Understanding Humes Fork

Humes fork describes how we refer to Kants critique of Hume, who separated knowledge into two types: facts based on ideasand facts based on experience.[1][2][3]

The general concept is that Hume asserts there are two distinct classes of knowledge, 1. rational (knowledge based on thoughts and ideas) and 2. empirical (knowledge based on experience in the material world), and that only the empirical can tell us useful things about the world (that we can only learn useful things about the world through experience). Meanwhile, Kant offers a rebuttal by attempting to prove that pure reason can tell us about the world (that we can learn useful things about the world based on ideasalone).

In other words, Hume says we can only know about the world through experiences in the physical world, and Kant says we can know about the world through ideas too.

Thus, Kant thinks both prongs of this two pronged fork of ideas and experience are useful, and Hume thinks only one prong is useful mostly everything else discussed below is a summary of Kants complex thoughts on Humes argument for experience-based empirical knowledge.

Before we explain everything in further detail, itll be helpful to introduce some more terms used by Kant and Hume when discussing this topic.

Humes Fork can be understood by comparing the following two prongs (dont worry if you dont understand the terms below yet; the point of this page is to explain them):

TIP: Humes 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 Humes fork by combining terms from each prong (specifically by proving the existence of a synthetic, necessary, a priori judgement/statement). See the story of how Hume inspired Kant(for more background on Hume and Kant), or see our page that focuses onthe a priori/a posteriori, the analytic/synthetic, and the necessary/contingentspecifically.

To understand all the terms we just used, it helps to know that they can be described by the following distinctions (where in each case one term relates to the rational and the other the empirical):

What do a priori and a posteriori mean? a priori means prior to experience (pureformal imagination and reason; rationalization not based on experience), anda posteriori means after experience (concepts we get from observation via our senses; based on empirical experience).

An example of thedifferencebetween ideas andexperience: All bachelors are unmarried (idea) vs. the bachelor is sitting in the chair (experience). We know the bachelor is in the chair because we see him sitting there (we can verify this with our senses, we dont need to rationalize it). We only know allbachelors aremarried because they arebachelors (we cant go around confirming each of the worlds bachelors is unmarried via our senses, we must rationalize it). We know all bachelors are married islogicallytrue, 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 atautology.

To get Kants Critique of Pure Reason (which is really a justification for using both empiricismand rationalism) it helps to understand a basic theory of knowledge(the general name for an epistemological theory of purereason, 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 of Humes and Kants arguments will suffice:

Despite Kants rationaliststance, after being awoken from his dogmatic slumber by HumesEnquiry, Kant abandons pure reason only for a slightly more nuanced epistemological theory (which mashes up pure reason and empiricism to show how they relate).

In other words, Kantsuccessfully synthesizes Humes ideas with his own in his masterworka Critique of Pure Reason, thus crossing Humes fork, by saying (paraphrasing), although all knowledge begins with the senses, we can use our experiences to inform our reason, and vice versa; We cant rely on our senses alone, but nor can we rely on pure rationalization.

Thus we can say, Kant crosses Humes fork by provingthat we can create a confirmable [via testing] synthetic a priori, a propositionthat is necessarilytrue and not dependent on itself, yetcant be proven viadirect empirical evidence (it can only be proven indirectly).

An example of a synthetic a priori that is necessarily true, and is provable indirectly (and therefore is objective), isE=mc2.

E=mc2is a rationalized idea, that is necessarily and objectively true (for observable physical bodies in spacetime) and not dependent on itself, yet cant be confirmed with direct experience (we can only confirm it indirectly via experiment).

GENERAL NOTE: Not every example we use on this page was given by Kant. When Kants example is clear and makes sense for a modern reader, we use it. When it is complex, or not directly said in his work, we opt for other examples.

