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The Glory of Philosophy: An Exoneration of Inductive Inference
ABSTRACT
At the very root of his critique of inductive inference, Hume unwittingly employed inductive inference. Hence his entire critical analysis suffers from the same defects he believed all induction suffers. Though Hume was correct when he declared that “custom” plays a fundamental role in inductive inferences, this applies only to the process of human thinking. However, the ideational content involved in all inductive inference is not established by mere custom but is selected according to objective and logical standards of judgment. With regard to the relations between cause and effect, Hume concluded these relations exists only in our mind. In so doing, he was focused too closely on the subjective or psychological side of things and failed to take into account the physical dynamic that objectively exists between causal conditions and their subsequent effects state. It is the physical existence of a dynamic, or energy-link, between a cause and its effect that differentiates causality from coincidence. Finally, I show that extreme skepticism falls by its own sword because it implicitly makes use of a presumed supra-human perspective.
The Glory of Philosophy: An Exoneration of Inductive Inference
It is well known that in the throes of Europe’s scientific revolution of the 14th century Francis Bacon sketched out the philosophical foundations of the newly emerging empirical sciences in his 1620 paean to inductive inference: Novum Organum.[1] Thereafter, for well over one hundred years, scientists and philosophers worked hand in glove in the belief that the new edifice of empirical knowledge they were raising was mounted upon a secure foundation.
Then came David Hume.
In his An Enquiry Concerning Human Understanding, Hume created a doctrine that cast grave doubt upon our ability to rely on inductive inferences. Although Hume personally advocated a “mitigated skepticism”[2], his criticisms not only tended to pull the rug out from under the new and rapidly expanding physical sciences, they also threw a cloak of insecurity over a vast area of human claims to reliable knowledge about the physical world.[3]
Now as most everyone admits (including Hume[4]), on a pragmatic level inductive inference works.[5] Accordingly, the workaday world has gone on much as though Hume never existed. But in philosophy his probing cut a wide swath. It is not that thinkers have been persuaded to abandon induction, so much as the inability to validate its virtues has continued to rankle in the philosophical breast. Over the years a host of writers have taken up this challenge[6], with counter claims ranging from apriorism,[7] “hardwired” thinking[8], “self-supporting” arguments[9], and stratagems to “evade”[10] the problem, to assertions that “there is no problem”[11] and the whole issue is “fictitious”.[12] Unfortunately, though most counter claims do make a valid point, none have succeeded in putting the specter of skepticism to rout, and the lament C. D. Broad voiced on the tercentenary of Bacon’s death remains yet: “May we venture to hope that when Bacon’s next centenary is celebrated the great work which he set going will be completed; and that Inductive reasoning, which has long been the glory of Science, will have ceased to be the scandal of philosophy”.[13]
Though it might appear all avenues have been exhausted in this matter and the field conceded to Hume, in fact that is not the case. I here offer a new and untried approach, one that is able to fully exonerate inductive inference and reassert the glory that (supposedly) prevailed in the philosophy of science from the time of Francis Bacon to the days of Hume.
First, a few brief and well-worn quotations from Hume will set out his position.
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… 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 tomorrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise.[14]
In response, it has been argued that, because “nature is uniform”[15] it is only reasonable to infer the sun will rise tomorrow just as it has always risen in the past. But Hume had anticipated this response.
All inferences from experience suppose, as their foundation, that the future will resemble the past, and that similar powers will be conjoined with similar sensible qualities. If there be any suspicion that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion. It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future; since all these arguments are founded upon the supposition of that resemblance.[16]
Others have claimed that, although predicting the future with complete certainty may be beyond us, we are still able to make probability predictions. In practice this is true. However, arguments advocating a probability approach do not address Hume’s philosophical concern. That is, if we wish to make a probability statement about the future, whether we base that statement upon the “frequency”[17] of past events or appeal to our level of “belief”[18], we must first assume the information we are using is in some way relevant to future events. But Hume’s concern was: how do we know any information we have is relevant to future events? Probability arguments, in his view, succumb to the same circular reasoning as other justifications of induction.
All our experimental conclusions proceed upon the supposition that the future will be conformable to the past. To endeavour, therefore, the proof of this last supposition by probable arguments, or arguments regarding existence, must be evidently going in a circle, and taking that for granted, which is the very point in question.[19]
According to Hume, all attempts at justifying induction beg the question. Furthermore, logic is unable to help us here because, “in all reasonings from experience, there is a step taken by the mind which is not supported by any argument or process of understanding”.[20] It is mere custom, he tells us, that drives inductive inference.
