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Popper-Peirce throwdown! (36 Views of Mount CritRat)

Charles Saunders Peirce writes about the methods of science in a way reminiscent of Popper. However, perhaps because he was a working scientist, he places much more emphasis on observation and experiment, making his approach more in keeping with what scientists actually do. I will illustrate by characterizing a particular series of experiments linking the gut microbiome to cognitive decline (in mice!)

About this series

C.S. Peirce

C.S. Peirce (annoyingly, pronounced “purse”) lived from 1839 to 1914. Bertrand Russell wrote in 1959 that “he was one of the most original minds of the later nineteenth century and certainly the greatest American thinker ever.“ Which, from a European, might be damning with faint praise.

He was trained in chemistry at Harvard, where he made an influential enemy, Charles William Eliot. He also offended an influential scientist, Simon Newcomb because he (Peirce) took up with another woman after his wife left him but before they were divorced. The same thing happened to me. The high point of my life was perhaps when I said “Dawn, this is my wife, Joan. Joan, this is my fiancée, Dawn,” and – as I’ve heard both of them say, just leaned back and smiled.

As a result – and because he could be a difficult person (possibly partly due to chronic trigeminal neuralgia, he never got the academic position he arguably deserved. Fortunately, this led him to much practical scientific work, largely for the United States Coast and Geodetic Survey. He got experience with the practical details of measurement of things like local gravity (via pendulums), the orbits of double stars, the brightness of stars, and the shape of the Milky Way.

However, he was an unreliable employee, so for the last 27 years of his life he lived (with his wife) in poverty. He wrote a lot, but not that much was published in his lifetime.

He was the inventor of the philosophical movement often called “American Pragmatism,” popularized (and somewhat distorted) by William James and John Dewey, but that doesn’t figure in this account.

Approaching truth

Peirce and Popper agree that induction (“every swan I’ve seen is white, therefore all swans are white”) is not a route to guaranteed truth. From this, Popper concluded that you must follow his conjectures-and-refutations approach, which also does not deliver guaranteed truth. To my mind, Popper doesn’t explain (in what I’ve read) why his methodology is correct and induction is bad. He merely asserts that his way is rational and other ways are not.

My own thinking is that the practice of looking for counterexamples (refutations) is probably more efficient than just looking for more examples – it’s a way of converging more quickly on what truth we can obtain.

Peirce is also interested in convergence, but he’s more of a social animal: he’s more comfortable with “the mob” (of scientists) being the judge. An example will help. Consider the problem of determining the speed of light. Peirce writes: Philosophical Writings of Peirce, Justus Buchler (ed.), 2001. “How to Make Our Ideas Clear,” p. 38.

“One man may investigate the velocity of light by studying the transits of Venus and the aberration of the stars; another by the oppositions of Mars and the eclipses of Jupiter’s satellites; a third by the method of Fizeau; a fourth by that of Foucault; a fifth by the motions of the curves of Lissajoux; a sixth, a seventh, an eighth, and a ninth, may follow the different methods of comparing the measures of statical and dynamical electricity. They may at first obtain different results, but, as each perfects his method and his processes, the results are found to move steadily together toward a destined centre. So with all scientific research. Different minds may set out with the most antagonistic views, but the progress of investigation carries them by a force outside of themselves to one and the same conclusion.”

At some point, everyone will agree that the speed of light is 299,792,458 meters per second. Except for a few people who dig getting ever more precision, everyone will move on and use the speed of light as a tool.

Peirce describes truth as “the end of inquiry.” You can take that as a mixture of three assertions:

1. Scientists (or people doing inquiry) have as their goal the discovery of truth. (It is the end toward which they’re working.)
2. When all people who are inquiring into the truth of a claim come to agree – and they all move on to something else – we might as well say the claim is true. He allows that people can be stubbornly attached to falsehood: “Our perversity and that of others may indefinitely postpone the settlement of opinion; it might even conceivably cause an arbitrary proposition to be universally accepted as long as the human race should last.” (ibid., p. 39) But he’s inclined to think that honest inquiry will tend to move toward consensus.
3. My metaphor is from the differential calculus: over time, investigation will converge on a limit value – which we might as well call the truth.