TIP: Kant proves that synthetic a priori judgements are possible early on in his Critique, pointing to mathematics (ex. 7 + 5 =12), geometry (a straight line between two points is the shortest), physics (F=ma), and metaphysics (God gave men free-will) as examples of synthetic a priori. The main question he then seeks to answer is, how are a priori synthetic judgements possible? Here we can note that since metaphysics, in its dealing with freedom, God, and the will, deals with the unknowable a priori, the key to figuring out the limits of our knowledge and the usefulness of rationalism is found not in metaphysical concepts like free-will but in more practical fields in which the physical and logical intersect like mathematics (including geometry) and physics. This is why Kant focuses on space and time as examples rather concepts such as free-will and morality. Still, make no mistake, Hume and Kant are both speaking to a bigger picture which includes pure metaphysics, ontology, theology, and other such areas of inquiry.

If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: For it can contain nothing but sophistry and illusion. Humes Enquiry.

TIP: As noted above, in his critique, Kant uses space and time as examples of useful a priori (offering geometry as an example of applying rational ideas about objects extended in space to the empiricalworld). With this in mind, we might also consider the concept of spacetime as a useful synthetic a priori concept, even though it is not confirmable directly with the senses. Kants justifications are complex and examples are sparse, but generally we can say he is pointing to the idea that rational laws like Newtons laws of physics are examples of useful a priori that tell us about the world. In this respect, proving synthetic propositions a priori useful isnt just about proving the usefulness of volumes of divinity or school metaphysics (from the theological to the moral metaphysics) it is about proving the usefulness of theoretical physics equations like those of Newton.[4][5][6]

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. conservatism,realism vs. idealism, and the general left-right argumentis essentially this same general argument. Each philosopher simply presents different ways to understand the underlying truisms of logic and reason.

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

To understand Humes fork, as presented by Kant in hisaCritique of Pure Reason, and named later by scholars, we need to define some terms that Kant used and/or coined:

The three basic distinctions we are working with (as noted above) are:

The terms used in those distinctions can be defined in terms of propositions (logical statements) like this:

This gives us four possibilities:

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

With all of that in mind, the main point here is that we can create: A necessarysynthetic a priori proposition that is not contingent or tautologicallike F=ma (thus crossing Humes fork). This type of judgement has both empirical and logical qualities and is a type of transcendental aesthetic.

What does transcendental mean in Kantian terms?An important but complex concept of Kant is the transcendental. Essentially each part of our discussion gets a transcendental, which generally describes where one category (like a priori, the rational, the logic) transcends into another (like a posteriori, the physical, the aesthetic). Important for our conversation is the Transcendental Aesthetic, which describes the a priori of empirical things (like space, time, geometry) from a physical perspective. Meanwhile, to flesh out the picture, Transcendental Logic describes the aspect of logic that relates to the empirical (like the categorizing of relations between objects) from a pure formal a priori perspective. A synthetic a priori like F=ma speaks to the transcendental aesthetic when we focus on the actual forces in the empirical world, and to transcendental logic in the way we speak about the proposition and categorize it. Learn moreKants Transcendental.

Phenomena and noumena: Kant also considers other terms likephenomena and noumena. Phenomena are the appearances and properties of things; that which constitutes what we can experience and sense. Meanwhile, noumena are posited objects or events that exist without sense or perception (that which, in theory, constitutes reality). In other words, the properties and effects of a thing that we can sense directly are phenomena, and the rest is noumena. All synthetic a priori judgements that tell us about the world are rationalizations about phenomena (like F=ma which describes the phenomena of force, mass, and acceleration). Understood loosely, 1. noumena is of the rational and phenomena is of the empirical, and 2.noumena is the thing-in-itself and phenomena is the effects (the manifestations of those things that can be perceived via the physical senses). TIP: See Platos theory of the forms(a theory of a noumenal world; as a metaphor at least) for more on different ways to understand noumena. NOTE: Empirically speaking, an object is a collection of properties (ex. a photon isnt a widget with properties as far as we know; the only way to describe a photon is to describe its properties, its phenomena). From this perspective there is only phenomena in the physical world and noumena is just a metaphysical idea (at best describing a collection of properties; directly observable or not). With that said, loosely speaking, it helps to understand that we can have useful knowledge of an object beyond what we can sense about an object directly. Still, the takeaway is the noumenal world may exist, but it is completely unknowable through human sensation and therefore it is a purely metaphysical concept.[7][8]

