Keith’s Conundrums: Is Science Real?

Keith Douglas

Last time, I received a joke from Alex B, a mention of what is called the “infinite monkey paradox”. I’ll analyze that one some other time; we’ve talked about similar puzzles in the past. (It is more or less similar to some aspects of Hilbert’s Hotel.)

I got a request from Steve Watson to write a column on the so-called pessimistic meta-induction and its somewhat dual argument, the “no miracles” argument. These are problems in the philosophy of science, and I’m pleased to take them up with everyone, and will do so after I deal with his first comment. It is true that heliocentrism vs. geocentrism can be looked at as a relativity of wrong question, a topic we will allude to in due course. However, there’s actually a better answer: I told the reader that I was going to pull the hair out of experts. This particular item is one place where it matters: acceleration is complicated, and “not all motion is relative” in the sense I glibly used it. In fact, in special relativity (not general), acceleration is an invariant, and in GR, it is too complicated for me to adequately explain (I run the limits of my understanding when I see it discussed). Einstein himself warned against the “everything is relative” misunderstanding – saying he should not have agreed to the name “relativity theory” – it should rather be called “the theory of spacetime invariants” instead, because it is even more about what is not relative.

On to the pessimistic meta-induction:

(Warning: the Wikipedia article here is pretty lousy. Also note that I’ve written in the timeless present, as if all parties are alive.)

The argument, supposed to be against a scientific realist, is due to Larry Laudan. Supposedly, the realist is committed to the idea that our presently successful theories are true or approximately true. However, we know from the history of science that successful theories of the past turned out to be false, so shouldn’t we be pessimistic about current theories? I consider myself a scientific realist¹, and use the terminology in more or less one of its standard ways, so our first problem is what the realist claims. Speaking sloppily (see the next item), we realists do not hold that current theories are true (more on “approximately true” later). Rather, the proper claim is that they are truth apt. If one reads what the antirealist claims, they either change the subject (whether justifiably or otherwise) to another non-correspondence notion of truth (e.g. Michael Dummett) or regard theories as calculational devices only (or other forms of instrumentalisms²). Sometimes this instrumentalism has a restricted scope: Pierre Duhem thinks one should be a realist in chemistry but not in physics. Bas van Fraassen thinks that somehow what is accessible directly through the senses can be theorized in truth apt ways, but once an “instrument” is needed³, theories become for calculations or “predictions” with no understanding that these are explanatory or reflect what is going on.

The second problem I see is that theories have no truth values if “theory” is used in the stronger way. Some authors, by contrast, use “theory” to be more or less synonymous with “hypothesis”⁴. They can use terminology however they want, but as we will see, a system of hypotheses is very different from an isolated one. 

A third is what Steve W. alluded to last time, which is the relativity of wrong. Another SW, the physics Nobel Laureate Steven Weinberg, has claimed that there has been one and only paradigm shift in physics and consequently all physics since Galileo is basically building upon itself. So Galileo is wrong, yes, but he’s more right than Aristotle, and Newton is more right than Galileo and Einstein than Newton and so on. For individual hypotheses, there are even theories of partial truth (Bunge worked on this, for example – and Popper worked on less successful versions⁵) as such. We then see that the partial truth of hypotheses and their consequences generally increases over time. There are exceptions at various times; sometimes two theories in the same domain cover now this aspect, now that, of the objects of study. The famous “wave-particle duality” is a historical example. One has to then investigate whether or not this sort of matter applies to the scientific area in question. It is in general plausible at first glance that different fields would be subject to different outcomes of the metainduction. 

Before I address the next way to see beyond the metainduction, I would like to address one complaint about what I’ve said here so far, preemptively. (The rest I will leave for responses to critics in the comments.) Fans of Kuhn might think that the comparison done with the relativity of wrong idea (and I’ve done one version – see also Asimov, where I borrow the phrase from) is itself misreading the history of science, that the views were not comparable and so we cannot even say that one is more or less correct than other, as they are in some sense about “different things”. It is notoriously hard to figure out what Kuhn was on about, and the late Susan Haack⁶ has pointed out that he and others have said something and also “taken it back”. However, I believe (and in the interest of the shortness ideas I keep to in these columns) that Kuhn’s strongest version is one that could matter here, and that version is provably wrong. Something cannot be both incomparable and about the same subject – Aristotle’s work on falling bodies is about falling bodies, and so is Galileo’s. This is formally provable in Bunge’s theory of reference, which was created in the 1970s to refute Kuhn and Feyerabend and other “meaning change theorists”. 

Weaker versions exist, and I believe that these can be handled in the discussion. Meanwhile, read Brock (The Norton History of Chemistry) or Kitcher (The Advancement of Science), for example) on Lavoisier, and how this plays out. Note that Brock will not address Kuhn directly – one can use the materials he presents to help, however.

Fourth, we have what I’ll call consilience, a term introduced into the philosophy of science by the 19th-century historian and philosopher of science, William Whewell, and more recently (1998) popularized by E. O. Wilson. I will ignore whether Wilson gets Whewell exactly right (he arguably doesn’t) and go with something like the common idea. This is that if many hypotheses lead to the same conclusion, we should be more confident in the matter. For example, there are many ways to traditionally measure the so-called Avogadro constant, and they all more or less come out the same. This suggests we are latching onto something important.

