Understanding Hume’s Fork

“Hume’s fork” describes how we refer to Kant’s critique of Hume, who separated knowledge into two types: facts based on ideas and facts based on experience.[1][2][3]

Before getting to the details and definitions of the term used below (i.e. don’t worry if you don’t understand these terms yet, we cover them below), Hume’s Fork can be understood by comparing these two “prongs”:

  • Empirical (facts based on experience), Relations of Facts – Statements about the world. These are syntheticcontingent, and knowable a posteriori. They are gained through empirical evidence (empiricism). Things we know through the senses. Ex. “An apple tastes sweet,” “the bachelor is sitting in a chair.”
  • Rational (facts based on ideas), Relations of Ideas – Statements about ideas. These are analytic, necessary statements (tautology) that are knowable a priori. They are known through reason (rationalism). Things we know through thought alone. Ex. “1+2=3,” “no apples are blue,” “all bachelors are unmarried.”

TIP: Hume’s fork = “a two-pronged fork in which the two prongs (rationalism and empiricism) never touch; or a fork in the road that never crosses.” Kant “crosses Hume’s fork”. See the story of how Hume inspired Kant (for more background on Hume and Kant).

A Summary of Kant’s Critique of Pure Reason and Hume’s Fork

To get Kant’s Critique of Pure Reason (which is really a justification for using both empiricism and rationalism) it helps to understand a basic theory of knowledge (the general name for an epistemological theory of pure reason, empiricism, ethics, metaphysics and such; what this theory is actually pointing at and the major focus of Hume and Kant).

In lieu of that, the following descriptions will suffice:

  • Hume tells us that we can only trust our our senses and experiences. Ideas born from our intellect alone tell us little about the real world (empiricism). TIP: See An Enquiry Concerning Human Understanding (written 1748; Kant wouldn’t have seen it until later). In that work Hume discusses his empirical theory of morals and his empirical theory of epistemology (what we can know). In the work he critiques pure reason so well that it caused Kant to dedicate a good decade to a rebuttal (sadly finished after Hume died).
  • Kant takes a mostly opposite stance, saying that while empirical data is useful, and that while all truth begins with the senses, we can only truly “understand” things using reason (rationalism)… after-all, our senses could be tricking us. TIP: See the Critique of Pure Reason (1781) where Kant, after being inspired by Hume, critique’s both his own style of pure reason and Hume’s absolutist skeptical empiricism (i.e. the title primarily refers to Kant’s critique of his own theories from his earlier works The Groundwork of the Metaphysic of Morals and The Metaphysics of Morals).

Despite Kant’s rationalist stance, after “being awoken from his dogmatic slumber” by Hume’s Enquiry, Kant abandons “pure reason” for a slightly more nuanced epistemological theory.

More specifically, Kant successfully synthesizes Hume’s ideas with his own in his masterwork a Critique of Pure Reason, thus “crossing Hume’s fork,” by saying (paraphrasing), “although all knowledge begins with the senses, we can use our experiences to inform our reason, and vice versa; We can’t rely on our senses alone, but nor can we rely on pure rationalization.”

Thus we can say, Kant “crosses Hume’s fork” by proving that we can create a confirmable [via testing] “synthetic” “a priori,” a proposition that is true and not dependent on itself, yet can’t be proven via direct empirical evidence (it can only be proven indirectly).

An example of a “synthetic” “a priori” that is provable indirectly is E=mc2, as it is true, but we can’t confirm it with direct experience (we can only confirm it indirectly via experiment). In his critique Kant uses space and time as examples of useful a priori, so we might also consider the concept of spacetime as something very real and useful, but not confirmable directly with the senses.[4][5][6]

TIP: I’m sure you are at this point wondering, “wait, what is an a priori?” Generally speaking, it is Kant’s term for “pure” rationalism (that which isn’t gleaned by direct experience; something that is logically independent of experience). We discuss definitions and examples of all the Kantian terms related to Hume’s Fork in detail below.

An example of the difference between ideas and experience: “All bachelors are unmarried” (idea) vs. “A bachelor is sitting in the chair” (experience). We know the bachelor is in the chair because we see him sitting there. We only know all bachelors are married because they are bachelors (we can’t go around confirming each of the world’s bachelors is unmarried via our senses). We know this logically because it is necessary for the sentence to be true, but it tells us nothing specifically about our world (it is a fact about an idea, not a fact about the world). It is redundant, what Hume calls a tautology.

