An Enquiry Concerning Human Understanding - The Ultimate Justification of Big Data, the Foundation of AI

This post was initiated by the post on causation in general and serves as my notes on reading Hume’s An Enquiry Concerning Human Understanding critically

Abbreviations
References to Hume’s original Enquiry Concerning Human Understanding are indicated by section and paragraph number. For example, a citation like EHU 7.21 refers to:

EHU: An Enquiry Concerning Human Understanding

7: Section VII, “Of the Idea of Necessary Connexion”

21: The 21st paragraph within that section.

What makes David Hume an Empiricism?#

Choosing to be on the side of empiricism is more of a “rational” choice, while knowing the why of being on that side is essentially subconscious. This section discusses what subconscious aspect of Hume made him to act as an empiricist.

We are moving beyond the intellectual reasons and into the realm of philosophical psychology. While we can’t psychoanalyze Hume directly, his own writings and biography point to a powerful subconscious disposition that made him a natural empiricist.

Philosophical Psychology
Being a truly fascinating and foundational field that bridges two of the most profound inquiries into the human condition, philosophical psychology is less a single, defined subject and more of a powerful intersection where the conceptual rigor of philosophy meets the empirical investigation of psychology.
While there isn’t one single book that covers everything around the topic of philosophical psychology for us to dive in deeply, there are several outstanding works that offer a deep and rewarding exploration of this area:

William James’s The Principles of Psychology (1890) (Volume 1 & Volume 2)

David Chalmers’s The Conscious Mind: In Search of a Fundamental Theory

At its core, the subconscious aspect that drew Hume to empiricism was likely a deep-seated skeptical temperament and a profound distrust of intellectual arrogance, which was solidified by a formative personal crisis.

A Temperamental Aversion to Dogma#

Rationalism, especially in its extreme forms like Leibniz’s, requires immense intellectual confidence. It asserts that the human mind, through pure reason, can grasp the ultimate structure of reality. This is a philosophy of certainty and grand systems.

Hume’s personality was the opposite. By all accounts, he was modest, good-humored, and deeply aware of the fallibility of human reason. His temperament was simply not suited to the dogmatic pronouncements of rationalism. He was psychologically inclined to doubt grand, abstract claims and to trust what was immediate and observable. Empiricism, with its humble starting point - “what can I actually see, hear, and feel?” - was a natural fit for a personality that was inherently wary of intellectual overreach.

The “Disease of the Learned”: A Formative Crisis#

The most compelling piece of evidence comes from Hume’s own life. As a young man, he threw himself into intense, abstract philosophical speculation, trying to find a rational foundation for everything. The effort drove him into a severe psychological crisis around the age of 18, a breakdown he later called the “Disease of the Learned.” He suffered from anxiety, listlessness, and an inability to think clearly.

He wrote that his salvation came not from more philosophy, but from abandoning it for a time:

“_I went under a course of bitters and anti-hysteric pills… I rode and walked… I also collected a share in a domestic society, and by my cheerfulness and good-nature, paid for the pleasure I enjoyed.”

This crisis taught him a lesson on a deep, subconscious level: pure reason, when pushed to its limits, is not only fallible but actively dangerous to human well-being. He learned firsthand that a healthy life is grounded not in abstract certainty, but in custom, habit, and sensory experience. His later philosophy, which champions custom over reason as the “great guide of human life,” is a direct reflection of this traumatic but formative discovery. He didn’t just think reason had limits; he felt them in his own nervous system.

A Grounded, Worldly Disposition 🍻#

Finally, Hume was not a reclusive academic. He was a man of the world - a historian, diplomat, and a beloved socialite known in Paris as “Le Bon David” (The Good David). He enjoyed conversation, good food, and games of backgammon.

This worldly disposition would have subconsciously drawn him to a philosophy that values the concrete and the observable over the ethereal. Empiricism is a philosophy of the here-and-now; it’s grounded in the same shared world of experience where people dine, converse, and live their lives. The grand, otherworldly systems of the rationalists would have seemed “cold, and strain’d, and ridiculous” to a man so comfortable and engaged with everyday reality.

What makes David Hume an “Extreme” Empiricism?#

In page xxix of Peter Millican’s introduction to An Enquiry Concerning Human Understanding, Oxford University Press 2007 there is a description of David Hume, who was relentlessly consistent in applying the core empirical principle to everything, including the inner workings of the mind itself:

The beginning of section 7. The Humean Revolution
… “he (David Hume) follows the spirit of Locke’s empiricism with respect to both the origin of ideas and factual discovery, but develops it far more consistently, ruthlessly dismissing all hints of pure rational insight and deploying powerful sceptical arguments to undermine even the ideal of causal intelligibility.”

Peter’s expression of “ruthlessly dismissing all hints of pure rational insight” is a clear manifestation of David Hume’s reputation as a somewhat “extreme” empiricist. What Mr. Millican didn’t discuss, which is also why I open up this section, is what drew David Hume to this somewhat extreme side over the spectrum between rationalism and empiricism.

While earlier empiricists like John Locke laid the groundwork by asserting that all knowledge comes from sensory experience, Hume took this idea much further. He relentlessly questioned what we can truly know if experience is our only guide, leading him to a profound skepticism about concepts that other philosophers (and common sense) take for granted.

Although followed by Hume, John Locke, however, had a much neutralized view and famously argued that all our ideas come from 2 sources:

sensation (data from the external world), and
reflection (observing the inner operations of our own minds).

This second source, reflection, is where Locke gives himself an out that Hume refuses to take.

Locke believed that through reflection, we can get ideas of things like “substance” and “causation.” He accepted that we can’t see the underlying substance that holds the properties of an apple together (its redness, roundness, etc.), but he assumed there must be something there - an “I know not what” - for those properties to inhere in. He took the mind’s ability to process and combine ideas as a reliable source for these more abstract concepts.

Hume takes Locke’s basic toolkit but applies it with ruthless consistency. He agrees that all ideas must be traced back to an impression (a direct sensory experience or feeling). If a concept, even an abstract one, cannot be traced back to a specific impression, Hume discards it as meaningless or, at best, a fiction of the mind.

In short, Locke allowed the mind’s reflective capabilities to generate ideas that weren’t strictly tied to raw sensory data, thereby preserving concepts like substance and a continuous self. Hume, on the other hand, insisted that every component of an idea, even those from reflection, must correspond to a direct, discrete impression. This uncompromising standard forced him to dismantle the very concepts that Locke and others took for granted, leading him down his uniquely skeptical and “extreme” path.

What that means is: Locke, in a sense, flinched where Hume did not, and this is where we are getting to the core: Locke flinched while Hume didn’t because they had fundamentally different projects and temperaments. Locke was a builder trying to construct a stable foundation for knowledge and society, whereas Hume was a diagnostician, relentlessly applying a single principle to see what would break.

John Locke: The Engaged Political Architect
Locke’s pragmatism is evident in how his life and work were directly aimed at solving concrete political and social problems.
Locke was not a secluded academic. He was a physician, a trusted political advisor to the Earl of Shaftesbury, and a key intellectual figure in the political intrigues of his time. He helped draft the Fundamental Constitutions of Carolina and was deeply involved in the planning that led to the Glorious Revolution of 1688, which established the supremacy of Parliament in England. His philosophy was forged in the midst of real-world political struggle.
Using writings as political tools, Locke wrote his most famous works with clear, practical goals:

Two Treatises of Government: This was not an abstract thought experiment. It was a direct argument against the divine right of kings and a powerful justification for the revolution he helped engineer. It provided the philosophical blueprint for modern liberal democracy.

