(P)robability

Alphabet Thoughts III

Here I outline 3 conceptions of probability that I learned about in a philosophy of math course, and note potential issues with each.

1. Subjectivism- Probability is subjective, like creating betting odds (ex. "I think its quite likely that the stock market will fall tomorrow, because…"). This method is useful because of it’s wide applicability, as well as it’s ability to call attention to diverse data sets and justifications.

Potential Issues: different people can have different intuitions and conclusions using the same information, as methods of interrogating information can vary. They can also be using different sets of information to justify their conclusions, resulting in apples to oranges comparisons.

2. Frequentism- You take a situation, figure out the possible results, then test over and over again to get results (ex. Taking a die, figuring out possible ways it can land, then rolling it a million times and considering how many times it lands on each side).

Potential issues: Not all events can be repeatedly tested, due to event rarity. For example, there is only one 2020 U.S national presidential election. Certain rare but repeating events are also difficult to model this way, for example certain cosmological events (such as comet passings). Additionally, there are practical limitations when it comes to repeating tests. Each new roll of the die will involve new circumstances (including slightly different air temperature, slightly different method of rolling, even minutely different gravity). Also, someone elsewhere must typically use a different die and rolling system (among other differences between situations). The philosopher David Hume covers similar issues in his famous Problem of Induction.

3. Conceptualism- You take a theoretical situation, list all results, then note their theoretical likelihood (stipulating the relative chance of each result). Ex. "We take a theoretically perfect 6 sided die. There are 6 possible results, so each side has a 1/6th chance of occurring"

Potential issues: The theoretical system in play doesn't exist out in the world. Due to physics, there is no perfectly equal 6 sided die, nor no way to roll a die that ensures perfect equality of outcomes. Thus the practical benefits of this method can be rather low.

Note from Alexandra: This post ends my blog hiatus! I hope to get back into the blog-writing more consistently, likely with some shorter examinations of topics I’ve studied in the past. My plan is to write a piece on Hume’s Problem of Induction next!