## Does science have a specific method: falsificationism

### 0.1 Introduction

So let’s assume the following:

1. empiricism: the scientific method relies in some way upon observations (even though we cannot accept these acritically)
2. the methodological assumption: the scientific method involves some sort of systematic method, but this method cannot be characterized in the way that the inductivist asserts

Perhaps one way to characterize the specific method of science is to say that the scientific method involves at least the following:

1. the initial proposal of conjectures (hypotheses)
2. the subsequent attempt to refute (falsify) these conjectures
3. upon refutation of the conjecture, a new hypothesis is proposed.

On this approach, no scientific theory is ever proven true. Instead, we get a picture of science where scientists propose and refute theories and, ideally, only the fittest scientific theory survives. Let’s call this general view of science falsificationism.

Science is an activity governed by a method where individuals consider a problem, gather data, look at previous explanations and then form a general hypothesis (the method in which this hypothesis is generated can be systematic). Next, scientists do not aim to prove this hypothesis by accumulating further observations. What they do instead is deduce testable predications from these hypotheses and try to look for observations that would falsify the hypothesis.

Note 1 The position of “falsificationism” is commonly attributed to its most notable champion: Karl Popper. The core ideas, however, are not new. 19th century American philosopher Charles S. Peirce (EP2:73-74) writes “The scientific man finds himself confronted by phenomena which he seeks to generalize or to explain. His first attempt to do this, though they will be suggested by the phenomena, can yet, after all, be reckoned but mere conjectures; albeit, unless there be something like inspiration in them, he never could make a successful step. Of those conjectures,–to make a long matter short,–he selects one to be tested. In this choice, he ought to be governed solely by considerations of economy. If, for example, the prospect is that a good many hypotheses to account for any one set of facts, will probably have to be taken up and rejected in succession, and if it so happens that, among these hypotheses, one that is unlikely to be true can probably be disposed of by a single experiment, it may be excellent economy to begin by taking up that. At last, however, a hypothesis will have been provisionally adopted, on probation; and now, the effort ought to be to search out the most unlikely necessary consequence of it and that can be thought of, and that is among those that are readily capable of being brought to the test of experiment. The experiment is made. If the prediction from the hypothesis fails, its failure may be so utter as to be conclusive; or, maybe, nothing more than an alteration of the defective theory need be undertaken. If, notwithstanding its unlikelihood, the prediction be verified, and if the same thing happens again and again, although each time the most unlikely of the (convenient) predictions has been tried, one begins to doff one’s cap to the rising star that nature herself seems to favor.”

Example 1 (Water Boiling) I believe that water boils at 100 Celsius. I test this hypothesis repeatedly and find that after a number of repeated tests, it boils at 100 Celsius. The hypothesis withstands my tests. Later on, I test this hypothesis at elevation and find that it does not boil at 100 Celsius. The hypothesis is refuted.

Example 2 (My Wife’s Lover) Suppose I think my partner is cheating on me. I may have some suspicions or I may be insecure (it doesn’t matter how I came to this hypothesis). To put my mind at ease, I develop a way to test my suspicion. If my wife is cheating on me, then a private detective following her for a week would find conclusive evidence of her infidelity. (If T, then p). I hire a private detective and after a week of trailing her, the detective reports that there are no signs of infidelity (not p). Thus, my theory has been shown to be falsified (not T).

Discussion 1 Offer up your own example of the method of falsification. First, come up with a falsifiable theory. Second, explain what observable phenomena would follow if that theory were true. Third, offer up a scenario that has that phenomena not follow. Fourth, explain what this does to the theory.

### 0.2 Modus Tollens

Earlier, it was noted that there are problems with characterizing the method of science as inductive. The falsificationist can characterize the method of science as having a deductive structure.

One way of characterizing this method is through the logical inference known as modus tollens (denying the consequent).

• P1: If theory (T) is true, then we should observe p rather than not-p.
• P2: We observe not-p (or we don’t observe p)
• C: Therefore, T is not true.

In other words, the method of science has a formal structure: If P, then Q, not-Q. Therefore, not-P

Another way of representing this structure is by falsifying universal statements using singular statements that contradict the universal statement.

• P1: All swans are white.
• P2: A swan observed at time t in location p was not white.
• C: It is not the case that all swans are white.