A Letter Concerning Toleration: This was a specific policy proposal arguing for religious freedom (for certain groups) to end the destructive religious wars that had plagued Europe.

An Essay Concerning Human Understanding: Even his major work on epistemology had a pragmatic aim. He stated his goal was to be an “under-labourer” to scientists like Newton, clearing away philosophical confusion to establish a firm foundation for scientific knowledge.

Locke’s philosophy was a means to an end: a stable, tolerant, and free society.

Locke’s primary goal was not just to see how far empiricism could go; it was to use empiricism to build a workable system. Writing in the wake of political and religious turmoil in England, his philosophy was a tool to establish a basis for science, morality, and stable government.

A Needed for Foundation: To justify his political philosophy - which relies on concepts like natural rights, property, and personal identity - he needed a persistent, continuous self. A mere “bundle of perceptions” wouldn’t be able to own property or enter into a social contract.
Common Sense as a Backstop: Locke’s philosophy is ultimately grounded in a kind of common sense. He accepted that we can’t directly perceive “substance,” but it was a necessary and common-sense assumption to explain how the qualities of an object (like an apple’s color and shape) are held together.
A Constructive Purpose: His empiricism was meant to clear away the rubbish of “innate ideas” and religious dogmatism so he could build something new. He wasn’t going to let his own tool demolish the very structure he was trying to erect. Therefore, he “flinched” from the most radical conclusions because they were destructive to his overarching constructive project.

Hume, living a generation later in the Scottish Enlightenment, had a different, more radical goal: to apply the “experimental method of reasoning to moral subjects.” He wanted to be the Isaac Newton of human nature, analyzing the mind with uncompromising rigor.

Consistency Was His Goal: Hume’s project was to take the empirical premise - that all ideas come from sensory impressions - and follow it to its absolute logical conclusion, no matter how uncomfortable. His aim was intellectual consistency above all else.
Destruction as Discovery: For Hume, discovering that concepts like causation, the self, and induction had no rational basis was the discovery. It wasn’t a failure of his system; it was the startling result of its successful application. He wasn’t trying to build a new house; he was stress-testing the foundations of the old one to see where they cracked.
Accepting the Unsettling Outcome: Hume famously admitted that once he left his study, he lived and acted like everyone else, believing in cause and effect out of habit. He was comfortable separating his devastating philosophical conclusions from the practical necessities of life. He didn’t need his philosophy to provide a comfortable or stable worldview.

In essence, Locke stopped where he did because going further would have undermined his practical and political goals. His “flinch” was a pragmatic choice. Hume, driven by pure intellectual curiosity, had no such reason to stop and therefore followed the chain of reasoning to its deeply skeptical end.

If Hume is the extreme of empiricism, who is the extreme of rationalism?
The most fitting counterpart for the extreme of rationalism is Gottfried Wilhelm Leibniz, whose system is arguably the most elaborate and counter-intuitive reality ever constructed from pure reason.
Leibniz’s philosophy is the ultimate expression of confidence in the power of the human mind to deduce the nature of reality. He believed that for everything that exists, there must be a sufficient reason why it is so and not otherwise. Starting from this principle, he constructed a complete metaphysical system that is profoundly strange and entirely a-priori (independent of experience).
His “extreme” position is best seen in two key ideas:

Monads: Leibniz argued that the universe is composed of an infinite number of simple, indivisible, non-physical substances he called monads. Each monad is a unique, soul-like entity with its own perceptions. What we think of as physical objects, and even our own bodies, are actually collections or colonies of these monads.

Pre-established Harmony: Since monads are non-physical, they cannot actually interact with each other. A billiard ball doesn’t “cause” another to move. Instead, Leibniz claimed that God, in his infinite wisdom, created all monads at the beginning of time and programmed them to unfold their perceptions in perfect harmony with one another. When we decide to raise our arm, the monads of our mind were pre-programmed to have that thought at the exact moment the monads of our arm were pre-programmed to rise.

This system, where nothing truly interacts and all events are just the synchronized unfolding of countless individual perspectives, is the pinnacle of a reality built from logic rather than observation.

Section I - Of the Different Species of Philosophy#

The first section of the Enquiry introduced 2 types of moral philosophies. The first type of moral philosophy Hume describes is the practical and inspirational kind. Its main goal isn’t to perform a deep, scientific analysis of morality but to make people want to be good. It treats humans as active beings who need guidance and motivation, not as purely rational creatures who need abstract theories.

A perfect example of this first type of moral philosophy is the Meditations by the Roman Emperor Marcus Aurelius.

His book is not a complex, academic treatise that tries to define the ultimate metaphysical foundation of “justice” or “courage.” Instead, it’s a personal journal filled with practical advice, reminders, and self-exhortations designed to make him a better person. His book is not a complex, academic treatise that tries to define the ultimate metaphysical foundation of “justice” or “courage.” Instead, it’s a personal journal filled with practical advice, reminders, and self-exhortations designed to make him a better person. When one reads the Meditations, they find passages like:

“Waste no more time arguing about what a good man should be. Be one.” “The best revenge is to be unlike him who performed the injury.”

This is Hume’s first type of philosophy in action. It’s not analyzing the concept of goodness; it’s giving us a direct, inspiring command to be good. It aims to stir our feelings and guide our actions, making virtue feel admirable and achievable. Think of it as a coach or a mentor for the soul.

In contrast, Hume’s second type of philosophy is the analytical and abstruse kind (which is what Hume himself practiced). This type is like a scientist dissecting human nature to understand the precise origins and principles of our moral beliefs. It asks questions like, “Where does our idea of ‘justice’ come from in the first place?” It seeks to explain morality, not just to promote it.

To break down this first section. Hume is essentially setting the stage for his entire book by dividing philosophy into 2basic types and explaining why he’s choosing the harder, more difficult path. Think of the two types of philosophy as a painter versus an anatomist, both studying the human form.

Like a painter, the goal of the “easy and obvious” philosophy is to create a beautiful and inspiring portrait of humanity, and to make us want to be a good person. It appeals to our emotions and passions. It uses beautiful language, stories of heroes, and practical examples to guide our actions. It paints virtue in attractive colors to make us admire it. The Meditations of Marcus Aurelius was designed to motivate us and guide us behavior. This philosophy is useful and popular because it directly helps people live better lives.

The “accurate and abstruse” (meaning difficult and complex) philosophy is the path Hume himself is taking. Like an anatomist, its goal is to understand the hidden structures of the human mind and the fundamental principles of human nature. It’s not trying to inspire someone, but to explain to them. It appeals to reason and dissects human thought, memory, and reasoning to see how they work. It’s precise, logical, and often very abstract. Hume’s own Enquiry is itself an example. He’s not telling us what to think, but trying to figure out how we think in the first place.

Hume knows most people prefer the painter. He admits that the anatomist’s work can seem cold, difficult, and useless. So, he ends the section by defending his approach. He argues that:

Accuracy Helps the Painter: A painter who understands anatomy can create a much more accurate and lifelike portrait. Similarly, inspirational philosophy is better when it’s based on a true understanding of human nature.
It’s the Only Way to Settle Debates: To end endless philosophical arguments, we need to get to the root of the problem by accurately mapping the powers and limits of the human mind as Hume stated:

“The only method of freeing learning, at once, from these abstruse questions, is to enquire seriously into the nature of human understanding, and shew, from an exact analysis of its powers and capacity, that it is by no means fitted for such remote and abstruse subjects.”
It’s a Noble Pursuit: Just like an astronomer studying the planets, there is inherent pleasure and value in understanding the “secret springs and principles” of our own minds.

