In both the Treatise and the first Enquiry, Hume provides two definitions of 'cause'. What does the second definition add to the first, and why did Hume think it necessary to introduce it?


Any discussion of Hume and his definitions of causation must be prefaced with a caution that Hume employs the concept of causation in two separate senses.   He employs the concept of causation as what I will call {cause(a)} -- the actual material, physical, scientific connection between an event (object) A and an event (object) B that exists (assuming the "outside world"does indeed exist) quite independent of any conscious mind.   He also employs the concept of causation as what I will call {cause(b)} -- the belief formed by some conscious mind about the necessary association of some event A and some event B.

In his exploration of the psychology of human beliefs, in his A Treatise of Human Nature(1), Hume explicitly proclaims that he does not deny the existence of {cause(a)}, but that it is the nature and origins of {cause(b)} that is the focus of his attention.   On the one hand, Hume talks about "cause"as a relationship between "objects"that we observe in our experience, and connect in our minds.   On the other hand, Hume talks about "secret"and "concealed"causes that we are unable to discover.   "'[T]is commonly allow'd by philosophers, that what the vulgar call chance is nothing but a secret and conceal'd cause.[Treatise I, III, xii]   Hume does not deny that there are "hidden"causes that underlie and explain the precedency and contiguity of observations in our experience.   But Hume clearly states that his

"intention never was to penetrate into the nature of bodies, or explain the secret causes of their operation.   …   For besides that this belongs not to my purpose, I am afraid that such an enterprise is beyond the reach of human understanding, and that we can never pretend to know body otherwise than by those external properties which discover themselves to the sense."

Hume's purpose in the Treatise is to "explain the nature and causes of our perceptions, or impressions, and ideas".[Treatise, I, II, v]   Hume, like Descartes and Locke before him, despairs of the ability of science to penetrate the "springs and principles, which are hid, by reason of their minuteness or remoteness"[Treatise, I, III, xii].

Hence it must be understood from the beginning that the two definitions of "cause"that Hume offers (and that the essay title refers to) are not definitions of {cause(a)}, but definitions of {cause(b)}.   They are definitions of the beliefs that human minds form about the nature of the causal relationship between two objects (or what we would call "events").   They do not pretend to be definitions of the mind independent connection between the two objects.

Hume's theory of mind -- that all ideas are preceded by impressions of sense -- is tightly linked to his account of "cause".   Having shown that ideas (or thoughts) arise from impressions, Hume needs to explain the natural affinity or relation that certain ideas have to other ideas. He does this by introducing the principles of the association of ideas.   These "principles of connexion"operate automatically, without conscious effort on our part (i.e. are a product of {cause(a)}),as a kind of "gentle force, which commonly prevails"[Treatise, I, I, iv].   He presents seven of these relations, divided into two groups -- a group of four relations that depend only on the ideas of mind and hence can be known a priori and with certainty; and a group of three that depend only on the impressions of our senses and hence cannot be known a priori or with certainty:-

a)   Objects of Knowledge and Certainty; Relations of Ideas; A Priori.

1.   Resemblance

2.   Proportion in quantity or number

3.   Degrees in any quality

4.   Contrariety

b)   Matters of Fact and Existence; Empirical.

5.   Identity

6.   Relations of time and place

7.   Causation

For Hume, causation is a relation dealing with matters of fact, and therefore is not something for which certainty is possible.   For Hume, therefore, causation is a matter of perceptual experience.

Hume acknowledges that we certainly have the idea of cause, but the thrust of his inquiry is the puzzle of where it comes from?   To fit within his theory of mind, the reasoning involved must be founded on either relations of ideas (a priori); or matters of fact or existence (empirical).   But Hume argues that the source is neither in any relations of ideas, nor in our experience.   In Hume's own words(2), from his Enquiry Concerning Human Understanding(3) [EHU, VII, II] --

1.   Every idea is copied from some preceding impression or sentiment.

2.   [W]here we cannot find any impression, we may be certain that there is no idea. [From 1.]

3.   In all single instances of the operation of bodies or minds, there is nothing that produces any impression … of power or necessary connection.

4.   In all single instance of the operation of bodies or minds, there is nothing that … can suggest any idea … of power or necessary connection. [From 2 and 3]

5.   [W]hen many uniform instances appear, and the same object is always followed by the same event; we begin to entertain the notion of cause and connection.

6.   [W]hen many uniform instances appear, and the same object is always followed by the same event; … [w]e then feel a new sentiment or impression, to wit, a customary connection in thought or imagination between the one object and its usual attendant…

7.   [T]his idea [of necessary connection] arises from a number of similar instances, and not from any single instance. [From 4 and 5]

8.   [This idea of necessary connection] must arise from that circumstance, in which the number of instances differ from every individual instance. [From 1 and 7]

9.   [T]his customary connection or transition of the imatination is the only circumstance in which they differ.

10. [T]his sentiment [i.e. the customary connection or transition or determination of the imagination] is the original of that idea which we seek for. [From 6, 8, and 9]

There is nothing that we can perceive in the bread (at least in Hume's time) that will determine in advance whether the bread will turn out to be nutritious or poisonous.   So the mind can never find the effect in the cause, no matter how close the scrutiny.   "Cause"is therefore not something that we sense.   Our idea of cause is therefore not based on an impression of sense.   It is not an object out in the world.   Causation is therefore not an empirical discovery.  

Nor is the effect is ever found within the cause.   The effect is totally different from the cause.   No matter how much we know about the cause, we cannot say in advance what the effect will be.   We can always conceive of the effect without the cause, or the cause without the effect.   Whatever the connection between the two, it is not logically contradictory to consider one without the other.   Causation is therefore not discovered by a priori reasoning.

Causation must therefore be an innate feature of our psychology.   All we see are two kinds of events, A and B, that display a consistent temporal sequence and spatial contiguity.   By observing a past regularity, through repetition we gradually acquire the belief in a necessary connection.   Thus "causation"is an invention of our minds to explain the consistent precedency and contiguity of events like A and B.   Cause ({cause(b)}) is a product ({cause(a)}) of human psychology, rather than an objective feature of the world out there.

Two questions can be asked whenever someone asserts that "A causes B."One is -- what is the nature of the relationship that is being asserted (i.e. "believed") between A and B?   What are the necessary and sufficient conditions for that relationship to actually exist as believed?   The other is -- what justification must the asserter have that those necessary and sufficient conditions obtain?   What must the asserter believe in order to have a justified belief that "A causes B"?   What we mean by causation is different from the grounds upon which we assert causation.(4)

It is for this reason that Hume sums up all of the relevant impressions in not one but two definitions of cause.   Just before the passage in the Treatise where Hume gives his two definitions of "cause,"he says:

"There may two definitions be given of this relation, which are only different by their presenting a different view of the same object, and making us consider it either as a philosophical or as a natural relation; either as a comparison of two ideas, or as an association betwixt them."[Treatise, I, III, xiv]

The two definitions he offers answer the two questions that can be asked -- what we mean by causation -- the philosophical relation, and what grounds we require in order to properly assert causation -- the natural relation.   He then immediately presents his definition of "cause"as a philosophical relation:

"an object precedent and contiguous to another, and where all objects resembling the former are placed in like relations of precedency and contiguity to those objects that resemble the latter."

This is followed, in the exact same paragraph, with his definition of "cause"as a natural relation:

"an object precedent and contiguous to another, and so united with it that the idea of the one determines the mind to form the idea of the other, and the impression of the one to form a more lively idea of the other."

To fully understand how these two definitions fit together, we must understand the difference that Hume draws between "philosophical relations"and "natural relations"beyond the simple distinction that Hume offers here - that a philosophical relation is a comparison of ideas, and a natural relation is an association of ideas.  

