I. Theory and experiments

Let’s use the following schema to represent the relationship between a theory T and an observation statement e:

T  ⊢ e           This says that T entails e, where e is something that can be decided by observation

「 e                This says that e is false

「 T               This says that T is false

In the context of theories, some theory T entails some observation statement e if the truth of theory T guarantees the truth of e. Conversely, if e is false, then the theory T is false.

E.g., Suppose Tis the theory that all metals expand when heated, and e is the statement that a particular sample of copper expands when heated. In this case, T  ⊢ e, since if the theory is true, the observation statement will be true. So, if e is false (i.e., if a particular sample of copper fails to expand when heated), then T (i.e., the theory that all metals expand when heated) is also false.

II. The Duhem Problem

Duhem argued that it is never possible to refute a theory in this way. The reason is that it isn’t possible to deduce any statement about what will be observed from a single hypothesis alone. Duhem said ‘an experiment in physics can never condemn an isolated hypothesis but only a whole theoretical group.’ (p.77)

Instead, the hypothesis in question will need to be combined with many other assumptions about background conditions, the reliability of measurements, the initial conditions of the system, etc.

For example, imagine that we want to test Newton’s theory of gravitation by the observation of the path of a comet. Recall from our lecture on Popper, that Newton’s universal law of gravitation:

m1m2

F = G

This says that the gravitational force (F) between two objects can be found by multiplying the gravitational constant (G) with the product of the masses of the two objects (m1 and m2) divided by the square of the distances between  the two objects (r2).

So, we can rephrase this in terms of entailment. Our question, then, is does our theory entail the observation of the comet’s path?

I.e., Our theory T is F = G  and our observation statement e will be the location of a comet at some time. But the equation above alone doesn’t predict the path of a comet. We also need:

-     The mass of the comet

-     The mass of other bodies in the solar system

-     Their relative positions and velocities

-     The initial position and velocity of the comet relative to other bodies in the solar system

-     The gravitational constant

We would also need to use Newton’s other laws of motion.

Suppose, then, that e is not as expected. Have we refuted Newton’s equation? It could be that Newton’s equation is false, but it could also be any other of our assumptions that are wrong (e.g., maybe the mass of the comet is not what we think).

The conclusion here is that the falsification of a theory is not as simple as the schema above suggests.

A more realistic schema for falsification would be the following:

(T & A)  ⊢ e

¬ e

¬ (T & A)

This says that T together with some set of auxiliary assumptions A entails e This says that e is false

This says that the conjunction of T and the auxiliary assumptions is false

¬ (T & A) means that either T is false, orA is false, or both T and A are false. So, we don’t know whether our theory or our auxiliary assumptions or both are incorrect when an observation “falsifies” a theory in this way.

III. Compare with Quine’s holism

If this objection sounds familiar, it should! Quine was influenced by Duhem’s worry when he argued for confirmational holism. This worry about testing scientific theories is sometimes called the Quine-Duhem Thesis. However, some philosophers object to putting Quine and Duhem’s objections together in this way because there  are some differences between Quine and Duhem’s positions.

Duhem’s position is less radical than Quine’s. They agree that an observation can tell us that something is wrong with the combination of our theory and our assumptions, it doesn’t tell us exactly what has been falsified. However, Quine makes the further (and much more radical) claim that we might even choose to give up the truths of mathematics or logic in the face of an observation that conflicts with our beliefs about the world.

Duhem formulates his non-falsifiability thesis as follows: “if the predicted phenomenon is not produced, not only is the questioned proposition put into doubt, but also the whole theoretical scaffolding used by the physicist.”

IV. Popper

What consequences does all this hold for Popper?

Recall Popper’s falsificationism: A hypothesis is scientific if and only if it has the potential to be refuted by some possible observation.

From the Duhem problem, it should be clear that there is no such thing as a completely conclusive refutation of a theory by an experiment. So you might think that if Duhem is right, then Popper’s falsificationism is in serious trouble. If we can’t refute a theory by some observation, then it doesn’t seem like we can use Popper’ s criterion to distinguish science from non-science.

However, Popper himself admits that there is no such thing as a completely conclusive refutation of a theory by an experiment. He appeals, instead, to the practice of science and agreement amongst a scientific community. He says  that in addition to a set of observation statements, there must also be a set of experimental procedures and  techniques, etc., that the relevant group of scientists agree on that allows them to determine the truth or falsity of each observation statement. This means that Popper thinks that falsificationism is only possible in science if there is intersubjective agreement amongst scientists about what is being tested on any given occasion.