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.[21]
Custom, then, is the great guide of human life. It is that principle alone which renders our experience useful to us, and makes us expect, for the future, a similar train of events with those which have appeared in the past.[22]
For 250 years these arguments of Hume have weathered all attempts to bring them down.[23] And yet, they are flawed. Under careful analysis we find Hume not only based his critique on ill-defined premises, he also shifts frames of reference, thereby giving his arguments an impression of cogency they do not really possess. Before examining these flaws, however, it is necessary to clarify some terms.
Learning and inferring.
Learning is the psychological process of forming new ideas and new idea-relations. Learning employs a variety of methods such as insight[24], trial and error[25], random exploration, and so forth. When a child comes to recognize his surroundings, his parents, and the family dog, he has formed new ideas. When he realizes that the family pet, Rover, the neighbor’s pet, Spot, and several other creatures resembling Rover are called dogs, he has learned to network those ideas into a specific relationship. The creating and colligating of ideas may come easily, as learning to recognize rainfall, or it may be an insight preceded by great mental effort, as Newton’s intuition that an apple and the moon are both attracted to the earth by the same force.
Inferring is not concerned with the formation of new ideas and idea-relations. Rather, (as it relates to induction) inferring is the process of expecting the facts we have already learned about the physical world to continue to hold beyond those occasions we have actually experienced. In other words, once a set of ideas and idea-relations are learned, they become the template we use for inductively inferring from the physically known to the physically unknown.
Another term having some ambiguity is inference. Normally it may be used to indicate either the process of inferring or a conclusion arrived at by inferring. I will continue to employ it in both capacities, while making an effort to keep its use contextually clear. The word induction will be used strictly to indicate a conclusion of an inductive inference.
Figure 1 schematically represents the mental operations involved in making a simple induction (admittedly, there is more going on psychologically, but the scheme is sufficient for present purposes). When the average adult looks out the window and experiences visual stimuli of water droplets falling from the sky, he instantly relates this information to his past learning and identifies (or learns) this is another instance of rain. This learned perception of “it is now raining” is immediately followed by a second process of remembering the idea-relation: “rain / has always made the ground wet”. From this past idea-relation he then infers the induction (conclusion) that “the ground will be wet”.
Seen as a sequence of logical thought, the present perception, “it is now raining” is the minor premise, the past learned idea-relation is the major premise, and the induction is the conclusion.
Although there is more to the story than Hume apparently realized, he was nonetheless correct in saying we make the kinds of inductive inference or “leap” diagrammed in Figure 1 without deliberation. That rain leads us to expect “the ground will be wet”, is the kind of automatic inference humans (and animals) make all the time. For, “the mind is carried by habit, upon the appearance of one event, to expect its usual attendant, and to believe that it will exist”.[26]
Now it is an essential part of human life to want our inductive inferences to be accurate. Indeed, it is crucial if we hope to obtain food, shelter, or avoid danger. To that end we strive to expand our learning base to as wide a premise as possible from which to make our induction. Rather than drawing our conclusion from a limited major premise, as in Figure 1, we desire to have major premises of universal scope (Figure 2). Not only is this a common and uncritical human practice, it is also one of the basic goals of philosophy, of science, and practically any systematized body of thought.
In the above diagram, the inductive “leap” is to a universal conclusion. This conclusion, coupled with the idea of rain, becomes an idea-relation that purports to cover all relevant cases - “rain will always make the ground wet”. Accordingly, this universal concept now becomes the major premise of our argument. Beginning with our minor premise (“it is now raining”) we inductively move up to the universal major premise, then by a process of deductive inference we draw the particular conclusion, “the ground will be wet”. Although this deductive conclusion is precisely the same as the conclusion arrived at inductively from the more limited major premise in Figure 1, because it is derived from a universal premise we feel it to be more secure (whether a universal premise truly is “universal” is, of course, another matter).
Historically there has been much confusion between learning and inferring.[27] The creation of a new universal hypothesis or theory (as Newton’s insight regarding universal gravitation) has often been mistakenly identified as an induction similar to that diagrammed in Figure 2. But it is not. There is a critical difference. When Newton saw an apple fall to the earth, and from this he supposedly got the idea that all bodies everywhere are attracted to one another, this was not a case of inductive inference. Though he drew a universal “conclusion” from a particular perception, his insight widened the class of falling objects to include other things such as the moon and the rise and fall of the tides. This introduced new ideas and new idea-relations. Therefore, the creating of his theory was a case of learning, not inferring. Had Newton merely said, all apples that become detached from the bough will fall to the earth, that would be a universal inductive inference from his specific experience. It introduces no new ideas or new idea-relations, it merely repeats or universalizes what is already known. In the creating of his theory Newton obviously employed both learning and inferring, however, it is important to keep the distinction clear.