Rationalism Vs Empiricism. This video works as a quick overview, see the lecture below for a full discussion of the ideas of Kant and Hume.

TIP: Hume and Kant are hardly the only ones having this debate. Locke is a famous empiricist. Plato and Aristotle have the argument indirectly. And liberalism vs. conservatismrealism vs. idealism, and the general left-right argument is essentially this same general argument.

Locke, Berkeley, & Empiricism: Crash Course Philosophy #6. Another look at the historic debate between rationalism and empiricism.

TIP: The title of the book Sense and Sensibility, by Jane Austin (1811), is a reference to the argument over passion and reason. Passion is historically associated with the female, and reason with the male.

Vocabulary Used by Hume and Kant: Defining Propositions, Empiricism, Rationalism, Skepticism, Analytics, Synthetic, a Priori, a Posteriori, Necessary, Contingent, Tautological and Related Terms

To understand Hume’s fork, as presented by Kant in his a Critique of Pure Reason, and named later by scholars, we need to define some terms that Kant used and/or coined:

  • Proposition: A logical judgement about two or more terms (a subject and a predicate; ex. “a bachelor is sitting in the chair” is a proposition or judgement about the subject, “a bachelor”, “sitting in the chair,” the predicate). In other words a proposition is a proposed logical judgement about at least two terms.
  • Empiricism: Knowledge through empirical evidence (information from the senses). Facts about the world.
  • Rationalism: Knowledge through ideas (information originating in our minds). Facts about ideas.
  • Skepticism: In this case, being skeptical that rationalism (pure reason) can result in true knowledge about the world. Can be interpreted broadly as skepticism about both empirical and rational knowledge. For instance, Kant suggests fusing the two styles as, “our senses themselves could be tricking us.”
  • Analytic proposition (or judgement): a proposition (AKA logical judgement) whose predicate concept is contained in its subject concept. A statement that is true by definition.  Ex. “All bachelors are unmarried.” The bachelor is unmarried because he is a bachelor.
  • Synthetic proposition: a proposition whose predicate concept is not contained in its subject concept but related. True by observation. Ex. “The bachelor is sitting in a chair” (nothing about sitting in a chair makes one a bachelor).
  • a priori proposition: a proposition whose justification does not rely upon experience. Moreover, the proposition can be validated by experience but is not grounded in experience. Therefore, it is logically necessary. What Hume called a tautology. Ex. “1 + 2 = 3,” or “all bachelors are unmarried.” It stands to reason all bachelors are unmarried, but I can’t meet every bachelor to confirm this empirically.
  • a posteriori proposition: a proposition whose justification does rely upon experience. The proposition is validated by, and grounded in experience. Therefore, it is logically contingent. Ex. “The bachelor is sitting in a chair” (yes, I can confirm the bachelor is in the chair empirically, via my senses, by looking).

This gives us four possibilities:

  • An Analytic a posteriori which are experience based propositions that can be shown to be true by their terms alone.
  • A Synthetic a posteriori which are experience based propositions that can be shown to be true by their terms alone.
  • An Analytic a priori which are propositions not based on experience that can be shown to be true by their terms alone.
  • A Synthetic a priori which are propositions not based on experience that can’t be shown to be true by their terms alone.

Furthermore, to round out this Kantian theory of knowledge, we can also define the following judgments:

  1. A necessary proposition (necessarily true): Any proposition which is necessarily true or necessarily false (the white cat is white; or, the white cat is not black). A necessary proposition is one where the truth value remains constant across all possible worlds.
  2. A contingent proposition (dependent on more information): Any proposition in which the truth of the proposition depends on more information. They are propositions that are neither “true under every possible valuation (i.e. tautologies)”, nor “false under every possible valuation (i.e. contradictions)”.
  3. Tautological proposition (necessarily true but redundant): That which must be true no matter what the circumstances are or could be (ex. the black cat is black; it is redundant to say the black cat is black).
  4. Contradictions (necessarily not true as it contradicts itself): That which must necessarily be untrue, no matter what the circumstances are or could be (ex. the bachelor is in a chair and not in a chair).
  5. “Possible” proposition (is true under certain circumstances): Are true or could have been true given certain circumstances (ex. x + y = 4).

