Even the definition which Anderson offers may, on a plain reading, be deficient. For I can think of a number of generalizations I’ve drawn in my life which I treat a certain and exceptionless even though they were not based on “a series of particular observations,” but in fact on single instances. For example, I distinctly remember burning my hand on a hot stove when I was a child. I did not need repeated experiences of this to drive home the causal relation between a touching a hot surface and experiencing sudden, intense, and lasting pain. One instance was plenty sufficient! Similarly, also when I was a child, I remember trying to plug something into a power outlet and getting shocked because one of my fingers was in contact with the plug’s metal prongs when it came into contact with the power source. Again, I did not need to repeat this experience in order to draw the generalization that doing this anytime, anywhere, was not a good idea. Once was enough!
So, I would say that there are in fact inductive generalizations which one can – and probably should – draw without reiteration. In fact, philosopher David Kelley, in his lecture Universals and Induction, goes so far as to say that “repetition plays no essential role in knowledge at all, not in induction, not in concept-formation, not in any reasoning process,” and his explanation is very cogent:
Whenever we reach certain conclusions about a given phenomenon, by observation or by inference, the occurrence of an exact repetition of that phenomenon does not allow us to draw any new conclusions, except the obvious conclusion that this has happened before. Repetition as such, the sheer fact of repetition, is epistemologically barren.
if I observe one thousand swans, and every one of those swans is white, I can infer inductively that probably all swans are white, and on that basis predict that any future swans I observe will (probably) be white.
For Anderson, the reliability of induction hinges – apparently exclusively – on one factor: the uniformity of nature:
Our inductive inferences about the natural world take for granted that nature is basically uniform across both space and time, such that observations in one location (e.g., in our solar system) are reliable indicators of how nature behaves in all other locations, and such that past observations are reliable indicators of future occurrences. If the principle of the uniformity of nature does not hold, then inductive inferences should not be considered reliable.
After introducing the topic of the uniformity of nature, Anderson asks point blank, apparently not expecting a serious answer:
On what basis do we assume that nature is in fact uniform across time and space?
My answer continues to be the same here: On the basis of the axioms, the primacy of existence, and the objective theory of concepts.
I am happy to explain this, but first I think it’s important to clarify what I take “uniformity of nature” to actually denote. The uniformity we observe in nature is essentially the concurrence of identity with existence. And this speaks to the first item in my answer – the axioms. The most basic recognition possible to the human mind is made explicit by the axiom of existence: “Existence exists – and only existence exists” (Leonard Peikoff, “The Analytic-Synthetic Dichotomy,” in Ayn Rand’s Introduction to Objectivist Epistemology, p. 109). In other words, things exist, there is a reality. Everything we perceive through our five senses provides a constant flow of objective input informing this fundamental recognition: everywhere we look, what we see is existence. Similarly with our other sense modalities.
Critics of Objectivism have protested this starting point by stammering “That doesn’t tell us what exists!” which of course is true when it comes to specifics. And it’s not meant to do this. But notice that this objection misses the point: the axiom of existence is a starting point - it is where cognition begins, namely with its first contact with objective reality; it is not where cognition ends. But notice what the objection takes for granted: it takes for granted that what exists has identity. To ask what exists assumes that what exists can be identified, and having identity, a nature, is a necessary precondition to being identifiable. The axiom of identity, then, is the fundamental recognition that to exist is to be something, to have identity, to be something specific - this as opposed to that, this as opposed to everything else.
Uniformity, then, is essentially the applicability of the axiom of identity to all existence. There is no such thing as an existent without identity, a thing without a nature, a thing that is nothing specific. To exist is to be something, and the axioms of existence and identity are our formal recognition of this fundamental fact.
