Tag: Isaac Newton

Deductive vs Inductive Reasoning: Make Smarter Arguments, Better Decisions, and Stronger Conclusions

You can’t prove truth, but using deductive and inductive reasoning, you can get close. Learn the difference between the two types of reasoning and how to use them when evaluating facts and arguments.

***

As odd as it sounds, in science, law, and many other fields, there is no such thing as proof — there are only conclusions drawn from facts and observations. Scientists cannot prove a hypothesis, but they can collect evidence that points to its being true. Lawyers cannot prove that something happened (or didn’t), but they can provide evidence that seems irrefutable.

The question of what makes something true is more relevant than ever in this era of alternative facts and fake news. This article explores truth — what it means and how we establish it. We’ll dive into inductive and deductive reasoning as well as a bit of history.

“Contrariwise,” continued Tweedledee, “if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.”

— Lewis Carroll, Through the Looking-Glass

The essence of reasoning is a search for truth. Yet truth isn’t always as simple as we’d like to believe it is.

For as far back as we can imagine, philosophers have debated whether absolute truth exists. Although we’re still waiting for an answer, this doesn’t have to stop us from improving how we think by understanding a little more.

In general, we can consider something to be true if the available evidence seems to verify it. The more evidence we have, the stronger our conclusion can be. When it comes to samples, size matters. As my friend Peter Kaufman says:

What are the three largest, most relevant sample sizes for identifying universal principles? Bucket number one is inorganic systems, which are 13.7 billion years in size. It’s all the laws of math and physics, the entire physical universe. Bucket number two is organic systems, 3.5 billion years of biology on Earth. And bucket number three is human history….

In some areas, it is necessary to accept that truth is subjective. For example, ethicists accept that it is difficult to establish absolute truths concerning whether something is right or wrong, as standards change over time and vary around the world.

When it comes to reasoning, a correctly phrased statement can be considered to have objective truth. Some statements have an objective truth that we cannot ascertain at present. For example, we do not have proof for the existence or non-existence of aliens, although proof does exist somewhere.

Deductive and inductive reasoning are both based on evidence.

Several types of evidence are used in reasoning to point to a truth:

  • Direct or experimental evidence — This relies on observations and experiments, which should be repeatable with consistent results.
  • Anecdotal or circumstantial evidence — Overreliance on anecdotal evidence can be a logical fallacy because it is based on the assumption that two coexisting factors are linked even though alternative explanations have not been explored. The main use of anecdotal evidence is for forming hypotheses which can then be tested with experimental evidence.
  • Argumentative evidence — We sometimes draw conclusions based on facts. However, this evidence is unreliable when the facts are not directly testing a hypothesis. For example, seeing a light in the sky and concluding that it is an alien aircraft would be argumentative evidence.
  • Testimonial evidence — When an individual presents an opinion, it is testimonial evidence. Once again, this is unreliable, as people may be biased and there may not be any direct evidence to support their testimony.

“The weight of evidence for an extraordinary claim must be proportioned to its strangeness.”

— Laplace, Théorie analytique des probabilités (1812)

Reasoning by Induction

The fictional character Sherlock Holmes is a master of induction. He is a careful observer who processes what he sees to reach the most likely conclusion in the given set of circumstances. Although he pretends that his knowledge is of the black-or-white variety, it often isn’t. It is true induction, coming up with the strongest possible explanation for the phenomena he observes.

Consider his description of how, upon first meeting Watson, he reasoned that Watson had just come from Afghanistan:

“Observation with me is second nature. You appeared to be surprised when I told you, on our first meeting, that you had come from Afghanistan.”
“You were told, no doubt.”

“Nothing of the sort. I knew you came from Afghanistan. From long habit the train of thoughts ran so swiftly through my mind, that I arrived at the conclusion without being conscious of intermediate steps. There were such steps, however. The train of reasoning ran, ‘Here is a gentleman of a medical type, but with the air of a military man. Clearly an army doctor, then. He has just come from the tropics, for his face is dark, and that is not the natural tint of his skin, for his wrists are fair. He has undergone hardship and sickness, as his haggard face says clearly. His left arm has been injured. He holds it in a stiff and unnatural manner. Where in the tropics could an English army doctor have seen much hardship and got his arm wounded? Clearly in Afghanistan.’ The whole train of thought did not occupy a second. I then remarked that you came from Afghanistan, and you were astonished.”

