17 Apr 2017

Hume (4.1) Enquiry concerning Human Understanding, “Sceptical Doubts concerning the Operations of the Understanding. Part I”


by Corry Shores


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[The following is summary. Any boldface in quotations or bracketed commentary is my own. Proofreading is incomplete, so there are still typos present. I apologize for the distractions. Block quotations of this text are copied from the Project Gutenberg online text.]





David Hume


An Enquiry concerning Human Nature


Section IV:

Sceptical Doubts concerning the Operations of the Understanding


Part I




Brief summary:

There are two sorts of objects of human reason or enquiry; 1) relations of ideas, which are certain on account of logical necessity, for example, “that three times five is equal to half of thirty” is consistent with the meanings of its terms and operators, but its negation is unconceivable for that reason also; and 2) matters of fact, which are possible, because their contraries are conceivable and are thus possible; for example: “the sun will rise tomorrow” is thinkable, but so is its contrary, “the sun will not rise tomorrow”; hence these claims are possible rather than certain. But we have much knowledge of matters of fact, and we often trust it to high degrees. We do so, because we assume there are causal relations that govern such events now and consistently in the future. All such knowledge of matters of fact, which include laws of physics, cannot be deduced a priori and thus is only gained by experience. Suppose you have had no experiences of certain sorts of objects before. Upon first seeing one, you would not be able to deduce what sorts of effects it will have upon other objects nor how other objects have some effect on it or are able to bring it about in the first place. We can only learn such things from experience. For example, upon first being shown a lodestone, we would not be able to deduce that it has magnetic interactions with other objects. It is only because we are so familiar with many objects that we mistakenly think that we can deduce their causal properties a priori. The reason we cannot make such deductions is that effects are completely different from causes, and they are not logically implied in the causes in a straightforward way. So suppose now that we have a collision of bodies, and we want to predict the effects on the basis of the physical causes. But suppose also that we are not allowed to appeal to prior observations. This means we can only imagine the effect. But what we imagine is arbitrary, as we can easily imagine opposite effects; for, the effects are not implied in the causes. Moreover, we can imagine different effects for various instances of the same situation rather than the same effect each time. Our knowledge of causality is always limited to our given spatial and temporal orientation. So we cannot broaden our knowledge to more ultimate causes holding universally. Also, the application of mathematics and geometry will not allow us to deduce a priori the effects of certain physical situations. This is because we cannot deduce a priori the laws of physics, which are required for applying our mathematical and geometrical tools when calculating outcomes.









[There are two objects of human reasoning or enquiry: 1) relations of ideas, which are logical certain (their contrary claims are contradictions), and include for example mathematical formulas; and 2) matters of fact.]


Human reason or enquiry has objects of examination. Of these there are two types:

1) Relations of Ideas, and

2) Matters of Fact.

Relations of ideas include geometrical, algebraic, and arithmetic objects. Relations of ideas also include any affirmation that is either intuitively or demonstratively certain. [I suppose an affirmation is to be understood perhaps as something like a proposition or statement or the like. One which is demonstrably certain I would think is one which has a proof for it. I am less certain what makes something intuitively certain, but it might be that it is immediately apparent to our sensory observation, or as he puts it in the Treatise of Human Nature, that it is “discoverable at first sight”. Let me quote from Book I, Part III, Section 1, Paragraphs 2–5. (p.70 or §§162-165 ( in the summary.

It appears, therefore, that of these seven philosophical relations, there remain only four, which depending solely upon ideas, can be the objects of knowledge said certainty. These four are RESEMBLANCE, CONTRARIETY, DEGREES IN QUALITY, and PROPORTIONS IN QUANTITY OR NUMBER. Three of these relations are discoverable at first sight, and fall more properly under the province of intuition than demonstration. When any objects resemble each other, the resemblance will at first strike the eve, or rather the mind; and seldom requires a second examination. The case is the same with contrariety, and with the degrees of any quality. No one can once doubt but existence and non-existence destroy each other, and are perfectly incompatible and contrary. And though it be impossible to judge exactly of the degrees of any quality, such as colour, taste, heat, cold, when the difference betwixt them is very small: yet it is easy to decide, that any of them is superior or inferior to another, when their difference is considerable. And this decision we always pronounce at first sight, without any enquiry or reasoning.

