Sunday, June 26, 2022

Same Old Song and Dance: Anderson on Induction... again

Christian apologist James Anderson has published yet another article on the problem of induction, this time as others essentially repeating the same superficialities from two decades ago, as though he has learned little in the intervening years: David Hume is still the prevailing authority on the topic of induction, and the problem of induction is “solved” by imagining an invisible magic being which ensures the uniformity of nature by means of sheer will. Nothing else really needs to be considered. The fact that he can point to academics who continue to be confused on the nature and basis of induction, as though this were even relevant, only serves to reinforce his theistic prejudices.

My views on the problem of induction have indeed evolved over the years. More and more I have come to the assessment that the problem of induction commits the fallacy of the stolen concept: the very framing of the problem of induction in fact tacitly assumes the validity of induction, and yet the validity of induction is what the problem essentially aims to call into question.

Take for example statements from Anderson’s own recent paper outlining the problem of induction is:

“An inductive inference aims to draw a general conclusion from a series of particular observations.”

Such a statement itself is a generalization as it is intended to apply to all instances of inductive inference. Although Anderson uses the singular here, it essentially states: every “inductive inference aims to draw a general conclusion from a series of particular observations,” which is to say: ALL inductive inferences do this. But if it’s the case that “inductive inferences cannot deliver absolute certainty,” on what basis does one form the generalization, stated here by Anderson as a solid, incontestable certainty, that all cases of inductive inference “aim… to draw a general conclusion from a series of particular observations”? At the level of its own genetic roots, the problem undermines itself.

In answer to this, one might say it’s a matter of definition: inductive inferences by definition “aim… to draw a general conclusion from a series of particular observations.” But this only moves the problem back a step: on what basis does one form such a definition, indeed one which applies to all instances of a general category? Do we just pull definitions out of thin air, or from some unmentionable nether region? In fact, such a counter is to be welcomed, because by asserting that this generalization about all inductive inferences is a matter of definition, the apologist would be conceding that concepts play a fundamental role here, for it is concepts which require definitions.

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.
Contrast this with Anderson’s own example of an inductive inference, which in his view requires ongoing sampling:
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.
Naturally the question arises: if repetition is required for inductive generalization, how many instances are sufficient to provide reliable content to said generalization? Is it ten instances? A hundred? Anderson’s “one thousand”? How does one arrive at such a figure without needing to enlist induction itself, which would lead to an infinite regress? On Anderson’s view, I would need to burn my hand a thousand times to draw the general conclusion that touching a hot surface (any hot surface) can cause pain, and then only probabilistically. Hopefully Anderson does not mind me going with my inductive process, which I conceive as applying the law of causality to entity classes (cf. here).

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.
Anderson does not make the case that other factors do not play a vital role in inductive reasoning (such as man’s mental activity), and seems satisfied to rest the matter exclusively on a metaphysical premise without considering the epistemological activity of human cognition. This has always struck me as rather odd because inductive reasoning is in fact a form of reasoning, and human minds are what perform tasks of reasoning! But in fact, ignoring the role of man’s mind in his efforts to reason inductively is what is to be expected given the apologist’s goal.

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?
That’s a tough one, eh?

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)
(Rand cautions that “the term ‘measurements omitted’ does not mean, in this context, that measurements are regarded as non-existent; it means that measurements exist, but are not specified” (Ibid., p. 12).)

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.
What should be clear in my points about concepts as open-ended integrations which include not only those particulars which we have perceived, but also those which we have not and never will perceive, is that the abstraction process makes time and place essentially irrelevant to what is included in conceptual integration. Time and place are basically omitted measurements in the sense that Rand explains. This means that the distinction between past and future has no fundamental bearing on the matter. The concept ‘shoe’ includes the pair of shoes which I possess now as well as the shoes I had in my seventh grade and the shoes which I will have five years from now, assuming I’m still alive. Since neither Hume nor Anderson enjoy the benefit of understanding induction in terms of its conceptual roots, this key point will continue to allude them and other thinkers who choose to remain uninformed on the nature of concept-formation and its bearing on the matter. Why is it that the concept ‘shoe’ can include all shoes which exist now as well as those which existed in the past and no longer exist and also those shoes which do not yet exist but will or may exist, and yet it is fallacious to infer that “past observations are a reliable guide to the future”? Indeed, we can infer this, not as the basis for justifying induction (for we have the axioms, the primacy of existence and the objective theory of concepts), but as a matter of extending the conceptual process across time and place in applying induction. Induction is already justified by forming our first concepts!

