Off-site Essay: The Relativity of Wrong

As I mentioned in last week's essay, I'm am switching to an every-other-week schedule for my Sunday essays. As I also mentiond, I do want to do something on the Sundays when I'm not posting an essay. I still haven't settled on precisely what I'd like to do, but I want to experiment with the idea of posting pointers to good off-site essays.


Isaas Asmiov was one of the most prolific writers of the twentieth century. In addition to being an acclaimed science fiction author, he is credited with writing over five hundred books (the exact count depending on how one counts his anthologies and collections where he was the editor). He was an equally prolific writer of essays. As impressive as the quanitity of his writings is, the quality of his work is just as remarkable. This is especially true of his intellectual popularizations. Asimov was justifiably considered a polymath and may well have been among the last of the world's rennaisance men, publishing to every category of the Dewey Decimal system with the sole exception of philosophy.¹

Of all his essays, my personal favorite is one titled The Relativity of Wrong. Many critics of science assume a naive stance of belittling science because science has a history of proving itself wrong time and again and, therefore, it is insinuated that we shouldn't put any trust in current theories because they could all be overturned during the next paradigm shift. Asimov deftly illustrates that "wrong" is a relative term and that the implicit assumption that wrong is an absolute mischaracterizes the way that science works.

I hope that you enjoy the essay as much as I have.

---

¹ Although none of his books dealt with philosophy, I would suggest that The Relativity of Wrong is about nothing less than epistemology.

The Force of Habit, part II

This is the second part of a two part essay. In the previous installment of the essay, I told an anecdote about habit and alluded to Hume’s belief that habit was sufficient, and necessary, to account for human beliefs and behaviors. In order to explain this, I took a brief explanatory journey through philosophy, epistemology, logic and deduction, ending with some observations regarding the limitations of deductive logic.

To recap, logic is intended to be a kind of truth mill. One of the limitations of deductive logic is that it can be argued that it doesn’t provide a mechanism to discover new truths so much as a means of clarifying our existing assumptions. This is because the conclusion of a deductive argument is already encapsulated in its assumptions.

Induction attempts to allow us to reach new truths by allowing us to reach conclusions which do not necessarily follow from their premises. It is important to stress that I am using the word “necessary” in a strict technical sense to mean something that logically required. In deductive logic, if we accept the premises of an argument, we are rationally constrained to accept the conclusion. The conclusion, in this sense, is necessary.

Where deduction offers us necessities, induction can only offer us probabilities. The cornerstone of inductive argumentation is the notion of inference. To illustrate the difference, let us consider the question of whether or not lions are carnivorous. Let us suppose that we have observed, over the course of years, any number of lions eating meat. If we constrain ourselves to deductive arguments, the only conclusion that we can draw from our observations is that some lions are carnivorous some of the time. No matter how many lions we’ve observed and no matter how often we’ve observed them, deduction does not allow us to logically discount the possibility that there is some population of lions that eats plants or that the lions that we’ve been observing are herbivorous when we aren’t observing them. Induction, however, allows us to infer, via our observations, that lions, as a whole, are carnivorous.

It should be immediately apparent that a strict reliance on deduction may not be able to tell us very much about the world and, furthermore, that what it can tell us will be hedged around with innumerable qualifications and caveats. Induction, by contrast, can allow us to make conclusions about the world that we could never reach through a process of strict deduction (citizens of the planet Vulcan to the contrary). There is a price to be paid though: certainty. While induction allows us to draw non-deductive conclusions, the conclusions are in no sense necessary. To illustrate this, we shall turn our attention from lions to swans.

Throughout most of the world, including Europe, Asia and Americas, swans are white. A natural philosopher from, say, the fifteenth century would have been perfectly within his inductive rights to infer that swans, as a whole, are white (with only the exceptions of diseased, deformed or altered animals). The preponderance of observation would have supported his conjecture. He would, however, have been wrong. Australian swans are black. With the discovery and exploration of Australia, the inductive inference would have been revealed to have been a leap to an unreal conclusion.

