Clarification and amplification of a parenthetical assertion
in my essay,
May 15, 2017
The principle of falsification: To be both meaningful and true, a statement about empirical reality must not only describe the world as it is, it must also, by implication, describe conditions in the world that would be found if the statement were false. As I stated in my essay, "Why Should We Trust the Scientist," when making a fact claim one must be prepared to say, "expect to find such-and such empirical conditions, to the exclusion of other describable conditions."
Today, many esteemed philosophers of science tell us that the falsifiability criterion is logically flawed. My reply: they are correct, but it doesn’t really matter. The criterion, though imperfect, remains robust and essential to scientific inquiry.
This reply requires an extended and somewhat technical justification, which is why I could not include it in the aforementioned essay.
To begin, formal logical inadequacy is not a barrier to empirical science. As David Hume demonstrated, induction, the foundation of such science, is based upon logical fallacies – two in particular: circularity and generalization. We will return to this point.
Let’s begin with some elementary logic.
At it’s root, a scientific proof by experiment or observation has the elementary form of the so-called hypothetical proposition, "if P, then Q." Affirm or deny the "P" (the "antecedent"), or affirm or deny the "Q" (the "consequent") and you will on get an "hypothetical syllogism." There are four possible forms, two of which are valid, and two of which are invalid.
1) If P, then Q. P. Therefore Q. (Affirming the antecedent. Valid).
2) If P, then Q. Not P. Therefore, not Q. (Denying the antecedent. Invalid)
3) If P, then Q. Not Q. Therefore not P. (Denying the consequent. Valid).
4). If P, then Q. Q. Therefore P. (Affirming the consequent. Invalid).
These rules can be demonstrated by simple interpretations:
1) If John has a son, then John is a parent. In fact, John has a
(Valid. Given the premises and conventional definitions, the conclusion is inescapable)
2) If John has a son, then John is a parent. In fact, John has no
(Invalid: he might have a daughter).
3) If John has a son, then John is a parent. In fact, John is not
4) If John has a son, then John is a parent. In fact, John is a
(Invalid. He might have a daughter instead).
These simple logical rules will be crucial to what follows.
Now let’s apply this to the Relativity/Eclipse observation.
5) If Relativity Theory is true, then in an eclipse the light from the star will appear at Point X, to the exclusion of all other possible locations.
There is a great deal wrong with this simple example, beginning with the fact that it commits the fallacy of affirming the consequent (4). So if relativity theory (an antecedent) predicts the appearance of a star at Point X, and that prediction is subsequently confirmed by observation (a consequent), how can we trust that alleged "confirmation" if the procedure is logically invalid? We do so by acknowledging that there might be other explanations, and then proceed to eliminate these rivals. Also the precision of the prediction can render the plausibility of alternative explanations to be extremely unlikely – though not logically impossible.
In addition, the antecedent (relativity theory in this case) is never a single assertion. It is always a compound of several assertions. We will return to this point shortly.
So much for empirical confirmation. What about falsification?
A naive interpretation of the falsifiability principle might go like this.
6) If Relativity Theory is True, then the light from the star will appear at point X.
The light does not appear at point X.
Therefore, the theory of Relativity is refuted.
The syllogism is valid (denying the consequent – (3)). But is it a falsification? Is this how we can describe how relativity might be false, even if it is in fact true? Not so fast!
A failure to find the star at the predicted Point X (a consequent), validly denies the truth of the antecedent. But in scientific observation and inquiry, the antecedent of the hypothetical syllogism is never a single premise. It is always a compound made up of numerous assumptions: (A&B&C&D...&N) with "N" the premise to be tested (e.g. E=MC2). All it takes to find an entire "conjunctive compound" false, is to falsify just one of the conjuncts. But which one (or more) is false? Neither the syllogism nor the experiment will tell you.
In the eclipse experiment, these "conjunctive" assumptions include the laws of optics, the reliability of the telescope mechanism, the laws of celestial mechanics, the honest reporting of the observers, etc.
"Replicability" and "experimental control" (altering conditions to eliminate untested assumptions, for example different observers and different equipment) all serve to minimize the possibility of an error among the conjunct assumptions. But in principle, total elimination of the possibility of error among the "base assumptions" is impossible.
So science is fallible. Who’da thunk it?
However, fallibility is not a weakness of science, it is its foundational strength, which opens science to perpetual advancement.. And the presence of logical fallacies in scientific method only shows us what we should already know: induction, the method of science, is not pure formal logic. And why not? For a myriad reasons, an elaboration of which would require a book to explain. There are many such books written by philosopher of science much more qualified than myself. But for a start, let’s return to David Hume.
Induction, as Hume cleverly pointed out, is founded on a fallacious circular argument: (a) Inductive method assumes that nature is uniform. And how do we know that nature is uniform? (b) By induction, of course!
In addition, induction commits the fallacy of generalization, as it infers from "some" to "all." Newton’s Laws of Motion apply to all moving bodies, even though all moving bodies have not been individually observed. And Gray’s Anatomy describes all human bodies, even though (fortunately) not all human bodies have been examined. Even so the surgeon confidently cuts open the body of the patient on the table, fully expecting to find the vital organs to be where Gray’s anatomy says they will be.
Generalization to all cases from individual confirming cases is just one of many inductive strategies. For more, Google "Mill’s Methods of Induction."
"So you have shown us that the falsifiability principle is logically flawed. Why then keep it?"
We should keep falsifiability as a valuable tool of analysis – an "heuristic device" as philosophers like to call it. When encountering a startling claim, it may be helpful to ask: "But what would it be like for your assertion to be false?" And if you can’t answer that -- if your assertion is true for all possible worlds -- then just what are you telling me about the world we live in?
"So why trust science at all if, as you say, it is shot through with logical fallacies?"
First of all, empirical science, qua empirical, is not an exercise in formal deductive logic. Scrupulously formal logic, because it is devoid of empirical reference, tells us nothing about the real world. In other words, formal logic is about "Ps" and Qs" referring to nothing in particular. It is not about fathers, sons and daughters, etc. These familial references cited above "interpret" the hypothetical syllogism. They do not prove validity. This is not to deny that deductive logic is an indispensable instrument in the toolbox of science. In fact, without formal logic (as advanced mathematics) the confirmation of E=mc2 by way of predicting an observed Point X in the eclipse experiment would be impossible, as would, for that matter, Einstein’s derivation of E=mc2. Empirical science is not "illogical," it is "extra-logical" a methodology designed, unlike formal logic (however in conjunction with formal logic), to yield information about the natural world. (See "Hypothetico-deductive method").
Why trust science? The pragmatist has the final word: because it works. As noted in the essay that prompted this response: