David Hume: Scepticism, Science, and Superstition

David Hume:Scepticism, Science,and Superstition 4. Hume’s Argument concerning Induction Dr Peter Millican Hertford College, Oxford

A Very Brief Overview • Suppose we see A followed by B again and again. When we next see an A, we naturally infer a B. But why? • A Priori insight? No: a priori, we can know nothing whatever about what causal effects A will have. “Intelligibility” is just an illusion. • Such factual inference is clearly based on extrapolating into the future the associations that we have observed.

Inferring Uniformity • What ground can we give for extrapolating from observed to unobserved? • Logical intuition? No. • Deductive reasoning? No: neither of these, because it’s clear that extrapolation could fail, so it can’t be a matter of pure logic. • Sensory knowledge? No: what we perceive of objects gives us no insight into the basis of their powers, hence no reason to extrapolate. • Experience? No: that would be circular.

Hume’s Argument in Context • The Argument in the Treatise • The Argument concerning Induction (“the Argument”) appears in Treatise I iii 6, the Abstract, and Enquiry IV. • In the Treatise, the Argument is embedded in an extended discussion of the origin of the idea of causal necessity. This distorts it: • A bit muddled about causal cf. “probable” inference; • Doesn’t clearly distinguish between psychological mechanism cf. epistemological foundation; • Also omits some important stages.

Hume’s Mature Argument • The Argument in Enquiry IV • Totally separated from discussion of the idea of causal necessity (in Enquiry VII); • Explicitly centred around epistemology: “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”? (E 4.3) • More complete than Treatise, e.g. explicit that senses and intuition cannot ground induction.

Inference from Impression to Idea • Treatise I iii 6 focuses on what Hume takes to be the paradigm causal inference: • After seeing A followed by B numerous times, we see an A (i.e. we have an impression of A) and expect B (i.e. we form a lively idea of B). • This tendency to infer from A to B underlies our ascribing A as the cause of B: “the necessary connexion [i.e. our belief in causal necessity connecting A to B] depends on the inference”, not the other way round (T 1.3.6.3).

Hume’s Fork • Enquiry IV starts from the distinction between “relations of ideas” and “matters of fact”. • Relations of ideas can be known a priori by inspecting ideas; hence their falsehood is inconceivable and they are necessarily true. • Matters of fact can be discovered only through experience, since their falsehood is conceivable and they are contingent (could be true or false). • This is a refinement of the distinction between types of relation in T 1.3.1.1-2.

Demonstrative and Probable • A Lockean distinction: • In demonstrative reasoning, each link in the inferential chain is “intuitively” certain (hence = “deductive” in the modern non-formal sense). • In probable reasoning, some links are merely probable (hence = “inductive” in a loose sense). • For Locke, both involve rational perception: • Reason perceives the links in a demonstrative argument, by “intuition”. • Reason also perceives probable connexions.

Hume on Types of Reasoning • In Treatise I iii 6, Hume employs Locke’s terminology. But in the Enquiry … • Demonstrative inference is also called “reasoning concerning relations of ideas”. • Probable inference is usually called “moral reasoning” or “reasoning concerning matter of fact” (I call this factual inference for short). • Factual inference is ampliative reasoning, which draws conclusions beyond what can be inferred a priori by relations of ideas.

Hume’s Factual Inference • Consider: Mars is red and round therefore Some round thing is coloured • The premise and conclusion are matters of fact, so is this “reasoning concerning matter of fact”? • Is the inference merely “probable”? No! • Does it go beyond “relations of ideas”? No! • Does justifying the inference require any appeal to experience or to causal relations? No! • So Hume (if he were to consider any example of this type) would have to count it as demonstrative.