Hume describes "natural relation"as the union of simple ideas into a complex idea guided by the one of the three principles of association -- resemblance, contiguity, and cause and effect."[Treatise, I, I, iv]   So in Hume's psychological analysis of the mind, a "natural relation"is one in which the presentation to our mind of one relatum naturally (by virtue of our innate nature) brings to our mind the other relatum.   As we would explain using modern evolutionary psychology, our minds have evolved so as to (learn to) naturally associate one relatum with the other.

A "philosophical relation"Hume declares is one that involves an "arbitrary union of two ideas in the fancy"[Treatise, I, I, v].   In other words, in a philosophical relation, any arbitrary pair of objects can be compared and found similar or different across some dimension of measurement.   It is a "scientific"comparison or comparative measurement of ideas, rather than an innately recognized association of ideas.   It must be noted that Hume does not say that any two arbitrary objects that have the philosophical relation of precedency and contiguity, also have the natural relation of association, and hence are cause and effect.   Rather he says that any two objects that have the philosophical relation in such a way, or that are "so united", that the two become associated in the mind, thereby become recognized as cause and effect.

To break Hume's first definition down into a modern format for a philosophical definition --

A causes B iff     (1) A and B are spatially contiguous,
                          (2) A is temporally precendent to B, and
                          (3) any object like A is temporally precendent and
                                          spatially continguous to B.

Now, condition (3) in this definition is not something that can ever be known with certainty.   So making a claim that some relationship between A and B is a causal one according to this definition is not something that anyone would ever be properly justified in doing.   However, there can be about the specific object pair A and B, something that generates in the mind a belief that condition (3) holds.   And this is what Hume refers to in the second definition as the pair being "so united that the idea of the one determines the mind to form the idea of the other".   And Hume specifies that this special uniting of the pair must consist of the habituation of the mind to their common association through repeated experience of the philosophical relationship of similar pairs.   This gives us the basis of the second definition .To break Hume's second definition down into a modern format for a philosophical definition, condition (3) from the first definition is replaced with a condition that described how we recognize that condition (3) is true.

A causes B iff     (1') A and B are spatially contiguous,
                          (2') A is temporally precendent to B, and
                          (3') we have formed the habit of mind of associating
                                           any object like A with an object like B (and vice versa).

So condition (3') provides the proper justification that we require in order to properly believe that condition (3) obtains.   The first definition examines the causal relation from the outside, as it were.   While the second definition examines the causal relation from the inside.   The first definition examines the causal relation as a philosophical (qua "scientific") relation, documenting the necessary comparison of ideas.   The second definition examines the causal relation as a natural (qua "innate") relation, documenting the habitual association that the mind requires in order to form the belief in a necessary causal connection.

Hume needs both definitions in order to provide a complete understanding of his concept of {cause(b)} since it is condition (3') that gives us the means of recognizing that condition (3) obtains.   Without that means, we could never justifiably recognize any "cause"at all.


Notes & References

(1)   Hume, David;   A Treatise of Human Nature, 1739.   Online Library of Liberty, URL = <>    
(Citations will be given in "Treatise, Book, Part, Section"format.)

(2)   Garrett, Don;   "The Representation of Causation and Hume's Two Definitions of ‘Cause'"in Nous, Vol 27, No 2 (June, 1993), pp 167-190

(3)   Hume, David;   An Enquiry Concerning Human Understanding, 1748.   Eighteenth-Century Studies, URL=<> (Citations will be given in "EUH, Section, Part"format.)

(4)   Richards, Thomas J.;   "Hume's Two Definitions of ‘Cause'"in The Philosophical Quarterly, Vol 15, No 60 (July, 1965), pp 247-253.

Gotterbarn, Donald;   "Hume's Two Lights on Cause"in The Philosophical Quarterly, VOl 21, No 83 (April, 1971), pp 168-171.

Morris, William Edward, "David Hume", The Stanford Encyclopedia of Philosophy (Winter 2008 Edition), Edward N. Zalta (ed.), URL = <>.

Russell, Paul;   "Hume's ‘Two Definitions'of Cause and the Ontology of ‘Double Existence'"in Hume Studies, Volume X, Number 1 (April, 1984), pp1-25.

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