TIP: As you can see a from the above, some terms are very similar, this is because all these terms speak to different aspects of what we can know. All of logic is a bit like that, sometimes we are talking about the process of thought, sometimes about the product. Sometimes about a judgement, sometimes about a term. A justification that relies on experience (a posteriori), and a statement that is true based on observation (synthetic) can use some of the same exact examples (as they are both speaking about an empirical judgement). Likewise, we can consider synthetic a priori terms, judgements, and categories (not just judgements/propositions/statements). Despite this, each term speaks to a different aspect of thought and has a slightly different meaning. In other words, many terms are similar, but they have specific meaning, and need to be considered on their own merit and in context.

NOTE: Humes fork is all about concepts pertaining to the validity of a single proposition. Meanwhile, propositional logic deals with the argument form which pertains to the validity of a argument consisting of multiple propositions. Logic can be thought of as a three step process, where first we consider terms/concepts, next we consider single logical propositions (what we are doing here), and then we move on to considering reasoned arguments consisting of multiple propositions. See a page on propositional logic and reasoning for the next step.

Below is a table that illustrates the above concepts and their relations.

Remember Kants goal was to prove Humes idea that pure rationalization tells us nothing about the world wrong, by proving the existence of anecessary synthetica priori (a statement not based on experience, that cant be shown to be true by its terms alone, but is necessarily true).

Ex. All bachelors are unmarried

Ex. The man is sitting in the chair

Ex. All bachelors are unmarried

Ex. All bachelors are unmarried. We cant personally ask every bachelor in the world if they are unmarried (does not rely on experience), but we know they are because a bachelor is by definition necessarily unmarried (the statement is tautological or redundant rationalized a priori).

TIP: Pure tautological reason. Logical.

F=ma

TIP: F=ma is necessarily true and not tautological, yet only indirect evidence can prove it (we cannot observe force, mass, and acceleration acting on bodies extended in space and time directly).

TIP: Although some statements can be contingent in this class. This class also contains statements that are necessarily true, but not tautological, andcant be proven by direct empirical evidence (they instead require testing and indirect evidence to prove). A sort of mix of pure reason and empiricism that crosses Humes fork and to which induction and deduction apply.

TIP: Transcendental(a mix of logic and empiricism).

Ex. the man is sitting in the chair

TIP: Produces a contradiction and can be ignored. There are noAnalytic a posteriori statements.

TIP: Some would argue that there are analytic a posteriori and they are needed forhypothetical judgements.

Ex. The man is sitting in a chair. I can confirm the man is sitting in the chair by looking (of course the truth of this statement is contingent on the man actually being in the chair in this case; it is conditional).

TIP: Pure empiricism. Empirical.

TIP:a priori anda posteriori are two key terms in Kantian philosophy. Kant coins their modern usage, but he borrowed them fromLatin translations of Euclids Elementsfrom about 300BC. 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 internalizingthe terms he introduces, after that one just needs to follow his arguments.[9]

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

With everything so far covered, lets now return to the two prong fork and discuss how to cross it.

First, for reference, here is an illustration of Humes Fork again for a visual:

To cross Humes fork is to show that we can make useful judgements that involve using a mix of terms from both categories.

The most useful mix is the one covered above, where we show that asynthetica priorithat is nottautological or contingent, but necessarilyand objectively true isnt just possible to create, but is actually useful.

However, other mixes like contingent synthetic a priori (a priori that depend on more information, like God gave man free-will, synthetic a priori terms are useful, or there are 11 dimensions of spacetime) are also useful.

The bottomline is that this whole practice shows us that using a mix of reason and empiricism tells us more about the world than empiricism alone.