This way of representing the formal structure of science is as follows: All Ps are Q. This P is not a Q. Therefore, it is not the case that all Ps are Q. In sum, while it is not possible to show that a scientific theory is true by induction, it is possible to show that a scientific theory is false deductively.

### 0.3 Falsifiability

The falsificationist places a condition on the type of hypothesis or conjectures permitted. Namely, hypotheses must be falsifiable.

Definition 1 (falsifiable) A hypothesis h is falsifiable if and only if there it is logically possible for there to be some observation (or collection of observations) that if established as genuine, would be inconsistent with the truth of the hypothesis.

Example 3 (Some falsifiable hypotheses)

1. Objects fall at a rate proportional to their mass.
2. Cancer can be fully cured by ingesting drug X.
3. All swans are white.
4. My husband is cheating on me.

Example 4 (Some unfalsifiable hypotheses)

1. All bachelors are unmarried men.
2. John will either go to the party or he won’t.
3. If we stay together, then we were meant to be. If we break up, then we were not meant to be.
4. God is loving.

The demand for only falsifiable hypotheses stems from the intuition that scientific theories ought to be informative about the world. If a hypothesis is falsifiable then it states what sorts of situations are not the case. For example, the claim that “objects fall at a rate proportional to their mass”, if true, states how we should see objects fall and in doing so tells us about ways we won’t see objects fall (e.g., objects won’t fall at a rate independent of their mass). “All swans are white” tells us that we won’t see any black, or blue, or green swans. In contrast, if a hypothesis is unfalsifiable, then it does not inform us about the world because it is consistent with any way the world might be. That is, “John will either go to the party or he won’t” does not tell us whether he will or he won’t go to the party.

### 0.4 How Falsifiable: Clarity and Precision

The quality of a scientific hypothesis might first be evaluated in terms of whether or it the hypothesis it proposes is falsifiable. Next, it might be evaluated according to the degree to which it is falsifiable. Tentatively, it might claimed that the more falsifiable a hypothesis is, the better. In other words, were two hypotheses being evaluated (${h}_{1}$ and ${h}_{2}$), assuming neither ${h}_{1}$ nor ${h}_{2}$ has been falsified, if ${h}_{1}$ is more falsifiable than ${h}_{2}$, then ${h}_{1}$ is a better hypothesis than ${h}_{2}$.

In exploring this claim, it is worthwhile to consider two different hypotheses and determine which of the two is more falsifiable:

1. Some bodies will fall at a rate proportional to their mass.
2. All bodies will fall at a rate proportional to their mass.

The more falsifiable theory is (2) since (i) it says everything (1) does but more and (ii) only one observation is required to falsify it.

Why ought we to accept the claim that the more falsifiable hypothesis is better?

First, if a hypothesis is not clear from the outset, then the hypothesis can always (potentially) be revised again and again to block any falsifying observation. In other words, the more obscure a hypothesis is, the more susceptible it is to ad hoc modifications.

Second, there is some relation to how precise a theory is and how falsifiable it is. That is, a hypothesis that says that all objects will fall at a rate between 4 and 10 m/s is less falsifiable than one that says it will fall at 10.00232 m/s. In other words, the precision and the falsifiability of a theory seem to go hand in hand. And, insofar as a precise theory is better than an imprecise theory, then so too a highly falsifiable theory is better than one that is less falsifiable.

### 0.5 Falsificationism and Progess: A simple account

From the theory of falsificationism, a theory of scientific progress can be obtained. Science progresses as follows:

1. There are problems that human beings encounter (many of these are the result of puzzling observations about things in the world) or questions that emerge.
2. Falsifiable hypotheses are proposed as solutions to these problems.
3. Individuals test these hypotheses
• Some hypotheses are refuted
• Others are not refuted and more rigorous testing ensues (often, new observations about the world emerge)
4. For the refuted hypotheses, new hypotheses are proposed, and these undergo testing.

As an illustration of the progress of science according to the falsificationist, Chalmers (in What is this thing called Science, pp.65-66) points to the question of how bats are able to navigate at night at speed given their poor eyes.