TIPa priori and a posteriori are two key terms in Kantian philosophy. Kant coins their modern usage, but he borrowed them from Latin translations of Euclid’s Elements from about 300 BC. In other words, Kant famously gave names to epistemological concepts, but he did so methodically (whether he borrowed the terms or coined them). The first step to understanding Kant is internalizing the terms he introduces, after that one just needs to follow his arguments.[7]

HINT: a priori kind of sounds like “pure,” it is pure formal rationalism. A posteriori, is the other one.

Defining Hume’s Fork

Again with our above definitions in mind, let’s look again at the “two prongs” of Hume’s Fork before we cross them:

  • Empirical (facts based on experience), Relations of Facts – Statements about the world. These are syntheticcontingent, and knowable a posteriori. They are gained through empirical evidence (empiricism). Things we know through the senses. Ex. “An apple tastes sweet,” “the bachelor is sitting in a chair.”
  • Rational (facts based on ideas), Relations of Ideas – Statements about ideas. These are analytic, necessary statements (tautology) that are knowable a priori. They are known through reason (rationalism). Things we know through thought alone. Ex. “1+2=3,” “no apples are blue,” “all bachelors are unmarried.”

In other words, as you may have noticed from that list of terms above, 1/2 the terms apply to the world of ideas (rationalism) and the other 1/2 apply to the world of things (empiricism).

Crossing Hume’s fork will, again to re-summarize this with everything thus far in mind, involve creating a synthetic a priori that is not tautological or contingent, but necessarily true (get it, we are mixing categories and “crossing forks” between the world of ideas and the world of experience to have even more understanding about the world than we would without crossing forks). See: A Priori and A Posteriori.

1. David Hume’s Fork and Immanuel Kant’s Synthetic A Priori. “Hume’s Fork” is a concept laid out by Kant to refute Hume and labeled by later philosophers.

TIP: As noted above, Kant’s analysis of the epistemological concepts discussed on this page starts in his earlier works like The Groundwork of the Metaphysic of Morals and The Metaphysics of Morals where he first properly lays down his Kantian ethics. In these texts he is giving names to fundamental dualities and concepts in an effort to better shed light on human understanding, just like he does in Critique. A main theory of his earlier works is that, in the realm of metaphysics and morals, “pure reason” can be used to know some truths (while other truths require the crossing of reason and empirical evidence). Hume counters this (albeit not talking directly to Kant), saying no human understanding can be gleaned from “pure reason” alone, and then Kant counters Hume in his Critique of Pure Reason saying “yes it can”. This confirms for us two things 1. an earnest exploration of these concepts requires reading multiple works of Hume and Kant 2. While both Kant and Hume care about science and politics, both are more interested in metaphysics and morality than justifying or debunking Newtonian physics.

TIP: Kant, like the Greeks, embraced the idea of a threefold division of philosophy into logic, physics, and ethics in his Groundwork. Kant starts the text by accepting that physics and ethics require a crossing of reason and empirical evidence, but rejected the idea for metaphysical morals and logic. Hume rejected the idea that any knowledge that wasn’t grounded in the empirical was knowledge at all. Kant ultimately tried to show that the fork could be crossed in all these realms allowing us to accept Newton’s F=ma and his Categorical Imperative.

Crossing Hume’s Fork

Kant’s crossing of Hume’s fork can be understood like this (my quotes below are meant for educational purposes, they never specifically said these things, their arguments are more complex and in different books):

  • Hume says, “we can’t cross this two-pronged fork of the empirical and rational… Throw Newton’s F=ma out the window, because it tells us nothing about the world”. “All knowledge begins with experience”. (See examples of Hume’s Empirical Naturalism).
  • Kant Says, “Though all our knowledge begins with experience, it does not follow that it all arises out of an experience. And, although all a posteriori judgments are indeed synthetic, not all necessary a priori judgments are analytic.” “We can and must cross the fork in terms of the a priori. We can create a necessary synthetic a priori. For example, we can use Newton’s laws of gravity to predict real world events, which we can than observe to be true empirically. Even when we can’t observe these events directly, we can observe effects and create theories that work 100% of the time. Hume is partially correct in that we can’t rely on pure reason alone. Our sensibility can inform our senses, but our reason can inform us as well” (See examples of Kant’s Synthetic A Priori Judgments and a Critique of Pure Reason).

An Example of a Synthetic a priori

A Synthetic a priori (an example of a “crossed fork”): A good example of crossing Hume’s fork is Newton’s laws (Kant gives a similar example of “every event has a cause” in his book).