Bounded by swans and lions, we come to the question of confidence. It is unfair to criticize induction for failing to be infallible. Inductive logic never promised infallibility, it only offered to provide us with conclusions that we could put a degree of confidence in. There, however, is the central question: how much confidence can we put into our inductive conclusions. This is where Hume enters the picture.

David Hume was a Scottish philosopher who lived in the 18th century. It must be stressed, up front, that Hume’s critiques of reason were not motivated by a hatred of rationality. Quite the contrary, Hume had a sincere desire to believe that a) humans were rational beings and b) that the universe was amenable to rational inquiry. Hume lived in an era where science was coming into a state of intellectual prominence. Science, at its heart, is an inductive philosophy. In simplified (very simplified) form, a scientist makes observations, forms a hypothesis, and performs experiments which seek to demonstrate of invalidate the hypothesis. The notion that observations can lead to a generalization (i.e., a hypothesis) is essentially inductive as is the notion that any amount of experimentation could validate the hypothesis (where deduction would insist that any given experiment could only logically apply to the specific circumstances of that particular experiment). Hume knew that induction was a powerful tool and wanted to demonstrate that it was rationally defensible.

Hume saw that one of the most productive methodologies of science was something called reductionism. This is where one takes a system and attempts to understand the system by reducing it to its parts. One might imagine a person seeking to understand the mechanisms of a pocket watch by carefully taking it apart and examining the cogs, gears and springs that comprise it. ¹ Hume sought to take the methodology of reduction and to use it to parse apart the component elements of reason.

The first thing that Hume did was to consider the question of causality. Causality is the property whereby a cause can be used to explain an event. If I kick a football (cause) it will be launched into the air (effect), for instance. Since many of our conclusions stem from the assumption that there is a causal relationship between events, Hume wanted to show that we could rationally rely on causation. Hume wanted to demonstrate that there is a necessary, logical relation between causes and effects (note the necessary clause – we’ll come back to that). I won’t detail his efforts except to note that he was vastly disappointed to discover that, no matter how he tried, he could not. The most he could conclude is that humans have an expectation that some events have a causal relation. If I put a pot of water over a fire, I expect that it will boil in due time. In Hume’s analysis, my expectation that the pot will boil can not be rationally justified.

From here, Hume considered the broader question of induction. How can any amount of observation lend itself to a conclusion, even if the conclusion is only expressed in terms of relative certainty?

One possible justification was to assume that the future must resemble the past. If the sun has risen throughout the course of human history each and every day, shall we not be confident that it will also rise tomorrow. Hume demonstrated, however, that there was nothing logically inconsistent in the notion that the future may diverge from the past regardless of how long the past has been consistent. Indeed, the notion that the past leads to a consistent future is little more than the assumption of causality rephrased.

Okay, if we can’t deductively affirm the future, might we not inductively do so? If the future has been consistent for billions of years, isn’t it probable that it will continue to be consistent tomorrow? Is this not an allowable inference? Ah, but now we’re trying to use induction to prove induction and that is nothing more or less than circular reasoning.

Hume’s sad conclusion was that although we do, in fact, heavily rely on inductive rationales, we have no rational foundation to our reliance. So, Hume asked himself, why is it that we do rely on them so persistently and insistently? Are we not, after all, rational animals? Hume decided that the only possible answer is that we were not rational animals. Our reliance upon causality and induction, in Hume’s view, ultimately came down to a single thing: habit.

In Hume’s thesis, humans were little more than bundles of perceptions bound by a sense of habit that was instinctually engraved within us. If we avoid sticking our hands into fires, it is not because we have rationally concluded that we will burn ourselves if we do, it is because we have a habitual aversion to fire. If we avoid leaping in front of fast moving vehicles, it is not because we have rationally inferred that we would likely be killed, but because we have developed a habitual avoidance of doing so. If, indeed, we believe that causes precede effects or that there is, in fact, such a thing as causes and effects, it is simply because we have grown accustomed to seeing the universe in such term. Latter day Humeans would go so far as to proclaim that the belief in cause and effect is nothing more than a kind of superstition.²

Was Hume right? I would say that depends on how we evaluate his thesis. I believe that Hume’s ultimate objection comes down to a desire that the induction can be deductively justified. Note Hume’s contention that there is no necessary relationship between the past and the future. The desire for necessity is a central hallmark of deductive logic. Since we already know that deduction can not lend itself to conclusions that aren’t implicit in its premises, I don’t think that we should be surprised that it can not be used to validate an epistemological tool whose primary function is to allow us to reach conclusions that aren’t entirely implicit within their premises. In this sense, we are criticizing a hammer for not being a screwdriver.