The second item in my answer is the primacy of existence. This fundamental principle is the formalized recognition that existence exists independent of conscious activity. As Ayn Rand observes: “that the task of man’s consciousness is to perceive, not to create, reality” (For the New Intellectual, p. 22; compare Leonard Peikoff: “that the role of the subject [of consciousness] is not to create the object, but to perceive it” and “The function of consciousness is not to create reality, but to apprehend it” (The Ominous Parallels, pp. 62 and 303). The recognition that consciousness perceives things which exists rather than conjures them ex nihilo is self-evident and fundamental, so much so that no adult thinker seriously questions the adage “wishing doesn’t make it so.” Consciousness does not have the power to simply revise reality at whim; if we don’t like something, we have to act to make things better, and that may or may not produce the outcome we desire. Reality does not conform to conscious activity, whether that’s wishing, hoping, imagining, preferring, willing, praying, throwing tantrums, etc.; consciousness must conform to reality. With respect to the uniformity of nature as understood above, this means that: if nature is uniform (i.e., if identity is concurrent with existence), this state of affairs is not the product of conscious activity – it is not an attribute that we can wish into being. If nature is uniform, it is uniform independent of conscious activity, and thus it is something we must discover and identify, not create or wish into existence.
Lastly, we come to the objective theory of concepts. This is the theory of concepts which Ayn Rand lays out succinctly in her book Introduction to Objectivist Epistemology, which I encourage visitors to my blog not merely to read, but to deeply study what Rand develops in those precious pages. Rand makes the case that the human mind forms concepts on the basis of perceptual input and that concepts expand man’s awareness beyond the range of his perception (the real heart of the problem of induction) by forming open-ended mental integrations which include not just those specific things we have actually perceived, but also others which are essentially like those things we have perceived but which we have not perceived and which we may never perceive. Rand explains that we do this through a process of abstraction, a step-by-step process which she describes and whose distinctive feature is the process of measurement-omission:
The basic principle of concept-formation (which states that the omitted measurements must exist in some quantity, but may exist in any quantity) is the equivalent of the basic principle of algebra, which states that algebraic symbols must be given some numerical value, but may be given any value. In this sense and respect, perceptual awareness is the arithmetic, but conceptual awareness is the algebra of cognition. (Introduction to Objectivist Epistemology, p. 18)
The concept ‘shoe’, for example, includes women’s size 6 as well as men’s size 12; shoes which are secured by laces as well as loafers (my personal preference!); shoes which are intended for use in sports as well as shoes worn by businessmen; shoes which are red and yellow as well as shoes which are solid black.
Notice that the concept ‘shoe’ includes those specific shoes which we have personally seen and handled as well as shoes which we have not personally seen or handled. My cousin in Virginia, whom I have not seen in many years, can call me on the telephone and tell me that he has recently purchased a new pair of shoes, and even though I have not seen these shoes – and maybe never will – I know right off what he’s talking about because I have already formed the concept ‘shoe’ and his new pair is just another unit that I can integrate into that concept now that I am aware that it exists. But notice also that the concept ‘shoe’ includes all shoes which will never otherwise enter my awareness: shoes which exist in China, in Slovakia, in South Africa, in India, in Peru, etc. Moreover, it includes shoes which used to exist but no longer exist. And, it includes shoes which do not yet exist but may or will exist in the future.
The take-away here is that just by forming the concept ‘shoe’ – or any concept, a skill which the human mind starts to develop in childhood, we are already forming general categories on the basis on specific examples, categories which expand our awareness beyond what we come into contact with personally. Thus, the role of concept-formation in inductive inferences is both fundamental and indispensable. Which means: no serious treatment of the topic of induction can be complete without understanding its basis in conceptualization. To put it succinctly, concept-formation provides the cognitive model for inductive generalizations.
Another important take-away here is that the conceptual understanding of induction pre-empts the stock objections which commonly accompany treatments of the problem of induction such as Anderson’s. Anderson provides an example of this objection in his paper:
A very common response is to suggest that the uniformity of nature, and thus the reliability of induction, has been confirmed empirically over time. Every time (or nearly every time) we’ve made predictions based on an inductive inference we’ve turned out to be correct, and therefore we’re justified in assuming that the same will be true in the future—in other words, that induction is generally reliable. The trouble with this answer, as Hume pointedly observed, is that it’s based on circular reasoning: it assumes the very thing in question, namely, that past observations are a reliable guide to the future. In other words, this answer tries to justify inductive inference with an inductive inference. That approach simply presupposes the reliability of induction rather than giving an independent justification for it. As Hume argued, it’s impossible in principle to justify induction on purely experiential grounds, because we will always have to extrapolate from what we have observed to what we haven’t observed.
