Axioms and Assumptions Are Made Up. How We Invented Paradigms To Change The World.
Paradigms are sets of rules accepted by groups of people working in a particular field.
Scientists agree to them while solving problems deemed important and worthy of a solution. Paradigms, comprised of axioms, i.e. things we hold as true, arise among scientific communities focused on a particular area or a problem. If you think about doing science or research as puzzle solving, the are the rules along which you agree to play, like you can only join puzzles together if they match with each other and can be pieced together effortlessly. They also talk about things one cannot do within a particular paradigm, like force the puzzles into a particular position.
A paradigm does not have to be accepted by all scientists working in a particular domain. Instead, it is common to see numerous subgroups of specialists within a field agreeing upon different axioms and working under numerous paradigms.
When a group of scientists including Claude Shannon (the founder of Information Science) and Marvin Minsky (considered one of the founding fathers of AI) gathered together in the Dartmouth Summer Research Project in 1956 didn’t expect they will not have solved AI by the time Autumn comes around. Obviously, they did not anticipate the emergence of two separate schools of doing AI neither, with the divide between symbolists and connectionists. The disputed between the two could be traced down to a disagreement of what intelligence really was. The former group believed that by setting rules and encoding symbols one can create intelligence, while the latter believed learning from experience, by running training on data and letting computers figure out a way, is better. It is the connectionists that emerged victorious (thus far) and it is their approach that lures behind modern machine learning approaches including neural networks and deep learning.
Paradigms enable groups to look at the same scenario and see the same things happening.
If you show five distinct connectionists how a trained neural network tells apart an image of a handwritten letter P from the letter R, they will say that what you see is an emerging intelligence. On the other hand if you show the same thing to the symbolists, they will say that it is just a bunch of random numbers predicting something, not even remotely close to an artificial intelligence.
Comparing two different paradigms and deciding which one is better with certainty is not possible. While it might seem that rules are more accurate versions of others, it's hard, if not impossible, to prove that one of them is superior. This is especially the case if they are distinct, like Newtonian and quantum mechanics. It is so because they tend to differ on fundamental questions and because they invariably take some axioms as true. Thus, they will have a hard time proving their case to people from another school which agrees upon other axioms instead. From this distinction emerges another important fact about paradigms.
Because people operating within a paradigm accept certain things as true, they also agree about what questions are important to solve and which ones are not.
If a hypothetical scientist accepts the ability to predict stuff as a sign of intelligence, he will not try to question this narrative, but instead move on to answer the question of how good certain predictions are and distinguish different types of intelligence.
Paradigms tend to have questions that they aim to solve while accepting answers to other questions as given.
This approach also proves quite effective, i.e. it allows researchers to focus on what they have agreed that matters and neglect other things. If a paradigm is stable, science progresses by answering questions with expected possible solutions. As Thomas S. Kuhn the author of Structure of Scientifc Revolutions says in his book:
As in manufacture so in science - retooling is an extravagance to be reserved
Most science progresses when paradigms are not questioned, because they are accurate enough for the scientists to pursue their investigations. Research under stable paradigms resembles the act of puzzle solving. People expect, more or less, what they should find, just like puzzle-solvers have an idea of what the finished puzzle will look like. Their paradigms supply them with theories that enable predictions of their outcomes. Their work is mostly figuring out how to get to the desired result, and how to do so with the most accuracy. Ian Hacking, in his introduction to Kuhn's Structure of Scientific Revolutions wrote:
Normal science does not aim at novelty but at clearing up the status quo. It tends to discover what it expects to discover. Discovery comes not when something goes right but when something is awry, a novelty that runs counter to what was expected. In short, what appears to be an anomaly.
Paradigms can change and they do so because we change opinions.
A paradigm shift is essentially revoking the accepted axioms. Comparing the paradigms before and after the shifts is not an easy task, and it will be anything but objective. Most of the time it is not feasible to find one paradigm superior to the other, because they tend to differ on fundamental questions. Moreover, the new paradigm will usually leave a lot of questions unanswered (as every paradigm does, especially more the recent ones) and there will be people that won't adopt it on this basis.
Kuhn explained that when a new paradigm is adopted, there is always opposition to it. Some researchers will tend to pursue their work just as it was before the shift occurred, and they will remain faithful to their ideas until their very last days. A change will take place nonetheless, as new scientists will go through education learning about the new paradigms and eventually replacing the older generations. This is common characteristic of a lot of changes. Because conservatives tend to offer a counterweight to the overly optimistic innovators, it's possible to keep the balance between the new and the old.
When we change the paradigms, we make the most progress.
While most science progresses when paradigms are stable, the most progress in science happens when the paradigms are changed. We already know what a paradigm shift is, but let's talk about why does it happen. Firstly, notice that paradigms are in no way objective, i.e. different groups might clash on particular questions and there is no answer that can be proved superior to others. The emphasis on which questions are important at a given time makes certain sets of axioms more suitable. When people find that their paradigm is unable to explain what is happening in the world, they look for new explanations.
Problem solving under a paradigm shift is different from problem solving during stable times. Instead of looking to come up with a more or less expected answer in creative ways, scientists relax fundamental assumptions and test which changes can explain the reality better. A new paradigm can become more popular, but never fully accepted, as it is not possible to convince everyone, especially on important topics. Also, there is no clear way to pinpoint when a new set of rules is really accepted, because more often then not, the novel approach needs time before it develops and becomes useful.
Think about the invention of a neural network. The concept was first proposed in 1943, by two researchers in order to present a simplified mathematical model of neurons. It took 14 years before the first trainable neural network, called the perceptron, was proposed in 1957. After this period, the idea of neural networks lost interest, as von Neumann's architecture took over the computing scene and popularized a logic based approach. By that time, most people have lost interest in neural networks, and discarded them as a plausible way to arrive at artificial intelligence. Then, with the idea of backpropagation suggested in 1980s neural nets shined again. A crucial moment came in 2012, when AlexNet was presented and went mainstream. In 2024, the Nobel Prize in Physics was awarded to John J. Hopfield and Geoffrey Hinton for their foundational discoveries and inventions that enable machine learning with artificial neural networks. It is unlikely that such an award would be given if backpropagation and AlexNet did not come about. It is also hard to say at which point did neural networks really took off and who in particular was their inventor.
New paradigms do not get us close to the truth.
Truth exists, perhaps only outside of Plato's cave and is not accessible to us. Science does not progress towards the truth or away from falsehood in a linear fashion of any sorts. We stumble, make mistakes, embrace ideas which are worse then their predecessors. This happened in the past, and it will happen again. It's foolish to believe that we can objectively evaluate our current approaches and judge that they are better than previous ones. A true scientist acknowledges that his understanding is limited, yet works on deepening it. The scientific method is not infallible, and there have been times where it lead us astray. Yet, it might just be the best thing we have.