Hume’s observation that using induction to support induction is, itself, circular does carry more weight. He is correct. We can not induce that induction is reliable for the very reason that it is the reliability of induction that is being questioned.

Here, I think, we must take a step back and ask ourselves what is meant when we say that something is reasonable. What, in fact, is this reason and rationality that we’re attempting to approach? Here we enter very murky waters. Some have narrowly defined reason has the human faculty for logic. If that’s the case, anything that qualifies as logic is, by definition, a basis for rational thought. The question then becomes one of whether or not induction is a type of logic. It is, at this point, that philosophy devolves into semantics. Some people define logic in terms of deduction claiming that anything that is non-deductive isn’t logical. Well, if that’s the cause, then it is tautological that induction isn’t reasonable, nor did we need Hume to challenge it. Others, by contrast, say that induction is, in fact, a form of logic. Again, we’re dealing with tautologies. If reason is the use of logic and induction is logic, then using induction is reasonable by definition. Clearly this isn’t a helpful line of inquiry.

George Lakoff and Mark Johnson have recently proposed a much broader conception of what reason is. They suggest that reason is “not only our capacity for logical inference, but also our ability to conduct inquiry, to solve problems, to evaluate, to criticize, to deliberate about how we should act, and to reach an understanding of ourselves, other people, and the world.”

I would summarize this as saying that reason is our capacity to reach conclusion via a methodical (and even methodological) process of thought. Reason is not infallible and, in fact, it is not always reliable but, when all is said and done, we have causes (good, bad or otherwise) for believing as we do. When Hume dismissed causality from the picture, he dismissed reason. The foundation of reason is, in fact, an assumption. It is the assumption that we can have cause to believe our conclusions. Like a logical axiom, this can not be demonstrated externally but must, instead, be accepted in the abstract. Sans that acceptance, reason can’t exist. Sans that acceptance, asking if we have cause to believe in reason isn’t even a coherent question since the predicate of the question is, itself, founded on the assumption that one ought not believe things without cause.

We do not live in an abstract world. We live in a concrete world. In the world we inhabit, fires don’t merely burn us theoretically nor do fast moving vehicles only impact us in terms of abstract hypothetical scenarios. We live in a world that requires us to interact with it. If our interactions are based on faulty evaluations (ergo, reasons), we can very easily be killed by our attempts to interact with it. In these terms, the inductive assumption, along with the causal assumption, aren’t merely conveniences of habit that we have adopted out of some indelible instinct, they are instruments of survival.

If we dismiss them, we are left with a world that is much like a car where the controls could be randomly reversed from moment to moment. In such a car, nothing you do could possibly matter because any attempt to accelerate or break or steer could cause you to crash. If you were to assume that your car was that kind of vehicle, it would be literally impossible to drive it. The only way that you can get from point A to point B is to drive with the assumption that turning the wheel a given direction will steer the car in the same direction, that one particular pedal accelerates the car and another decelerates it, and so forth and so on. Even when your assumptions are betrayed (say by a cut brake line) you need to have those working assumptions as a default. The alternative is a paralysis of action.

The world requires us to make decisions. Reason and all of its tools, including induction, allow us to make those decisions. They represent our best effort to do so and we judge their success by our continuing survival. To reduce this necessity to a cluster of habits wrapped around a bundle of perceptions is, I believe, an error of its own kind.

---

¹As a quick aside, there are a lot of ignorant criticisms of reductionism that are little more than lampoons of this method by implying that reductionists invariably miss the forest for the trees. The goal of real-world reductionism is to take the knowledge of a systems parts and to recombine those parts into a new synthesis that allows us to understand the whole in terms of the interaction of its parts.