To summarize, Kants crossing of Humes 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):

For more reading, see:A Priori and A Posteriori.

TIP: As noted above, Kants analysis of the epistemologicalconcepts discussed on this page starts in his earlier works likeThe Groundwork of the Metaphysic of MoralsandThe Metaphysics of Moralswhere he first properly lays down hisKantian 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 isthat, in the realm of metaphysics and morals, pure reason can be used to know some truths (while other truthsrequire the crossing of reason and empirical evidence). Hume counters this (albeitnot 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 Reasonsaying yes it can. Thisconfirms forus two things 1. an earnest exploration of these concepts requires reading multiple works of Hume and Kant 2. While bothKant and Hume care about science and politics, both are moreinterested 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 acceptingthat 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 wasnt grounded in the empirical was knowledge at all. Kant ultimately tried to showthat the fork could be crossed in all these realms allowing us to accept NewtonsF=ma and hisCategorical Imperative. Generally we can say that Kant asserts that even pure metaphysical a priori can be useful knowledge, as long as it can trace a path back to the empirical (this being the concept of the transcendental).

Synthetic a priori examples (examples of crossing Humes fork):

As noted above, in his Critique of Pure Reason, Kant generally points to mathematics (ex. 7 + 5 =12), geometry (a straight line between two points is the shortest), physics (F=ma), and metaphysics (God gave men free-will) to show synthetic propositions a priori possible (again, some of these are my examples).

Specifically, Kant tells us we should focus on mathematics (including geometry) and physics. Thus, Kant zeroes in on the a priori concepts/terms of space and time to justify his ideas about synthetic propositions a priori.

While he spends a lot of time describing every aspect of the general concept, he does not spend a lot of time offering concrete examples of synthetic a priori statements (see: why some of these examples are mine).

With that in mind, good examples of crossing Humes fork (AKA of not only synthetic a priori statements, but necessary and objective synthetic a priori) can be found inNewtons laws(Kant gives a nod to the Laws of Motion as containing synthetic a priori and gives a similarexample of every event has a cause in hisbook).

Lets take the second law, the one we use an example above, which can be represented as F=ma(Force equals mass time acceleration in an inertialframe).

F=ma is synthetic, as the predicate concept is not contained in its subject concept (nothing about forceinherently equals mass time acceleration). But also,these concept are (by most measures) a priori because force, mass, and acceleration cant be experienced directly (they are relations and effects of physical bodies in spacetime, represented by values in an equation, but they are not themselves tangible things).

Or, if we want to make the case for the empirical qualities of mass, force, and acceleration (denoting their transcendental aesthetic or mixed qualities), we can still say at least that the general rule F=ma is nota posteriori. After-all, we cant confirm a Newtons second law on a far off planet, we have to use our reason to know it is true.

Newtons third law also works in this respect. His third law states: when 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 cant set about testing every object, just asone cant confirm every bachelor, yet again we can use experiments to know this theory is true.

All this to say, pure ideas can tell us a lot about the empirical world, but only if we can find that place where facts about ideas transcends to world of ideas and begins to tell us facts about the world (a place that differs by subject).

Kants examples of space and time as synthetic a priori: Kant crosses forks by using space and time in his book. Considering spacetime (the theoretical construct which speaks to real phenomena) is most certainly of the synthetic a priori class, I would say he got it fairly right in his first attempt (although some will be skeptical of this). For Kant, according to the book Understanding Kant, First, time is not empirical as neither coexistence nor succession have ever come within human perception (1929, p. 74). Second, time is a pure intuition because it is a necessary component of all intuitions (1929, p. 74). Third, time has only one dimension and this knowledge is not gained through experience, therefore time is a priori (1929, p. 75). Finally, different times are all part of one and the same time there are no separate or individual times (1929, p. 75).The thing to get here is that space and time are pure a priori (they arent tangible things), but yet they can tell us useful things about the empirical a posteriori world (in this vein, other statements that contain objective synthetic a priori knowledge include mass and energy are equivalent and time is relative to frame of reference; both of these statements are examples that concern what Kant calls the transcendental aesthetic). Consider the following Kant quotes from Section II. Of Time below as well:

Thus our conception of time explains the possibility of so much synthetical knowledge a priori, as is exhibited in the general doctrine of motion, which is not a little fruitful.

