In part one, I defended Popper and his criterion of falsifiability from the Duhem-Quine thesis. I examined Popper’s position and revealed that not only was Popper aware of the Duhem-Quine problem before most of his critics, but that he also proposed a methodological solution to it. In part two, I will attempt to demonstrate that the Duhem-Quine thesis is either false, insofar as it’s interesting, or trivial, insofar as it’s true. In either case, the Duhem-Quine thesis no longer stands as a refutation of Popper’s criterion of falsifiability.
The positivists demanded that all meaningful propositions be empirically decidable–both verifiable and falsifiable. Difficulties arose, however, with respect to scientific hypotheses, because they couldn’t be verified. For example, scientific hypotheses aren’t just about the past but also the future, and it’s impossible to verify an event which hasn’t happened yet. Even putting aside doubts regarding the veracity of our observations, it’s seemed impossible to verify scientific hypotheses. Therefore, scientific hypotheses were apparently meaningless. The positivists attempted to solve this problem by using an alternate logic–induction. Supposedly, the mistake had been to presume that meaningful propositions must be deductively verifiable. If, instead, meaningful propositions need only be inductively verifiable (while remaining deductively falsifiable) then the meaningfulness of scientific hypotheses could be restored. However, problems arose with respect to the logic of induction–what justifies the use of induction? What exactly is inductive verification, and why is it epistemically valuable? How do we measure the strength of inductive inferences? What is the relationship between induction and parsimony? And more besides. The positivists had sought to reduce all meaningful discourse to the contents of, and logical derivations from, sense experience. But they encountered insurmountable difficulties that forced subsequent generations to abandon their programme.
Karl Popper wasn’t a positivist. Whether a proposition could be reduced to sense experience was, in Popper’s view, irrelevant to either its meaningfulness or its scientific status. For Popper, scientific hypotheses need only be empirically testable and, since they weren’t verifiable, that meant they were falsifiable:
I shall not require of a scientific system that it shall be capable of being singled out, once and for all, in a positive sense; but I shall require that its logical form shall be such that it can be singled out, by means of empirical tests, in a negative sense: it must be possible for an empirical scientific statement to be refuted by experience.
Popper noted that verifiability and falsifiability are asymmetrical with respect to empirical observation. That is, no finite set of observations could verify a scientific hypothesis, but a single recalcitrant observation could falsify it. By demanding only falsifiability from scientific hypotheses, Popper obviated the need for any logic of induction. Empirical testing, then, required nothing more than regular truth-preserving deduction.
As for the origin of scientific hypotheses, which induction was sometimes thought to explain, Popper said:
The initial stage, the act of conceiving or inventing a theory, seems to me neither to call for logical analysis nor be susceptible of it. The question how it happens that a new idea occurs to a man–whether it is a musical theme, a dramatic conflict, or a scientific theory–may be of great interest to empirical psychology; but it is irrelevant to the logical analysis of scientific knowledge.
In order that a hypothesis might be evaluated by scientific criteria or be subject to empirical tests, it must first been submitted to examination. Where it came from matters little except to the psychologist or historian. To the scientist, what matters is whether the hypothesis might solve an extant problem, whether it’s a promising explanation, and whether it can be tested empirically.
While the demand that scientific hypotheses be verifiable became mired in logical quandaries, the contrary demand of falsifiability appeared to suffer no comparable difficulties. We can represent the logic of falsification by the retransmission of falsity from conclusion to premises in a valid argument. That is, if the conclusion is false, then at least one of the premises must be false. A prediction, then, is the valid deduction (⊨) of an observation (O) from a scientific hypothesis (H):
H ⊨ O
For the purpose of logic, we put aside questions regarding the veracity of our observations, such as whether we’re being fooled by an illusion or a dream, and we simply concern ourselves with logical relations. On this account, the logic of falsification appears decisive–if a scientific hypothesis predicts an observation which clashes with experience, then that scientific hypothesis is falsified. There is no ambiguity or wiggle room, and nothing more than elementary deduction is required to complete the argument.
The Duhem-Quine thesis, however, challenges the logic of falsification. We cannot, it’s claimed, predict any observation from scientific hypotheses alone, because we must include auxiliary hypotheses among our premises. For example, we cannot predict where a cannon ball will land from Newton’s laws alone, because we must include assumptions about the shape and mass of the cannon ball, the position and orientation of the canon, the composition of the gunpowder, the gravitational pull of the earth, resistance of the atmosphere, and so on. An extreme variant of the thesis would also include metaphysical presuppositions, such as scientific realism, determinism, or even the laws of logic. With our auxiliary hypotheses in tow, we can now characterise a prediction as the valid deduction (⊨) of an observation (O) from a scientific hypothesis (H) with the conjunction of auxiliary hypotheses (A1 through to An):
H & (A1 & … An) ⊨ O
Even putting aside questions regarding the veracity of our observations, the logic of falsification no longer appears decisive–if a scientific hypothesis predicts an observation which doesn’t occur, then that scientific hypothesis might be false, or perhaps some auxiliary hypothesis is false instead. There is now ambiguity and wiggle room, and something more than pure deduction seems necessary to complete the falsification. Popper himself explained the problem:
By this mode of inference we falsify the whole system (the theory as well as the initial conditions) which was required for the deduction of the statement p, i.e. of the falsified statement. Thus, it cannot be asserted of any one statement of the system that it is, or is not, specifically upset by the falsification.
The scientist’s problem is similar to what a teacher faces when she returns to the classroom to discover a vulgar word scrawled on the blackboard. She turns to the class and demands the culprit step forward and take responsibility, but she is confronted by silence. A few bottoms squirm in their seats. She looks over at the usual suspects, snickering in the corner. Her gut says one of them is responsible, but which? None of them will confess the truth, and the school has a strict policy against torture. Besides, there’s the possibility that someone else is to blame or the whole class conspired together. The vulgar word on the blackboard is testament to an act of defiance, but the source cannot be traced. The teacher’s quandary corresponds to that a scientist faces when interpreting the results of his experiments. An apparent falsification attests to some error, but logical analysis alone cannot trace its origin.