Observation and theory

Peirce describes his approach as “fallibilism.” If you have a hypothesis, of course it will likely be wrong, and of course you’d want to put it to some test. But Popper is entirely concerned with how a theory could be logically incorrect (can be used, via deductive mathematics and logic, to make false predictions, whereas Peirce seems most concerned with theories that are incomplete and how observation grows theory.

A simple case is measurement error. Peirce writes:

“In those sciences of measurement which are the least subject to error – metrology, geodesy, and metrical astronomy – no man of self-respect ever now states his result, without affixing to it its probable error; and if this practice is not followed in other sciences it is because in those the probable errors are too vast to be estimated.”

The critical rationalists seem entirely uninterested in measurement error, treating it as something the experimenters should take care of on the way to making their binary confirmed/refuted judgment. So the purpose of measuring spectral lines is to check whether their location fits theory. They do not acknowledge the oddity that such lines aren’t lines but rather bands. They don’t ask “why?” and as a result don’t see how that question has answers that prompt new theory.

A more complex case is given in Peirce’s account of Kepler’s work on planetary orbits. “Abduction and induction” in Philosophical Writings of Peirce, Justus Buchler (ed.), 2001. (archive.org) He chides J.S. Mill for (allegedly) “den[ying] that there was any reasoning in Kepler’s procedure. He says it is merely a description of the facts. He seems to imagine that Kepler had all the places of Mars in space given him by Tycho’s observations; and that all he did was to generalize and so obtain a general expression for them.” – that is, Mills claimed a pure inductive procedure not different from concluding that all swans are white. Peirce claims it required a great deal of non-inductive reasoning.

The problem (as I understand it) was this:

1. The Ptolemaic (earth-centered) theory “agrees with the appearances, although there were various difficulties in making it fit exactly.” Those difficulties required kludges: epicycles and equants.

2. The Copernican theory originally inherited the kludges of Ptolemy. For example, it did not actually put the sun at the center of the universe with everything orbiting around it. Instead, if I understand correctly, it orbited around a central point, as did all planets. (That is, they all orbited around the same point, not a different center for each planet’s orbit. I think.)

3. At that point, Copernican theory could be seen as a mathematical transformation of Ptolemaic theory: one that is purely instrumental, not necessarily true, and not allowing any new predictions. Kepler wanted better evidence for the heliocentric universe than that. He also knew (as Ptolemy did not) that the Sun is much bigger than the Earth: at least 15 times bigger. So it seemed sensible for the Sun to have a stronger causal role in planetary motion – that it wasn’t just one planet of many.

How did Kepler proceed?

1. Because of epicycles (a planet’s orbit is not it moving around a circle, but around a circle that’s itself moving in a circle), each planet has a point where it’s furthest from the center and a point where it’s nearest. Draw a line between the two (“the line of apsis”). Kepler looked looked at the apsides (plural of “apsis”) for the Earth and Mars. “[He] utilized various observations [drink!] most ingeniously to infer that they probably intersected in the sun” (not the center of the sun’s supposed orbit).

2. From this, Kepler thought it reasonable just to put the sun, immobile, at the center. That has consequences for when you take observations to support calculation of an orbit. “Thence it followed that the proper times at which to take the observations of Mars for determining its orbit were when it appeared just opposite the sun-the true sun-instead of when it was opposite the mean sun, as had been the practice.” “Carrying out this idea, [Kepler] obtained a theory of Mars which satisfied the longitudes at all the oppositions observed by Tycho and himself, thirteen in number, to perfection.”

3. “But unfortunately; it did not satisfy the latitudes at all and was totally irreconcilable with observations [drink!] of Mars when far from opposition.” However, it was progress that allowed him to make a leap from the earlier notion that planets sweep out a constant angle per unit time and replace it with the idea that they sweep out a constant area.