²This conjecture isn’t one that’s solely embraced by philosophical dilettantes and fuzzy-headed mystics. Among its proponents were such heavyweight philosophers and rationalists as Bertrand Russell.

The Force of Habit, part I

I know a nifty little trick for getting the ketchup (or catsup if we want to be pretentious) out of its bottle. Most people upend the bottle and try to pound it from the back. This doesn’t work very well because the ketchup forms a plug in the neck of the bottle due to the ketchup’s viscosity. The only way for the liquid to flow is for air to enter the bottle but the neck is purposely designed to restrict the flow of air in order to make the ketchup seem “thicker”. Pounding the back of the bottle can force some of the ketchup out by overcoming the viscosity of the ketchup by the direct application of kinetic force but this tends to result in splatter and it’s not much more efficient then simply waiting for the air to slowly bubble up through the neck.

A better way to achieve this is to hold the bottle at a shallow angle above the plate and to sharply tap the bottle on the neck perpendicular to the axis of the bottle. This forces the ketchup against the opposite side of the neck, allowing air to flow past the gap. Not only doesn’t the ketchup splatter but once it starts to flow it tends to continue flowing reducing the effort it takes to get it out while simultaneously making it pour at a reasonable rate. Give it a try and see for yourself.

I’ve shown this trick to quite a few people over the years. The curious thing, though, is that, of all the people I’ve shown this little technique too, not a single one, to the best of my knowledge, has adopted it. They continue pounding the backs of their bottles, or digging the ketchup out with a knife, or simply waiting for the ketchup with a stoic patience. I’ve often wondered why no one chooses to adopt a method that is clearly superior to what they’ve been doing. Over the years I’ve come to the conclusion that the answer is habit. People pick up a certain method of getting the ketchup out of the bottle at a fairly early age and become so accustomed to it that they can’t change — can’t even think to change — even when a better way is demonstrated to them.

Habits are powerful things. Some habits are good, like brushing one’s teeth after ever meal, some are bad, like picking one’s nose, but they all exert a compelling force that makes it difficult to break them. In fact, we have a special term to describe adverse habits that are nearly impossible to break by force of will: addictions. It takes no act of genius to see that habits are an important part of human behavior and that we can’t really understand why we act as we do unless we factor them into our considerations, but are habits powerful enough to explain all of our actions? Are they, in fact, required to explain why we act as though we live in a universe that is consistent and predictable? Hume thought so.

In order to understand why Hume thought this, it’s necessary to understand a bit about induction which, in turn, requires us to know a bit about logic, which requires us to know a bit about epistemology which, finally, requires us to understand something about philosophy in general. Don’t worry, unlike my last epic, this won’t take too long (I’ll be done next week — I promise!)

When you bring up the subject of philosophy, a lot of people immediately roll their eyes. To them, philosophy is nothing more or less than a bunch of ever-educated snobs splitting endless semantic hairs. To be fair, there is a lot to that stereotype. Much of what goes on in academic circles is tantamount to quibbling over definitions (although such quibbles often do have a point and a purpose) and much of what passes for deep contemplation is more than a little silly (I’ll save that discussion for when I’m in the mood to tackle postmodernism); however, the basic goal of philosophy is, I believe, worthwhile. That goal is nothing less than an attempt to pursue truth. That can be truth with a small T, meaning the pursuit of facts about the universe and certain abstracts such as justice and ethics, or it can be Truth with a big-T, meaning that which is absolute, eternal and immutable, qualities that have led some theologians to identify Truth as being synonymous with God (and lest you be tempted to pedantics, theologians are typically concerned with God and not gods but, again, that’s a topic for another time). In this essay, we’re going to be concerned with the former kind of truth.

Philosophy has two grand divisions (and various lesser ones). One division, ontology, deals with question of existence. One often finds ontologists talking about the nature of existence and asking questions about the essence of entities. The other division, which will concern us, is epistemology. The subject of epistemology is knowledge. Many of us are familiar with Descartes’ demon where Descartes posited the existence of an infinitely powerful deceiver. He asked himself what we can know given the possibility that such a deceiver exists. Descartes conclusion was that the only thing we could know was our own existence: cogito ergo sum. This is an example of an epistemological reduction, but let's not get too sidetracked.