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!
If a justification of the presumption that nature is uniform were all that’s needed for induction, how is it that my cat cannot draw inductive generalizations like I can? The answer here is no mystery: unlike my cat, I can form concepts. As we saw above, the formation of our first concepts, a skill my cat will never be able to develop, human minds are already on the road to inductive generalization since concepts expand man’s awareness beyond the range of his senses.

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


Justin Hall said...

As I understand it, Hume was using concepts to call into question the epistemological foundations of concepts. It does not take a genius to see the problem here.

Bahnsen Burner said...

Hello Justin,

Great to see your comment!

In terms of fundamentals, I think you’re entirely right. At root, the real issue here is how the mind is capable of knowledge beyond the range of one’s senses. The answer is: we form concepts. Concepts expand human awareness beyond what one perceives by the process of abstraction. To deny the validity of induction is essentially to deny the validity of awareness beyond the scope of one’s senses. But if one denies the validity of awareness beyond what he perceives, how would he be able to ascertain and validate the general conclusion that awareness beyond the range of the senses is not possible? This is where the stolen concept involved in the matter germinates and takes root.

If induction is a conceptual process, and Hume et al. are simply ignorant of what this means, then the self-undermining nature of the problem of induction will likely be lost on them. But once one grasps the fact that just in framing the problem of induction, one needs to make use of concepts – i.e., the means by which the human mind expands its awareness beyond the range of the senses – it becomes clear that the mind has already formed categories which are general in scope, encompassing an endless series of units into a single mental whole. If that does not already get us on the road to inductive reasoning, what does?

In the end Hume’s problem like trying to argue for the conclusion “all generalizations are rationally unjustifiable.” Such a conclusion would fall by its own sword. After all, if the problem of induction were seeking to conclude merely that some inductive conclusions were not valid, it would have no teeth against induction as such. Only to the extent that the conclusion of the problem of induction is intended to have sweeping consequences for inductive reasoning as such – i.e., generally, would it have any claim to a serious philosophical problem. But then it would simply cancel itself out.

Perhaps what’s happening is that those championing the problem of induction are engaging in the fallacy of self-exclusion: the conclusion of the problem of induction applies to all generalizations *except* the conclusion that all generalizations are not rationally justifiable. But by then the jig is up.


Robert Kidd said...

Thank you, Dawson, for this latest post. This is a really good one. I guess people who are used to taking things on authority don't question Hume. And theists think that all atheists worship him or something.

"Naturally the question arises: if repetition is required for inductive generalization, how many instances are sufficient to provide reliable content to said generalization? Is it ten instances? A hundred? Anderson’s “one thousand”? How does one arrive at such a figure without needing to enlist induction itself, which would lead to an infinite regress?"


I can't wait for Anderson to come here and defend his paper. I'll just keep hitting the refresh button because he'll be eager to do so and it'll just be a few minutes.

Robert Kidd

Jason mc said...

Another really good post.

I imagine presuppositionalists and hyper-sceptics alike would dispute the claim that touching hot stoves is painful, as an item of certain knowledge possible to learn from instances of touching them. Touching stoves isn't enough to get a full understanding of the way the physiology of the human nervous system interprets intense heat as pain. Whether a full understanding of this will ever be within grasp is unknown. The presupper says God has this full understanding, and this somehow justifies the human claim, or maybe just for theists?

I'd say we don't need a full understanding, only a partial one, and for that, one touch is enough. The factual details about the nervous system will explain why, and explain exceptions e.g. it may not hurt at all if my senses are numbed with drugs. (That would be an exception that proves the rule, when the rule is better understood.)

The days of intense Christian-atheist debates in blog comments are over, I reckon, because Christians have decided to concentrate their energies elsewhere. Islam is the real threat as an alternative basis for civilisation. Atheism isn't a real demographic contender, apparently, because secular societies' reproduction rates are so low.

I've been enjoying observing the intellectual battles at the historic Speakers Corner at Hyde Park. To any potential visitor to London I'd strongly recommend experiencing a Sunday afternoon at the corner! Right now, Muslims dominate the space. A few Christian groups try to hold ground too. The level of debate is all over the place. You can get a sense of what it's like via YouTube videos.

