Sir William Osler's take on probability:
Variability is the law of life, and as not two faces are the same, so no two bodies are alike, and no two individuals react alike and behave alike under the abnormal conditions which we know as disease. This is the fundamental difficulty in the education of the physician, and one which he may never grasp, or he takes it so tenderly that it hurts instead of boldly accepting the axiom of Bishop Butler, more true of medicine than of any other profession:"Probability is the guide of life." Surrounded by people who demand certainty, and not philosopher enough to agree with Locke that "Probability supplies the defect of our knowledge and guides us when that fails and is always conversant about things of which we have no certainty," the practitioner too often gets into a habit of mind which resents the thought that opinion, no full knowledge, must be his stay and prop.
Kahneman and Tversky differentiate between subjective and objective judgment of probability:
Subjective judgments of probability are important because action is often based on beliefs regarding single events. The decisions of whether or not to buy a particular stock, undergo a medical operation, or go to court depend on the degree to which the decision maker believes that the stock will go up, the operation will be successful, or the court will decide in her favor. Such events cannot be generally treated as a random sample from some reference population, and their judged probability cannot be reduced to a frequency count. Studies of frequency estimates are unlikely to illuminate the processes that underlie such judgments. The view that "both single-case and frequency judgments are explained by learned frequencies (probability cues), albeit by frequencies that relate to different reference classes" (Gigerenzer, 1991, p. 106) appears far too restrictive for a general treatment of judgment under uncertainty. First, this treatment does not apply to events that are unique for the individual and therefore excludes some of the most important evidential and decision problems in people's lives. Second, it ignores the role of similarity, analogy, association, and causality. There is far more to inductive reasoning and judgment under uncertainty than the retrieval of learned frequencies.
Probability theory is a useful concept to help us align our beliefs with the state of the world at a certain point in time. Herbert Weisberg adds to the definition of probability:
A probability is a mental construct. In this sense, it is entirely subjective, or personal, in nature. However, probability must also have something to do with observations in the outside world.
This is a great overview of the concept of probability by assistant professor Anna Mahtani:
Lsewebsite. "LSE Philosophy: Anna Mahtani." YouTube. YouTube, 15 Apr. 2015. Web. 02 July 2017.
Understanding probability and logic is not only important for science and statistics, but also for understanding judgment and decision making.Tweet to @jvrbntz