We might proceed, after the same manner, in fixing the proportions of quantity or number, and might at one view observe a superiority or inferiority betwixt any numbers, or figures; especially where the difference is very great and remarkable. As to equality or any exact proportion, we can only guess at it from a single consideration; except in very short numbers, or very limited portions of extension; which are comprehended in an instant, and where we perceive an impossibility of falling into any considerable error. In all other cases we must settle the proportions with some liberty, or proceed in a more artificial manner.

I have already I observed, that geometry, or the art, by which we fix the proportions of figures; though it much excels both in universality and exactness, the loose judgments of | the senses and imagination; yet never attains a perfect precision and exactness. It’s first principles are still drawn from the general appearance of the objects; and that appearance can never afford us any security, when we examine, the prodigious minuteness of which nature is susceptible. Our ideas seem to give a perfect assurance, that no two right lines can have a common segment; but if we consider these ideas, we shall find, that they always suppose a sensible inclination of the two lines, and that where the angle they form is extremely small, we have no standard of a right line so precise as to assure us of the truth of this proposition. It is the same case with most of the primary decisions of the mathematics.

There remain, therefore, algebra and arithmetic as the only sciences, in which we can carry on a chain of reasoning to any degree of intricacy, and yet preserve a perfect exactness and certainty. We are possest of a precise standard, by which we can judge of the equality and proportion of numbers; and according as they correspond or not to that standard, we determine their relations, without any possibility of error. When two numbers are so combined, as that the one has always an unite answering to every unite of the other, we pronounce them equal; and it is for want of such a standard of equality in extension, that geometry can scarce be esteemed a perfect and infallible science.

(Hume, Treatise, p.70-71)

But we need to distinguish intuitively certain relations of ideas from matters of fact. Perhaps intuitive certainty here is not an issue of sensory observation necessarily but is rather a matter of the knowledge of the relation being obtained immediately on account of its obviousness. So, what we know by demonstration requires steps in reasoning, but what we know by intuition is immediately obvious.] Hume gives some examples of relations of ideas. [It seems they are demonstrably certain, and it seems his point here is to emphasize that their certainty is of the sort that no existing thing could challenge them.] These examples are mathematical equations where the relations between the terms are certain.

All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic; and in short, every affirmation which is either intuitively or demonstratively certain. That the square of the hypothenuse is equal to the square of the two sides, is a proposition which expresses a relation between these figures. That three times five is equal to the half of thirty, expresses a relation between these numbers. Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence.

(online text, or Hume 18)




[Matters of fact are possible rather than certain, because their contrary claims are not contradictions, as for example, “the sun will rise tomorrow”.]


The other kind of objects of human reason or enquiry are matters of fact. [First consider something like the above examples of relations of ideas: 2+2=4. It would be a contradiction to say: 2+2≠4.  We cannot even conceptualize what it means, given that its meaning could not be consistent with the meanings of its terms and operators. Now consider the sentence, “the sun will rise tomorrow”. This we can conceptualize. Also consider its negation, “the sun will not rise tomorrow.” This we can conceptualize also. In other words, the contrary of such a proposition is conceivable, and thus in a sense possible.]

Matters of fact, which are the second objects of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality. That the sun will not rise to-morrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise. We should in vain, therefore, attempt to demonstrate its falsehood. Were it demonstratively false, it would imply a contradiction, and could never be distinctly conceived by the mind.

(online or 18)




[We will now ask how we come to trust matters of fact even though they are only possible.]