TIP
Section I is Hume’s mission statement: He’s telling us he’s not going to be a painter who inspires us but an anatomist who will dissect human thought to provide a clear and accurate map of the mind.

Section II - Of the Origin of Ideas#

Section II is where Hume lays down the central principle of his entire philosophy by saying that everything in our mind can be divided into 2 categories, distinguished only by their force and vivacity:

TIP
Think of the mind as a room containing original paintings and faded photocopies.

Impressions (The Original Paintings 🎨): These are our direct, vivid experiences. This includes sensory perceptions (seeing, hearing, touching), emotions (love, hate), and desires. When we see the color red, feel the warmth of the sun, or feel a pang of anger, we are having an impression. They are the strong, lively, original paintings of experience.
Thoughts or Ideas (The Faded Photocopies 📄): These are the faint copies we make of our impressions when we think, remember, or imagine. Remembering the color red, thinking about the sun’s warmth, or recalling a time we were angry are all ideas. They are less forceful and vivid than the original experience, just like a photocopy is less vibrant than the original painting.

The key takeaway is simple: impressions are the raw data of experience; ideas are just faint copies of that data. After establishing this distinction, Hume makes his radical claim:

Every idea in our mind is ultimately a copy of a past impression

This is the cornerstone of his empiricism. He argues that we cannot think of anything that we haven’t first experienced through our senses or feelings. He offers 2 “proofs” for this:

Just try it (EHU 2.6): Challenge ourselves to think of something that doesn’t trace back to an impression. Even a fantastical creature like a golden mountain is just a combination of two ideas (gold + mountain) that we originally experienced as impressions.
The case of a blind man (EHU 2.7): A person born blind has no impression of the color red. Consequently, they have no idea or concept of what “red” is. This shows that without the initial impression, the corresponding idea cannot exist.

Hume, being an honest philosopher, then presents a single counter-example to his own rule - an exception of the missing shade of blue 🟦 (EHU 2.8). Imagine someone has seen every shade of blue except for one specific shade. If all the shades of blue they have seen are laid out in a row, from darkest to lightest, with a gap for the one they’ve never experienced, could they imagine that missing shade?

Hume says, “Yes, I believe they could.”

This seems to contradict his main rule because the person would be forming an idea of a color without a direct impression of it. However, he dismisses this as a single, peculiar instance that is so minor it doesn’t really undermine his overall principle.

Putting our fingers on a modern perspective where Hume’s 18th-century model of the mind clashes with modern psychological insights, we see that Hume’s framework has no room for the concept of the subconscious, and this is one of its major limitations when viewed from our perspective today.

Hume is building a model based entirely on conscious experience. The concept of a structured, active subconscious - a hidden part of the mind that processes experiences and influences behavior - is a much later invention, largely from the 19th and 20th centuries (think Freud, Jung, and modern cognitive science).

By taking the influence of subconsciousness into account, we could postulate that even though we cannot feel the intensity of a past experience, subconscious mind had already consumed that experience and subconsciously affect our thought and behaviors; we just don’t know this extra level of subconscious vivacity. If we add up this level of subconscious vivacity, we could state that the Hume’s memorized vivacity and our subconscious vivacity add up to match the intensity of impression.

In fact, the exception of “missing shade of blue” (Thank you, Hume; you are indeed honest) exactly highlights the effects of the subconscious mind which shall be the root cause helping us to figure out that missing shade mentally

For Hume, the mind is the sequence of perceptions we are aware of. Therefore, when he uses a word like “vivacity”, he means its felt, conscious quality. He’s making a phenomenological claim: the immediate sensation of seeing a bright red apple simply feels stronger and more forceful than the memory of that apple an hour later. The idea of a “subconscious vivacity” is a concept that exists entirely outside of his framework.

Past experiences shape our thoughts and behaviors in powerful ways that are not consciously accessible. Concepts like implicit memory, priming, and unconscious bias are all examples of past impressions having a potent, ongoing “vivacity” that we don’t feel directly. A traumatic event, for example, can have a far more powerful and lasting effect on a person’s behavior (a kind of “subconscious vivacity”) than the immediate, vivid impression of drinking a cup of tea, even if the memory of the trauma is repressed and feels less “vivid” than the memory of the tea.

Facing the argument that the subconscious is the faculty that allows us to generate the new idea of missing blue shade 🟦, which acts as a very compelling and modern interpretation, Hume, however, would likely explain it using the tools he did have. He wouldn’t need to invoke a subconscious. Instead, he would argue that the mind is using its natural ability to recognize relationships between ideas in this way:

The mind observes the series of blue shades.
It perceives the relationship between them - a steady, ordered progression from dark to light.
It then performs an operation of imagination based on this observed relationship, taking the idea of the shade on one side and the shade on the other, and generating a new idea that fits logically in the middle.

For Hume, this would be a subtle function of the conscious mind’s ability to compare and relate the ideas it already has, rather than a mysterious process bubbling up from a hidden depth. But imagination itself has to be examined first: is Hume’s “imagination” just a product of experience, or is it a hidden, active power that his own principles can’t account for?

Humean System Failure#

The “missing shade of blue” is a major problem for Hume’s model. It’s the one instance where Hume admits the imagination seems to do the impossible: create a new simple idea (a specific shade of blue) without a corresponding prior impression.

How does Hume’s system handle this? Frankly, it doesn’t handle it well. His probable explanation is that the imagination is performing a special kind of operation. It’s not creating from nothing, but rather observing the relationship between the existing shades (the ordered gradient) and then interpolating the missing piece. It’s like seeing the numbers 2 and 4 and figuring out the number 3.

Hume’s Official Position: Imagination as a “Copy and Paste” Faculty
For Hume, the imagination is fundamentally a secondary and derivative power. It’s like a mental artist working with a limited set of paints—the “paints” being the simple ideas that are themselves faded copies of our impressions. The imagination’s powers are restricted to manipulating this existing material in a few ways:

Compounding: Combining ideas (a horse + a horn = a unicorn).

Transposing: Rearranging ideas (a man’s head on a lion’s body).

Augmenting or Diminishing: Making ideas larger or smaller (a normal-sized man vs. a giant).

In this view, the imagination is strictly a posteriori. It cannot invent a new “paint” (a new simple idea) from scratch. It can only recombine what the senses have already provided. So, when Hume explains a complex idea, he must be able to break it down into the simple sensory impressions it came from.

But as one could rightly imply, this is a bit of a cheat. The ability to perceive such an abstract “relationship” and then generate a new idea to fit into it seems like a far more active and powerful mental faculty than simple “copy and paste.” Hume himself treats it as a singular, trivial exception, but for critics, it’s a thread that, if pulled, could unravel his whole system.

The Kantian Alternative: An Active, Structuring Mind#

The intuition that there might be a “subconscious process” or a more fundamental power at play is precisely the kind of thinking that led Immanuel Kant to his philosophical revolution.

For Kant, the “missing shade” problem wouldn’t be a weird exception; it would be proof of his central thesis. Kant argued that the mind is not a passive recipient of sense data. Instead, it actively structures our experience using innate, a priori concepts.