Another take-away that is often lost on those who take Hume seriously, is that the problem of induction, to the extent that it is a problem, cannot be addressed merely by justifying the presumption that nature is uniform. Nature is indeed uniform in the sense that identity is concurrent with existence: whatever exists has identity. That’s well and good, but that does not provide illumination on the cognitive nature of induction. By resting the matter entirely on the uniformity of nature, treatments like Anderson’s ignore the role performed by the human mind on the matter, which is key to it all! As I pointed out in my own blog entry Presuppositionalism and Induction: Thoughts on the Uniformity of Nature:
If nature is uniform, it is uniform not only in my experience, but also in my cat’s experience. However, my cat will never be able to draw the generalization that dropping eggs will result in them breaking and spilling their contents. But I can!
It should be no surprise that concept-formation never enters into consideration of the problem of induction in treatments like Anderson’s, not only because his very purpose in raising the problem of induction in the first place is to argue for the existence of something that we can only imagine, but because his worldview – the Christian worldview – has no theory of concepts to begin with. Since knowledge is concepts, lacking a theory of concepts is a fatal liability for anything posturing as a comprehensive worldview: it means it has no account for knowledge as such. Clueless about the conceptual nature of human cognition, apologists exploit what is mysterious to themselves in order to validate worship of something that “must always remain mysterious to man” (Cornelius Van Til, The Defense of the Faith, p. 14), namely the god which believers enshrine in their imagination. By clinging to the ever-mysterious, the apologist remains in the dark and never finds the light switch.
Anderson notes that “solutions to the problem of induction have been offered, but none has been widely accepted and the issue has proven to be an enduring challenge.” Whether a solution has been “widely accepted” or not is irrelevant to its cogency. I would think that Anderson would understand this. After all, how “widely accepted” is the “solution” which Anderson endorses? And yes, if thinkers are looking for a solution in the wrong place, I would expect the original problem to constitute “an enduring challenge.”
Anderson believes that “At the heart of the problem is the fact that only an omniscient being could possess direct and infallible knowledge of the uniformity of nature across space and time.” I do not see that Anderson has supplied an argument for this. It seems that the problem of induction is being treated here as just another in a long series of god-of-the-gaps type of apologetic, to wit: “I have no idea how to solve the problem of induction, but we draw inductive conclusions nevertheless, therefore there must be a God!” And given Anderson’s deep investment in his religious confession, it’s hard to shake off the suspicion that this was his desired outcome all along.
In essence, Anderson offers an appeal to magic, not by means of sound reasoning, but by means of imagination: a supernatural consciousness which the believer concocts in his imagination has the power to wish uniformity onto the elements of reality, and reality conforms accordingly, just because. This is a two-fold violation of the primacy of existence – a principle which Anderson’s own affirmations take for granted (for no doubt he would not claim that his statements are true because he wants them to be true). This is far from a serious philosophical position. But what alternative to the imagination does Anderson offer here? How can anyone reliably distinguish between what Anderson calls “an omniscient being” from something which Anderson may merely be imagining? Blank out. And how does positing “an omniscient being” move us forward in any way toward understanding what the human mind does when drawing inductive inferences? At best, it’s a distraction; at worst, it’s a formula for keeping thinkers in the pitch black of anti-conceptual darkness.
Now maybe there’s a reader (or several?) who thinks I’m wrong, either partly or entirely, in my conception of induction, my defense of inductive reliability, or my challenges to Anderson’s viewpoint. If so, please feel free to use the comments section to voice your concerns. Maybe I am wrong. If I am wrong, how will I discover that I’m wrong if no one steps forward to show me the light? If we grow in our knowledge, what have we lost that’s worth protecting?
by Dawson Bethrick