The process of falsificationism proceeds first by proposing the hypothesis that bats actually navigate with their eyes. Next, an experiment is designed to test this where bats are blindfolded. Bats are able to navigate when blindfolded and so the hypothesis is falsified. A new hypothesis is proposed, e.g. that they use their eyes and various squeaks to navigate. Scientists then proceed to test this hypothesis by either covering their ears or their mouths and having them navigate an obstacle course. When bats fail to adequately navigate the course, it is not proven that bats navigate with their ears and by emitting squeaks but only that this hypothesis has not been falsified. It is not proven because other explanations are possible and future observations may falsify the theory.

### 0.6 Naive vs. Sophisticated Falsificationism

Let’s contrast two different versions of falsificationism.

Definition 2 (Simple falsificationism) Simple falsificatonism is the theory that science ought to proceed by (i) proposing hypotheses that are falsifiable yet not already falsified and (ii) test these hypotheses by way of observation and experiment.

Definition 3 (Sophisticated falsificationism) Sophisticated falsificatonism is the theory that science ought to proceed by (i) proposing hypotheses that are falsifiable yet not already falsified, (ii) testing these hypotheses by way of observation and experiment, and (iii) replacing rejected hypotheses with new hypotheses that are more falsifiable than their predecessors.

The central difference between the simple and sophisticated versions of falsificationism concern the issue of replacement of falsified hypotheses. According to the simple falsificationist, once a hypothesis has been falsified, it can be replaced with any falsifiable hypothesis that purports to solve the problem. According to the sophisticated falsificationist, this is insufficient. Replacement hypotheses need to be more falsifiable than the hypotheses they are seeking to replace. The reason for this condition is to prevent ad hoc modifications to a theory. That is, some hypotheses might start out as falsifiable but continually resort to modifications that are made simply to avoid falsifying observations (some even being transformed into totally unfalsifiable hypotheses).

Definition 4 (ad hoc modification) A modification to a theory is an ad hoc modification if and only if the modification adds to or replaces or alters a component of the theory but this alteration has no new testable consequences that are not already found in the original theory.

#### 0.6.1 Examples of ad hoc modifications

Example 5 (Invisible Unicorns.) Suppose I say that there is a unicorn in the room. In fact, he is in the closet. This is a startling claim but one that is easily falsifiable by looking in the close to see if there is a unicorn. Quite unsurprisingly, there is no unicorn in the closet. You have falsified my theory! But, I might change my theory so as to avoid abandoning my theory. “Ah!” I say “but it is in the closet. It is just that the unicorn is invisible! No one can see it, hear it, touch it, and no consequences follow from it being in the room.”

Here I have engaged in a modification to my theory so as to avoid it being falsified. I have modified the hypothesis so that there are no testable consequences that are not already found in the original theory. In this particular example, I’ve modified it so radically that there are no testable consequences at all!

Example 6 (Popper on Freudian Psychoanalysis.) Suppose an individual is suffering from neurosis. One might propose the theory that all neuroses are the result of being punished for some sexual act and so the patient’s neurosis is the result of being punished for some earlier sexual act. But now suppose there is falsifying evidence. No, the individual was never punished for such an act. At this point, the theory might get revised to say that all neuroses are the result of being punished for some actual sexual act or some non-sexual act that is later unconsciously sexualized so the patient’s neurosis is the result of being punished for some earlier actual or perceived sexual act. This transforms a potentially falsifiable claim into one that is unfalsifiable!

Example 7 (Bread Nourishes) This particular example is taken from ?, p.70-71. Suppose someone hypotheses that “bread nourishes”. That is, they claim that when wheat is grown, converted into bread, and eaten by human beings, it will nourish them. Suppose, however, that a certain batch of bread grown and made in the normal way poisons a group of people. This appears to falsify the general theory that “bread nourishes”.

One might, however, modify the hypothesis that “bread nourishes” by simply excluding that particular batch of bread from the theory. That is, rather than bread nourishes, the theory contends that “all bread nourishes except that particular instance of bread that poisoned people”. This is an ad hoc modification. There are no new testable consequences that are not already found in the original hypothesis.

Example 8 (Galileo and the moon’s invisible substance) The moon (and all celestial bodies) were once thought to be perfect spheres (no mountains or craters). However, with the invention of the telescope, Galileo observed that the moon was not a perfect sphere and contained mountains and craters.

In response to this falsifying observation, the theory was modified in the following way: the moon was a perfect sphere and the appearance of craters and mountains were an illusion for there was an invisible substance that filled in these gaps. This is an ad hoc modification since there are no new testable consequences that are not found in the original hypothesis.