A Humean would say we see the relationships between colors.
A Kantian would say our mind imposes a structure of relationships (like quantity and degree) onto our sense perceptions in order to make sense of them.

For Kant, the imagination is not just a reproductive faculty but a productive one. It’s a fundamental power that synthesizes raw sensory data into the structured, coherent world we experience. The ability to generate the missing shade would be a perfect, small-scale example of the mind’s innate power to complete a pattern and structure reality.

Section III - Of the Association of Ideas#

Section III is very short but incredibly important. Hume is identifying the secret, universal forces that guide our train of thought. He argues that while our thoughts seem wild and random, they are actually connected by a 3 simple, powerful principles.

TIP
Think of it as a kind of “mental gravity”. Just as gravity is the invisible force that pulls objects together in the physical world, there are invisible forces that pull our ideas together in the mental world. Hume identifies three such forces.

Resemblance (Likeness): This is the simplest principle. When we have an idea, our mind has a natural tendency to drift to other ideas that are similar to it. For example, seeing a photograph of our friend immediately makes us think of our actual friend. The picture resembles the person, so our mind makes the connection effortlessly.
Contiguity in Time or Place (Nearness): Our minds tend to connect ideas that are near each other in either time or space. For instance, if we mention the Eiffel Tower, it’s almost impossible not to think of Paris. The two are so closely associated in place that one idea naturally calls up the other. Similarly, thinking about a specific historical event might lead us to think about what happened immediately before or after it (nearness in time).
Cause or Effect (Connection): This is the most powerful and important principle for the rest of Hume’s book. When we think of an event (a cause), our minds automatically jump to the event that usually follows it (the effect), and vice versa. If we think of a wound, we almost can’t help but think of the pain that follows it. The wound is the cause, and the pain is the effect. This connection feels so strong and automatic that it seems unbreakable.

Those who are thinking critically, just as Hume would want us to, easily notice that Hume doesn’t offer a formal, logical “proof” for the 3 principles, and that can feel like he’s building his entire system on an unproven assumption. 🤔

From Hume’s perspective, his “proof” isn’t a mathematical deduction; it’s an observational claim. As a committed empiricist, he’s not trying to prove that these principles must be true from some abstract, a priori reason. Instead, he is making a descriptive claim about how the mind works based on introspection.

His argument is essentially this: “Look at your own mind. Watch your thoughts flow. I have, and I’ve found that all the connections between ideas can be categorized under these three headings: Resemblance, Contiguity, and Cause/Effect.”

He’s not a geometer starting with axioms. He’s more like a naturalist who has spent countless hours observing an ecosystem (the mind) and is now presenting his findings: “In this entire ecosystem, I’ve only ever seen three types of interaction between the creatures (ideas). Here they are.”

His challenge to the reader, although not stated explicitly, is an empirical one: “If you disagree, find me an example of two ideas that are connected in your mind, but where the connection isn’t one of these three.” By presenting the principles as a comprehensive explanation, he shifts the burden of proof to the skeptic to find a counter-example.

Section IV - Sceptical Doubts concerning the Operations of the Understanding#

In this section Hume, the careful anatomist of the mind, takes the simple tools he has established and uses them to perform a devastating dissection of human reason.

Part I: Building the Case and Posing the Ultimate Question#

Hume begins by dividing all human knowledge into 2 distinct categories:

Relations of Ideas (EHU 4.1), which are the certain truths of mathematics and logic. We know “a triangle has three sides” with perfect certainty just by understanding the definitions; the opposite is a logical contradiction. This realm is certain, but it tells us nothing about the world itself.
Matters of Fact (EHU 4.2), the second category and the one he is truly interested in, is all knowledge that comes from experience, from science to everyday observation. Hume makes the crucial point that the contrary of any matter of fact is always possible. “The sun will not rise tomorrow” is a perfectly intelligible thought(see tip below), not a logical contradiction. This immediately raises the question (EHU 4.3): if our knowledge of the world isn’t logically certain, what is it based on?

Intelligible Thought
In the context of Hume and his contemporaries, an “intelligible thought” simply means a thought that is conceivable by the mind without involving a logical contradiction. It’s a test for logical possibility. A thought is “intelligible” if we can form a clear idea of it. It doesn’t mean the thought is true or even likely, only that it isn’t self-contradictory nonsense.
For Hume, intelligibility is a crucial tool. He basically argues that if we can clearly conceive of something happening, then it’s logically possible. We can easily imagine “The sun will not rise tomorrow”. The world continues to spin, but the sun is gone. It’s a coherent picture in our mind, so it is logically possible and implies no logical contradiction. We cannot, however, form a clear mental picture of “I drew a four-sided triangle”. The very definition of a triangle (three sides) contradicts the property we’ve given it (four sides). It is inconceivable, logically impossible, and therefore unintelligible.
Hume later uses this to prove that our knowledge of the world (“Matters of Fact”) isn’t based on pure logic. Since we can intelligibly conceive of the future being different from the past, there can be no purely logical proof that it will be the same.
The importance of “intelligibility” goes all the way back to the Ancient Greeks, particularly Plato, who divided reality into 2 realms:

The Sensible World: The physical world we perceive with our senses. It is constantly changing, imperfect, and a source of mere opinion.

The Intelligible World: The world of perfect, eternal, and unchanging “Forms” or “Ideas” (like the perfect Form of Justice, or the perfect Form of a Triangle). We cannot see this world with our senses; we can only grasp it with our intellect (in Greek, nous).

For Plato, the “intelligible” realm was the source of true knowledge and was, in fact, more real than the physical world. The word itself comes from the Latin intelligibilis, meaning that which can be understood by the intellect.
Later, the Rationalist philosophers like Descartes and Leibniz built on this. For them, what is “clear and distinct” to the intellect - what is truly intelligible - was the foundation of all certainty. Hume, in his typically skeptical way, takes this classical and rationalist term and uses it for his own empiricist purpose: not to establish what is true, but merely to test what is logically possible.

Hume’s answer is that all our reasoning about matters of fact is founded on the relation of Cause and Effect (EHU 4.4). This is the principle that allows our minds to go beyond the immediate evidence of our senses and memory. When we see light and feel heat, we infer a fire is the cause. When we find a watch on a desert island, we infer a watchmaker was the cause. This is the chain of reasoning that connects all our beliefs about the world.

Now Hume asks the next, deeper question: how do we arrive at our knowledge of cause and effect? (EHU 4.5) He argues forcefully that this knowledge (cause and effect) can never be attained by reasoning a priori (before experience). He gives his famous example of a hypothetical Adam, a man with perfect rational faculties but no experience of the world. Adam could not, simply by examining the transparency and fluidity of water, deduce that it could drown him. The effect is a completely different event from the cause, and no amount of logical analysis of the cause can ever reveal the effect. Even after we have experience, Hume argues, our reasoning only helps us organize what we’ve already observed. Science never reveals the secret “power” or “energy” by which one object produces another; it only describes the constant conjunction of events we have seen. (EHU 4.6-9)

Having demolished the idea that reason can discover causality, Hume concludes that all our knowledge of cause and effect must be founded entirely on Experience (EHU 4.10-13). But this, he shows, is not a real answer; it just pushes the question back one step. He then arrives at the ultimate problem of the section. He uses the example of bread: I have eaten bread in the past and it has nourished me. I see a piece of bread now that looks and feels the same, and I confidently conclude that it will also nourish me. This inference seems simple, but Hume reveals it contains a hidden, massive assumption. He asks: what is the logical process that allows me to take my past experiences and extend them into the future? (EHU 4.14)

Part II: The Skeptical Conclusion#

Part 2 begins with Hume stating that no one has yet provided a satisfactory answer to his question.