(From Sir Arthur Conan Doyle’s A Study in Scarlet)

Inductive reasoning involves drawing conclusions from facts, using logic. We draw these kinds of conclusions all the time. If someone we know to have good literary taste recommends a book, we may assume that means we will enjoy the book.

Induction can be strong or weak. If an inductive argument is strong, the truth of the premise would mean the conclusion is likely. If an inductive argument is weak, the logic connecting the premise and conclusion is incorrect.

There are several key types of inductive reasoning:

  • Generalized — Draws a conclusion from a generalization. For example, “All the swans I have seen are white; therefore, all swans are probably white.”
  • Statistical — Draws a conclusion based on statistics. For example, “95 percent of swans are white” (an arbitrary figure, of course); “therefore, a randomly selected swan will probably be white.”
  • Sample — Draws a conclusion about one group based on a different, sample group. For example, “There are ten swans in this pond and all are white; therefore, the swans in my neighbor’s pond are probably also white.”
  • Analogous — Draws a conclusion based on shared properties of two groups. For example, “All Aylesbury ducks are white. Swans are similar to Aylesbury ducks. Therefore, all swans are probably white.”
  • Predictive — Draws a conclusion based on a prediction made using a past sample. For example, “I visited this pond last year and all the swans were white. Therefore, when I visit again, all the swans will probably be white.”
  • Causal inference — Draws a conclusion based on a causal connection. For example, “All the swans in this pond are white. I just saw a white bird in the pond. The bird was probably a swan.”

The entire legal system is designed to be based on sound reasoning, which in turn must be based on evidence. Lawyers often use inductive reasoning to draw a relationship between facts for which they have evidence and a conclusion.

The initial facts are often based on generalizations and statistics, with the implication that a conclusion is most likely to be true, even if that is not certain. For that reason, evidence can rarely be considered certain. For example, a fingerprint taken from a crime scene would be said to be “consistent with a suspect’s prints” rather than being an exact match. Implicit in that statement is the assertion that it is statistically unlikely that the prints are not the suspect’s.

Inductive reasoning also involves Bayesian thinking. A conclusion can seem to be true at one point, until further evidence emerges and a hypothesis must be adjusted. Bayesian updating is a technique used to modify the probability of a hypothesis’s being true as new evidence is supplied. When inductive reasoning is used in legal situations, Bayesian thinking is used to update the likelihood of a defendant’s being guilty beyond a reasonable doubt as evidence is collected. If we imagine a simplified, hypothetical criminal case, we can picture the utility of Bayesian inference combined with inductive reasoning.

Let’s say someone is murdered in a house where five other adults were present at the time. One of them is the primary suspect, and there is no evidence of anyone else entering the house. The initial probability of the prime suspect’s having committed the murder is 20 percent. Other evidence will then adjust that probability. If the four other people testify that they saw the suspect committing the murder, the suspect’s prints are on the murder weapon, and traces of the victim’s blood were found on the suspect’s clothes, jurors may consider the probability of that person’s guilt to be close enough to 100 percent to convict. Reality is more complex than this, of course. The conclusion is never certain, only highly probable.

One key distinction between deductive and inductive reasoning is that the latter accepts that a conclusion is uncertain and may change in the future. A conclusion is either strong or weak, not right or wrong. We tend to use this type of reasoning in everyday life, drawing conclusions from experiences and then updating our beliefs.

A conclusion is either strong or weak, not right or wrong.

Everyday inductive reasoning is not always correct, but it is often useful. For example, superstitious beliefs often originate from inductive reasoning. If an athlete performed well on a day when they wore their socks inside out, they may conclude that the inside-out socks brought them luck. If future successes happen when they again wear their socks inside out, the belief may strengthen. Should that not be the case, they may update their belief and recognize that it is incorrect.

Another example (let’s set aside the question of whether turkeys can reason): A farmer feeds a turkey every day, so the turkey assumes that the farmer cares for its wellbeing. Only when Thanksgiving rolls around does that assumption prove incorrect.

The issue with overusing inductive reasoning is that cognitive shortcuts and biases can warp the conclusions we draw. Our world is not always as predictable as inductive reasoning suggests, and we may selectively draw upon past experiences to confirm a belief. Someone who reasons inductively that they have bad luck may recall only unlucky experiences to support that hypothesis and ignore instances of good luck.