#### 0.6.2 Examples of non ad hoc modifications

Example 9 (Bread Nourishes) This particular example is taken from ?, p.72. Suppose someone hypotheses that “bread nourishes”. That is, they claim that when wheat is grown, converted into bread, and eaten by human beings, it will nourish them. Suppose, however, that a certain batch of bread grown and made in the normal way poisons a group of people. This appears to falsify the general theory that “bread nourishes”.

One might, however, modify the hypothesis that “bread nourishes” by saying that “all bread nourishes except for bread that is made with wheat effected by a particular fungus”. This modification is not ad hoc because there are testable consequences that are not present in the original hypothesis. The experiment for testing bread simply involving taking some bread and seeing if it nourishes. In the new hypotheses there is the new experiment that involves taking bread with (and without) a certain fungus and testing to see if it nourishes or not.

Example 10 (The motion of Uranus and the discovery of Neptune) This particular example is taken from Chalmers’s What is this thing called Science, p.73. Consider the orbit of Uranus and the Newtonian laws of motion. In the nineteenth century, Uranus appeared not to travel according to the Newtonian laws of motion. This then appears to falsify Newtonian gravitational theory.

One might, however, keep the Newtonian gravitational theory by postulating what we know about the world. That is, to explain Uranus’s strange deviation from Newtonian gravitational theory, Leverrier and Adams postulated a new (unobserved) planet near Uranus. Given the deviation from Newtonian theory, the approximate size and location of the object was postulated. This modification to the theory (particular certain assumptions about how the world is) is not ad hoc because it is independently testable. That is, it contains a testable consequence not found in the original theory.

Later, it was discovered that there was a planet influencing the orbit of Uranus: Neptune!

### 0.7 Criticisms of Falsificationism

Objection 1 (Falsifying observations: reject the theory or the observation?) A number of scientific theories face falsifying observations, but there is no way to determine whether we ought to reject the theory or reject the observation.

Example 11 (Copernicus and naked eye observations.) The Copernican theory is inconsistent with naked eye observations of Venus and Mars.

Objection 2 (The Duhem-Quine Problem (or Duhem’s Holism).) The falsificationist model gives the impression that the scientific method is systematic because it is algorithmic (there are a set of rules that allow us to compute the answer to a particular problem or question) and realistic in that it is tied to the observable world. But, let’s consider a problem for the above account known as the Duhem-Quine problem. Consider that formal models of scientific activity are said to consist of five parts: the predication (p), the theory (T), and initial conditions (ic), auxiliary universal statements (aus), and idealizations (i):

• the prediction (p): a sentence that describes a phenomena to occur
• the theory (T): sentences that specify various universal statements, e.g. laws of nature like “force is equal to mass times acceleration”
• initial conditions (ic): a set of singular statements specifying current states, relations, etc., e.g. there exists a planet u, planet u is at position p1 at t1.
• auxiliary universal statements (aus): statements that underlie the specification of or determination of initial conditions, e.g. aus1 = statements regarding how telescopes (or other technological devices) work.
• idealizations (i): simplifications necessary for doing calculations, e.g. i1 = the only bodies that exist in our solar system are the sun and planets.

Note that the number of auxiliary hypotheses, idealizations, and initial conditions are often extremely high and are sometimes not explicitly formulated. We previously stated that an isolated theory T allows us to deduce a prediction p. The falsification method said that if we observed not-p, then T would be falsified. But, that is an oversimplification of what actually goes on. Consider Newton’s three laws of motion as it is specified schematically below:

• Theory: $T$ = Newton’s Laws
• Initial conditions: $i{c}_{1}$, $i{c}_{2}$, $i{c}_{3}$, $i{c}_{4}$, …, $i{c}_{n}$
• predictions: ${p}_{1}$, ${p}_{2}$, ${p}_{3}$
• Auxiliary universal statements: $au{s}_{1}$, $au{s}_{2}$, $au{s}_{3}$, $au{s}_{4}$, …, $au{s}_{n}$
• Idealizations: ${i}_{1}$, ${i}_{2}$, ${i}_{3}$, ${i}_{4}$, …, ${i}_{n}$

