It seems to me that the only objects of the abstract sciences or of demonstration are quantity and number, and that all attempts to extend this more perfect species of knowledge beyond these bounds are mere sophistry and illusion. As the component parts of quantity and number are entirely similar, their relations become intricate and involved; and nothing can be more curious, as well as useful, than to trace, by a variety of mediums, their equality or inequality, through their different appearances. But as all other ideas are clearly distinct and different from each other, we can never advance farther, by our utmost scrutiny, than to observe this diversity, and, by an obvious reflection, pronounce one thing not to be another. Or if there be any difficulty in these decisions, it proceeds entirely from the undeterminate meaning of words, which is corrected by juster definitions. That the square of the hypotenuse is equal to the squares of the other two sides cannot be known, let the terms be ever so exactly defined, without a train of reasoning and enquiry. But to convince us of this proposition, that where there is no property, there can be no injustice, it is only necessary to define the terms, and explain injustice to be a violation of property. This proposition is, indeed, nothing but a more imperfect definition. It is the same case with all those pretended syllogistical reasonings, which may be found in every other branch of learning, except the sciences of quantity and number; and these may safely, I think, be pronounced the only proper objects of knowledge and demonstration.
All other enquiries of men regard only matter of fact and existence; and these are evidently incapable of demonstration. Whatever is may not be. No negation of a fact can involve a contradiction. The non-existence of any being, without exception, is as clear and distinct an idea as its existence. The proposition which affirms it not to be, however false, is no less conceivable and intelligible, than that which affirms it to be. The case is different with the sciences, properly so called.5 Every proposition which is not true, is there confused and unintelligible. That the cube root of 64 is equal to the half of 10 is a false proposition, and can never be distinctly conceived. But that Caesar, or the angel Gabriel, or any being never existed, may be a false proposition, but still is perfectly conceivable, and implies no contradiction.
The existence, therefore, of any being can only be proved by arguments from its cause or its effect; and these arguments are founded entirely on experience. If we reason a priori, anything may appear able to produce anything. The falling of a pebble may, for aught we know, extinguish the sun; or the wish of a man control the planets in their orbits. It is only experience which teaches us the nature and bounds of cause and effect, and enables us to infer the existence of one object from that of another. Such is the foundation of moral reasoning, which forms the greater part of human knowledge, and is the source of all human action and behaviour.
Moral reasonings are either concerning particular or general facts. All deliberations in life regard the former; as also all disquisitions in history, chronology, geography, and astronomy.
The sciences which treat of general facts, are politics, natural philosophy, physic, chemistry, &c. where the qualities, causes and effects of a whole species of objects are enquired into.
Divinity or Theology, as it proves the existence of a Deity, and the immortality of souls, is composed partly of reasonings concerning particular, partly concerning general facts. It has a foundation in reason, so far as it is supported by experience. But its best and most solid foundation is faith and divine revelation.
Morals and criticism are not so properly objects of the understanding as of taste and sentiment. Beauty, whether moral or natural, is felt, more properly than perceived. Or if we reason concerning it, and endeavour to fix its standard, we regard a new fact, to wit, the general tastes of mankind, or some such fact, which may be the object of reasoning and enquiry.
When we run over libraries, persuaded of these principles, what havoc must we make? 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 matters of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.
Specimen Questions
1 Explain Hume’s distinction between ‘relations of ideas’ and ‘matters of fact’. Why did he think much traditional metaphysics should be ‘committed to the flames’?
2 Hume suggests that in order to understand the laws of nature and all the operations of bodies we depend entirely on experience, and that the effects of causes cannot be known a priori or through reason alone. What is his argument and is he right?
3 ‘The contrary of every matter of fact is still possible; because it can never imply a contradiction’ (Hume). Explain and critically discuss.
Suggestions for Further Reading (Including Internet Resources)
1 See readings on Hume at the end of Part I, section 7. See also ch. 3 of D. F. Norton (ed.), The Cambridge Companion to Hume (Cambridge: Cambridge University Press, 1994).
2 For a good overview of Hume's philosophy see D. Garrett, Hume (Abingdon: Routledge, 2015); and, for more detailed analysis, J. Bennett, Locke, Berkeley, Hume (Oxford: Clarendon, 1971).
3 For online resources such as the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy see Part I, section 7 above.
4 An excellent introduction to Hume is P. Millican’s General Philosophy lecture from 2010 http://podcasts.ox.ac.uk/26-david-hume recorded for Oxford University, and also his subsequent series of podcast lectures on ‘David Hume and the first book of his Treatise of Human Nature’ (2012), http://podcasts.ox.ac.uk/series/introduction-david-humes-treatise-human-nature-book-one. See also D. Robinson’s Oxford lecture on Hume and causation from the lecture series ‘Reid’s Critique of Hume’ (2014), http://podcasts.ox.ac.uk/hume-causation.
5 You may also want to listen to a stimulating episode of the BBC program In Our Time presented by M. Bragg at https://www.bbc.co.uk/programmes/b015cpfp.
Notes
* David Hume, An Enquiry Concerning Human Understanding [1748]. Extracts from Section IV, part 1, and Section XII, part 3; with some changes of spelling and punctuation. There are many editions, including that by Tom L. Beauchamp (Oxford: Oxford University Press, 1999), which contains a useful introduction for students.
1 1 Treatise, Bk I, part iv, section 3, para. 7.
2 2 Ibid., para. 2.
3 3 Hume argues elsewhere that our tendency to generalize on the basis of limited experience is based more on custom and habit than on any sound reasoning: see below, Part VII, extract 5 and extract 6.
4 4 For more on why Hume maintains this, see Part VII, extract 6.
5 5