In The 12 Secrets of Persuasive Argument, the authors write:

In inductive arguments, focus on the inference. When a conclusion relies upon an inference and contains new information not found in the premises, the reasoning is inductive. For example, if premises were established that the defendant slurred his words, stumbled as he walked, and smelled of alcohol, you might reasonably infer the conclusion that the defendant was drunk. This is inductive reasoning. In an inductive argument the conclusion is, at best, probable. The conclusion is not always true when the premises are true. The probability of the conclusion depends on the strength of the inference from the premises. Thus, when dealing with inductive reasoning, pay special attention to the inductive leap or inference, by which the conclusion follows the premises.

… There are several popular misconceptions about inductive and deductive reasoning. When Sherlock Holmes made his remarkable “deductions” based on observations of various facts, he was usually engaging in inductive, not deductive, reasoning.

In Inductive Reasoning, Aiden Feeney and Evan Heit write:

…inductive reasoning … corresponds to everyday reasoning. On a daily basis we draw inferences such as how a person will probably act, what the weather will probably be like, and how a meal will probably taste, and these are typical inductive inferences.

[…]

[I]t is a multifaceted cognitive activity. It can be studied by asking young children simple questions involving cartoon pictures, or it can be studied by giving adults a variety of complex verbal arguments and asking them to make probability judgments.

[…]

[I]nduction is related to, and it could be argued is central to, a number of other cognitive activities, including categorization, similarity judgment, probability judgment, and decision making. For example, much of the study of induction has been concerned with category-based induction, such as inferring that your next door neighbor sleeps on the basis that your neighbor is a human animal, even if you have never seen your neighbor sleeping.

“A very great deal more truth can become known than can be proven.”

— Richard Feynman

Reasoning by Deduction

Deduction begins with a broad truth (the major premise), such as the statement that all men are mortal. This is followed by the minor premise, a more specific statement, such as that Socrates is a man. A conclusion follows: Socrates is mortal. If the major premise is true and the minor premise is true the conclusion cannot be false.

Deductive reasoning is black and white; a conclusion is either true or false and cannot be partly true or partly false. We decide whether a deductive statement is true by assessing the strength of the link between the premises and the conclusion. If all men are mortal and Socrates is a man, there is no way he can not be mortal, for example. There are no situations in which the premise is not true, so the conclusion is true.

In science, deduction is used to reach conclusions believed to be true. A hypothesis is formed; then evidence is collected to support it. If observations support its truth, the hypothesis is confirmed. Statements are structured in the form of “if A equals B, and C is A, then C is B.” If A does not equal B, then C will not equal B. Science also involves inductive reasoning when broad conclusions are drawn from specific observations; data leads to conclusions. If the data shows a tangible pattern, it will support a hypothesis.

For example, having seen ten white swans, we could use inductive reasoning to conclude that all swans are white. This hypothesis is easier to disprove than to prove, and the premises are not necessarily true, but they are true given the existing evidence and given that researchers cannot find a situation in which it is not true. By combining both types of reasoning, science moves closer to the truth. In general, the more outlandish a claim is, the stronger the evidence supporting it must be.

We should be wary of deductive reasoning that appears to make sense without pointing to a truth. Someone could say “A dog has four paws. My pet has four paws. Therefore, my pet is a dog.” The conclusion sounds logical but isn’t, because the initial premise is too specific.

The History of Reasoning

The discussion of reasoning and what constitutes truth dates back to Plato and Aristotle.

Plato (429–347 BC) believed that all things are divided into the visible and the intelligible. Intelligible things can be known through deduction (with observation being of secondary importance to reasoning) and are true knowledge.

Aristotle took an inductive approach, emphasizing the need for observations to support knowledge. He believed that we can reason only from discernable phenomena. From there, we use logic to infer causes.

Debate about reasoning remained much the same until the time of Isaac Newton. Newton’s innovative work was based on observations, but also on concepts that could not be explained by a physical cause (such as gravity). In his Principia, Newton outlined four rules for reasoning in the scientific method:

  1. “We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.” (We refer to this rule as Occam’s Razor.)
  2. “Therefore, to the same natural effects we must, as far as possible, assign the same causes.”
  3. “The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.”
  4. “In experimental philosophy, we are to look upon propositions collected by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, ’till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.”