Now suppose that Newton’s theory says we should see ${p}_{1}$ but we are actually presented with $not-{p}_{1}$. Given the theory complex and the falsifying observation, logically, we are justified in saying that the theory complex is false:

• P1: If $T$ AND $i{c}_{1}$, $i{c}_{2}$, $i{c}_{3}$, $i{c}_{4}$, …, $i{c}_{n}$ AND $au{s}_{1}$, $au{s}_{2}$, $au{s}_{3}$, $au{s}_{4}$, …, $au{s}_{n}$ AND ${i}_{1}$, ${i}_{2}$, ${i}_{3}$, ${i}_{4}$, …, ${i}_{n}$, then ${p}_{1}$
• P2: $not-{p}_{1}$
• C: Therefore, not ($T$ and $i{c}_{1}$, $i{c}_{2}$, $i{c}_{3}$, $i{c}_{4}$, …, $i{c}_{n}$ AND $au{s}_{1}$, $au{s}_{2}$, $au{s}_{3}$, $au{s}_{4}$, …, $au{s}_{n}$)

Notice that the theory itself has not been show false. Rather what has been falsified is some part of the theory-complex, initial conditions, auxiliary hypotheses, and idealizations. Thus, the falsifying instance does not directly falsify the theory but hits the entire system. Or, as Duhem puts it:

The only thing the experiment teaches us is that among the propositions used to predict the phenomenon and to establish whether it would be produced, there is at least one error; but where this error lies is just what it does not tell us.

It was claimed that science is systematic and doesn’t engage in ad hoc modifications. Even though some falsifying observation does not directly falsify the theory but hits the entire system, the falsification method says we should not modify the initial conditions, the auxiliary statements, or the idealizations. We ought to reject the theory and move forward. But science does not work like this!

Example 12 (Falsifying the Copernican theory) If we simply reject the theory, Copernicus’s theory that the earth travels around the sun would have been denied (see Barker & Kitcher, p.20-21). Galileo “saved” the Copernican theory by modifying one of the initial conditions (ic), i.e. the size of the universe.

Example 13 (Orbit of Uranus) If we simply reject the theory, then Newton’s gravitational theory would have been denied when it was shown to conflict with the orbit of Uranus. But Adams and Leverrier “saved” Newtonian physics by modifying one of the initial conditions (ic), i.e. they changed the initial conditions by positing another planet that exerted a gravitational force on Uranus

Objection 3 (Many new theories stands against a wealth of falsifying observations.) When the Copernican universe was proposed, it stood against the Aristotelian-Ptolemaic universe. The philosopher Aristotle claimed that the universe was divided into the sub-lunar and super-lunar regions. The sub-lunar region consisted of the earth to the moon’s orbit while the super-lunar region extended from the moon to the stars. The Aristotelian universe is a finite universe. The stars in the sky are fixed to a sphere with nothing behind them.

All super-lunar objects (e.g. the planets) are composed of a perfectly spherical and incorruptible substance and they moved in a circular orbit around the earth which sat at the center of the universe (see Figure 1).

Figure 1: Aristotle’s universe

The problem with this picture of the universe is that while planets appear to move from West to East against a fixed background of stars, when observed from Earth planets will occasionally appear to change direction, moving from East to West. This change in direction is known as “retrograde motion”. One way that retrograde motion was accounted for was by the introduction of epicycles. That is, planets would orbit their circle of orbit around the earth (Figure 2)

Figure 2: Aristotle’s universe with epicycles

Copernicus argued that the sun, rather than the earth, was at the center of the universe and that the earth (and all other planets) orbited the sun. The initial benefit of this theory is that it can explain retrograde motion without epicycles. Namely, retrograde motion is only a perspective effect.

However, despite the smoother (less ad hoc) explanation of retrograde motion, Copernicus’s theory stood against not only the accepted world-view but the observations that the Aristotelian-Ptolemaic theory could easily explain. These include:

1. if the earth orbits on its axis and is traveling around the sun, then why do objects when dropped from heights (e.g. a tower) fall directly to the ground rather than some distance away (e.g. a number of yards away).
2. if the earth orbits on its axis and is travelling around the sun, then why don’t objects not bound to the ground fly around, e.g. small rocks.
3. if the Copernican system is true, then why do Mars and Venus always look the same size with the naked eye. If their distance relative to the earth changes, then they should change sizes.