Does anyone else here have anything like this institution in their locality? I believe there's one in Singapore, established in imitation of London's. It'd be interesting to see how Objectivism fares in this environment.

If it's them or Islam, for my part, it's not western chauvinism that makes me hope the Christians can win.

Jason MC

Ydemoc said...

Hey Dawson,

Another great entry! Many times I will select certain key points that you make in your writings, then drag and drop them as text clippings into my philosophy folder. This time I consider your entire entry a key point, so I'll be dragging and dropping the whole thing!

Thanks again!


Robert Kidd said...

Hi Dawson,

I have a question. Isn't this insistence that induction is unreliable because at some point in the future or in a different part of the universe, the laws or regular order of the universe might be different a moot point given the context in which we employ induction, namely our lives here on Earth? I mean if I see someone fall off a hundred foot tall building, I know just with that one instance that I don't want to fall off that building myself, even if in some freak cases the person doesn't die but is horribly injured. I don't need the certainty of death to know with certainty that that fall would be detrimental to my life. What difference would it make to me that on another planet with lighter gravity I would survive that fall without injury? I live on Earth, and I have to act accordingly. I don't see this aspect of the so called problem of induction talked about.

Robert Kidd said...

I guess what I'm asking is do we really need that level of absolute certainty from induction? isn't 99 or even 98 percent good enough in regards to choosing our actions that determine the course of our lives. It seems that Anderson is dropping a huge context.

Bahnsen Burner said...

Hi Robert,

Thanks for your question. Lots can be said on this topic, but generally I think the way one would go about answering the kind of question you raise revolves around what one takes the purpose of knowledge to be. Apologists tend to treat knowledge almost as an end to itself, or at least as a means of aligning the mind with a fault-finding, unforgiving supernatural being whose demands can never be fully satisfied (regardless of what they say outwardly on the matter). Any spot or blemish is to be magnified and excoriated without mercy. "You better be absolutely sure if you're going to claim certainty, because Wo unto You if you aren't!"

In my view, the purpose of knowledge is to help us live, regardless of what some alleged supernatural being might demand or want. Hence the kind of example you raise - yes, witnessing such a harrowing tragedy would be more than enough to tell me: be careful in high places.

Incidentally, I was reading recently about the experience of Alan Magee, a B-17 gunner who fell out of his aircraft at 20,000 feet during a bombing raid in France in January 1943. He had no parachute, but nevertheless he survived the fall. He had crashed into the glass roof of a railroad station, which broke his fall. He reported that as he was falling, he prayed to "The Almighty" to save his life and of course attributed his survival to the intervention of the supernatural (see here: I wonder how many apologists would try to replicate the incident for themselves. After all, Jesus saves, right?

Of course, if there were supernatural beings which could intervene and suspend natural laws as Christians claim, then induction is out the window. I could say that my cat sprouted wings and began to recite Chinese poetry - what true believer could consistently say "That's not possible!"?


Robert Kidd said...

Thank you for your answer, Dawson. That is an amazing story of the soldiers falling out of a bomber. I read once about a sky diver whose shoot didn't open and he landed in a marsh. The soft marsh mud acted like the glass roof and he survived. I'd not want to experience either scenario, though. I'd imagine one would relive that experience every night in a nightmare. Wow!

Your question of whether an apologist would want to test his faith reminds me of when I lived in eastern North Carolina. There was a religious sect out in the mountains of the western part of the state that would pass a rattlesnake around during the service because the bible says that if you have faith, you won't be harmed. They would feed the snake the night before and put it in a refrigerator so that it was sluggish first. I guess their faith wasn't all that strong. This went on for several months until the preacher got bitten and almost died.

My go-to whenever a theist asks me what would convince me is to ask them to move a mountain. I think this is a completely legitimate request since Mathew 17:20 says clearly that if one has the faith of a mustard seed, one can say to the mountain move and it will move. They don't like this very much and they get angry and accuse me of wanting to test God which is a no-no. So then I ask them if they don't have the faith of a mustard seed why should I. Crickets every time.

I once did a post on a Christian forum titled: God, a solution to a problem that doesn't exist. I explained why the question of who created the universe is fallacious. Seems Anderson is doing the same thing; dropping context to create a problem so that he can insert his god as the solution.

Thanks, Dawson.

Have a great evening,

Robert Kidd