In 1843, philosopher John Stuart Mill published A System of Logic, which further refined our understanding of reasoning. Mill believed that science should be based on a search for regularities among events. If a regularity is consistent, it can be considered a law. Mill described five methods for identifying causes by noting regularities. These methods are still used today:

  • Direct method of agreement — If two instances of a phenomenon have a single circumstance in common, the circumstance is the cause or effect.
  • Method of difference — If a phenomenon occurs in one experiment and does not occur in another, and the experiments are the same except for one factor, that is the cause, part of the cause, or the effect.
  • Joint method of agreement and difference — If two instances of a phenomenon have one circumstance in common, and two instances in which it does not occur have nothing in common except the absence of that circumstance, then that circumstance is the cause, part of the cause, or the effect.
  • Method of residue — When you subtract any part of a phenomenon known to be caused by a certain antecedent, the remaining residue of the phenomenon is the effect of the remaining antecedents.
  • Method of concomitant variations — If a phenomenon varies when another phenomenon varies in a particular way, the two are connected.

Karl Popper was the next theorist to make a serious contribution to the study of reasoning. Popper is well known for his focus on disconfirming evidence and disproving hypotheses. Beginning with a hypothesis, we use deductive reasoning to make predictions. A hypothesis will be based on a theory — a set of independent and dependent statements. If the predictions are true, the theory is true, and vice versa. Popper’s theory of falsification (disproving something) is based on the idea that we cannot prove a hypothesis; we can only show that certain predictions are false. This process requires vigorous testing to identify any anomalies, and Popper does not accept theories that cannot be physically tested. Any phenomenon not present in tests cannot be the foundation of a theory, according to Popper. The phenomenon must also be consistent and reproducible. Popper’s theories acknowledge that theories that are accepted at one time are likely to later be disproved. Science is always changing as more hypotheses are modified or disproved and we inch closer to the truth.

Conclusion

In How to Deliver a TED Talk, Jeremey Donovan writes:

No discussion of logic is complete without a refresher course in the difference between inductive and deductive reasoning. By its strictest definition, inductive reasoning proves a general principle—your idea worth spreading—by highlighting a group of specific events, trends, or observations. In contrast, deductive reasoning builds up to a specific principle—again, your idea worth spreading—through a chain of increasingly narrow statements.

Logic is an incredibly important skill, and because we use it so often in everyday life, we benefit by clarifying the methods we use to draw conclusions. Knowing what makes an argument sound is valuable for making decisions and understanding how the world works. It helps us to spot people who are deliberately misleading us through unsound arguments. Understanding reasoning is also helpful for avoiding fallacies and for negotiating.

FS Members can discuss this article on the Learning Community Forum.

Inertia: The Force That Holds the Universe Together

Inertia is the force that holds the universe together. Literally. Without it, things would fall apart. It’s also what keeps us locked in destructive habits, and resistant to change.

***

“If it were possible to flick a switch and turn off inertia, the universe would collapse in an instant to a clump of matter,” write Peter and Neal Garneau in In the Grip of the Distant Universe: The Science of Inertia.

“…death is the destination we all share. No one has ever escaped it. And that is as it should be, because death is very likely the single best invention of life. It’s life’s change agent; it clears out the old to make way for the new … Your time is limited, so don’t waste it living someone else’s life.”

— Steve Jobs

Inertia is the force that holds the universe together. Literally. Without it, matter would lack the electric forces necessary to form its current arrangement. Inertia is counteracted by the heat and kinetic energy produced by moving particles. Subtract it and everything cools to -459.67 degrees Fahrenheit (absolute zero temperature). Yet we know so little about inertia and how to leverage it in our daily lives.

Inertia: The Force That Holds the Universe Together

The Basics

The German astronomer Johannes Kepler (1571–1630) coined the word “inertia.” The etymology of the term is telling. Kepler obtained it from the Latin for “unskillfulness, ignorance; inactivity or idleness.” True to its origin, inertia keeps us in bed on a lazy Sunday morning (we need to apply activation energy to overcome this state).

Inertia refers to resistance to change — in particular, resistance to changes in motion. Inertia may manifest in physical objects or in the minds of people.

We learn the principle of inertia early on in life. We all know that it takes a force to get something moving, to change its direction, or to stop it.

Our intuitive sense of how inertia works enables us to exercise a degree of control over the world around us. Learning to drive offers further lessons. Without external physical forces, a car would keep moving in a straight line in the same direction. It takes a force (energy) to get a car moving and overcome the inertia that kept it still in a parking space. Changing direction to round a corner or make a U-turn requires further energy. Inertia is why a car does not stop the moment the brakes are applied.