[I am not entirely certain about the points in this paragraph, but they might be the following. First suppose it is dawn and you see the sun rising. We note that “the sun is rising”. I am not sure if this is an intuitively certain relation of ideas. But at any rate, our example of matters of fact is the claim that the sun will rise tomorrow. What Hume might here be asking is, how can we be relatively sure of the truth of such claims? We have memories of past sunrises and sensory evidence of the current one, but how do then draw the inference that tomorrow it will rise? My guess is that his next point is that by trying to answer this question, we might find that philosophy has been in error regarding such knowledge, and also that it might do philosophy good to try to rectify such errors. I quote for your interpretation.]

It may, therefore, be a subject worthy of curiosity, to enquire what is the nature of that evidence which assures us of any real existence and matter of fact, beyond the present testimony of our senses, or the records of our memory. This part of philosophy, it is observable, has been little cultivated, either by the ancients or moderns; and therefore our doubts and errors, in the prosecution of so important an enquiry, may be the more excusable; while we march through such difficult | paths without any guide or direction. They may even prove useful, by exciting curiosity, and destroying that implicit faith and security, which is the bane of all reasoning and free enquiry. The discovery of defects in the common philosophy, if any such there be, will not, I presume, be a discouragement, but rather an incitement, as is usual, to attempt something more full and satisfactory than has yet been proposed to the public.

(online / 18-19)




[We draw such inductive inferences under assumptions of causal relations that must be holding.]


[I again am not certain here, but the points might be the following. All such reasonings of matters of fact involve the assumption that there are (physical) causal reasons for why the inference holds. Perhaps in the sunrise example, we assume that there are astrological causes for why it happens. This would seem to be like his example here of finding a watch on a deserted island and concluding once humans had been there. For, their presence would cause there to be such evidence. He says in these cases it is “constantly supposed, that there is a connexion between the present fact and that which is inferred from it”. I am not sure if it is necessarily physical causality. In the first example, a man infers that his friend is somewhere else on the basis of certain facts, like finding a letter from the friend indicating her absence or remembering the friend’s intentions to go somewhere. This evidence could be physically tied to the friend’s absence, act of leaving, or resolve to leave, but maybe Hume means by cause and effect something more like certain indicators causing one’s inference, which would then be the effect of that cause of knowledge. Let me quote, but I am inclined to think he means a physical cause for the evidence rather than the evidence causing the knowledge:]

All reasonings concerning matter of fact seem to be founded on the relation of Cause and Effect. By means of that relation alone we can go beyond the evidence of our memory and senses. If you were to ask a man, why he believes any matter of fact, which is absent; for instance, that his friend is in the country, or in France; he would give you a reason; and this reason would be some other fact; as a letter received from him, or the knowledge of his former resolutions and promises. A man finding a watch or any other machine in a desert island, would conclude that there had once been men in that island. All our reasonings concerning fact are of the same nature. And here it is constantly supposed that there is a connexion between the present fact and that which is inferred from it. Were there nothing to bind them together, the inference would be entirely precarious. The hearing of an articulate voice and rational discourse in the dark assures us of the presence of some person: Why? because these are the effects of the human make and fabric, and closely connected with it. If we anatomize all the other reasonings of this nature, we shall find that they are founded on the relation of cause and effect, and that this relation is either near or remote, direct or collateral. Heat and light are collateral effects of fire, and the one effect may justly be inferred from the other.

(online / 19)





[If we base our trust in matters of fact on cause and effect, then we need to know how we obtain knowledge of cause and effect.]


We must determine how we gain knowledge of cause and effect in order to know why we can trust matters of fact, which are grounded in causal relations.

If we would satisfy ourselves, therefore, concerning the nature of that evidence, which assures us of matters of fact, we must enquire how we arrive at the knowledge of cause and effect.

(online / 19)




[We never obtain knowledge of the causes of some object or its effects, upon our first experience of such a thing. Thus causal knowledge is not a priori.]