(EHU 4.15-21) Hume then proceeds to prove that no such rational answer can ever be given. He argues that the inference from past to future cannot be demonstrative (based on Relations of Ideas), because there is no logical contradiction in imagining that the course of nature might change. Nor can the inference be probable (based on Matters of Fact), because that would be a circular argument. We would be using past experience to prove that past experience is a reliable guide for the future. We are assuming the very thing we are trying to prove.

(EHU 4.22-23) Hume concludes that this monumental belief - that the future will be like the past - has no foundation in reason or understanding whatsoever. The bedrock of all our scientific and everyday knowledge is an assumption that cannot be rationally justified. He has led us to a skeptical precipice, showing that a chain of reasoning we use every moment of our lives is, from a purely logical standpoint, an irrational leap in the dark.

The Kantian Awakening
This is the very argument that, as Immanuel Kant famously wrote, “first interrupted my dogmatic slumber”. Kant saw the devastating power of Hume’s conclusion. He agreed with Hume that causality could not be derived from experience. But he could not accept that it was merely an irrational habit of mind. Kant’s entire philosophical project in the Critique of Pure Reason was an attempt to save causality from Hume’s skepticism.
His revolutionary solution was to propose that causality is neither a feature of the world we discover (as the rationalists thought) nor a mental habit we develop (as Hume concluded). Instead, Kant argued that causality is an a priori category of the understanding - it is one of the innate rules, like a piece of operating software, that our mind imposes on raw sensory data to structure it into the coherent, cause-and-effect world we experience. For Kant, we don’t learn causality from experience; it is a precondition for us to be able to have intelligible experience at all.

Section V - Sceptical Solution of these Doubts#

In this section, Hume provides his solution to the profound problem of induction he raised in Section IV.

Part I#

He begins by praising “Academical” or moderate skepticism, not as an end in itself, but as a healthy, humbling force that limits our oversized philosophical ambitions to topics we can actually investigate (EHU 5.1). He then immediately re-states the problem: having proven that Reason cannot justify our inference from past to future, we are left in a dire skeptical position (EHU 5.2).

Hume’s solution is to propose a different, non-rational principle: custom or habit (EHU 5.5). This is the key to his entire “science of man.” He explains that after we observe two events, like “flame” and “heat,” in constant conjunction, our mind forms a habitual, automatic association between them. The next time we see a flame, this habit forces our mind to expect heat. This step is not an act of reason; it is an instinct. Without this principle of custom, Hume argues, we would be as helpless as infants. Our past experience, which only tells us about specific past moments, would be entirely useless for navigating the future. We would be incapable of acting or planning. Therefore, he famously concludes, “Custom, then, is the great guide of human life.” (EHU 5.6) It is this principle alone that makes our experience useful and allows us to function in the world.

Parallel Between “Custom and Habit” and “Big Data Analytics”#

Big Data analytics is, in many ways, the technological and mathematical embodiment of Hume’s principle of Custom. The parallel is incredibly strong in the sense that:

Both are based on induction, not deduction
- Hume’s Custom: The mind observes a “constant conjunction” in the past (Event $A$ has always been followed by Event B). From this data set, it forms a non-rational but powerful expectation that $A$ will be followed by $B$ in the future.
- Big Data Analytics: A model is fed a massive data set of past events. It identifies statistical correlations (this “constant conjunction” of data points). From these patterns, it generates a probabilistic prediction about the future (e.P., a person who bought X and Y is 80% likely to buy Z).
Both focus on correlation, not true causation

This is the most crucial link. Hume’s central point is that we never see the “secret power” or logical “cause” that connects $A$ to B. We only see that they happen together.

Modern machine learning models, especially “black box” deep learning models, do the exact same thing. A model can tell us that people with a certain browsing history are highly likely to click on a specific ad, but it doesn’t (and can’t) tell you the why in any deep, philosophical sense. It’s just an extremely powerful correlation engine. It’s operating on “constant conjunction,” not on an understanding of the necessary connection.

Big Data analytics can be viewed as a system that has taken Hume’s psychological principle of Custom, removed it from the fallible human mind, and instantiated it in a mathematical algorithm, making it faster and more powerful than any individual’s “habit” could ever be. It’s the ultimate tool for a world operating on Humean principles: we don’t need to know why things happen, we just need a perfect record of what has happened.

From this parallel, can we conclude that David Hume’s Enquiry to be the very foundation of Big Data? We shall postpone the answer for now and resume and fully expand this important topic in Section X, because there are still related fundamentals we are about to cover

”Humean” Investigation on Personality#

According to Hume, if custom is the great guide of human life, we would choose our future action based on our past experience. We can then say a person’s deeds today reflects his or her past experience. Or put it in another way, a person’s past experience shaped their future action. This opens up an extremely interesting topic of practicality: how to read one person deeply through his or her past experience?

For Hume, what we call “personality” is, in many ways, the sum of a person’s habits and customs. Because he argued the “self” is just a “bundle of perceptions,” our character isn’t a fixed, essential soul. Instead, it’s a set of predictable mental pathways carved by our past experiences.

This leads directly to the question of how to “read” someone. From this perspective, “reading” a person isn’t a mystical art. It’s a “Humean” investigation. We in this case are empiricists studying another person, looking for the underlying patterns that their past has created.

Here are a few ways to approach this, moving from a Humean to a Kantian perspective:

The Humean Method: Look for “Constant Conjunctions”

Hume’s big idea for causation was “constant conjunction.” We can’t see the why, but we can see the what - what events are always paired together. To read a person, we do the same.
- Look for patterns, not single actions. A person “being rude once” tells us nothing. A person who is consistently deferential to authority figures but dismissive of subordinates reveals a deep-seated “custom” about power. This custom was learned, not invented.
- Identify their triggers. What impressions (events) are constantly conjoined with what passions (emotions)? For example:
  - Does criticism (impression) always lead to defensiveness (passion)? This suggests a past where criticism was threatening.
  - Does a story of injustice (impression) always lead to anger (passion)? This reveals a deeply ingrained value, likely from their own experiences with injustice.
- Listen to their “Principles of Association.” In Section III, Hume named the “mental gravity” that connects ideas. Listen to how a person’s thoughts flow.
  - Resemblance: What do they compare things to? “My new boss is just like my overbearing father.” This reveals the past lens through which they see the present.
  - Contiguity: What memories pop up based on a place or time? Their story of “home” reveals the emotional foundation of their life.
  - Cause & Effect: How do they explain their own life story? The “causes” they assign for their successes and failures (“I succeeded because I worked hard,” or “I failed because the system was against me”) reveal their core explanatory “custom.”
The “Passion” Method: Find the Slaves

Hume famously said, “Reason is, and ought only to be the slave of the passions.” This gives us a powerful tool. To read a person, don’t just listen to their “reasons” - those are just the justifications. Instead, try to identify the underlying passion (the desire, fear, or insecurity) that their reason is serving. A person’s past experiences teach them which passions are most important (e.g., the need for security, the desire for approval, the fear of abandonment).

For example, A person might give us 10 “reasons” for why they must buy a bigger house. The Humean method is to look for the “master” passion. Is it a desire for status (from a past of feeling insignificant)? Is it a passion for security (from a past of instability)? The “reasons” are just the mind’s “habits” for serving that master passion.