“Demonstrative” => a priori? • But this is controversial: many Hume interpreters have claimed that he counts an inference as “demonstrative” only if its premise(s) – and hence its conclusion – are a priori. Consider … • “Were [any matter of fact] demonstratively false, it would imply a contradiction, and could never be distinctly conceived by the mind.” (E 4.2) • “whatever is intelligible, and can be distinctly conceived, implies no contradiction, and can never be proved false by any demonstrative argument or abstract reasoning à priori.” (E 4.18)

Is Demonstrative Reasoning Limited to Mathematics? • “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.” (E 12.27) • But Hume’s account of this limit is in terms of the relative clarity of mathematical and moral ideas. • So if we want to find a posteriori demonstrative arguments of any complexity, we have to look to applied mathematics …

Hume on Applied Mathematics • Hume’s most explicit discussion of “mixed mathematics” is in Enquiry Section IV: • “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 . . . if, by any contrivance . . . we can encrease the velocity of that force, so as to make it an overmatch for its antagonist.”(E 4.13)

The momentum of a body is equal to its mass multiplied by its velocity. • In any collision the total momentum of the colliding bodies (in any given direction) is conserved. Before … 25,000 m/s 4 m/s 2 kg 10,000 kg After …

“Geometry assists us in the application of this law . . . 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.” (E 4.13) • “Mathematics, indeed, are useful in all mechanical operations . . . But ’tis not of themselves they have any influence. . . . Abstract or demonstrative reasoning . . . never influences any of our actions, but only as it directs our judgment concerning causes and effects.” (T 2.3.3.2)

“No Matter of Fact is Demonstrable” • Let proposition P be: “All crows are black.” • Suppose I say:“P is demonstrable.”Ridiculous, you would say! How can I possibly claim to demonstrate that all crows are black? • “Well”, I reply, “here’s my demonstration”: 1. All birds are black. 2. All crows are birds. All crows are black. • That’s a demonstrative argument, isn’t it?

“Demonstrate” = “Deductively Prove” • When we say “P is demonstrable” (or “P is deductively provable”), we don’t just mean: • “Some deductively valid argument or other can be found which has P as a conclusion.” • Instead, we mean something like: • “P can be proved using some deductively valid argument, from premises that we know with absolute certainty to be true. • So it is no surprise at all to find Hume stating that “no matter of fact can be demonstrated”.

Humean “Demonstration” • In short, an argument is “demonstrative” if it is deductively valid (in the informal sense: its premises logically entail its conclusion). • Useful examples of such argument occur mostly in mathematics, pure or applied, because mathematical ideas are precise enough to allow complex trains of inference. • One matter of fact can be demonstrated from another, but no matter of fact can be demonstrated tout court (i.e. a priori).

UP: The Uniformity Principle • In the Treatise • “If reason determin’d us [to infer B from A], it wou’d proceed upon that principle, that instances of which we have had no experience, must resemble those of which we have had experience, and that the course of nature continues always uniformly the same.” (T 1.3.6.4) • This seems conditional: IF reason is involved, THEN it must be based on this principle. • But the principle seems implausibly strong.

The Uniformity Principle (2) • In the Enquiry • “all our experimental conclusions proceed upon the supposition, that the future will be conformable to the past”. (E 4.19) • No suggestion of conditionality (cf. also E 5.2: “in all reasonings from experience, there is a step taken by the mind” corresponding to UP). • More vague than UP in Treatise, and so more plausible: we expect the future to “resemble”(E 4.21) the past, but not copy exactly.

The Uniformity Principle (3) • UP is Implicit, not Explicit • Hume is not suggesting, even in the Enquiry, that we think of UP explicitly when making inductive inferences (cf. T 1.3.8.13). • Rather, in making an inductive inference, we manifest the assumption of UP, in basing our inferential behaviour on past experience. • Compare: we manifest the ascription of causal necessity between A and B, when we infer from A to B (cf. T 1.3.6.3 above).

A Sketch of the Argument • Part (i) • Concludes that all factual inferences to the unobserved are founded on experience. • Pivot • Hence all factual inferences to the unobserved are founded on UP. • Part (ii) • But UP has no rational foundation. • So factual inference is not founded on Reason.

The Part (i) Argument • Factual inference is founded on causation • Causation is the only relation that enables us to infer from one thing to another. • All knowledge of causal relations is founded on experience • A priori, we can know nothing of causation. • The “Founded on” Relation is Transitive • i.e. if x is founded on y, and y is founded on z, then it follows that x is founded on z.