The heavier a vehicle is, the harder it is to overcome inertia and make it stop. A light bicycle stops with ease, while an eight-carriage passenger train needs a good mile to halt. Similarly, the faster we run, the longer it takes to stop. Running in a straight line is much easier than twisting through a crowded sidewalk, changing direction to dodge people.

Any object that can be rotated, such as a wheel, has rotational inertia. This tells us how hard it is to change the object’s speed around the axis. Rotational inertia depends on the mass of the object and its distribution relative to the axis.

Inertia is Newton’s first law of motion, a fundamental principle of physics. Newton summarized it this way: “The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavors to preserve its present state, whether it be of rest or of moving uniformly forward in a straight line.”

When developing his first law, Newton drew upon the work of Galileo Galilei. In a 1624 letter to Francesco Ingoli, Galileo outlined the principle of inertia:

I tell you that if natural bodies have it from Nature to be moved by any movement, this can only be a circular motion, nor is it possible that Nature has given to any of its integral bodies a propensity to be moved by straight motion. I have many confirmations of this proposition, but for the present one alone suffices, which is this.

I suppose the parts of the universe to be in the best arrangement so that none is out of its place, which is to say that Nature and God have perfectly arranged their structure… Therefore, if the parts of the world are well ordered, the straight motion is superfluous and not natural, and they can only have it when some body is forcibly removed from its natural place, to which it would then return to a straight line.

In 1786, Immanuel Kant elaborated further: “All change of matter has an external cause. (Every body remains in its state of rest or motion in the same direction and with the same velocity, if not compelled by an external cause to forsake this state.) … This mechanical law can only be called the law of inertia (lex inertiæ)….”

Now that we understand the principle, let’s look at some of the ways we can understand it better and apply it to our advantage.

Decision Making and Cognitive Inertia

We all experience cognitive inertia: the tendency to stick to existing ideas, beliefs, and habits even when they no longer serve us well. Few people are truly able to revise their opinions in light of disconfirmatory information. Instead, we succumb to confirmation bias and seek out verification of existing beliefs. It’s much easier to keep thinking what we’ve always been thinking than to reflect on the chance that we might be wrong and update our views. It takes work to overcome cognitive dissonance, just as it takes effort to stop a car or change its direction.

When the environment changes, clinging to old beliefs can be harmful or even fatal. Whether we fail to perceive the changes or fail to respond to them, the result is the same. Even when it’s obvious to others that we must change, it’s not obvious to us. It’s much easier to see something when you’re not directly involved. If I ask you how fast you’re moving right now, you’d likely say zero, but you’re moving 18,000 miles an hour around the sun. Perspective is everything, and the perspective that matters is the one that most closely lines up with reality.

“Sometimes you make up your mind about something without knowing why, and your decision persists by the power of inertia. Every year it gets harder to change.”

— Milan Kundera, The Unbearable Lightness of Being

Cognitive inertia is the reason that changing our habits can be difficult. The default is always the path of least resistance, which is easy to accept and harder to question. Consider your bank, for example. Perhaps you know that there are better options at other banks. Or you have had issues with your bank that took ages to get sorted. Yet very few people actually change their banks, and many of us stick with the account we first opened. After all, moving away from the status quo would require a lot of effort: researching alternatives, transferring balances, closing accounts, etc. And what if something goes wrong? Sounds risky. The switching costs are high, so we stick to the status quo.

Sometimes inertia helps us. After all, questioning everything would be exhausting. But in many cases, it is worthwhile to overcome inertia and set something in motion, or change direction, or halt it.

The important thing about inertia is that it is only the initial push that is difficult. After that, progress tends to be smoother. Ernest Hemingway had a trick for overcoming inertia in his writing. Knowing that getting started was always the hardest part, he chose to finish work each day at a point where he had momentum (rather than when he ran out of ideas). The next day, he could pick up from there. In A Moveable Feast, Hemingway explains:

I always worked until I had something done and I always stopped when I knew what was going to happen next. That way I could be sure of going on the next day.