The Limit of the Humean View
Immanuel Kant would have found the profound limitation of this entire approach. Hume’s model, if taken to its extreme, is deterministic. It suggests a person is nothing but a bundle of past programming, helplessly acting out their “customs.”
Kant would argue that while Hume is right about our empirical character (our bundle of habits and desires), we, however, also have a “noumenal” or “intelligible” self. This is our rational, free will. This is where someone on the other side can potentially:

Observe their own Humean habits.

Stop and reflect.

Choose to act against their past programming, not because of a “passion,” but because of a “principle” they have rationally chosen (the Categorical Imperative).

So, to truly read a person deeply, we must look for 2 things:

Their Humean Character: What is their “default programming”? What are their habits, triggers, and ruling passions, all built from their past? This will predict 90% of their actions.

Their Kantian Character: What happens when they are tested? Do they have the self-awareness to see their own programming? Do they have the strength to override their “customs” for a moral principle? This reveals their capacity for freedom.

The deepest way to read a person is to understand this fundamental tension: the pull of their Humean past versus the potential of their Kantian freedom.

Part II#

Having established Custom as the cause of our expectations, Hume moves on to Part II to ask a new, related question: What is the nature of this expectation? He frames this as the difference between Fiction and Belief. Our imagination is free to conjure any idea, such as a golden mountain, but we don’t believe it exists. What, then, is this thing called “belief”? What is the difference between such a fiction of golden mountain and belief of its non-existence (EHU 5.10)? He argues it cannot be a separate “idea” that we add to the concept; we have the same set of ideas for “a golden mountain” whether we believe in it or not. (EHU 5.10)

The difference, he concludes, must be in the feeling or “manner of conceiving” the idea (EHU 5.11). This is his famous definition of Beliefe: (EHU 5.12) it is “a more vivid, lively, forcible, firm, steady conception of an object, than what the imagination alone is ever able to attain.” A belief is simply an idea that is felt with a particular force and vivacity, making it feel “real” and present to the mind. This, he argues, is precisely the feeling that Custom produces. When the habit of mind carries us from a present impression (seeing a flame) to its usual partner (the idea of heat), it infuses that idea with the vividness of the initial impression.

Hume describes this process as an unavoidable, instinctive “act of the mind,” as natural as feeling love or hate. It is a “pre-established harmony” not of divine design, but of natural psychological principles. To support this, he shows that his other, weaker principles of association - Resemblance (seeing a picture of a friend) and Contiguity (being physically near home) - also work to enliven our ideas, though none so powerfully as Cause and Effect. It is this powerful, custom-driven link of causality that forms the basis for all our beliefs about history (which relies on testimony) and science (which relies on induction). In sum, our entire system of belief about the world is not a product of rational calculation but a necessary, instinctive, and “felt” component of our human nature.

Section VI - Of Probability#

This section is a brilliant extension of Hume’s arguments from Section V, where he explained how our minds form a 100% certain Belief when our experience is totally consistent (a “constant conjunction,” like a flame always burning).

In this section, he asks the obvious next question: What happens when our experience is inconsistent or uncertain? Hume argues that our belief isn’t an “on/off” switch but a “dimmer switch” 🎛️ that scales precisely with our experience.

In a world filled with the phenomenons of probability, when our past experience is mixed (e.g., an event has happened 60 times one way and 40 times another), our mind performs a kind of automatic, unconscious arithmetic. Each past instance (both the 60 and the 40) creates a small “impulse” or “push” on our imagination, thanks to the principle of Custom. These competing impulses then “battle” in the mind. The side with the “superior number” of past instances (the 60) ultimately wins and determines our final expectation. The force of the winning side, however, is diminished by the opposing force of the minority (the 40).

The result is that we form a probable belief. We don’t feel the 100% certainty we feel with a flame, but we feel a partial assurance that is directly proportional to the statistical evidence.

TIP
This section perfectly reinforces again “Big Data” analogy. Hume is explicitly describing the human mind as a natural probabilistic engine. It doesn’t just learn from a perfect “constant conjunction”; it is a sophisticated mechanism that weighs all past data, calculates the “probabilities,” and produces a “feeling” of belief that is scaled to the strength of the evidence.

Jumping from Section VI to X#

We shall jump to section X for now without breaking the conceptual continuity. In fact, many people read Section X immediately after the sections we have covered so far on induction and probability.

Sections IV, V, & VI are Hume’s theory of “matters of fact”, where

IV: We have no rational proof for them.
V: We believe in them because of Custom.
VI: Our belief scales with Probability based on experience.

Section X is the “Application”: “Of Miracles” is Hume’s most famous and dramatic application of this entire theory. He’s taking the rules of evidence and belief he just established and applying them to the most extreme case possible: a claim that contradicts all of human experience (i.e., a miracle).

The sections we would be skipping (VII, VIII, and IX) are also “applications” or deeper dives, but they run on parallel tracks:

Section VII (“Of Necessary Connection”): This is a brilliant, deep dive into the origin of the idea of “cause.” It’s foundational to his core philosophy but not strictly necessary for understanding the miracles argument.
Section VIII (“Of Liberty and Necessity”): This applies his theory of causation to the free will debate.
Section IX (“Of the Reason of Animals”): This supports his theory by showing animals also learn from “custom.”

You can easily come back to these later. Jumping from Probability (VI) to Miracles (X) is a direct and exciting path, as it’s essentially a complex probability problem.

Section X - Of Miracles#

This section is the dramatic climax of the first part of the Enquiry. It’s where Hume takes his “sceptical” tools - his theory of belief, custom, and probability - and applies them to one of the most controversial and important topics of his day. Hume provided a single, decisive argument that a rational person should never believe in a miracle, even when presented with testimony from others. His argument is a “battle of evidence” based on the principles of probability we just learned in Section VI

Hume starts by praising an English archbishop, John Tillotson for using an experience-based argument against a specific Catholic doctrine. He’s cleverly showing that even the most pious thinkers use his methods (reasoning from experience) when it suits them.

John Tillotson’s writing against Catholic doctrine
The Roman Catholic doctrine of transubstantiation claims that bread and wine, when blessed in the ceremony of the Christian Eucharist, are substantially changed into the body and blood of Christ…
John Tillotson, a Protestant preacher, attacked Roman Catholicism, who ultimately became archbishop of Canterbury. He argued against transubstantiation on the basis that our only evidence of its truth is from the reported sense experience of the Disciples, but this must be balanced against the clear evidence of the senses that transubstantiation is false.
Hume’s argument against miracles, as we shall see pretty soon, is structurally parallel

Now Hume starts to set up his weapon to attach the concept of “Miracle”:

Testimony is Probabilistic: Testimony, as Hume pointed out, is usually a “common, useful, and necessary” (EHU 10.4) guide to reality. He establishes that we trust testimony not because of any a priori logic, but only because of experience (Custom) (EHU 10.6). Having stated that a proof is inevitable while probability is variable (EHU 10.6), Hume stated that testimony is essentially probabilistic. He points out that our experience also teaches us that testimony is fallible. We must weigh the probability of the testimony by considering the witness’s character, the number of witnesses, their potential bias, and how they deliver the news.
Assumption: Hume postulate that the winning side between two contrasting experiences is essentially weighting the probabilities of each side (EHU 10.8)
Defining “Miracle”: Assuming that the theist will understand a miracle as being an event that is contrary to nature’s normal ways of working, brought about by the intervention of some invisible spirit, Hume thus confines the scope of a “Miracle” by defining a miracle as a violation of a law of nature, and a law of nature as something established by “a firm and unalterable experience (EHU 10.12)”.