The Pivot • All factual inference is founded on experience. • All inference from experience is founded on the Uniformity Principle. • Because it requires that we extrapolate from our experience, on the basis that what we have not yet experienced will be similar. • Hence all factual inference is founded on the Uniformity Principle.

The Part (ii) Argument • In Treatise I iii 6 • “let us consider all the arguments, upon which [UP] may be suppos’d to be founded; … these must be deriv’d either from knowledge [i.e. demonstration] or probability”. (T 1.3.6.4) • We can conceive a change in the course of nature, so UP cannot be demonstrably true. • Probable reasoning must be causal, and so founded on UP. Hence it cannot itself provide a foundation for UP, on pain of circularity.

Enquiry IV Part (ii) • Four “Kinds of Evidence” • “It is common for Philosophers to distinguish the Kinds of Evidence into intuitive, demonstrative, sensible, and moral”. (Letter from a Gentleman, 1745, p. 22) • In the Enquiry, Hume argues explicitly that UP cannot be founded on what we learn through the senses, nor on intuition. • Hence he rules out all four “kinds of evidence”, not just demonstrative and probable inference.

A Sceptical Argument • All this seems to imply that Hume’s argument is genuinely sceptical. • It starts by showing that all factual inference is founded on the Uniformity Principle; • Then goes on to undermine every possible rational foundation for UP; • Then draws from this the conclusion that factual inference has no rational foundation. • This way of arguing does not make sense unless the argument has sceptical intent.

The Gap in Hume’s Argument • The Uniformity Principle is not founded on: • demonstrative argument • because a change in the course of nature is possible, whereas any demonstrative argument would have to yield total certainty; • probable argument • because any probable argument is itself founded on experience and hence on the Uniformity Principle. • But what if we could find a way of arguing probabilistically but a priori? • Hume just assumes this to be impossible.

Deductivist Interpretations • Antony Flew and David Stove • Interpret Hume as a deductivist, who just takes for granted that any argument which is less than certain is therefore useless. • Tom Beauchamp, Annette Baier etc. • Interpret Hume as an anti-deductivist, whose argument proceeds from deductivist assumptions, but whose ultimate point is to undermine deductivism by showing its inability to provide any basis for factual inference.

“Mediums” and Deductivism • When Hume says a “medium” is needed to prove UP (he doesn’t speak of UP as itself a medium), he need not be presupposing a deductive paradigm of inference: • Arguments do not always need a “medium” to get from premiss to conclusion (e.g. T 1.3.7.5n). • Even when they have one, that “medium” can be merely “probable” (Dialogues 143). • Hume sees that inductions are incurably fallible even if nature is uniform (e.g. T 1.3.15.11).

Refuting Deductivist Interpretations • Why Canvass a Probable Argument for UP? • On the deductivist and anti-deductivist interpretations, Hume’s canvassing of a “probable” foundation for UP makes no sense – on deductivist principles, no merely “probable” argument can provide a foundation for anything. • The Balance of Hume’s Scepticism • Hume does appear to view his argument as genuinely sceptical, but he certainly doesn’t proceed on deductivist assumptions elsewhere: indeed he is a strong advocate for induction.

Is Hume an Inductive Sceptic? • Does Hume deny that inductive inference is founded on any sort of rational insight into why nature should be uniform? • YES! • Does Hume think that all inferences about “matter of fact” are equally hopeless, so that there’s no rational ground for preferring one to another? • NO!

The “No Argument” Interpretation • Don Garrett and Harold Noonan • Garrett (1997) and Noonan (1999) claim that Hume is only concerned to show that inductive inferences are not caused byargument, i.e. that there is no process of ratiocination that leads us to infer inductively. • David Owen • Owen (1999) claims that Hume is only ruling out inference by intermediate steps, what he understands by Lockean “reason”.

