An Enquiry Concerning Human Understanding - Hume's Inductive Explanation of Induction
C. Cheng, March, 2001
On Hume's Inductive Proof of Induction
After Leibniz’s rationalist account of the principle of causation, David Hume publishes his counter account with an empirical approach. Hume specifically counters Leibniz’s claim that “all predicate is contained in the subject”. Rather, he affirms empirical and inductive inquiry and the use of common sense. As with his other writings, Hume attempts to analyze principles and theories - be they political, economical, or philosophical – in accordance with human nature. In chapter four and five of An Enquiry Concerning Human Understanding, Hume dissects and analyzes causal principles through investigating the faculties of human understanding. From that, he draws the conclusion that the idea of causation comes from mere experience and has no reasonable foundation. Hume asserts that experience in turn becomes a propensity and develops the habit or custom of causal beliefs. Hence, custom sounds like a causal process or agency itself, and thus appears to be circular. Yet, through a comprehensive study of Hume’s appeal, assumptions, and analysis, it is apparent that his doctrine is neither circular in logic nor begging itself for answer.
Hume begins his inquiry by analyzing the human processes of understanding. He notes that man reasons from relation of ideas and matters of fact. Relation of ideas is strictly logical, wherein ideas correlate and draw conclusions, which is “either intuitively or demonstratively certain” (108); i.e., the predicate is contained in the subject and hence can be equated. These demonstrative propositions are “discoverable by mere operation of thought, without dependence on what is any where existent in the universe” (108). On the other hand, matter of fact can render its contrary possible, for it cannot be justified by demonstrative logic (and hence proven right or wrong): “it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness [to be true]” (108). In other words, understanding by matters of fact (or probable reasoning) is the process of inductive inference from perceptions.
Distinguishing the two faculties of human understanding, Hume proceeds to circumscribe probable reasoning (ex matter of fact) as reasoning ex cause and effect. He claims that much of knowledge is conceived through senses and memory; beyond senses and memory, there is no essential affirmation. The rising and setting of the sun, the fall of an apple, etc., are examples of this gender of knowledge. Hume further notes;
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 evidence of our memory and senses. (109)
Hume gives several examples: a man receiving a French stamp would assume the letter to have come from France, a machine in a remote island will imply that there are people on the island, etc. From this, Hume claims that whenever the mind asserts something about events in the world that exceeds the boundaries of memory and present perception, the reasoning traces causes to effects and effects to causes (24). I.e., a letter is mailed and hence caused by someone, and a maker must have caused a machine, for cause and effect, according to Hume, have tempo, spatial, and necessary connections. These are assertions requiring past inferences to reason out the unknown circumstance, rather than demonstratively reasoning and discerning. Hence, Hume maintains that all such matter-of-fact inferences are ultimately causal inferences.
Reasoning with causal inferences (i.e. matter of fact reasoning) is not one of demonstrative reasoning, for it is purely from experiences and founded on the basis of belief. Hume notes;
The knowledge of this reason is not, in any instance, attained by reasons a priori; but arises entirely from experience, when we find, that any particular objects are constantly conjoined with each other. Let an 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. (109)
The knowledge that fire burns and water drowns, as Hume provides in the examples, cannot possibly be deduced and demonstrated through their respective material properties. Thence, causal inferences are not based on relations of idea and not demonstrable. The more frequently the mind experiences a connection between the two types of events, i.e. cause and effect, fire and burn, water and drown, the more confidently the mind would expect the first event to be followed by the second. The foundation of causal inferences is the belief arisen from repetitive experience and patterns of recurring phenomena. Probable reasoning, Hume notes, compels the mind to “put trust in past experience and make it the standard of …future judgment” (115).
Yet, this claim, like all inductive inferences, has an assumption. In order for the inferences to hold substance, and in order for all empirical experience to be of value, the future must resemble the past. This assumption is necessary in order to hold past inferences as a tool for future understanding: “All inferences from experience suppose, as their foundation, that the future will resemble the past” (117). This is to say, inductive inferences naturally assume that the pending circumstance will resemble the inference, such that the knowledge from empirical experiences can be applied. Without this assumption, all causal inference will be trivial, as they hold no validity. On the other hand, this may not be too brave an assumption for general inductive reasoning; certain occurrence does repeat over time and its recurrence can affirm this assumption.
As proven, inductive inferences lack the support of reason (even granting their assumptions). Hence, it must be driven by another “principle of equal weight and authority”(120) in human nature (29). Hume identifies the human psychological account of habit in response to the “skeptical doubts” he has raised on induction. The “skeptical solution” asserts that experiences have conditioned the mind such that it produces a propensity for the mind to expect the type of outcome experience has taught. Hume calls the mechanism custom, or habit: “Wherever the repetition of any particular act or operation produces a propensity to renew the same act or operation, without being impelled by any reasoning or process of the understanding, we always say, that this propensity is the effect of custom” (121). According to Hume, the subconscious and semi-deterministic force called custom (for probable reasoning), along with reason (for demonstrative reasoning), drives the mind to understand and conceive as it does. As to what causes that propensity and what constitutes that inclination for the mind to operate in this mechanism, Hume notes that there can be no intelligible answer:
By employing that word [custom], 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 out conclusions from experience. (121)
The above claim can partly answer the accusation on Hume, that his doctrine is a circular logic. This is because the “custom” Hume introduces sound like a causal process or agency of causal beliefs. The doctrine Hume asserts appears to be circular, for custom, which is a product of repeated practice, becomes the cause of the causal belief, which then in turn causes causal inference and hence probable reasoning. Yet, Hume is not trying to investigate into the nature and essence of the principle of causation, rather, he is laying out the mechanism and the grounds on which it operates. Were he trying to explain the principle of causality with the cause of custom, then we will run into circular logic. In fact, Hume is not trying to use logic, for it is nonsensical and impossible to analyze probable reasoning with logic (115). Hume merely provides the answer for how causal inferences functions, not what it is or why it is; he is not trying to qualify or explain the principle of causation itself, he merely explains how man comes to use it, how it infers and how it becomes a mechanism through custom. Thus, Hume is only using the principle of causality (which he has inductively taken as true) to explain various psychological and mental tendencies to causal beliefs (which produces the propensity to understand through causal inference, without ever appealing to the context of causal principles). Since logic is never used in the process of understanding causal inferences, it is not circular logic. It is a mere attempt to draw a psychological analysis on the issue of causation.
Although Hume merely makes what appears to be trivial and commonsensical observation and analyzes the psychological phenomena on causality and draws no definitive assertion, he does not conclude that inductive inferences are worthless or that man should avoid using them. He notes that causal inferences are normal and important mental functions for cognition. Without the influence of custom and the habitual use of induction, which leads the mind to assume that future resembles the past, there can be no factual sciences or even knowledge in general (123). In fact, induction is used in excess in daily lives, in academic and scientific fields, and even in mathematics. The many examples ranging from weather prediction to deriving Fermat’s last theorem show the importance of the assumption of in-tempo recurrence. Hence, despite the absence of any claim, his analysis remains relevant and of importance.
Through investigating the doctrine of causal inference, it is apparent that Hume has not contradicted himself; he never intends to draw any logic beyond circumscribing mere observations and providing a psychological basis for inductive mental actions that has no rational basis. Indubitably, his empirical approach to the inquiry is a commonsensical one, to the extent where it may appear trivial. But nonetheless, he attempts to counter the rationalists’ extremities without discrediting their validities (that is, demonstrative reasoning). It is no surprise that Hume paved the way for Kant to draw a synthesis for the two opposing schools of thought.