Hume believes laws of nature, as supported by proof is deterministic and intrinsically bears a probability extremely close to $1.0$ (e.g. $0.999\dots$ ), whereas a testimony-based miracle due to is intrinsic probabilistic anti-law nature cannot even reach a counter probability that’s even close to $1.0$ . Lastly, since Hume postulate that the winning side is essentially weighting the probabilities of each side, we should always disbelieve miracle when confronted with a law of nature.

To conclude for Part I, Hume states his famous maxim:

“That no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish” (EHU 10.13)

In Part II, Hume argues that even if a miracle could theoretically be proven, no miracle claim in human history has ever come close to meeting the high bar set in Part I.

Disputing Religious Authority#

A critical mind, on touching Hume’s conclusion of “Christian religion being founded on Faith”, shall quickly sense Hume’s political purposes against the Christian dogmatism during his time of living. In fact, section X is arguably one of the most potent political and cultural essays Hume ever wrote. It was not just an abstract philosophical puzzle; it was a direct, deliberate, and radical assault on the very foundation of religious authority in 18th-century Europe.

Hume was a central figure of the Enlightenment, a period defined by its attempt to replace dogma and superstition with reason and empirical evidence. His conclusion about faith was the final, devastating blow of his argument.

TIP
In his introduction to An Enquiry Concerning Human Understanding, Oxford University Press 2007, Peter Millican had an excellent narrative on the historical and European cultral background on which Hume developed his philosophical ideas. It is strongly recommended to read those pages which helps enormously to understand why Hume this section, i.e. for his rivalry on the religious authority of Church.
The rest of this sub-section is mostly relating Peter’s whole theme in his introduction, which describes the deterioration of Christian church authority during European’s Enlightenment period, in the context of “Miracle”.

Hume’s argument was aimed at a very specific target: the “Evidentialist” school of Christian theology. For centuries, and especially in the 17th and 18th centuries, the established churches didn’t just ask for blind faith. They claimed to have rational proof of their divinity. Their central argument was:

Miracles are acts of God that violate the laws of nature.
The Bible (and other testimony) provides reliable historical accounts of miracles (e.g., the resurrection).
Therefore, these miracles prove that the Christian revelation is true.

This was the intellectual and legal basis for the Church’s power. Miracles were their primary evidence.

Hume’s goal was to take this “evidence” and show that, according to the very rules of evidence we use in all other parts of life (in science, in law, in history), it was inadmissible. He was attempting to publicly disqualify religion’s main proof from the court of enlightened reason.

When Hume concludes that a Christian “is sensible of the weakness of human reason… and… believes in miracles… with a faith, which subverts all the principles of his understanding,” he is not making a respectful compromise. He is, in effect, saying:

“Gentlemen, I have just spent an entire chapter proving, on your own terms of evidence and experience, that belief in your miracles is rationally impossible. The only way you can continue to believe them is to admit that you are making an irrational leap—a ‘faith’ that is the opposite of reason, not its partner. You must choose: either join us in the world of reason, or stay in your world of faith. You cannot have both.”

This was a radical political act. He was attempting to force a divorce between philosophy/science and theology, walling religion off into a private, non-rational sphere where it could no longer claim to have a “proof” that gave it authority over public life, law, and education.

NOTE
Hume himself was known as “the Great Infidel.” His skepticism cost him university positions and made him a highly controversial figure. Section X was his most direct challenge to the dogmatism he saw as the main obstacle to human progress.

Ultimate Philosophical Justification for Big Data Analytics#

So much for the political side stories. Now we have all the required theories and context to resume our discussion unfinished in Section V. We first answer the question directly: No, Hume’s Enquiry is not the technical foundation of Big Data, but it is, arguably, its ultimate philosophical justification. This is a subtle but crucial distinction so let’s break it down a little bit:

Hume Defined the Problem that Big Data Solves#

Hume’s philosophy is the problem statement. He famously demonstrated that we have no logical, rational basis for believing the future will resemble the past. We have no access to the “secret power” of causation. Instead of reason, he said we are forced to rely on Custom or Habit. We observe a “constant conjunction” of events (Event $A$ is always followed by Event B), and our mind builds an instinctive expectation.

Hume’s Argument: Induction is a “Feeling”
Hume’s core problem is that we observe “constant conjunction” ( $A$ is always followed by $B$ ). This creates a Custom or Habit in our mind, which in turn produces a vivid Belief (a “feeling”) that $B$ will follow $A$ in the future.
His killer point was that there is no logical step that connects “I have seen $A$ followed by $B$ 1,000 times” to “I know $A$ will be followed by $B$ the 1,001st time.” This, he said, is a “leap of faith” we all make, guided by instinct, not reason. This is a psychological explanation.

For 200 years, this was seen as a devastating skeptical problem. But Big Data and machine learning looked at Hume’s conclusion and, in effect, said: “What if that’s not a bug, but a feature?” Modern predictive analytics works on a purely Humean principle. A machine learning model does not understand why $A$ causes $B$ (it has no access to “causality”). It is fed a massive data set of past events (Hume’s “experience”), identifies “constant conjunctions” (correlations), and builds a powerful, probabilistic model to predict the future (Hume’s “custom” or “habit,” but formalized as an algorithm).

Big Data is, in essence, the industrial-scale application of Hume’s “Custom.” It’s what we get when we stop worrying about the “why” of causation and focus all our energy on the “what” of correlation.

The Technical Foundation Came from Hume’s Opponents#

This is the most fascinating part of the story. The actual mathematical foundation of Big Data was not built by Hume’s followers, but by people who were trying to solve the very problem he created.

The true mathematical ancestors of data science are figures like Thomas Bayes and Pierre-Simon Laplace.

Hume’s Enquiry (specifically his essay skeptical of miracles) was published in 1748. It caused a huge stir. In the 1760s, Richard Price published the work of his late friend, Thomas Bayes. Price used Bayes’s Theorem (as we now call it) to argue against Hume, showing mathematically how the testimony of multiple independent witnesses (data points) could make a very improbable event (a miracle) become believable. This was the birth of Bayesian statistics: a mathematical method for updating our “custom” or “belief” when new data arrives.

The “original reference” for the Bayes’s Theorem itself is Thomas Bayes’s paper, which he never published. His friend, Richard Price, found it among his notes after his death and presented it to the Royal Society.

Title: An Essay towards solving a Problem in the Doctrine of Chances
Published in: Philosophical Transactions of the Royal Society of London (1763)

We will not, however, find the modern, algebraic formula of

P(H|E) = \frac{P(E|H) \cdot P(H)}{P(E)}

Instead, Bayes’s “essay” is a dense, 20-page solution to a single “Problem”:

Problem: “Given the number of times in which an unknown event has happened and failed: Required the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability that can be named.”

So, where did the modern equation above come from? That was the work of the French mathematician Pierre-Simon Laplace in Théorie analytique des probabilités (“Analytic Theory of Probabilities,” 1812) and his earlier Philosophical Essay on Probabilities. Laplace independently rediscovered and generalized Bayes’s principle, giving it the powerful algebraic form we use today. He was the one who famously applied this logic to Hume’s other problem (Section IV), creating “Laplace’s Rule of Succession” to calculate the probability of the sun rising tomorrow.