Later on in the book, he describes another method, which was to write just one sentence:

Do not worry. You have always written before and you will write now. All you have to do is write one true sentence. Write the truest sentence that you know. So, finally I would write one true sentence and go on from there. It was easy then because there was always one true sentence that I knew or had seen or had heard someone say. If I started to write elaborately, or like someone introducing or presenting something, I found that I could cut that scrollwork or ornament out and throw it away and start with the first true simple declarative sentence I had written.

We can learn a lot from Hemingway’s approach to tackling inertia and apply it in areas beyond writing. As with physics, the momentum from getting started can carry us a long way. We just need to muster the required activation energy and get going.

Status Quo Bias: “When in Doubt, Do Nothing”

Cognitive inertia also manifests in the form of status quo bias. When making decisions, we are rarely rational. Faced with competing options and information, we often opt for the default because it’s easy. Doing something other than what we’re already doing requires mental energy that we would rather preserve. In many areas, this helps us avoid decision fatigue.

Many of us eat the same meals most of the time, wear similar outfits, and follow routines. This tendency usually serves us well. But the status quo is not necessarily the optimum solution. Indeed, it may be outright harmful or at least unhelpful if something has changed in the environment or we want to optimize our use of time.

“The great enemy of any attempt to change men’s habits is inertia. Civilization is limited by inertia.”

— Edward L. Bernays, Propaganda

In a paper entitled “If you like it, does it matter if it’s real?” Felipe De Brigard[1] offers a powerful illustration of status quo bias. One of the best-known thought experiments concerns Robert Nozick’s “experience machine.” Nozick asked us to imagine that scientists have created a virtual reality machine capable of simulating any pleasurable experience. We are offered the opportunity to plug ourselves in and live out the rest of our lives in permanent, but fake enjoyment. The experience machine would later inspire the Matrix film series. Presented with the thought experiment, most people balk and claim they would prefer reality. But what if we flip the narrative? De Brigard believed that we are opposed to the experience machine because it contradicts the status quo, the life we are accustomed to.

In an experiment, he asked participants to imagine themselves woken by the doorbell on a Saturday morning. A man in black, introducing himself as Mr. Smith, is at the door. He claims to have vital information. Mr. Smith explains that there has been an error and you are in fact connected to an experience machine. Everything you have lived through so far has been a simulation. He offers a choice: stay plugged in, or return to an unknown real life. Unsurprisingly, far fewer people wished to return to reality in the latter situation than wished to remain in it in the former. The aversive element is not the experience machine itself, but the departure from the status quo it represents.

Conclusion

Inertia is a pervasive, problematic force. It’s the pull that keeps us clinging to old ways and prevents us from trying new things. But as we have seen, it is also a necessary one. Without it, the universe would collapse. Inertia is what enables us to maintain patterns of functioning, maintain relationships, and get through the day without questioning everything. We can overcome inertia much like Hemingway did — by recognizing its influence and taking the necessary steps to create that all-important initial momentum.

***

Prime Members can discuss this on the Learning Community Forum.

End Notes

[1] https://www.tandfonline.com/doi/abs/10.1080/09515080903532290

The Danger of Oversimplification: How to Use Occam’s Razor Without Getting Cut

Occam’s razor (also known as the ‘law of parsimony’) is a problem-solving principle which serves as a useful mental model. A philosophical razor is a tool used to eliminate improbable options in a given situation, of which Occam’s is the best-known example.

Occam’s razor can be summarized as such:

Among competing hypotheses, the one with the fewest assumptions should be selected.

The Basics

In simpler language, Occam’s razor states that the simplest solution is correct. Another good explanation of Occam’s razor comes from the paranormal writer, William J. Hall: ‘Occam’s razor is summarized for our purposes in this way: Extraordinary claims demand extraordinary proof.’

In other words, we should avoid looking for excessively complex solutions to a problem and focus on what works, given the circumstances. Occam’s razor is used in a wide range of situations, as a means of making rapid decisions and establishing truths without empirical evidence. It works best as a mental model for making initial conclusions before adequate information can be obtained.

A further literary summary comes from one of the best-loved fictional characters, Arthur Conan Doyle’s Sherlock Holmes. His classic aphorism is an expression of Occam’s razor: “If you eliminate the impossible, whatever remains, however improbable, must be the truth.”