Knowledge of causality cannot be obtained a priori. This is evident from the fact that upon first seeing some sort of object the likes of we have never experienced before, we cannot discern the causes bringing it about or the effects it can have.

I shall venture to affirm, as a general proposition, which admits of no exception, that the knowledge of this relation is not, in any instance, attained by reasonings a priori; but arises entirely from experience, when we find that any particular objects are constantly conjoined with each other. Let an object be presented to a man of ever so strong natural reason and abilities; if that object be entirely new to him, he will not be able, by the most accurate examination of its sensible qualities, to discover any of its causes or effects. Adam, though | his rational faculties be supposed, at the very first, entirely perfect, could not have inferred from the fluidity and transparency of water that it would suffocate him, or from the light and warmth of fire that it would consume him. No object ever discovers, by the qualities which appear to the senses, either the causes which produced it, or the effects which will arise from it; nor can our reason, unassisted by experience, ever draw any inference concerning real existence and matter of fact.

(online / 19-20)




[There are many examples where the only way we can obtain knowledge of causes and effects for some thing is by experiences with it. We can only know the way a magnet causes certain movements only by seeing its attractional behaviors.]


[Hume will now give examples for sorts of causal relations that can only be discovered by experience and thus are not a priori. I am not sure, but the first one might be something like the following. We have two polished slabs of marble. We affix one atop the other. I am not sure if we use something to bind them or not. We find that it is easier to separate them by applying pressure parallel to the surfaces that meet than by applying pressure down upon the pieces, perpendicular to those meeting surfaces. In other words, the slabs are more apt to slide past one another when the pressure follows the plane of separation. I am guessing. The other examples are that we cannot know that gunpowder is explosive until we see how it reacts to ignition, and we cannot know that a material is magnetic until we see its attractional behaviors. Or at least, we cannot deduce these properties a priori. I am not sure about his next point, but it might be the following. Some of our causal knowledge involves complicated systems, like the bodies of humans and animals. We know that bread or milk is good for humans but not for lions, but this knowledge we could only have obtained from experience. For, the systems are so complex that we cannot understand their workings in perfect detail, and instead we must experiment with them.]

This proposition, that causes and effects are discoverable, not by reason but by experience, will readily be admitted with regard to such objects, as we remember to have once been altogether unknown to us; since we must be conscious of the utter inability, which we then lay under, of foretelling what would arise from them. Present two smooth pieces of marble to a man who has no tincture of natural philosophy; he will never discover that they will adhere together in such a manner as to require great force to separate them in a direct line, while they make so small a resistance to a lateral pressure. Such events, as bear little analogy to the common course of nature, are also readily confessed to be known only by experience; nor does any man imagine that the explosion of gunpowder, or the attraction of a loadstone, could ever be discovered by arguments a priori. In like manner, when an effect is supposed to depend upon an intricate machinery or secret structure of parts, we make no difficulty in attributing all our knowledge of it to experience. Who will assert that he can give the ultimate reason, why milk or bread is proper nourishment for a man, not for a lion or a tiger?

(online / 20)





[It is only because of our deep familiarity with the workings of many things that we might mistakenly think that we can deduce causal relations like the transfer of motion without ever first witnessing such events.]


We have become so familiar with the workings of many things that we mistakenly conclude that we would have been able to deduce for example “one Billiard-ball would communicate motion to another upon impulse; and that we needed not to have waited for the event, in order to pronounce with certainty concerning it”:

But the same truth may not appear, at first sight, to have the same evidence with regard to events, which have become familiar to us from our first appearance in the world, which bear a close analogy to the whole course of nature, and which are supposed to depend on the simple qualities of objects, without any secret structure of parts. We are apt to imagine that we could discover these effects by the mere operation of our reason, without experience. We fancy, that were we brought on a sudden into this world, we could at first have inferred that one Billiard-ball would communicate motion to another upon impulse; and that we needed not to have waited for the event, in order to pronounce with certainty concerning it. Such is the influence of custom, that, where it is strongest, it not only covers our natural ignorance, but even conceals itself, and seems not to take place, merely because it is found in the highest degree.

