In GEB, the protagonists are the Tortoise and Achilles. I think this particular passage is about the french translation that Hoefstader proof-read (as he's fluent in French); the French translator called the Tortoise "she", because "tortue" is of feminine gender so most "tortues" characters are naturally female in French.

Not quite. Achilles and the Tortoise originally came from an essay by Lewis Carroll. Hofstadter had borrowed them for GEB, and in doing so also borrowed their gender -- or so he thought. In reality when he went back to check, long after publication, he realized that Lewis Carroll had left the Tortoise completely genderless.

I dug up the book to check, and in the 20th anniversary preface page 16 and 17, a few lines before the previous quote there is :

"Mr Tortoise, meet Madame Tortue A few years later, a wholly unexpected chance came along to make amends, at least in part, for my sexist sin."

And here comes the French translators part:"[...] they rather gingerly asked me if I would ever consider letting them switch the Tortoise's sex to female."

So I don't see what's the contradiction you're trying to point out.

Then it's probably my mix-up. An extremely similar passage occurs in Metamagical Themas, in which Hofstadter describes a conversation in which he first realized that he may have only assumed that Carroll's Tortoise was male. I've likely confused one with the other.

This I wonder about: do feminine and masculine (and nueter) pronouns indicate gender when used for non-people beings, or must they match the word of those things?

    Ich hab' eine Hase, die wir Hans nennen.

The pronoun is feminine to match the word Hase, even though the hare is male as indicated by his name.

    Oder würde man "Der [die Hase] heißt Hans" sagen?

In french, the article or pronoun must match the word gender too, it's always "une tortue", even if it's "une tortue male". There are often two different words for male and female animals, though: "un lièvre" (male hare), "une hase" (female hare).

Hase, being masculine, is a bad example here.

But cat, Katze (feminine), and dog, Hund (masculine), work. There are versions of these words for the opposite sex, Kater and Hündin, but there are used rarely. So 'Ich habe eine Katze, Felix' and 'Ich habe einen Hund, Bella' would be perfectly acceptable even though the gender of the noun doesn't match the sex of the animal.

> This I wonder about: do feminine and masculine (and nueter) pronouns indicate gender when used for non-people beings, or must they match the word of those things?

In french at least, words themselves have gender irrespective of the subject's gender. And pronouns usually match the word's gender. So a tortoise is feminine even if it's a male, so's a sparrow, a mole, a goat or a stork. Then, there may be subsets of the original word for each of the genders (or further differentiations by age). "Goat" in general is feminine but buck ("bouc") is masculine for instance.

Cf. the so-called Sapir-Whorf Hypothesis / linguistic relativity.

http://en.wikipedia.org/wiki/Linguistic_relativity

Interesting. That also seems to back up my point that languages just make words sound masculine or feminine, even if not explicitly defined like in the Romantic languages (French, Portuguese, Spanish, Italian, others of similar origin). The fact that they are in a footrace seems to suggest they were lifted from their original myths though.

The race between the tortoise and Achilles (or sometimes Achilles and the arrow) is the common illustration of the best known Zeno's paradox: https://en.wikipedia.org/wiki/Zenos_paradoxes