However, there’s a fifth and related matter that makes that previous example problematic. These are the standards for (SI) units that reflect our best theoretical understanding – or try to. Consequently, certain items which used to be hypotheses get enthroned into units. To use another example – the case of the Avogadro constant is parallel – one cannot now measure the (vacuum) speed of light, exactly. The speed of light is assumed constant, and one is really checking how long the meter is!

(History of philosophy aside: Wittgenstein argued that the standard meter (which existed before the decision about the current standards) was the only object in the world for which one cannot say that it is greater or less or equal to a meter in length⁷. Now one can, if one wants to use the platinum bar and etchings that Wittgenstein used as a “standard”.)

This is related to the sixth matter, convergence. This is very much related to consilience and was written about at great length by Bunge in 2003. As so understood, convergence is what happens between disciplines that were previously disjoint and now share referents: for example, immunology joins with neuropsychology (already a converged discipline) and endocrinology, to form his favourite, psychoneuroendocrinimmunology. The idea here is that because the fields start sharing a reference, they form a greater web of mutual support. Those who know “Quine’s web of belief” may hear echoes of that; Bunge’s notion is in a way more social, as it does not take place in any one brain. There is a final aspect to consider, which is alluded to in Steve’s bit about the “no miracles” argument. This is that it would be massively unlikely that a complete falsehood would result in any success at all. This is often poo-pooed as a response, with the pessimist claiming that ‘surely phlogiston has no truth to it’. I think this dismissal can be responded to my 3rd  category, but I’ll leave it at almost that for now. However, I am also somewhat worried that this can be taken another direction, which I think requires the “relativity of wrong” answer to work. Take, for example, approximations. If one calculates the period of a pendulum (say), the simplest model of this system includes idealizations that make the calculation approximate. These include (amongst others) that the acceleration due to gravity is constant, that the mass of the bob is all that matters (not of the string), the string does not stretch, there is no air resistance (so also that the string is “thin” and the bob very smooth and spherical), and that the amplitude of swing is “small”. In spite of all of that, one can calculate very accurately, in certain contexts, the period of the pendulum. So, yes, the anti-realist critic is right – that this is a nest of falsehoods, allowing a correct prediction – for a while. However, the critic does fail to notice the relativity of wrong, as stated. Try making a prediction using Aristotle’s physics! (One simply can’t.⁸) But she also fails to notice something further. I’ve enumerated – because developing the model for the calculation requires it, or at least makes it easier to see what they are – the areas where quite possibly the model breaks down. Take the small amplitude of swing – this is my favorite because it is not a physical idealization in the same ways others are.

In this model, a more careful model makes use of the sine of the angle of swing, but this makes solving the resulting differential equation much harder, so we use the “small angle approximation”, i.e., that sine theta is roughly theta when theta is “small”. This is not like the others – we’ve ignored, by contrast, the fact that acceleration due to gravity is not constant, which then in turn leads to a simplification of the equation. Can you imagine finding a situation where you’d have to use Newton’s law of gravitation to find the period of a pendulum, never mind general relativity?⁹ 😊 I am somehow reminded of my realization that Douglas Adams’ joke about the way a human can fly is to throw themselves towards the ground and miss – is actually describing, sort of, how orbits work!

Anyway, enough for now – as stated, I am being very elliptical and look forward to lots of reaction. This is a conversation starter, not a paper. 😊

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1. Hereafter, I will always use “realist” to mean “scientific realist”. There are other kinds, and I am not, for example, a mathematical realist. ↩︎
2. I am not going through at all the various antirealist positions here. Another time, perhaps. ↩︎
3. At the Nagel Lectures I attended while at CMU, a fellow graduate student asked him if this entailed that anyone wearing glasses has to be antirealist about what is seen through them. “Yes.” This should strike people as very odd, in my view, and shows a clear problem with a “dividing line instrumentalism”. A sorites style paradox almost looms here, for one thing. ↩︎
4. In mathematics and most mathematicised fields, a theory is what it is in (most) logic, which is a set of elements (called propositions, sentences, whatever, depending on the logic) closed under a consequence relation. ↩︎
5. Almost all theories of partial truth assume that v(~p) = 1-v(p), which is likely wrong and where they traditionally founder. Bunge has one (vol. 5 of the Treatise on Basic Philosophy) that does not do this – it, however, makes the theory of truth not truth functional, alas.… ↩︎
6. Next month I might do an honouring-Haack column (she died a few weeks ago at the time of writing). Any thoughts, folks? ↩︎
7. Logicians will spot that Wittgenstein holds that there are truth value “gaps” here! ↩︎
8. It is not, however, true, to say that there were no exact factual sciences in antiquity – there were: astronomy, geometric optics, and eventually statics (Archimedes). ↩︎

9. This hides a very interesting question that in my view the antirealist cannot answer: “Why would you want to complexify a theory?” Incidentally, this comes up in the context of Ptolemaic astronomy. Ptolemy is not an anti-realist, contrary to some presentations, however. Maybe sometime I’ll do a “myths in the history of the philosophy of science” column. 😊 If you are reading this you may wonder about Duhem on chemistry – thanks to B. Wray 25+ years ago for reminding me of this one!