(online / 20)




[We cannot know the causes and effects of objects, and thus we cannot know any of the laws of nature or the workings of physical objects, except by experience. This is because effects are totally different from their causes and cannot be deduced from them.]


Hume will now convince us that all knowledge of the laws of nature and the workings of physical objects can only come from experience. We first suppose that we are to explain the effects that some object will cause. But we are not allowed to consult any past experiences with it. Our only other recourse then is to invent or imagine an event where the object exhibits its effect. But, there is a problem with this approach. [The reasoning might be the following. An effect follows directly from its cause. But the effect is completely different than its cause, so much so, that there is nothing conceptually inherent to the cause that implies with any certainty the effect. We might for example claim that the motion of one billiard ball will be transferred to the next upon impact. But how do we know that without having first discovered that motion is transferable?]

But to convince us that all the laws of nature, and all the operations of bodies without exception, are known only by experience, the following reflections may, perhaps, suffice. Were any object presented to us, and were we required to pronounce concerning the effect, which will result from it, without consulting past observation; after what manner, I beseech you, must the mind proceed in this operation? It must invent or imagine some event, which it ascribes to the object as its effect; and it is plain that this invention must be entirely arbitrary. The mind can never possibly find the effect in the supposed cause, by the most accurate scrutiny and examination. For the effect is totally different from the cause, and consequently can never be discovered in it. Motion in the second Billiard-ball is a quite distinct event from motion in the first; nor is there anything in the one to suggest the smallest hint of the other. A stone or piece of metal raised into the air, and left without any support, immediately falls: but to consider the matter a priori, is there anything we discover in this situation which can beget the idea of a downward, rather than an upward, or any other motion, in the stone or metal?

(online / 21)




[Also, without the benefit of experience, we can imagine more than one effect for the same cause.]


[Suppose we are trying to explain the effects of one body striking another, without consulting prior experience. We already noted that whatever we choose to imagine the effect to be, it is an arbitrary choice, as even the opposite effect is imaginable. Also, our very assumption that there is only one possible effect is as well an arbitrary choice, as we can imagine the effects varying in each instance.]

And as the first imagination or invention of a particular effect, in all natural operations, is arbitrary, where we consult not experience; so must we also esteem the supposed tie or connexion between the cause and effect, which binds them together, and renders it impossible that any other effect could result from the operation of that cause. When I see, for instance, a Billiard-ball moving in a straight line towards another; even suppose motion in the second ball should by accident be suggested to me, as the result of their contact or impulse; may I not conceive, that a hundred different events might as well follow from that cause? May not both these balls remain at absolute rest? May not the first ball return in a straight line, or leap off from the second in any line or direction? All these suppositions are consistent and conceivable. Why then should we give the preference to one, which is no more consistent or conceivable than the rest? All our reasonings a priori will never be able to show us any foundation for this preference.

(online / 21)





[Thus we cannot know causes simply a priori, so we always must appeal to experience.]


Hume than summarizes the above points.

In a word, then, every effect is a distinct event from its cause. It could not, therefore, be discovered in the cause, and the first invention or conception of it, a priori, must be entirely arbitrary. And even after it is suggested, the conjunction of it with the cause must appear equally arbitrary; since there are always many other effects, which, to | reason, must seem fully as consistent and natural. In vain, therefore, should we pretend to determine any single event, or infer any cause or effect, without the assistance of observation and experience.

(online / 21-22)




[Since our knowledge of cause is limited to local situations, we cannot know much about ultimate causes holding universally.]


