“It’s turtles for quite a way down, but at some point it’s solid bedrock.”

Just once, I’d like to hear the above expression..

It can’t always be turtles all the way down, right? Cos if it was, we wouldn’t need the expression. Kind of like if everything was red, we wouldn’t need any words for colors.

1. Jonathan (another one) says:

Recursion.

• Don Baccus says:

Unbounded vs. bounded recursion. Regardless of any role a turtle might play.

2. Andrew (not Gelman) says:

So you’re a Wittgenstein person rather than a Quine person? “If I have exhausted the justifications I have reached bedrock, and my spade is turned. Then I am inclined to say: ‘This is simply what I do.'” (PI 217)

And all shades and textures of red are the same, so we’d just need the one word? Much as “brown” is all I need to describe the colour of my tea, coffee, dining table, and rug.

• Andrew (not Gelman) says:

But, what would solid bedrock look like? As I see it all explanations depend on unquestioned assumptions that seem more obvious than the thing to be explained. “Why did the car crash?”. “Because the road was slippery”. “Why was the road slippery?” “Because it had been raining”. “And are all surfaces slippery when wet?”? No. “So why was that particular surface slippery when wet?” Because molecular structure??? And why is the molecular structure that way? Turtles, eventually.

And don’t get me started on “the” cause of something.
The cause of the crash was the fact that the driver was drunk.
The cause of the crash was the fact that the road was slippery.
The cause of the crash was the fact that the camber on the road was too steep.
The cause of the crash was that somebody pulled out suddenly without giving the driver time to stop

All of the above could be true, so probably not just the one turtle, even if you believe the buck stops with them.

3. Having turtles all the way down is unique. There are many ways for a stack of turtles to end, in contrast — bedrock, a molten core, a black hole at the center of the turtle galaxy, a secret lair in a sewer, etc. Too many possibilities for a simple, catchy expression.

4. Ian says:

They must be fractal turtles.

5. Eric says:

I think it something to do with the distribution of heirarchical structures in nature. In practice, if you are given a natural hierarchy, it will either have a “few” levels til it reaches the bottom level, or it will be recursive, and therefore, countably infinite.

For example, consider an animal food chain. We might ask: if we descend from predator to prey, when do we reach vegetation (aka the bottom level of the hierarchy). Perhaps in some environments, the chain can become quite convoluted. But I doubt it extends past, say, twenty animals.

So in order for the phrase, “It’s turtles quite a way down, but it reaches bedrock” to be applicable, you would need a pseudo-recursive structure: one that naively looks infinite, but actually terminates at some large integer value. I would conjecture that such structures are actually quite rare, so they are outside of normal human intuition.

6. Renzo Alves says:

Although I can’t quite recall where, Bertrand Russell cited William James for this. Williams James asked a woman what the turtle was standing on (she had previously claimed that the earth was supported on the back of a turtle), after a couple iterations, she told him “it’s no use Mr. James, it’s turtle all the way down” (to the best of my recollection.) It was an obvious reference to the argument that God made everything but wasn’t herself made by anything (and the obvious follow-up, if God didn’t need to be made, why did everything else?) Indeed everything is the way it is because it is the best way to be in the best of all possible worlds (according to Leibniz, parodied by Voltaire.)

7. Joshua says:

Eventually the turtles at the bottom die, decompose, get compressed under enormous pressure, and form bedrock.

8. Carlos Ungil says:

So below the elephants and the turtles it’s rock all way down?

That’s funny, because according to wikipedia: “The exact origin of the phrase is uncertain. In the form “rocks all the way down”, the saying appears as early as 1838.”

9. Mendel says:

Maybe it’s better to say, it’s space all the way up?

• Andrew (not Gelmanj says:

Yah. Space. Deffo. Innit. Just curiious whethther there’s a fact of the matterr.

10. “There is some solid bedrock at some point, but after that it’s turtles all the way down”

11. John Richters says:

… the bedrock is a slippery slope.

12. Ben says:

It could be turtles arranged in a circle. Or like some sort of turtle ringworld.

I Googled the expression and was surprised that the idea more the turtles are getting bigger (you find under one turtle, another larger turtle: https://en.wikipedia.org/wiki/Turtles_all_the_way_down).

I always thought of this like nested dolls, so like there was a little turtle in the big turtle, etc.

13. Andrew writes:

It can’t always be turtles all the way down, right? Cos if it was, we wouldn’t need the expression.

From a set theory point of view, you want to think about ordinals vs. cardinals (set theory 101). There are all sorts of non-isomorphic orderings of a simple countably infinite set. For example, the naturals and positive rationals have the same cardinality (also set theory 101), but are not isomorphic orderings; same for two copies of the naturals laid end to end (a second stack of turtles where the uppermost turtle on the second stack is lower than the lowest turtle on the first stack).

From a linguistics point of view, I don’t understand your argument. We use idioms when they’re relevant, not in variations for every possible application. Don Baccus nailed the operative distinction of when we apply it (unbounded recursion). Not every expression does double duty. For instance, the expression “it’s raining cats and dogs” for hard rain doesn’t have an alternative form “raining hamsters and gerbils” for less strong rain.

• Yup, it’s simply all semiotics but semiotics ain’t simple ;-)

My immediate interpretant of “turtles all the way down” is don’t expect a satisfying answer.

14. michael schwartz says:

Isn’t this just Thomas Aquinas and the Unmoved Mover all over again?