The philosopher Carl G. Hempel, in his 1965 essay “Studies in the Logic of Confirmation,” brought to light a central paradox in the scientific method as it is commonly understood. This is called Hempel’s Ravens Paradox, and it deals with inductive reasoning, which is the first step in any scientific method: Observing and forming a hypothesis.

Hempel’s Ravens Paradox

Suppose you see a raven, and you note that it is black. “Hmm,” you say, “that raven was black.” Sometime later you notice a couple more ravens, and they also are black. “What a coincidence,” you remark, “those ravens are black too.” Time goes by and you see many more ravens. And it happens that all the ravens you see are black. “This is beyond coincidence,” you might reasonably think, and with the instincts of a good and observant scientist you form a hypothesis: All ravens are black.

Inductive Reasoning

There are always limits to an experimental apparatus, even if the apparatus is just a matter of observing as many ravens as possible to check their colour. Nonetheless, we feel justified in saying that each new observation of a black raven tends to confirm the hypothesis, and in time, if no green or blue or otherwise non-black ravens are observed, our hypothesis will eventually come to have the status of natural law.

The Limitation

Logically put, our hypothesis “all ravens are black” has the form of a conditional, that is, a statement of the form “if A then B.” In short, we are saying that if a given object is a raven, then that object is black. According to the laws of logic, a conditional is equivalent to its contrapositive. That is, a statement of the form “if A then B” is equivalent to the statement “if not B then not A.” This rule of logic is incontrovertible.

The Flaw In Our Logic

Our hypothesis “all ravens are black” therefore has the equivalent form “all non-black things are non-ravens,” or more precisely, “if an object isn't black then it is not a raven.” Consequently, if every sighting of a black raven confirms our hypothesis, then every sighting of a non-black non-raven equally confirms our hypothesis.

The Illogical Conclusion

Very well, you might say, but maybe every sighting of a non-black non-raven really does confirm, even if only to an infinitesimal degree, the hypothesis that all ravens are black. After all, if we could, somehow, check every non-black object in the universe, and if none of them were ravens, our statement that all ravens are black would be proved.

The Bottom Line

Stashed ideas

Hempel’s Ravens Paradox | Platonic Realms

In order to sharpen our reasoning skills, we must have a good grasp of our own cognitive biases, as well as the basic laws of the universe.But in a dynamic world, new laws are constantly emerging.The editors over at <a href="http://edge.org/">Edge.org </a>asked some of the most influential thinkers in the world — including neuroscientists, physicists and mathematicians — what they believe are the most important scientific concepts of the modern era.We've highlighted 35 of the concepts here (please check the website for credits to authors whose essay highlights the theory)

Background

Decades of cognitive research shows that "our minds are finite and far from noble. Knowing their limits can help us become better reasoners..."Perhaps the most dire consequence is that human beings tend to be better at remembering evidence consistent with their beliefs."

Cognitive humility

Our brains can only hold so much information at once. When there's too much "information overload," we tend to get distracted easily and not retain what we're learning."Working memory is what brain scientists call the short-term store of information where we hold the contents of our consciousness at any given moment — all the impressions and thoughts that flow into our mind as we go through the day."

Cognitive load

When presented with too many choices — no matter how beautiful or beneficial — it can be overwhelming, and we are paralyzed by indecision.That's why having constraints, or any sort of limits, is beneficial and leads to solutions. In fact, "much creativity emerges from constraint satisfaction...". Einstein had one of his major breakthroughs when he realized that "time need not pass at a constant rate."

Constraint satisfaction

"Biologists have joined with social scientists to form an altruism debunkery society" — pushing the belief that every altruistic act is done in self-interest.But a new concept, "contingent superorganisms," says that we live life on a few different hierarchies. The idea is that when you reach a higher level, you are willing to put the success of the group or a higher cause above one's own. This is what drives militaries, fire departments, and rock bands.

Contingent superorganisms

The Copernican Principal is the idea that we are not special — that the universe is much larger, and we have a rather insignificant role."The paradox of the Copernican Principle is that by properly understanding our place, even if it be humbling, we can only then truly understand our particular circumstances. And when we do, we don't seem so insignificant after all."

Copernican principle

We are attracted to ideas and concepts that are easy to accept or digest.For example, round numbers are cultural attractors — they're "easier to remember and provide better symbols for magnitudes." Efficiency is another powerful cultural attractor.But just because we are drawn to specific concepts, does not mean that they are the best ones to apply to any given situation.

Cultural attractor

When information travels through multiple channels, it's easy for some elements of the message to get distorted — by biases, or simple human error.The effect of the spread of misinformation is "cumulative error." Living in an age where information can travel across the world in nanoseconds, this concept has never been more real or dangerous.

Cumulative error

Cycles explain everything — especially, at the basic level: evolution and biology. Cycles can be disrupted. Also watch out to see which cycles are doing all the work."All the 'magic' of cognition depends, just as life itself does, on cycles within cycles of re-current, reflexive information-transformation processes, from the biochemical scale within the neuron to the whole brain sleep cycle, waves of cerebral activity and recovery revealed by EEGs."

