Aretē

When working in science, one is faced with a problem if he tries to assert the truth of a hypothesis based on the satisfaction of its predictions. The problem is that of induction. Given the logical statement, “if H, then P,” P is necessarily true if H is true, but P being true is not sufficient for the truth of H. Said in another way, H implies P, but P doesn't say anything about H. Applying this to hypotheses and predictions, one would say, “If a given hypothesis is true, it is necessary that the things it predicts are also true. But finding true things in the world tells you nothing of the truth of hypotheses.” Karl Popper acknowledges this shortcoming and offers a solution: falsification.

While it is not logically valid to move from the truth of P to the truth of H, it is valid to move from the falsification of P to the falsification of H. That is, because H implies P, if P is not the case, then it follows logically that H is not the case either. Popper latches onto this idea and formulates a scientific methodology that measures progress with respect to the falsification of hypotheses. He attempts “to characterize the falsifiability of a theory by the logical relations holding between the theory and the class of basic statements.” Basic statements are “self-consistent singular statements of a certain logical form—all conceivable singular statements of fact” (84). Here Popper places emphasis on basic statements, because these are the type of statement that he takes to be fundamental in observation; for example, “this chair here is blue,” is a basic statement. Note that basic statements are existential statements. Theories make universal statements. The inductive problem arises when moving from the existential statements (observations) to the universal statements of the theory. But to show that a universal statement is false, all that is needed is a single incompatible existential statement.

Popper writes: “A theory is to be called ‘empirical’ or ‘falsifiable’ if it divides the class of all possible basic statements unambiguously into the following two non-empty subclasses. First, the class of all those basic statements with which it is inconsistent… and secondly, the class of those basic statements which it does not contradict (or which it ‘permits’)” (86). So a theory needs to sort basic statements into two baskets. We start with every conceivable basic statement in a basket, then we pick out all the ones that contradict the theory and put them in the other basket. These are what Popper calls “potential falsifiers” (86). They're called “potential” falsifiers because they're simply statements which if true, would make the hypothesis false. They needn't necessarily actually be true.

Popper continues, “It may be added that a theory makes assertions only about its potential falsifiers. (It asserts their falsity.) About the ‘permitted’ basic statements it says nothing” (86). For the very reason the ‘permitted’ basic statements are ‘permitted’, a theory says nothing about them. They are completely logically unrelated (remember that our basic statements are self-consistent—that is, they aren't, by themselves, contradictory. If they were, then anything could be derived from them, including the theory).

Given all that, Popper takes the game of science to be one of falsification. Experiments are to be designed in such a way as to falsify a given theory, as that is the only way we can actually make empirical statements about theories. To make this seemingly hopeless endeavor worthwhile, Popper articulates a methodology to go along with the logical structure which, he hopes, allows us to measure scientific progress. The first rule he imposes is, “The game of science is, in principle, without end” (53). Because there are an infinity of hypotheses, with an infinity of potentially falsifying basic statements to test, the game will never cease. But this does not imply hopelessness, for we certainly learn something from the act of showing a theory to be false. Namely, that the theory is false! Obviously, we want our theories to be useful for answering further questions about the world, so in finding that a theory we come up with is false, we know, through the falsifying basic statements, a bit more about the features of the world in question. To be able to use those theories which haven't been falsified, Popper adds a second rule: “Once a hypothesis has been proposed and tested, and has proved its mettle, it may not be allowed to drop out without ‘good reason’. A ‘good reason’ may be, for instance: replacement of the hypothesis by another which is better testable; or the falsification of one of the consequences of the hypothesis” (54-55). This rule is meant to protect against the usual objections to conventionalism. Replacing a theory with another one should only be done if it is being replaced with a better-testable theory. This ultimately strengthens the scientist's position, as a better-testable theory is more easily falsified.

The methodological rules Popper lays down are the main difference between his view and conventionalism. A conventionalist chooses whatever theory best fits his purposes, while Popper's theories are dictated to him by the logical structure around basic statements. At some level, though, Popper's falsificationism adopts some portions of conventionalism. For example, Popper agrees with the conventionalist in that even at the level of basic statements, we run into problems.

Popper differentiates between occurrences and events. The distinction can best be understood as follows: an event is described by basic statements of the form “x exists” or “x happens”. Occurrences are specific instances of an event; for example, “there is a blue chair here right now,” or “the light in this room is currently on.” Further, when we make an observation, we make a statement of the form “I see a blue chair here now, “ or “I see that the light in this room is currently on.” The problem mentioned previously lies in our observations. There is no logical basis for moving from statements of the form “I see x” or “I observe x” to statements of events. This is the little conventionalist in Popper coming out. Because there is no logical basis for making such moves, Popper speaks of “inter-subjective testability” and “agreeing” that a given event-statement is true. This feature of Popper's view makes it more appealing than standard conventionalism, because it shifts the emphasis from the very general to the very specific. The hope is that it's a much easier jump to make from “I see x” to “x exists” than to simply accept a general theory on no such grounds.

last updated 2 years ago #