Let’s take the second law, F=ma (Force equals mass time acceleration in an inertial frame). It is synthetic, as the predicate concept is not contained in its subject concept (nothing about force inherently equals mass time acceleration). But also, it is loosely also a priori because it can’t be experienced directly, and well, it’s certainly not a posteriori as we can’t confirm a F=ma on a far off planet, but we can know it’s true using reason.

His third law also works, which states: one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

One can’t set about testing every object just as one can’t confirm every bachelor, yet again we can use experiments to know this theory is true.

TIP: This article contains an excellent analysis of the synthetic a priori The Importance of the Synthetic A Priori in Kant’s First Critique.

Using a Synthetic a priori to Cross forks: Equations like Newton’s F=ma or Einstein’s E=mc2 are Pure Reason (Pure Logic) despite being both true and not tautological. Yet we can’t confirm they tell us anything about the world until we test and confirm them via experiment and actually physically “cross forks” (we have to not only create a “Synthetic a priori”, but prove it is true empirically). Even though we can’t reach out and touch their forms directly, we confirm those equations “are true”, as they can help us to predict what we will observe with perfect accuracy. Thus they are great examples of a “synthetic a priori”. The complex part is dealing with “Synthetic a priori” that can’t be proven, such as is the case with Moral Philosophy…

…Trying to Cross the forks of Moral Philosophy: On this page we are dealing with crossing the forks of natural philosophy (AKA natural science), in other words, we are just showing you how the empirical and logical forks can cross. However, both Kant and Hume apply their theories to morality and ethics (they are, so to speak, also seeing if they can cross the more ethereal forks of ethics and metaphysics). Hume says morality is purely informed by the senses (that ALL knowledge that can tell us useful facts is empirical – period); Kant says we can have useful knowledge of the empirical, logical, ethical, and metaphysical, despite the more obvious benefits of the empirical. It stands to “reason”, if we can cross the forks of natural philosophy, why can’t we cross the forks of moral philosophy? A main goal of Kant is to figure out if we can create a confirmable metaphysical “synthetic a priori”. Long story short, Kant believes that we can have facts about pure philosophy, but that we can’t create a provable metaphysic “synthetic a priori”. In other words, we can have true facts about metaphysics… but we can’t prove it empirically. Learn about crossing forks and human understanding in terms of the physical, logical, ethical, and metaphysical.[8]

…And a Book Full of Proofs and Arguments

The above summary of Kant’s argument was gleaned from the over 1,000 pages of his work.

The gist is that Kant attempted to prove that we can use facts about ideas to prove facts about the world. That “Pure Reason” can be used to prove the existence of a synthetic a priori, crossing the tongs of Hume’s Fork, and thus saving Newton’s laws and science itself in the process.[9]

This we can conclude, Kant rebutted Hume in an effort to show that knowledge can be found in both “the necessary and contingent (concerning reality), the a priori and a posteriori (concerning knowledge), and the analytic and synthetic (concerning language); In short, useful human knowledge can be found in both reason and empirical sensory evidence, and each form of human understanding can tell us about the other.”

Prof. Paul Guyer – Hume, Kant, and the Passion for Reason

TIP: Think about the scientific method. We have ideas and define experiments; we do experiments and come up with more ideas; rinse and repeat. We formulate theories and we test a hypothesis based on theoretical mathematics or ideas. Modern science IS the crossing of Hume’s fork.

TIP: We credit Kant with saving science, but Hume also saved science. Before Hume (in the Age of Reason) empiricism was starting to be abandoned for Pure Reason (Newton doesn’t always offer proofs for instance). Long story short, Hume and Kant are both sages and both important. Kant’s a Critique of Pure Reason exemplifies a key moment in history (and it is largely a testament to Hume’s importance as well as Kant’s).


  2. Synthetic A Priori Knowledge
  3. Hume’s fork
  4. Critique of Pure Reason: Introduction B
  5. The Importance of the Synthetic A Priori in Kant’s First Critique
  6. Rationalism vs. Empiricism
  7. A Priori and A Posteriori
  8. Analytic / Synthetic Distinction – The possibility of metaphysics
  9. Hume’s Fork

"Hume’s Fork Explained" is tagged with: Epistemology, Immanuel Kant, Liberalism, Metaphysics, Morality, Senses, Theories

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