[I am quite uncertain about the next point, but I will guess it is the following. We begin by acknowledging that all knowledge of cause must come from experience. This means we can only be relatively certain about the causality of specific things (as future experiences could give new data that modifies our current knowledge). But we cannot know about more ultimate causes whose effects are widespread over space and time. For, out ability to experience such more widespread causes is far too limited to our current spatio-temporal orientations. Let me quote, as I am guessing:]

Hence we may discover the reason why no philosopher, who is rational and modest, has ever pretended to assign the ultimate cause of any natural operation, or to show distinctly the action of that power, which produces any single effect in the universe. It is confessed, that the utmost effort of human reason is to reduce the principles, productive of natural phenomena, to a greater simplicity, and to resolve the many particular effects into a few general causes, by means of reasonings from analogy, experience, and observation. But as to the causes of these general causes, we should in vain attempt their discovery; nor shall we ever be able to satisfy ourselves, by any particular explication of them. These ultimate springs and principles are totally shut up from human curiosity and enquiry. Elasticity, gravity, cohesion of parts, communication of motion by impulse; these are probably the ultimate causes and principles which we shall ever discover in nature; and we may esteem ourselves sufficiently happy, if, by accurate enquiry and reasoning, we can trace up the particular phenomena to, or near to, these general principles. The most perfect philosophy of the natural kind only staves off our ignorance a little longer: as perhaps the most perfect philosophy of the moral or metaphysical kind serves only to discover larger portions of it. Thus the observation of human blindness and weakness is the result of all philosophy, and meets us at every turn, in spite of our endeavours to elude or avoid it.

(online / 22)





[We also cannot deduce a priori the effects of physical causes using mathematics and geometry, because they can only aid in making predictive calculations that are already guided by observation.]


[The points and reasoning here might be the following. One might object that we can use mathematics and geometry to deduce a priori the laws of physics and thereby also to make predictions. For example, if we have all the relevant quantities, like mass and speed, and all the relevant spatial determinations like direction of the motion, we might then simply calculate the effects of a collision of moving bodies. However, while these mathematical and geometrical determinations, along with their appropriate operations, can help us produce our calculations, they do not establish from the beginning that certain sorts of motion will result from certain given circumstances. We first need to observe the sorts of causes and their effects before incorporating mathematical techniques to make predictions. Perhaps a better way to put it is the following. We can have all the mathematical and geometrical tools possible, but in order to apply them, we need to know the laws of physics that govern the situations we are studying. But no law of physics can be known a priori, because as we noted we can imagine opposing effects resulting from certain causes.]

Nor is geometry, when taken into the assistance of natural philosophy, ever able to remedy this defect, or lead us into the knowledge of ultimate causes, by all that accuracy of reasoning for which it is so justly celebrated. Every part of mixed mathematics proceeds upon the supposition that certain laws are established by nature in her operations; and abstract reasonings are employed, either to assist experience in the discovery of these laws, or to determine their influence in particular instances, where it depends upon any precise degree of distance and quantity. Thus, it is a law of motion, discovered by experience, that the moment or force of any body in motion is in the compound ratio or proportion of its solid contents and its velocity; and consequently, that a small force may remove the greatest obstacle or raise the greatest weight, if, by any contrivance or machinery, we can increase the velocity of that force, so as to make it an overmatch for | its antagonist. Geometry assists us in the application of this law, by giving us the just dimensions of all the parts and figures which can enter into any species of machine; but still the discovery of the law itself is owing merely to experience, and all the abstract reasonings in the world could never lead us one step towards the knowledge of it. When we reason a priori, and consider merely any object or cause, as it appears to the mind, independent of all observation, it never could suggest to us the notion of any distinct object, such as its effect; much less, show us the inseparable and inviolable connexion between them. A man must be very sagacious who could discover by reasoning that crystal is the effect of heat, and ice of cold, without being previously acquainted with the operation of these qualities.

(online / 22-23)







Hume, David. 2007. An Enquiry concerning Human Nature. Peter Millican (ed.). Oxford: Oxford University.

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Or if otherwise noted:

Hume, David. 1979. A Treatise of Human Nature. L.A Selby-Bigge (ed.). Oxford: Clarendon Press.

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