Time and space are, therefore, two sources of knowledge, from which, a priori, various synthetical cognitions can be drawn. Of this we find a striking example in the cognitions of space and its relations, which form the foundation of pure mathematics. They are the two pure forms of all intuitions, and thereby make synthetical propositions a priori possible.

We have now completely before us one part of the solution of the grand general problem of transcendental philosophy, namely, the question: How are synthetical propositions a priori possible? That is to say, we have shown that we are in possession of pure a priori intuitions, namely, space and time, in which we find, when in a judgement a priori we pass out beyond the given conception, something which is not discoverable in that conception, but is certainly found a priori in the intuition which corresponds to the conception, and can be united synthetically with it. But the judgements which these pure intuitions enable us to make, never reach farther than to objects of the senses, and are valid only for objects of possible experience.

Kant onSECTION II. Of Time.

Using a Synthetic a priori to Cross forks:Equations like Newtons F=ma or EinsteinsE=mc2arePure Reason (Pure Logic; a Priori) despite being both necessarily true (valid statements / very strong theories) and not tautological (not purely analytic). Yet we cant confirm theytell us anything about the world until we test and confirm themvia experiment and actually physically cross forks (we have to not only create a Synthetic a priori, but prove it is true empirically via testing). Even though we cant reach out and touch their forms directly, we confirmthoseequations are true, as they canhelp usto predict what we will observe with perfect accuracy (and thus we can treat them as scientific theories). Thus equations like these are good examples ofa synthetic a priori. The complex part is dealing withSynthetic a priori that cant be proven, such as is the case with Moral Philosophy

Trying to Crosstheforks of MoralPhilosophy: On this page we are mainly 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 theirtheories to morality and ethics(they are, so to speak, also seeing if they can cross the more etherealforks 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, ifwe can cross the forks of natural philosophy, why cant we cross the forks of moralphilosophy? A main goal of Kant is to figure out if we can create a confirmable metaphysical synthetic a priori. Long story short, Kantbelieves that we can have facts about pure philosophy, but that we cant create a provable metaphysic synthetic a priori. In other words, we can have true facts about metaphysics and they can be very useful, but we cant prove it empirically (as by its nature there is a sub-category of metaphysics that is a priori). Learn about crossing forks and human understanding in terms of the physical, logical, ethical, and metaphysical.[10]

TIP: Confused? The following article contains an excellent analysis of the synthetic a priori The Importance of the Synthetic A Priori in Kants First Critique.

The above summary of Kants argument was gleaned from theover 1,000 pagesof his work.

The gist is that Kantattempted to provethat we can use facts about ideas to prove facts about the world. That Pure Reason can be used toprove theexistence of asynthetic a priori, crossing the tongs ofHumes Fork, and thus saving Newtons laws and science itself in the process.[11]

Thus we can conclude, Kantrebutted Hume in an effort to show thatknowledge canbe foundinboththe necessaryandcontingent (concerning reality), the a priorianda posteriori (concerning knowledge), and the analyticandsynthetic(concerning language); In short, useful human knowledge can be foundin both reason and empirical sensory evidence, and each form of human understanding can tell us about the other.

TIP: Think about the scientific method.We have ideas and define experiments; we do experiments and come up with more ideas; rinse and repeat. Weformulate theories and we test a hypothesis based on theoretical mathematics or ideas. Modern science IS the crossing of Humes 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 doesnt always offer proofs for instance). Long story short, Hume and Kant are both sages and both important. KantsaCritique of Pure Reasonexemplifies akey moment in history (andit is largely a testament to Humes importance as well as Kants).

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Hume's Fork Explained - Fact / Myth