Cycles

The belief that there is much more time before us than has already elapsed. This creates a more expansive view of the world and the potential of the universe."Our sun is less than halfway through its life. It formed 4.5 billion years ago, but it's got 6 billion more years before the fuel runs out."

Deep time

It's a tool that researchers use to prevent against subconscious bias when performing experiments.Understanding the need for double-blind experiments would help the rest of the population understand their inherent subjective, everyday biases, and guard against generalization and impress upon people the need for critical thinking.

Double-blind control experiment

"Effective theory is one of the more important notions within science — and outside it. The idea is to determine what you can actually measure and decide, given the precision and accuracy of your measuring tools, and to find a theory appropriate to those measurable quantities.

Effective theory

As technology makes us more interconnected, there are more cross-overs between groups and populations. For example, there are more intermarriages."These effects are potentially beneficial for the improvement of cognitive skills, from two perspectives. We call these the 'expanding in-group' and the 'hybrid vigour' effects."

Expanding in-group

We all affect each other incidentally, especially in an interconnected world. Externalities are the unintended positive and negative side effects these interactions have."Externalities are increasingly important in the present era, when actions in one place potentially affect others half a world away."

Externalities

"Failure is not something to be avoided but something to be cultivated... It is a sign of weakness and often a stigma that prohibits second chances.Yet the rise in the West is in many respects due to the rise in tolerating failure. Indeed, many immigrants trained in a failure-intolerant culture may blossom out of stagnancy once moved into a failure-tolerant culture. Failure liberates success."

Failure liberates success

Our attachment to the familiar keeps us from taking risks and making real strides and breakthroughs. We often don't accurately assess the risk/benefit ratio; our irrational fears get in the way of real progress. "If the public could be brought to a greater understanding of how to evaluate the risks inherent in exploring future technology, and the merits of accepting some short-term risk in the interests of overwhelming greater expected long-term benefit, progress in all areas of technology — especially biomedical technology — would be greatly appreciated."

Fear of the unknown

Some behaviours we exhibit we blame on instinct. But what we believe to be instinct may, in fact, be learned behaviour over time — or a "fixed-action pattern." This has many implications, including the fact that, as rational creatures, we can change what we believe to be instinctive."Given an understanding of our fixed-action pattern, and those of the individuals with whom we interact we — as humans with cognitive processing powers — could begin to rethink our behaviour patterns."

Fixed-action patterns

We often believe that a certain, different set of circumstances would dramatically change our lives. But the truth is, factors like income and health are less indicative of overall happiness."The mismatch in the allocation of attention between thinking about a life condition and actually living it is the cause of the focusing illusion."

Focusing illusion

These are the layers of understanding that exist between the external reality and our own perception of the world. These systems of layers become more interconnected as we develop habits. Learning to ride a bike was hard; but after a while it's like second nature."The general concept of hidden layers captures deep aspects of the way minds — whether human, animal, or alien; past, present, or future — do their work."

Hidden layers

"Holism is colloquially described as 'The whole is greater than the sum of its parts.'Perhaps the most impressive is that carbon, hydrogen, oxygen, nitrogen, sulfur, phosphorus, iron, and a few other elements, mixed in just the right way, yield life... There is a kind of awesome synergy between the parts.Just look at DNA, and other much broader systems, like cities, that operate only if each individual element does its part."Holism does not come naturally. It is an appreciation not of the simple but of the complex ."

Holism

When any single event occurs, there are many possibilities as to the cause of the event. But the truth often lies in what is the single most reasonable, best explanation for the event. "Many of our most rancorous scientific debates — say over string theory or the foundations of quantum mechanics — have been... which competing criteria for judging explanations [of] best ought to prevail."

Inference to the best explanation

The greatest insights and inventions are the product of multiple people. It's never just a single person; everyone's standing on someone's shoulders."In hindsight we often find that if one scientist did not make a particular discovery, some other individual would have done so within a few months or years of the discovery...We are reluctant to believe that great discoveries are part of a discovery kaleidoscope and are mirrored in numerous individuals at once."

Kaleidoscopic discovery engine

We give names to everything in order to understand the world. But in doing this, we sometimes undermine, or simplify, the true nature of an organism or process. "Naming" keeps us from asking further, deeper questions about the nature of something. It's also important not to over-associate words, which leads to misunderstanding — for example, "theory [is] a strong idea in science while vague in common discourse."

Name game

"Because so many scientific theories from bygone eras have turned out to be wrong, we must assume that most of today's theories will eventually prove incorrect as well ."Accepting the belief that many of our theories are "fundamentally provisional and quite possibly wrong," we can better listen to and empathize with others' ideas.

Pessimism meta-induction

In zero-sum games, there's a clear winner and a clear loser. In positive-sum games, "everyone wins.""In a positive-sum game, a rational, self-interested actor may benefit the other actor with the same choice that benefits himself or herself." Some competition will always be zero-sum — such as the competition for mates.