The direct argument between the two ideas was about Hume’s specific use of it in this section “Of Miracles.” This is where ones engineering background will make this click.

Hume argues that a “miracle” is, by definition, a violation of a “law of nature.” A law of nature is something we believe in because of “a firm and unalterable experience” (i.e., a massive amount of past data). In modern terms, he’s comparing two probabilities:

$P(\text{Miracle})$ : The probability of the miracle, and
$P(\text{False Testimony})$ : The probability that the witnesses are lying or deluded

Hume argues that $P(\text{Miracle})$ is, by definition, infinitesimally small (based on all our past experience) and that $P(\text{False Testimony})$ is always higher than this. Therefore, a rational person should always reject the testimony. This is an absolute conclusion.

Reverend Richard Price, who published Bayes’s work, saw Hume’s argument and realized it was a testable, mathematical problem. He essentially accused Hume of doing the math in his head and getting it wrong.

Let’s use Bayes’s Theorem. We want to know the probability that a miracle happened given that we have testimony for it: $P(M|T)$ :

P(M|T) = \frac{P(T|M) \cdot P(M)}{P(T)}

where

$P(M|T)$ is the Posterior Belief, which is what we want to find (the probability the miracle is real)
$P(M)$ is the Prior Belief, which is Hume’s “law of nature.” We can agree with Hume that this is incredibly small. Let’s say $P(M) = 1 \times 10^{-20}$ .
$P(T|M)$ is the Likelihood, which is the probability we would get this testimony if the miracle actually happened. Let’s say the witnesses are 90% reliable, so $P(T|M) = 0.9$ .
$P(T)$ : The total probability of hearing the testimony. We expand this using the law of total probability:

$P(T) = P(T|M)P(M) + P(T|\neg M)P(\neg M)$

Here, $P(T|\neg M)$ is the key: the probability of the testimony if the miracle did not happen. This is Hume’s “falsehood of the testimony.” Hume’s mistake was in thinking his tiny prior $P(M)$ made the whole thing impossible. The Bayesians showed that extraordinary evidence can overcome an extraordinary prior.

Let’s define a “witness” to be a testimony of “I saw this miracle happened” where in fact this miracle never physically happened. One witness is certainly unreliable. But what about 10 independent witnesses of such? In this case, the prior $P(M)$ stays the same (it’s still $10^{-20}$ ). But the probability of 10 independent people all lying or being deluded in the exact same way is astronomically small. This is the equivalent of mathematically stating that “given the miracle didn’t actually happen, the probability of 10 people all say the miracle did happen” is very small, i.e. $P(T|\neg M)$ . Hence the probability of the testimony if the miracle didn’t happen ( $P(T|\neg M)$ ) shrinks exponentially.

At a certain point, the $P(T|\neg M)$ term can become much smaller than the $P(M)$ - extraordinary evidence overcome an extraordinary prior, in which case Hume’s own rule is satisfied: the falsehood of the testimony ( $P(T|\neg M)$ ) has become “more miraculous” (i.e., less probable) than the miracle itself $P(M)$ .

What is Hume’s own rule?
Earlier in this section we discussed this rule:

“That no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish” (EHU 10.13)

Literally, Hume is stating that “You cannot justify the miracle unless you prove that opposite side of miracle is more probable”

Mathematical Justification for Data Mining#

A direct mathematical and philosophical consequence of the Bayesian framework that Price and Laplace championed is entire modern discipline of outlier analysis (or anomaly detection) in Data Mining.

The debate between Hume and Price/Bayes was the 18th-century, philosophical version of the core question in modern data mining: “When I see a data point that contradicts all my other data, what should I do?”

Hume’s Model: “Discard the Outlier”

Hume’s argument in “Of Miracles” is the classic, non-statistical approach to outliers.
- The Outlier: A “miracle” (e.g., a single data point of a man rising from the dead).
- The Model: The “Law of Nature” (e.g., a massive data set of billions of points showing dead men stay dead).
- Hume’s Conclusion: The outlier must be an error. The model (“law of nature”) is based on a “firm and unalterable experience,” so any data point that contradicts it is, by definition, “false testimony” or a measurement error.
- The Action: Discard the outlier. It’s irrational to believe it.
This is a brittle model. It’s great at describing the “norm,” but it has no way to rationally process a “black swan” event.
The Bayesian Model: “Weigh the Outlier”

The Bayesian framework created by Price and Laplace provided the first formal, mathematical tool to challenge Hume’s rigid conclusion.
- The Outlier: A “miracle” (an anomalous data point).
- The Model: A “prior probability” (our belief based on past data, which is very strong, but not 100%).
- The Bayesian Conclusion: The outlier could be an error, OR it could be a true, new, revolutionary piece of data. How do we decide? We use probability to weigh two competing hypotheses:
  1. Hypothesis A (The “Error” Hypothesis): What is the probability this data point is “false testimony” (a measurement error, a lie, a bug in the sensor)?
  2. Hypothesis B (The “Miracle” Hypothesis): What is the probability this event actually happened (it’s a real, though rare, event)?
  Bayes’s Theorem gives us the engine to weigh $P(\text{Hypothesis A }|\text{ Evidence})$ against $P(\text{Hypothesis B }|\text{ Evidence})$ .
This is the mathematical justification for outlier detection. We don’t just discard the anomaly. We quantify the evidence for it.

Think of fraud detection, which is a classic data-mining problem:

The Model (Prior): 99.999% of our credit card transactions fit a predictable pattern (location, amount, time).
The Outlier: A $5,000 charge for scuba gear in another country.
A Humean Analyst would say: “This contradicts the ‘law of nature’ of your spending. It must be fraud. Block it.”
A Bayesian Analyst (the actual algorithm) says: “This is a ‘miracle,’ an event with a tiny prior probability. But let’s check the testimony. Was a PIN used? Did the chip work? Is the store legitimate?”

If the “testimony” (the new data) is extraordinarily strong (e.g., a PIN was used, and we bought airline tickets two days ago), the model’s belief will shift. It will conclude that the falsehood of this “testimony” is less probable than the “miracle” itself.

The concept of an “outlier” is just an observation. But we have seen that the rational framework for deciding what to do with it - the very heart of data mining - is a direct consequence of the mathematical logic that Bayes, Price, and Laplace created to solve Hume’s problem.

What makes David Hume an Empiricism?#

A Temperamental Aversion to Dogma#

The “Disease of the Learned”: A Formative Crisis#

A Grounded, Worldly Disposition 🍻#

What makes David Hume an “Extreme” Empiricism?#

Section I - Of the Different Species of Philosophy#

Section II - Of the Origin of Ideas#

Hume’s Blind Spot - Subconsciousness#

Humean System Failure#

The Kantian Alternative: An Active, Structuring Mind#

Section III - Of the Association of Ideas#

Section IV - Sceptical Doubts concerning the Operations of the Understanding#

Part I: Building the Case and Posing the Ultimate Question#

Part II: The Skeptical Conclusion#

Section V - Sceptical Solution of these Doubts#

Part I#

Parallel Between “Custom and Habit” and “Big Data Analytics”#

”Humean” Investigation on Personality#

Part II#

Section VI - Of Probability#

Jumping from Section VI to X#

Section X - Of Miracles#

Disputing Religious Authority#

Ultimate Philosophical Justification for Big Data Analytics#

Hume Defined the Problem that Big Data Solves#

The Technical Foundation Came from Hume’s Opponents#

Mathematical Justification for Data Mining#