The Controversial Concept of Probability: A Deep Dive into Steven Pinker's Explanation
Steven Pinker, in his discourse on probability, addresses the complex and often conflicting interpretations mathematicians and philosophers have put forth. The concept of probability, particularly in the context of one-time events, is far from straightforward.
Probability of Repeated Events: The Long-Run Frequency Interpretation
The meaning of probability for an event that is repeated many times is relatively simple: it refers to the frequency in the long run. For instance, when rolling a fair die, each face tends to appear approximately 1/6 of the time. This straightforward interpretation simplifies our understanding of probabilities in recurring scenarios.
Probability of One-Time Events: An Uncertain Realm
The interpretation of probability for one-time events, such as the outcome of a future election or a random competition, is much more complex. It often involves our subjective expectations and confidence levels. For example, Nate Silver, founder of 538, predicted the 2020 election outcome with a 90% confidence level, reflecting his subjective credence, or belief, in the event.
Another approach to interpreting one-time events is through the perspective of logical possibilities. In the Monty Hall Problem on Let's Make a Deal, with three doors, each has an equal 1/3 chance of concealing the big prize. Understanding how opening a door changes the probability to 2/3 is a classic example of using logical possibilities to assess probabilities in unique situations.
Types of Probability Interpretations
The varied interpretations of probability include numerous philosophical understandings, such as the frequentist, subjective, and evidential warrant perspectives.
Frequentist Interpretation
The frequentist view interprets probability as the frequency of an event in a large number of trials. For instance, the statement “there is a 7 out of 10 chance of rain tomorrow” means that out of every ten similar days, seven will be followed by rain. However, this interpretation can be challenging when attempting to define “relevant respects” for comparison.
Subjective Credence
The subjective credence view, exemplified by the Bayesian approach, involves assessing the probability based on one's personal belief. In the case of the rain prediction, if your belief swings from 50% on Sunday to 55% on Monday to 70% on Tuesday, you are updating your prior estimates with new evidence. This approach allows for a flexible and dynamic understanding of probabilities.
Evidential Warrant
Pinker's reference to evidential warrant suggests a middle ground between frequentism and subjectivism. It posits that while we might not be completely certain, we can base our expectations on a strong likelihood. The concept implies that we have substantial evidence to support our beliefs, yet we are not entirely sure, as evidenced by the 70% confidence level in the rain prediction.
Formalist Approach
A formalist approach to probability involves a structured and mathematical framework. This perspective might involve using formal logic and mathematical models to interpret and calculate probabilities, even in the context of unique or one-time events.
Conclusion: Understanding the Complexity of Probability
In summary, the interpretation of probability is a complex and nuanced topic, with various philosophical schools of thought. Steven Pinker's point about the disagreement over the definition of probability serves as a reminder that the concept is far from universally agreed upon.
The appreciation of these different interpretations allows us to approach probability from multiple angles, enhancing our understanding and predictive capabilities in various scenarios.