Refuting Garrett and Owen (1) • According to Garrett and Owen, “reason” for Locke and Hume means quite specifically our faculty of inference, a sub-faculty of “the understanding”. • But this seems wrong (see slides 37-48): • Writers of the time all seem to have used “reason” and “the understanding” equivalently. • They apparently meant to refer to a general faculty of rational perception rather than a more specific faculty of inference.

Refuting Garrett and Owen (2) • The Logic of the Part (ii) Argument • Hume’s Part (ii) argument makes no sense on the Garrett/Owen reading: • UP plays a role in the causation of factual inference; • UP is not itself caused by a process of raticination; • Therefore inductive inference is not caused by any process of ratiocination • This is a complete non-sequitur. Inductive inference could be caused by a process of ratiocination that involves UP!

Refuting Garrett and Owen (3) • Causation by Argument, or Foundation in Reason? • If Hume were only concerned to prove that ratiocination plays no role in the causation of induction (i.e. factual inference), then: • His argument would be incomplete, because he does nothing to rule out the possibility that induction could be caused by bad argument. • Much of his Enquiry argument would be redundant, as he would have no need to refute the idea that induction is founded on intuition or sensation.

Is Lockean Reason Inferential? • Don Garrett (1997): • “‘Reason’, according to Locke, is the faculty of the ‘discovering and finding out of Proofs’, ‘laying them in a clear and fit Order’, ‘perceiving their Connexion’, and ‘making a right conclusion’ (ECHU IV.xvii.3). Reason is thus a faculty of finding, presenting, appreciating, and being moved to belief by arguments. …” (pp. 26-7) • “for Locke, ‘reason’ is simply the inferential or argumentative faculty of the mind.” (p. 85)

Is Humean Reason Inferential? • Don Garrett (1997): • “Similarly for Hume, reason is the faculty of reasoning: of making inferences, or providing, appreciating, and being moved by arguments.” (p. 27) • David Owen (1999): • “Hume sometimes uses ‘understanding’ and ‘reason’ as synonyms, though strictly speaking the understanding is a more inclusive faculty than reason.” (p. 142)

Locke on Reason as Inference “The greatest part of our Knowledge depends upon Deductions and intermediate Ideas: And in those Cases [where we achieve only probability rather than knowledge] we have need to find out, examine, and compare the grounds of their Probability. In both these Cases, the Faculty which finds out the Means, and rightly applies them to discover Certainty in the one, and Probability in the other, is that which we call Reason.” (Essay IV xvii 2) • See also Essay IV xvii 14, IV xx 16.

Locke on Reason as Intellect • “The Word Reason … stands for a Faculty in Man, That Faculty, whereby Man is supposed to be distinguished from Beasts, and wherein it is evident he much surpasses them.” (Essay IV xvii 1, cf. IV xix 4) • “Nothing that is contrary to, and inconsistent with the clear and self-evident Dictates of Reason, has a Right to be urged, or assented to, as a Matter of Faith …” (Essay IV xviii 10) • “But if they know it to be a Truth, they must know it to be so either by its own self-evidence to natural Reason; or by the rational Proofs that make it out to be so.” (Essay IV xviii 11)

Locke on Reason as Perception (1) “we … looke for noe greater certainty then what our eyes can afford us, the whole evidence of this assureance being noe more then what the word Demonstration doth naturaly import; which is to shew any thing as it is & make it be perceived soe that in truth what we come to know this way is not by proofe but intuition, all the proofe that is used in this way of knowledg being noe thing else but shewing men how they shall see right … without useing arguments to perswade them that they are soe” (Draft B of Locke’s Essay, 1671, p.153)

Locke on Reason as Perception (2) “Inference … consists in nothing but the Perception of the connexion there is between the Ideas, in each step of the deduction, whereby the Mind comes to see, either the certain Agreement of Disagreement of any two Ideas, as in Demonstration, in which it arrives at Knowledge; or their probable connexion, on which it gives or with-holds its Assent, as in Opinion. … For as Reason perceives the necessary, and indubitable connexion of all the Ideas or Proofs one to another, in each step of any Demonstration that produces Knowledge; so it likewise perceives the probable connexion of all the Ideas or Proofs one to another, in every step of a Discourse, to which it will think Assent due. …” (Essay IV xvii 2).

