Part Of: Philosophy of Science sequence
Content Summary: 900 words, 9 min read

Does science describe the world? Let me frame this foray into philosophy of science as a dialectic.

The Exchange

It is a brisk spring evening, just before sunset. Achilles and the Tortoise are taking their ritualized evening stroll down a winding country road. Their discussions vary wildly, but typically center around some current events or some random bit of science news.

• Achilles comments out of the blue: “Tortoise, I can’t help but notice that you seem to place too much weight in scientific claims.”
• “Do you really doubt the existence of the electron?” the Tortoise counters. “I mean, if particle physics got that wrong, then how could it wield such predictive power?”
• Achilles’ pace slows, as he puzzles over the Tortoise’s reply. “But doesn’t it strike you as arrogant to believe we were lucky enough to be born in an age where science got it right? I would probably credit my skepticism to my reading of scientific history, at watching long lines of scientific theories crumble and fall.”
• Tortoise replies: “Achilles, I have a slogan I like to tell people, to explain my way of thinking. When people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you really think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together.”
• Tortoise continues: “My point is simply that your binary notion of truth must become more subtle. It seems better to say that modern theories (such as general relativity) approximate older theories (like Newtonian mechanics).”

Now,  in case you haven’t heard these arguments before, Achilles is Thomas Kuhn and Tortoise is Isaac Asimov. I have found the appeal to approximation compelling, and so (I submit) do most scientists. However, here is the depth at which most people stop. Let us instead swim further… let us listen more carefully to Achilles.

• Achilles gathers his thoughts. “When you read your textbooks, Tortoise, how many hours do you spend perusing the history section?”
• “Not many, Achilles.” The Tortoise seems neither apologetic nor proud of this fact. “While Tortoises do in fact live for 200 years, my time is still finite. I’d rather let my mind reside near the state of the art.”
• “Of course learning about history is not for everyone, Tortoise… but I have. Consider what it would feel like to read science textbooks from my eyes. Naturally enough, these texts are written by the victors of scientific disputes… but their history sections without fail do violence to the actual thinking of their predecessors.” Achilles’ speech is picking up speed. “Tortoise, if you study history like I do, your nose would smell propaganda, as mine does.”
• Achilles drives his point home: “Shouldn’t this stench give you pause, Tortoise?  Your claim about scientific revolutions approximating their predecessors strikes you as intuitive, but do historians concur? In fact, you stand at odd with the facts of scientific revolutions. General relativity was not conceived as a generalization of classical mechanics. What relativistic concept does the Newtonian concept of simultaneity ‘approximate’? It does not! Consider also the ether. It was not approximated, it was trashed! Your notion of approximation seems misguided, my friend.”

This is the Kuhnian critique of scientific realism. Most philosophers consider the strongest reply to go as follows:

Startled at his inability to defend his vague notions, Tortoise spends the next several months studying scientific histories, and trying to improve his theory of approximation. Spring turns into summer… but then one day, Tortoise feels ready to return to this topic:

• “Achilles, do you remember our conversation about scientific histories?”
• “Of course I do, Tortoise!”
• “Well, It seems to me that you’ve put your finger on something important. I’ve spent time poring over memoirs of past intellectual giants as you have, and I definitely now see what you mean by the ‘smell of propaganda’. But Achilles, I think I’ve noticed something else, something important”.
• Tortoise continues: “When I look at the debates between competing theories, my cherished notion of approximation cannot be resuscitated. But! When I compare the equations of new theories to the ones they replace, I do see an approximation. For example, I cannot recover the Newtonian dogma of flat three-dimensional space, but if I assume the speed of light is infinite, I can recover the Newtonian equation of gravity directly from general relativity.”
• Tortoise concludes: “Achilles, it seems to me that the only continuity in science is in its laws. I will no longer claim to know that electrons are real, or that spacetime is curved. Concepts may not refer. It is only the relationship between concepts, the formal structure of a mature theory, that lasts”.

Condensing The Argument

The above conversation is based on (Worrall, 1989) Structural Realism: The Best Of Both Worlds?. We can compress the above as follows:

1. Realists advance the no-miracles argument: the predictive power of science seems too implausible unless its theories somehow refer to reality.
2. Anti-realists counter with pessimistic meta-induction: previously successful theories have been discarded; who are we to say that our current theories won’t meet the same fate.
3. The approximation hypothesis is where these two arguments connect meaningfully: isn’t it more accurate to call older theories approximations rather than worthless?
4. It is notoriously difficult to describe what “approximation” means.
5. Some realists have conceded that scientific narratives tend to fail, but produce compelling evidence that scientific equations tend to persist. This position is known as structural realism (where formulae structure means more than the meaning of the variables).