A number of mathematical and scientific studies have backed up its validity and lasting relevance. In particular, the principle of minimum energy supports Occam’s razor. This facet of the second law of thermodynamics states that, wherever possible, the use of energy is minimized. In general, the universe tends towards simplicity. Physicists use Occam’s razor, in the knowledge that they can rely on everything to use the minimum energy necessary to function. A ball at the top of a hill will roll down in order to be at the point of minimum potential energy. The same principle is present in biology. For example, if a person repeats the same action on a regular basis in response to the same cue and reward, it will become a habit as the corresponding neural pathway is formed. From then on, their brain will use less energy to complete the same action.

The History of Occam’s Razor

The concept of Occam’s razor is credited to William of Ockham, a 13-14th-century friar, philosopher, and theologian. While he did not coin the term, his characteristic way of making deductions inspired other writers to develop the heuristic. Indeed, the concept of Occam’s razor is an ancient one which was first stated by Aristotle who wrote “we may assume the superiority, other things being equal, of the demonstration which derives from fewer postulates or hypotheses.”

Robert Grosseteste expanded on Aristotle’s writing in the 1200s, declaring that:

That is better and more valuable which requires fewer, other circumstances being equal… For if one thing were demonstrated from many and another thing from fewer equally known premises, clearly that is better which is from fewer because it makes us know quickly, just as a universal demonstration is better than particular because it produces knowledge from fewer premises. Similarly, in natural science, in moral science, and in metaphysics the best is that which needs no premises and the better that which needs the fewer, other circumstances being equal.

Early writings such as this are believed to have led to the eventual, (ironic) simplification of the concept. Nowadays, Occam’s razor is an established mental model which can form a useful part of a latticework of knowledge.

Examples of the Use of Occam’s Razor

Theology

In theology, Occam’s razor is used to prove or disprove the existence of God. William of Ockham, being a Christian friar, used his theory to defend religion. He regarded the scripture as true in the literal sense and therefore saw it as simple proof. To him, the bible was synonymous with reality and therefore to contradict it would conflict with established fact. Many religious people regard the existence of God as the simplest possible explanation for the creation of the universe.

In contrast, Thomas Aquinas used the concept in his radical 13th century work – The Summa Theologica. In it, he argued for atheism as a logical concept, not a contradiction of accepted beliefs. Aquinas wrote ‘it is superfluous to suppose that what can be accounted for by a few principles has been produced by many.’ He considered the existence of God to be a hypothesis which makes a huge number of assumptions, compared to scientific alternatives. Many modern atheists consider the existence of God to be unnecessarily complex, in particular, due to the lack of empirical evidence.

Taoist thinkers take Occam’s razor one step further, by simplifying everything in existence to the most basic form. In Taoism, everything is an expression of a single ultimate reality (known as the Tao.) This school of religious and philosophical thought believes that the most plausible explanation for the universe is the simplest- everything is both created and controlled by a single force. This can be seen as a profound example of the use of Occam’s razor within theology.

The Development of Scientific Theories

Occam’s razor is frequently used by scientists, in particular for theoretical matters. The simpler a hypothesis is, the more easily it can be proved or falsified. A complex explanation for a phenomenon involves many factors which can be difficult to test or lead to issues with the repeatability of an experiment. As a consequence, the simplest solution which is consistent with the existing data is preferred. However, it is common for new data to allow hypotheses to become more complex over time. Scientists chose to opt for the simplest solution the current data permits while remaining open to the possibility of future research allowing for greater complexity.

Failing to observe Occam’s razor is usually a sign of bad science and an attempt to cover poor explanations. The version used by scientists can best be summarized as: ‘when you have two competing theories that make exactly the same predictions, the simpler one is the better.’

Obtaining funding for simpler hypothesis tends to be easier, as they are often cheaper to prove. As a consequence, the use of Occam’s razor in science is a matter of practicality.

Albert Einstein referred to Occam’s razor when developing his theory of special relativity. He formulated his own version: ‘it can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.’ Or “everything should be made as simple as possible, but not simpler.” This preference for simplicity can be seen in one of the most famous equations ever devised: E=MC2. Rather than making it a lengthy equation requiring pages of writing, Einstein reduced the factors necessary down to the bare minimum. The result is usable and perfectly parsimonious.

The physicist Stephen Hawking advocates for Occam’s razor in A Brief History of Time:

We could still imagine that there is a set of laws that determines events completely for some supernatural being, who could observe the present state of the universe without disturbing it. However, such models of the universe are not of much interest to us mortals. It seems better to employ the principle known as Occam’s razor and cut out all the features of the theory that cannot be observed.

