Richard James
PHIL362
Prof Lawson
Paper Assignment
Carl Hempel argues scientific hypothesis testing involves auxiliary hypotheses, challenging Karl Popper’s claim that a single failed prediction can conclusively falsify a scientific hypothesis. This discussion begins with an exposition of Falsificationism from Popper, examining his argument with the logic of Modus Tollens, which claims one failed prediction falsifies a scientific hypothesis. In contrast, Hempel asserts hypotheses are never tested in isolation, as they depend on auxiliary assumptions which complicate the straightforward falsification Popper asserts. This paper will explore them both, contrast their positions, and examine how Hempel’s rationale, drawing from Brahe, highlights limitations in Popper’s methodology, despite Modus Tollens being deductively valid.
Karl Popper asserts that scientists should reason by following The Logic of Falsification, which asserts that one failed prediction can conclusively falsify a scientific hypothesis. Popper suggests this strict criterion ensures that scientific theories remain empirically testable and subject to rejection of contrary evidence. Popper formalizes this theory with the logic of Modus Tollens, which takes the logical form - if the hypothesis, H, is true, then we should observe I. Or, If H, then I. Therefore, if we observe I is false, then H must be false. Or ‘not I’, therefore, ‘not H’. Modus Tollens is deductively valid and through it, one can surmise that if a theory is true, then certain predictions should follow. Conversely, the same can also be stated that if a prediction is observed to be false, then the theory itself must be false. To illustrate this, Popper refers to Einstein’s prediction about light bending around the sun, and how the experiment by Eddington in 1919 confirmed Einstein’s prediction (Popper, 6). Thus, Popper illustrates that had Eddington’s experiment shown no bending of light, Einstein’s theory would have been falsified.
Carl Hempel argues that in actual scientific practice, hypotheses are never tested in isolation, rather they rely on auxiliary hypotheses which help generate predictions. With this, Hempel challenges Popper’s idea that one failed prediction automatically falsifies a theory, and his reasoning follows – scientific testing involves not only the hypothesis H, but also auxiliary assumptions, A. H and A together yield a prediction, I, or if (H & A), then I, or with multiple assumptions, if (H & A1 … & AN), then I. Conversely, if I is false, then we cannot immediately conclude that H is false because A might be wrong instead. This is the Logic of Falsification with Auxiliary Hypotheses, which postulates when auxiliary hypotheses are involved, the logical consequence of a failed prediction, ‘not I’, does not directly lead to ‘not H’, but instead opens multiple possibilities where H might be false, ‘not H’, and auxiliary assumption might be false, ‘not A’, or the experimental conditions might be flawed. Thus, Hempel argues Popper’s falsification is less straightforward, requiring scientists to assess whether the failure stems from the hypothesis itself, auxiliary assumptions, or experimental conditions before rejecting the main theory .
Hempel goes on to describe Tycho Brahe, and how he rejected Copernicus' heliocentric model partly because he observed no stellar parallax. Essentially, Copernicus’ model would have predicted stellar parallax if the Earth moved (Hempel, 18). Hempel argues with the use of Popper’s strict falsification logic, the lack of parallax, ‘not I’, should refute heliocentrism, ‘not H’. However, Hempel points out Brahe did not consider an auxiliary hypothesis, that stars could be farther away than people thought. Eventually, technology improvements with telescopes revealed stellar parallax and it confirmed heliocentrism. This example demonstrates how auxiliary hypotheses can prevent scientific theories from being prematurely discarded. Rather than refuting heliocentrism, the negative result led scientists to revise auxiliary assumptions about stellar distances.
In summary, this paper exposes Hempel’s assertion of why falsification is more complex than Popper suggests. While Modus Tollens is logically valid, and from the perspective of Einstein’s theory and how Eddington’s experiment confirms Einstein’s prediction, scientific falsification is rarely this straightforward because predictions usually depend on multiple interconnected assumptions. A failed prediction does not necessarily mean that the core hypothesis is false, but it may instead point to flaws in auxiliary hypothesis or experimental methods. In the case of Tycho Brahe, limitations in technology and underestimations in stellar distance, which were classified as failures in both experimental conditions and auxiliary assumptions, caused heliocentrism to be prematurely discarded. This example challenges Popper’s strict view that a single failed prediction can conclusively refute a scientific hypothesis, underscoring the complexity and nuance of real scientific reasoning.