Positive-sum games

Much of the world operates in powers of 10. Understanding scaling laws, like Richter scales that measure earthquakes or of "that between the volume of the brain's cortical white matter" — where computing takes place — would give us more perspective on the depth of events, matter, and ourselves."The spatial scales are also immense. Our space-time trajectory is a very tiny part of the universe, but we can at least attach powers of 10 to it and put it into perspective."

Powers of 10

Our expectations — and if they are met or not — greatly influence how we perceive the world, and ultimately, our quality of life.Predictive coding "concerns the way the brain exploits prediction and anticipation in making sense of incoming signals and using them to guide perception, thought and action."

Predictive coding

"Randomness is a fundamental limit to our intuition ; it says that there are processes we can't predict fully. It's a concept that we have a hard time accepting, even though it's an essential part of the way the cosmos works."But some random events — like random collections of atoms — are so absolute, that we can predict the outcome of that "randomness" with pure certainty.

Randomness

Freud inspired the idea of the irrational subconscious, but many of today's scientists dispute that idea.Instead they are bridging the conscious and unconscious — and insisting that we operate on both levels, and have an awareness of this connection, more than we think. "Our conscious understanding of probability, for example, is truly awful, in spite of the fact that we unconsciously make subtle probabilistic judgments all the time."

Rational unconsciousness

The idea that we perceive ourselves to be better than we are; to claim responsibility for success and blame others for failure ."In everyday life, more than nine in ten drivers are above-average drivers, or so they presume. In surveys of college faculty, 90 percent or more have rated themselves as superior to their average colleague."

Self-serving bias

The belief that what we perceive is what's normal, not taking into account the full extend of the past nor potential for future events.The syndrome is named after scientist Daniel Pauly, who said that each generation accepts "as a baseline the stock size and species composition that occurred at the beginning of their careers, and uses this to evaluate changes. When the next generation starts its career, the stocks have further declined, but it is the stocks at that time that serve as the new baseline."Therefore what is "normal" is constantly changing.

Shifting baseline syndrome

"Skeptical empiricism, the kind exemplified by the carefully thought-out and tested research in science at its best. It differs from plain empiricism" — which is simply the observation of results of the world around us.Put more simply, it is important for us to be skeptical about the world around us and not blindly accept what we believe to be "truths."

Skeptical empiricism

We overly-attribute breakthroughs to luck. But successful people regularly put themselves in positions — by studying, relentlessly working, pursuing the truth — where they encounter luck ."We should each invest a few hours a week in reading research that ostensibly has nothing to do with our day jobs, in a setting that has nothing to do with our day jobs, in a setting that has nothing in common with our regular workspaces."

Structured serendipity

The belief that we have a single self is false. In fact, we have multiple identities, or "subselves." "Each of us has a set of functional subselves — one dedicated to getting along with our friends, one dedicated to self-protection, one dedicated to winning status, another to finding mates..."

Subselves and the modular mind

Umwelt is the idea that we blindly accept the reality of the world around us ."It would be useful if the concept of the umwelt were embedded in the public lexicon. It neatly captures that idea of limited knowledge, of unobtainable information, of unimagined possibilities."

Umwelt

"We humans are terrible at dealing with probability. ... Our irrational fears and inclinations are costly ."We place too great a weight on the possibility of rare, major events occurring to us — for example, the lottery, or a plane crash — but not enough weight into the effects of lesser events."Making good decisions requires concentrated mental effort, and if we overdo it, we run the risk of being counterproductive through increased stress and wasted time. So it's best to balance and play, and take healthy risks."

Uncalculated risk

When I found this article, I didn't expect to not know most of these ideas from school already. These concepts are interesting in the way that they either perfectly describe the world we live in, or puts it in a whole new light- either way, it was enlightening!

My stuff

35 Scientific Concepts That Will Help You Understand The World

There is a branch of philosophy concerned specifically with how we justify our beliefs. The chief concern of "epistemic justification" is determining what counts as a good reason for believing something and how we come about those reasons. While there is a smorgasbord of different theories, one of the bigger is known as "coherentism."Coherentism is a view that settles for circular reasoning. It does so knowingly because the alternatives are just as bad, if not worse.

Epistemic justification

It is a great theory to call out the inconsistencies of others, but it has been criticized for allowing circular reasoning.The problem is that coherentism has been criticized on these very internalist grounds. If we can be justified in believing things based on no other authority than my own beliefs, then it allows the possibility of any outlandish beliefs.

Critics of coherentism

Epistemic justification is the area of philosophy that asks: what counts as enough to justify a belief? Coherentism is the theory that states a belief is justified insofar as it coheres or is consistent with our other beliefs. It is a great theory to call out the inconsistencies of others, but it has been criticized for allowing circular reasoning.

Hempel’s Ravens Paradox | Platonic Realms

35 Scientific Concepts That Will Help You Understand The World

Your beliefs are much harder to justify than you think

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