Isaac Newton used Occam’s razor too when developing his theories. Newton stated: “we are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.” As a result, he sought to make his theories (including the three laws of motion) as simple as possible, with the fewest underlying assumptions necessary.

Medicine

Modern doctors use a version of Occam’s razor, stating that they should look for the fewest possible causes to explain their patient’s multiple symptoms and also for the most likely causes. A doctor I know often repeats, “common things are common.” Interns are instructed, “when you hear hoofbeats, think horses, not zebras.” For example, a person displaying influenza-like symptoms during an epidemic would be considered more probable to be suffering from influenza than an alternative, rarer disease. Making minimal diagnoses reduces the risk of over treating a patient, or of causing dangerous interactions between different treatments. This is of particular importance within the current medical model, where patients are likely to see numerous different health specialists and communication between them can be poor.

Prison Abolition and Fair Punishment

Occam’s razor has long played a role in attitudes towards the punishment of crimes. In this context, it refers to the idea that people should be given the least punishment necessary for their crimes.

This is to avoid the excessive penal practices which were popular in the past, (for example, a Victorian could receive five years of hard labour for stealing a piece of food.) The concept of penal parsimony was pioneered by Jeremy Bentham, the founder of utilitarianism. He stated that punishments should not cause more pain than they prevent. Life imprisonment for murder could be seen as justified in that it may prevent a great deal of potential pain, should the perpetrator offend again. On the other hand, long-term imprisonment of an impoverished person for stealing food causes substantial suffering without preventing any.

Bentham’s writings on the application of Occam’s razor to punishment led to the prison abolition movement and our modern ideas of rehabilitation.

Crime solving and forensic work

When it comes to solving a crime, Occam’s razor is used in conjunction with experience and statistical knowledge. A woman is statistically more likely to be killed by a male partner than any other person. Should a female be found murdered in her locked home, the first person police interview would be any male partners. The possibility of a stranger entering can be considered, but the simplest possible solution with the fewest assumptions made would be that the crime was perpetrated by her male partner.

By using Occam’s razor, police officers can solve crimes faster and with fewer expenses.

Exceptions and Issues

It is important to note that, like any mental model, Occam’s razor is not failsafe and should be used with care, lest you cut yourself. This is especially crucial when it comes to important or risky decisions. There are exceptions to any rule, and we should never blindly follow a mental model which logic, experience, or empirical evidence contradict. The smartest people are those who know the rules, but also know when to ignore them. When you hear hoofbeats behind you, in most cases you should think horses, not zebras- unless you are out on the African savannah.

Simplicity is also a subjective topic- in the example of the NASA moon landing conspiracy theory, some people consider it simpler for them to have been faked, others for them to have been real. When using Occam’s razor to make deductions, we must avoid falling prey to confirmation bias and merely using it to backup preexisting notions. The same goes for the theology example mentioned previously – some people consider the existence of God to be the simplest option, others consider the inverse to be true. Semantic simplicity must not be given overt importance when selecting the solution which Occam’s razor points to. A hypothesis can sound simple, yet involve more assumptions than a verbose alternative.

Occam’s razor should not be used in the place of logic, scientific methods and personal insights. In the long term, a judgment must be backed by empirical evidence, not just its simplicity. Lisa Randall best expressed the issues with Occam’s razor in her book, Dark Matter and the Dinosaurs: The Astounding Interconnectedness of the Universe:

My second concern about Occam’s Razor is just a matter of fact. The world is more complicated than any of us would have been likely to conceive. Some particles and properties don’t seem necessary to any physical processes that matter—at least according to what we’ve deduced so far. Yet they exist. Sometimes the simplest model just isn’t the correct one.

Harlan Coben has disputed many criticisms of Occam’s razor by stating that people fail to understand its exact purpose:

Most people oversimplify Occam’s razor to mean the simplest answer is usually correct. But the real meaning, what the Franciscan friar William of Ockham really wanted to emphasize, is that you shouldn’t complicate, that you shouldn’t “stack” a theory if a simpler explanation was at the ready. Pare it down. Prune the excess.

I once again leave you with Einstein: “Everything should be made as simple as possible, but not simpler.

Occam’s razor is complemented by other mental models, including fundamental error distribution, Hanlon’s razor, confirmation bias, availability heuristic and hindsight bias. The nature of mental models is that they tend to all interlock and work best in conjunction.