Chapter 1: The Nature of Skepticism

Embracing skepticism involves maintaining an inquisitive attitude towards truth. Rather than being a guiding philosophy for life, skepticism serves as a philosophical approach to all ideas, including life philosophies. This perspective aligns with Simone de Beauvoir's assertion that certain individuals can derive universal insights from the often chaotic realm of philosophical systems, which she referred to as a "conscious venture into lunacy" (The Prime of Life 178).

A contemporary skeptical perspective hinges on three foundational principles inherited from ancient skeptics like Carneades and Cicero. Two of these concepts—coherentism and fallibilism—have been explored in previous discussions. The third, probabilism, is our current focus.

Carneades introduced the term "pithanon," denoting likelihood or persuasiveness, while Cicero adapted it to "probabilis," giving rise to the modern term probability. Although neither philosopher possessed the quantitative framework we now apply to probability, they argued that it is rational to provisionally accept ideas supported by solid arguments and relevant evidence, always remaining open to the possibility of being mistaken.

Since the 18th century, Bayes' theorem has emerged as a valuable tool for refining the intuitions of Carneades and Cicero. The Reverend Thomas Bayes published a brief paper in 1763, which, although initially overlooked, gained prominence in the 20th century for addressing complex problems dependent on conditional probabilities. I believe Bayes' theorem, along with the decision-making philosophy called Bayesianism, is crucial for modernizing the insights of these ancient thinkers.

The Problem of Skepticism in Modern Contexts

Let’s briefly examine Bayes’ theorem. It focuses on conditional probabilities—how likely an event is based on knowledge of another related event. This conditionality can either heighten or diminish the likelihood of the original event.

For instance, if I'm contemplating whether it will rain today, I might first glance outside and see clear skies. This observation decreases the probability of rain. However, upon hearing a weather report indicating approaching clouds, I would reassess my initial estimate and raise the probability of rain, as satellite imagery is typically a more reliable indicator than a mere glance out the window.

This reasoning, applicable in both everyday life and scientific inquiry, is encapsulated by Bayes' theorem:

P(A|B) ~ P(B|A) x P(A)

Here, “|” indicates conditional probabilities, “~” signifies proportionality, and “P” represents various probabilities associated with events A and B.

In our weather example, A denotes rain, while B represents the satellite imagery. Thus, the probability of rain given the satellite images, P(A|B), can be expressed in relation to the probability of observing those images if rain were indeed imminent, P(B|A), multiplied by the a priori probability of rain, P(A), based on my earlier observation of sunny weather.

As we analyze this, we notice that while P(A) is low due to the sunny conditions, P(B|A) remains high since the satellite images indicate cloud movement. Consequently, the posterior probability of rain, P(A|B), becomes higher than the prior estimate.

In simpler terms: we start with an initial estimate of an event's likelihood, gather empirical evidence related to that event, and adjust our probability based on the new information. This updated probability can then serve as a new prior for further evidence. This process continues until we achieve a reasonable level of confidence in our understanding—or until our resources for data collection are exhausted.

As a more intricate example, consider a medical researcher investigating the effectiveness of three different vaccines during a viral outbreak. Initially, the researcher would assign equal probabilities to the efficacy of each vaccine. However, as data is collected, the researcher might find that vaccines 1 and 2 perform well, while vaccine 3 does not. This would lead to an increase in confidence for vaccines 1 and 2, while the confidence in vaccine 3 would decrease. The researcher would continue to adapt their estimates based on incoming data.

A crucial aspect of this approach is that as long as the updated probabilities rise, confidence in the effectiveness of vaccines 1 and 2 will increase. However, absolute certainty is never achieved, as new data may alter these trends.

To understand posteriors better, think of them as your degree of belief in the truth of a statement (e.g., the efficacy of a vaccine or the likelihood of rain). Posteriors are probabilities that range from 0 to 1 (or 0% to 100%). They will never reach these extremes within the context of Bayes’ theorem because setting priors to either extreme would render them unchangeable by new evidence. Such a stance would reflect closed-mindedness and dogmatism, which is contrary to the skeptical approach advocated by Carneades, Cicero, and Bayes.

Responses to Skepticism: Exploring Bayesian Perspectives

At this point, you might question whether my discussion has been about subjective or objective priors—whether the priors reflect personal belief or can be derived independently. The answer is that, for our discussion, the distinction is not essential. I provided examples of both: my initial belief about rain was subjective, while the likelihood of the three vaccines was objectively calculated.

Bayesian theorists have demonstrated that, provided enough rounds of updates are made based on new evidence, it doesn’t matter where one starts; the posteriors will ultimately align with true probabilities, though this may take time. For skeptics, probabilities represent estimates of subjective beliefs, and this form of quantification is a significant advancement compared to the qualitative assessments available to Carneades and Cicero.

This three-part series has illustrated that modern skeptics—or any thoughtful individuals—can build upon the insights of ancient philosophers like Carneades and Cicero while incorporating modern epistemological concepts. The three pillars of skepticism—coherentism, fallibilism, and probabilism—interact to form a rich understanding of knowledge.

Coherentism encourages us to view knowledge as an interconnected web of beliefs and observations. Changing our minds involves altering or replacing parts of this web. The web is anchored by fundamental principles such as logic and direct observation—our primary sources of knowledge. Fallibilism reminds us that our understanding is provisional, as both reason and perception are reliable yet fallible. Meanwhile, probabilism facilitates the continual updating of our beliefs based on new evidence.

Together, these pillars create the intricate tapestry of human knowledge, while also instilling a sense of humility regarding our understanding. We must always be open to the possibility of being incorrect, and if we are, the rational response is to adapt our beliefs accordingly.