This blog post delves deeply into the logic of how empirical evidence, when combined with different evaluation methods like elimination, inductivism, and Bayesianism, produces conflicting hypothesis selections.
When we must choose one hypothesis among competing ones, we make our judgment by examining the relevant empirical evidence. Regarding how to consider empirical evidence, three main approaches can be considered. First, elimination involves formulating multiple hypotheses and then progressively discarding competing hypotheses based on empirical evidence, ultimately selecting the remaining hypothesis. This method is useful when a true hypothesis clearly exists among several, and empirical evidence can definitively exclude the others. However, the elimination method offers no help when empirical evidence simultaneously fits multiple hypotheses. For example, empirical evidence of recent favorable economic indicators could fit both the hypothesis that the Korean economy is growing healthily and the hypothesis that risk factors are increasing despite external growth. In such a situation, neither hypothesis can be excluded based solely on the given empirical evidence, so the elimination method fails to provide grounds for hypothesis selection.
Classical inductivism overcomes the limitations of elimination by enabling selection even among hypotheses not excluded by empirical evidence. According to classical inductivism, the more empirical evidence aligns with a specific hypothesis, the more reliable that hypothesis becomes. This perspective allows us to select hypotheses by considering the entirety of relevant empirical evidence. For example, consider the case of designating one of two new drugs, both expected to have similar efficacy, as a health insurance-covered medication. Classical inductivism advises selecting the drug that showed more positive results in various clinical trials, based on a comprehensive consideration of the trial outcomes for both drugs. Of course, classical inductivism also reaches the same conclusion as elimination for drugs showing negative effects in clinical trials.
However, classical inductivism cannot quantitatively assess how much empirical evidence supporting a specific hypothesis increases its credibility. Bayesianism resolves this issue as follows. Before acquiring new empirical evidence, let us denote the credibility we hold regarding a specific hypothesis as a value between 0 and 1, called the ‘prior probability’. A confidence level of 0 means we are certain the hypothesis is false, while 1 means we are certain it is true. Bayes’ theorem provides a clear computational method showing how this prior probability changes into a ‘posterior probability’ through new empirical evidence. Bayesianism refers to the difference between the posterior probability and the prior probability as the ‘strength of the evidence,’ which is used to determine how strongly new empirical evidence supports a hypothesis. Therefore, if a particular piece of empirical evidence does not change the confidence level of the hypothesis, the strength of that evidence is zero.
Consider an example. Suppose an air conditioner company, based on various climate data, hypothesizes that next summer’s temperatures will be higher than the average of the past decade, leading to increased air conditioner sales. Given a prior probability of 0.6 for this hypothesis, suppose new evidence emerges suggesting that next year’s economy will improve, boosting consumer spending on appliances. If applying Bayes’ theorem results in the posterior probability of the given hypothesis increasing to 0.8, then the strength of the new evidence for this hypothesis is 0.2. Thus, Bayesianism offers a significant advantage by expressing the relationship between evidence and hypotheses with precise quantitative values, enhancing the rigor of hypothesis selection.
However, despite this usefulness, criticism of Bayesianism is also raised. One prominent criticism is that the hypothesis evaluation method proposed by Bayesianism does not align with how scientists actually conduct research. Bayesianism analyzes the relationship between evidence and hypotheses through probability calculations. Critics argue, however, that in practice, scientists often use different forms of evidence evaluation rather than performing such probability calculations. In this context, Bayesianism is criticized as a theory that does not correspond to actual scientific practice. In response, some Bayesian statisticians counter that Bayesianism is not a theory describing how scientists actually evaluate hypotheses, but rather a theory presenting normative standards scientists ought to follow. Viewed this way, Bayesianism can be understood less as a technical description of actual scientific research and more as a theoretical stance offering normative guidance on how to handle the relationship between evidence and hypotheses.
