to explore metaphysics (Study of Being) including the nature of existence, substance, causality, and the ultimate nature of reality. His understanding of first-order categories and truth claims played a crucial role in his exploration of these profound philosophical questions.
Aristotle’s analysis of language and the structure of propositions, combined with his categorisation system, provided the conceptual foundations for the future development of mathematics, computation, formal logic, philosophy, and science making his ideas critical to the development of the history of thought and in doing so, profoundly influencing the future direction and progress of Western Civilisation.
The emergence of Inductive Reasoning and Empiricism
“The deductive method is the mode of using knowledge, and the inductive method the mode of acquiring it”…
– Henry Mayhew
“Induction makes you feel guilty for getting something out of nothing … but it is one of the greatest ideas of civilisation”…
– Herbert Wilf
Sir Francis Bacon is generally regarded as one of the pioneers of the Scientific Revolution, and his ideas are captured in his seminal work Novum Organum (New Instrument or New Method), published in 1620.
A publication that lays out the scientific method that became the foundation of the Scientific, Industrial and Digital Revolutions that would follow.
In the work, Bacon was critical of the prevailing orthodoxy anchored in deductive reasoning and Aristotelean Term Logic, which he believed had become rigid and inhibited our progress in revealing new knowledge.
He recognised that such reasoning could be grounded in false assumptions (axioms/premises) and perpetuate pre-existing beliefs (orthodoxies & dogma).
Instead, he advocated for a new method of scientific inquiry based on a systematic and organised approach of observing, experimenting, and collecting data from the Natural World.
The importance of empirical evidence and inductive reasoning, where general conclusions are drawn from specific observations.
A World where Mother Nature checks the maths.
Induction is the process of generalisation (abstraction and reductionism), based on a sufficient number of specific observations or examples to determine a value.
It combines logical processes of abstraction with intuition.
It relies on a Principle of Symmetry between Explanation and Prediction.
Given the complexity, uncertainty and emergent qualities of our Material World, it is probabilistic in nature.
Recognising the limits of observations (i.e. finite phenomena) which cannot eliminate all uncertainty (e.g. Knightian Uncertainty).
It, therefore, remains a contingent explanation and prediction based on the available evidence.
The emergence of Abductive Reasoning and the Pragmatic Maxim – a guiding normative principle for Logic and Abstraction
“Logic and metaphysics make no special observations, but they rest upon observations which have been made by common men”…
— Charles Sanders Peirce
19th and 20th Century Charles Sanders Peirce, an American philosopher and polymath, made significant contributions to the field of logic and reason, mainly through his development of abductive reasoning, the pragmatic maxim and semiotic triadic.
These ideas depart from purely deductive and inductive approaches to reason, offering a more holistic understanding of how we arrive at new knowledge.
Abductive reasoning involves forming a hypothesis to explain an observed phenomenon.
Unlike deductive reasoning, which moves from general principles to specific conclusions, or inductive reasoning, which generalises from particular observations, abduction begins with unexplained observations and suggests a plausible explanation (inference to the best explanation).
Like Francis Bacon’s inductive reasoning, this process recognises the inherent uncertainty and fallibility of human cognition.
The pragmatic maxim, a cornerstone of Peirce’s philosophy, provides a normative principle for reasoning and logic.
It suggests that the meaning or truth of an idea is linked to its practical implications.
According to Peirce, we understand concepts by considering their effects on our experience if they were true.
The pragmatic approach underscores knowledge’s practicality and emphasises the importance of real-world application.
Abductive reasoning extends Aristotle’s deductive reasoning and term logic by recognising the emergent nature of reason.
It recognises that the process of revealing new knowledge begins with new plausible relationships of meaning — imaginative leaps — to arrive at a hypothesis.
It highlights the fundamental role of hypotheses in scientific inquiry and the progress in Science.
“All significant breakthroughs are break -“withs” old ways of thinking”…
— Thomas Kuhn
Peirce’s approach incorporates the notion of generating new ideas and theories, providing a framework for scientific discovery beyond established principles.
“No part of the aim of normal science is to call forth new sorts of phenomena; indeed those that will not fit the box are often not seen at all. Nor do scientists normally aim to invent new theories, and they are often intolerant of those invented by others”…
— Thomas Kuhn
It also extends the frontier of reason beyond Aristotle’s deductive and Bacon’s inductive reasoning to our embodiment and meaning-making in the World.
Recognising the role of the Semantic Mind — Relationships of Meaning, our Semantic Abstraction of the World and the development of Semantic Languages.
Extending the nature of thought and the somatosensory process beyond the body.
While Aristotle emphasised the certainty of deductive conclusions derived from given premises, and Bacon championed systematic empirical observation to induce general principles, Peirce’s abductive method integrates and extends these two processes of reason.
It acknowledges the need for deduction and induction, but grounds both of these in a higher-order notions of meaning.
The process of revealing new relationships of meaning where the meaning of concepts are tied to their practical effects (Pragmatic Maxim).
New plausible explanations and understandings based on revealing new relationships of meaning in the form of a hypothesis.
Peirce’s ideas of abductive reasoning and the pragmatic maxim revolutionise how we approach logic and reason.
- Introducing new relationships of meaning — plausible explanations — hypothesis — into the structures of how we reason;
- Recognising the complexity, uncertainty and emergent qualities of the World we inhabit and the contingent & emergent nature of Knowledge;
- Providing a guiding normative principle to logic and reason through the Pragmatic Maxim that couples the meaning of concepts to its practical effects;
- Introducing into the concept of Reason the role of Semiotics to both Abduction (Pragmatic Maxim and Semiotic Triadic) and Induction (Altersense — Double Consciousness — Semiotic Signs (Icons) in the form of the Human Sensory Experiences (Phenomena — Altersense); and
- Re-establishing the Dyadic Relationship of Reason — Primacy of Human Consciousness and Primacy of Existence via the Semiotic Triadic (Observer (Conscious Self) — Sign — Observed) for the process of Abduction and part of the process of Induction.
“Semiotics, at its core, is logic”…
— Charles Sanders Peirce
Reason was now a combination of Meaning, Being and Thought or stated slightly differently, Semiotics (Study of Meaning & Habits), Metaphysics (Study of Being) and Logic (Study of Thought).
Conclusion — The Triadic of Reasoning: Meaning, Being and Thought
The Triadic of Reasoning and Inference ( the mental act of getting from premise A to conclusion B)
“Thus, the maxim of pragmatism, if true, fully covers the entire logic of abduction. It remains to inquire whether this maxim may not have some further logical effect. If so, it must in some way affect inductive or deductive inference”…
– Charles Sanders Peirce
“So we must start from this dual nature of intelligence as something both biological and logical”
—Jean Piaget
In The Triadic of Reason: Part 2 I will illustrate the nexus between Semantics, Metaphysics and Logic to highlight the shift to an integrated nature of reason.
Beyond Cartesianism and Nominalism.
It will walk through the coupled relationships between Abduction, Induction & Abduction and highlight the limits of logic (nominalism, cartesianism, abstraction & reductionism).
The shortfalls of types of reasoning (deductive or inductive) undertaken by humans or increasingly by semiotic sign machines (e.g. classical computing or machine learning) which are increasingly decoupled and anchored in more and more abstraction.
The Crisis of Modernity and Post-Modernity — A Primacy of Human Consciousness increasingly without a Primacy of Existence.
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