Locke’s Scepticism about Faculties • Locke ridicules the language of faculties as a source of philosophical error, and declares himself inclined to forego it completely were it not that faculty words are so much in fashion that “It looks like too much affectation wholly to lay them by” (Essay II xxi 17‑20). • When we refer to man’s “understanding”, all we can properly mean is that man has a power to understand. • It is a serious mistake to speak of our faculties “as so many distinct Agents”. • “the understanding, or reason, whichever your lordship pleases to call it …” (First Letter to Stillingfleet, III 70)

Hutcheson on the Faculties “Writers on these Subjects should remember the common Division of the Faculties of the Soul. That there is 1. Reason presenting the natures and relations of things, antecedently to any Act of Will or Desire: 2. The Will, or Appetitus Rationalis, or the disposition of Soul to pursue what is presented as good, and to shun Evil. … Below these [the Antients] place two other powers dependent on the Body, the Sensus, and the Appetitus Sensitivus, in which they place the particular Passions: the former answers to the Understanding, and the latter to the Will.” Illustrations upon the Moral Sense (1728), SB §450

Price on Reason and Sense “The power, I assert, that understands; or the faculty within us that discerns truth, and that compares all the objects of thought, and judges of them, is a spring of new ideas. … Sense presents particular forms to the mind; but cannot rise to any general ideas. It is the intellect that examines and compares the presented forms, that rises above individuals to universal and abstract ideas. … Sense sees only the outside of things, reason acquaints itself with their natures. … Feeling pain, for example, is the effect of sense; but the understanding is employed when pain itself is made an object of the mind’s reflexion …“ A Review of the Principal Questions in Morals (1758), SB §590-2

Price on Reason as Perception “In a word, it appears that sense and understanding are faculties of the soul totally different: … The one not discerning, but suffering; the other not suffering, but discerning; and signifying the soul’s Power of surveying and examining all things, in order to judge of them; which Power, perhaps, can hardly be better defined, than by calling it, in Plato’s language, the power in the soul to which belongs … the apprehension of Truth.” A Review of the Principal Questions in Morals (1758), SB §593

Butler on Reason • Joseph Butler too identifies “reason” with “the understanding”, and views it as essentially perceptual: “… as speculative reason may be neglected, prejudiced, and deceived, so also may our moral understanding be impaired and perverted … This indeed proves nothing against the reality of our speculative or practical faculties of perception …” Analogy of Religion (1736), Part I Chapter vi §19

Hume on Reason • Hume also identifies “reason” with “the understanding”, and views it – initially at least – as an essentially perceptual faculty, contrasted with “the imagination”. • For more on this, see §2 of Peter Millican, “Hume’s Sceptical Doubts Concerning Induction”, chapter 4 of Reading Hume on Human Understanding (OUP, 2002). • After Hume has proved that inductive inference depends on “the imagination”, the terminology gets a bit more complicated (op. cit.§2)

Hume’s ‘Sceptical Solution’ • Hume sums up his sceptical conclusion about the foundation of induction thus: ‘we … conclude … that, in all reasonings from experience, there is a step taken by the mind, which is not supported by any argument or process of the understanding’ (E 5.2) • He then goes on: ‘If the mind be not engaged by argument to make this step, it must be induced by some other principle of equal weight and authority …’

Custom or Habit • Hume gives the principle a name, but makes no pretence to understanding its ultimate basis: ‘This principle is CUSTOM or HABIT. By employing that word, we pretend not to have given the ultimate reason of such a propensity. We only point out a principle of human nature, which is universally acknowledged, and which is well known by its effects. Perhaps, we can push our enquiries no farther, or pretend to give the cause of this cause; but must rest contented with it as the ultimate principle, which we can assign, of all our conclusions from experience.’ (E 5.5)

David Hume: Scepticism, Science, and Superstition