   At this point, Kepler was still assuming circular orbits, so I don’t know how angle vs. makes an observable difference if the sun is at the center. Perhaps this is another shift (like from Ptolemaic to heliocentric cosmology) that produces no new predictions but readies you to look in a new direction. A quote from Richard Feynmann comes to mind: Richard Feynman, The Character of Physical Law, 1967, p. 53, emphasis mine.

   “Mathematically each of the three different formulations [of the law of gravitation], Newton’s law, the local field theory and the minimum principle, gives exactly the same consequences. What do we do then? You will read in all the books that we cannot decide scientifically on one or the other. That is true. They are equivalent scientifically. It is impossible to make a decision, because there is no experimental way to distinguish between them if all the consequences are the same. But psychologically they are very different in two ways. First, philosophically you like them or do not like them; and training is the only way to beat that disease. Second, psychologically they are very different because they are completely unequivalent when you are trying to guess new laws.”

   … because:

4. “Subsequently, finding [drink!] that the planet moves faster at ninety degrees from its apsides than it ought to do, the question is whether this is owing to an error in the law of areas or to a compression of the orbit. He ingeniously proves that the latter is the case.”

5. That is, the orbit isn’t a perfect circle. But what is it? An egg shape? Or what?

   “He accomplished [finding that planets move in ellipses] by his incomparable energy and courage, blundering along in the most inconceivable way (to us), from one irrational hypothesis to another, until, after trying twenty-two of these, he fell, by the mere exhaustion of his invention, upon the orbit which a mind well furnished with the weapons of modern logic would have tried almost at the outset.“ “The Fixation of Belief”, in …. p. 6

It’s instructive to contrast this description of the interaction between observation and theorizing with Lakatos' account of Newton’s development of his theory of gravitation. In that case, In the Beginning Were the Words: specifically, Newton’s three laws of dynamics and his inverse-square law for gravitation. Lakatos describes Newton as then applying those laws to a succession of more and more realistic thought experiments. Observation doesn’t play any role in Lakatos' story. It only occurs when Newton is correcting the Astronomer Royal’s observations [spit!] by schooling him on a new theory of refraction. “Thus Newton constantly criticized and corrected Flamsteed’s observational theories. Newton taught Flamsteed, for instance, a better theory of the refractive power of the atmosphere; Flamsteed accepted this and corrected his original ‘data’. One can understand the constant humiliation and slowly increasing fury of this great observer, having his data criticized and improved by a man who, on his own confession, made no observations himself.” I’m suspicious of this account of Newton, given that his Optics was an experimental work full of observation, and given Kuhn claims that Lakatos grossly undervalues experiment in other “rational reconstructions” of science.

Peirce, from my point of view, rings more true.

Abduction

Whereas the critical rationalists treat theory development as a black box, Peirce is interested in the how. His contribution was the idea of abduction (alternately, “retroductive reasoning”). It’s a guideline for reasoning backward from effects to causes. Consider the classical syllogism:

The structure is premise + observation = conclusion. Abduction puts the observation first:

Deductive logic promises that true premises will produce true conclusions. Abduction offers no guarantee, so it must be tested by making predictions and testing them. One prediction might be “Paul, if asked, will answer that he is, in fact, a priest.” Another might be that “Paul understands Church Latin.”

Peirce would approve, I think, of combining these two predictions into a single test, such as asking Paul “Dic mihi: esne sacerdos?” and getting the reply “Ita” rather than “huh?”. In his opinion, it is irrational to work hard on an expensive test when you could do a simpler one and use the time saved to find out more about reality. For this reason, he places less emphasis on predictions being “bold” (surprising if confirmed, having a low subjective probability of occurring), though those are the most interesting (have the highest subjective probability of leading to theory change/growth, more abduction, and further observations that might produce further surprises.

He would also, I expect, not rush to label a “huh?” as a refutation. You might have encountered a priest who didn’t know Latin. (Such are more common today, but I assume there were some even in Peirce’s time.) He would (subject to economics) prefer a variety of different tests (beyond straight replications) because those are more likely to add up to something we can agree is likely enough to be true that it’s safe to depend on it while doing further science.