Most philosophers believe that knowledge isn’t quite so elusive, although it is worth noting that it’s difficult to even devise a good definition of knowledge. Epistemologists contrast knowledge with belief. Beliefs are propositions that individuals hold to be true. A given belief may or may not, of course, be true. Knowledge represents a particular category of belief. It is not sufficient that one holds a true belief in order for one to have knowledge. If I believe that the planets trace out elliptical orbits around the sun because they are being tugged by invisible space elephants, my belief that the planetary orbits are elliptical is true but is, never the less, based on an ignorant belief (elephants, etc). Likewise, if I happen to accurately guess next week's lottery numbers, my guess does not indicate a state of knowledge (assuming, of course, that I’m not psychic) no matter how firmly I am convinced of its truth beforehand. One of Plato’s great contributions to philosophy was giving us a definition of knowledge that has held up fairly well for over two millennia. His definition is that knowledge is a state of true, justified belief. Of course that leaves us with the question of what constitutes justification. A general rule of thumb that I like is that one is justified in one’s beliefs if one could convince an unbiased, rational agent that your beliefs are merited. Even this can be challenging as evidenced by the so-called Gettier counterexamples which explore the question of accidental knowledge.

Leaving aside the thorny question of how we should define knowledge, epistemology also concerns itself with the generation of knowledge. How do we go about discovering truths? This is where logic enters the picture. I think the best way to think of logic is that it’s a kind of truth mill. At one end of the mill, you put in propositions which are considered to be true, you crank the handle and, from the other end, pop out new truths. The field of logic has a number of different mills to choose from. Most people have encountered the syllogism mill:

All men are mortal
Socrates is a man
Therefore, Socrates is mortal.

A syllogism consists of a major premise, a minor premise and a necessary conclusion, which is to say that, if we accept both premises, we are rationally constrained to accept the conclusion. As such, syllogisms are an early form of logic known as deductive logic. The hallmark of deduction is that their conclusions necessarily follow from the arguments (or premises) that lead up to them. In this respect, logical deduction is very much like a mathematical proof (indeed, many argue that deduction is properly a type of mathematics).

Deduction is a strong form of reasoning. It has two primary limitations, however. The first limitation is that a deductive argument is only as good as its premises. By example, you will sometimes hear it said that it is impossible to prove or disprove the existence of God. Strictly speaking, this isn’t true. There are dozens of logically consistent deductive proofs for the existence of God. There are also dozens of equally consistent proofs that God does not exist. Clearly both sets of arguments can’t be true but deduction isn’t, strictly speaking, about determining truth, it’s about making conclusions that are true if the premises that lead up to those conclusions are true. This is, obviously, a major caveat. If I start with the major premise that all dogs are gods and follow it with the minor premise that all gods must be worshipped then I can logically conclude that all dogs must be worshipped. Somehow I don't see many people accepting either the major or minor premise. Unfortunately, a logical argument can’t be used to establish the validity of its own premises (such attempts represent the fallacy of circular reasoning). Logicians try to get around this by limiting their predicates to “universally accepted truths”. When it comes to addressing important questions, though, such universal acceptance is difficult to come by.

A more subtle limitation of deduction concerns the sorts of truths that you can reach using it. As noted, the conclusion of a logical argument flows directly and necessarily from its arguments. If you think about this a bit it should be clear that this means that any truth you reach via deduction was already present in its premises. As such, deduction is less about generating truths than clarifying things which have been agreed to be truth. Such clarifications can be useful (we wouldn’t knock the Pythagorean theorem by complaining that it’s already contained in Euclid’s axioms) but it doesn’t really satisfy the primary goal of logic which is the generation (or discovery, if you prefer) of new truths. Enter induction.

Next week, I’ll detail what inductive logic is all about, why Hume had a problem with it, and argue that our reliance on it is rational in spite of Hume’s convictions to the contrary.