The charge of the Duhem-Quine thesis is that falsification is logically arbitrary. Even assuming the veracity of our observations, they cannot entail the truth or falsity of any scientific hypothesis. A falsifying observation, like inductive verification, must go beyond valid inference to establish its conclusion. Therefore, according to this view, the criterion of falsifiability fares no better than verifiability. Contrary to Popper, empirical testing cannot proceed according to regular truth-preserving deduction after all.
My charge, however, is that the Duhem-Quine thesis is merely an elaborate way of denying the veracity of our observations. Therefore, it employs a double-standard against the falsifiability criterion and, moreover, is merely an indirect way of stating that all observation is theory-laden–a position that Popper is famous for espousing.
What we observe depends on how we explain our experience. Suppose we experience standing on the bank of a river in the presence of a large white bird with a orange and black bill. If we explain our experience of as the product of a dream, then we will not claim to have observed a white swan. However, if we explain our experience as the consequence of a white swan, then we might claim to have observed a white swan. We only interpret our experience as an observation because we bring to it an explanation of how the existence of something explains the experience.
However, if our explanation of our experience is mistaken, then so might be our observation. This is why, for Popper, there is nothing foundational about experience. An experience doesn’t mean anything–it has no content–without an explanation. An explanation consists of laws, principles, circumstance, and so on, which cannot be derived from, or justified by, the experience. The experience is the thing to be explained (the explanandum) rather than the thing doing the explaining (the explanans). There are, then, no observations without theories, assumptions, and expectations through which to interpret experience. Therefore, explanation must come before observation, both logically and genetically. This is what it means to say that all observation is theory-laden, and it’s also why Popper did not regard any falsification as conclusive and irrevocable; our observations are theoretically loaded and logically irreducible to experience. For Popper, all falsifications are tentative and, in principle, may be overturned in the course of scientific progress.
A falsifying observation is theoretical construct, but what theories, assumptions, and expectations is it constructed from? Auxiliary hypotheses. For example, when testing Newton’s laws by firing a canon ball, our observation is a product of auxiliary hypotheses–the shape and mass of the canon ball, the position and orientation of the canon, the composition of gunpowder, and so on–and our experience. Newton’s laws are falsified when, in conjunction with the auxiliary hypotheses, they fail to explain our subsequent experience. To deny an auxiliary hypothesis is tantamount to denying the veracity of the observation, because it would change our explanation and, ipso facto, the content of our observation. Indeed, any falsifying observation can be trivially transformed into a corroborating observation by denying or modifying auxiliary hypotheses, and vice versa. For Popper, auxiliary hypotheses cannot be arbitrarily varied relative to a falsifying observation, because the content of that observation depends on how the auxiliary hypotheses make sense of experience.
The Duhem-Quine thesis, as its normally presented, treats observations as non-theoretical, like an experience without an interpretation. Such “observations” are devoid of content–they aren’t statements or propositions that have logical consequences. While our experience may remain explicable if we falsify an auxiliary hypothesis in lieu of Newton’s laws, it also amounts to a denial that any falsifying observation happened. In this way, the Duhem-Quine thesis, insofar as its true, can be reduced to the claim that our observations are theory-laden and irreducible to experience, and it amounts to little more than questioning the veracity of our observations. However, when discussing the logical relations between theory and observation, this is precisely what we’re not concerned with!
This might be a more accurate formulation of the logic of falsification.
H ⊨ (A1 & … An) → E
The observation, in this case, is a material conditional, where the auxiliary hypotheses are the antecedent and some basic description of our experience is the consequent. In fact, our experiences aren’t statements, and even a very basic description of an experience is theory-laden, so there remains nothing foundational or incorrigible about basic descriptions. We can no more put experiences into a logical argument than we can atoms, swans, or cannonballs, because they’re not propositions or statements. In any case, a conditional is false if, and only if, its antecedent is true and its consequent is false. Given this formulation, then, a falsifying observation occurs when the auxiliary hypotheses are true and the predicted experience is false. What we’re attempting to capture here is the theory-ladenness of observation by showing the dependence of the falsifying observation upon our various theories, assumptions, and expectations.
As Fred Dretske is reputed have said, ‘one man’s modus ponens is another man’s modus tollens‘. There is nothing–neither in logic nor experience–which forces us to accept any observation. We could even adopt a strong anti-realist position that nothing but our experiences exists and abandon any pretense of explaining them. However, questions of when and why we might assent to a particular scientific hypothesis or falsifying observation were the subject of Part One. If the Duhem-Quine problem is reducible to the claim that any purported falsification may be mistaken, then I contend that it’s a trivial thesis. It is especially perverse to bring this objection against Popper, who not only stressed the corrigibility of observation, but was also a thoroughgoing fallibilist.
The Duhem-Quine thesis, however, is false with respect to oft-repeated claim that it’s always possible to preserve a scientific hypothesis from an apparent falsification by revising auxiliary hypotheses in its stead. This result depends on an implicit denial of the theoretical character of even the simplest observation. The thesis artificially separates our theories, assumptions, and expectations–or auxiliary hypotheses–from our observation, as though we could vary the former indefinitely without changing the content of the latter. When testing hypotheses, we assent to an explanation of our experience such that we might get a falsifying observation, otherwise we’re only pretending to test the hypothesis, i.e. it isn’t a test if we’re determined to excuse every apparent failure come what may. It’s a simple task, then, to reformulate the logic of falsifiability in such a way to restore its logical validity.