The critical rationalists, it seems to me, long for the certainty of deductive logic, know you can’t – alas – get that sort of certainty from science, and but have

Him as observer…

End with Popper quote. Contrast with Peirces “it’ll all work out eventually”. The crit rats like having enemies.

Unlike the critical rationalist, Peirce cares greatly about the expense of testing, arguing that using an expensive/difficult test when a simple one would do is wasting time that should be used to find out more about the universe.

it’s downright irrational to use an expensive/difficult test when a simple one would do. Given there’s a vast universe of facts left to uncover, you have to consider the opportunity cost of testing:

Priests (in Peirce’s time) all knew , so a testable prediction is “Paul will understand

required some kludges (epicycles and equants) to make it fit the observational evidence.

• Ptolemaic theory The difficulties came down to the philosophical requirement that all planets move in circles, sweeping out the same angular distance per day. But that’s absolutely not what we see from our perspective at the

  One difficulty is that the planets do not move steadily around the earth, covering the same angle in each day. The angular velocity changes – from Earth’s perspective, Mars even sometimes moves backwards. Because of the philosophical assumption that everything to do with orbits must be perfect circles, this required epicycles: Mars orbited around the center point of a circle, and that center point itself orbited around Earth. The margin picture shows that (and more).

  The “more” is required because that still wouldn’t work. Another philosophical requirement was that a planet

For the numbers to work out, the planets would still have to move with different angular velocities at different times. That, for philosophical reasons, wasn’t allowed. So, in what seems a massive kludge, another “center” is added to the circle, called the “equant.” The center of the epicycle moves in a perfect circle

• At the time of Kepler, there was not the notion that the sun was motionless at the center of everything. Rather, (I think), the sun moved in a circle, and the planets revolved around that in such a way that it cancelled out the motion of the sun. “Now this hypothesis, as Copernicus himself understood its first outline, merely modifies the theory of Ptolemy so far as [to] impart to all the bodies of the solar system one common motion, just what is required to annul the mean motion of the sun.”

the Ptolemaic assumptions that (a) planets move in circles and (b) they move at a constant speed along those circles, he accepted epicycles. (They’re necessary to match apparent changes of speed as observed from earth.) The picture to the right shows a Copernican version of the orbits of Mars and the Earth. (Click to enlarge.)

2. Because he knew (measurement! drink!) The military historian Bret Deveraux usually adds “drink!” after he mentions Clausewitz, the implication being that such mentions happens so often it’s like a drinking game in a bar, one in which you’re likely to end up hammered. Example. Example. Example. See also: buzzword bingo. that the sun was at least 15 times the diameter of the earth, it seemed plausible it had some causal connection to the rotation of the planets.
3. He was starting from assumptions that

That makes an interesting contrast to Lakatos’s account of Newton’s work on gravitation.

That sort of thing smacks of reasoning to theory via inductive arguments, which is not good behavior.

Observation

The development of tests is somewhat different from Popper’s. Popper approaches the development of a test by first requiring a prediction (a more specific truth-valued statement logically/mathematically derived from the abstract theory under test), which is then tested to yield a “confirmed” or “refuted” answer. A good prediction is one that has, in what has to be a subjective judgment, a high probability of being wrong (which Popper characterizes as a “bold” prediction).

Peirce advocates for observation as a way to determine where a theory is weak, but not just that. His regard for observation as a driver for creativity is perhaps his greatest difference from the critical rationalists.

For example, Popper rarely (if ever) speaks of using a collection of observations as the inspiration for a theory. That smacks of induction, and he is dead set against induction. In contrast, Peirce lauds Kepler for his blending of observation, induction, and intuition.

Peirce – as a professional observer – centers the act of observation over a more abstract prediction. The designer of an observation or experiment asks “What could I measure that would provide the most information about what’s wrong with the theory?” This shifts some of the creativity of science toward