Bridging syntax and semantics with Quine’s Gavagai

Quine has an ar­gu­ment show­ing that you can never be sure what words mean in a for­eign lan­guage:

Quine uses the ex­am­ple of the word “gav­a­gai” ut­tered by a na­tive speaker of the un­known lan­guage Arunta upon see­ing a rab­bit. A speaker of English could do what seems nat­u­ral and trans­late this as “Lo, a rab­bit.” But other trans­la­tions would be com­pat­i­ble with all the ev­i­dence he has: “Lo, food”; “Let’s go hunt­ing”; “There will be a storm tonight” (these na­tives may be su­per­sti­tious); “Lo, a mo­men­tary rab­bit-stage”; “Lo, an un­de­tached rab­bit-part.” Some of these might be­come less likely – that is, be­come more un­wieldy hy­pothe­ses – in the light of sub­se­quent ob­ser­va­tion.

What does this mean from the per­spec­tive of em­piri­cally bridg­ing syn­tax and se­man­tics?

Well, there is no real prob­lem with “gav­a­gai” from the em­piri­cal per­spec­tive; the fact that there seems to be one is, in my view, due to the fact that the syn­tax-se­man­tic dis­cus­sion has fo­cused too heav­ily on the lin­guis­tic as­pects of the prob­lem.

Let be the sym­bol in the Arunta speaker’s brain that ac­ti­vates when they say “gav­a­gai”. As Quine said to­wards the end of his quote, “some of these might be­come less likely – that is, be­come more un­wieldy hy­pothe­ses – in the light of sub­se­quent ob­ser­va­tion.” Re­lat­edly, Nick Bostrom ar­gues that in­de­ter­mi­nancy is a “mat­ter of de­gree”.

In prac­tice, this means is that if, for in­stance, r=”A rab­bit is there” and s=”A storm is com­ing tonight”, then, if we ac­cu­mu­late enough ob­ser­va­tions, the is go­ing to be pre­dic­tive of bet­ter than it is of , or vice versa. Thus there is an em­piri­cal test for whether cor­re­sponds to some of these hy­pothe­ses.

But what about u=”An un­de­tached rab­bit-part is there”? It may be very difficult to find a situ­a­tion that dis­t­in­guishes be­tween u and r in prac­tice—so does stand for “rab­bit”, or “un­de­tached rab­bit-part”?

Similarly to the ex­am­ple of the neu­ral net in the pre­vi­ous post, is a sym­bol for both r and u. If no ex­per­i­ment can dis­t­in­guish be­tween the two—or, at least, if no ex­per­i­ment can dis­t­in­guish be­tween the two in any typ­i­cal en­vi­ron­ment that any Arunta speaker would ever ex­pe­rience—then they are syn­ony­mous (or, equiv­a­lently, they are strongly within each other’s web of con­no­ta­tions).

If we pre­sented the speaker with a situ­a­tion far out­side their typ­i­cal en­vi­ron­ment, then we might be able to dis­t­in­guish r from u—but we’d be un­cer­tain if ‘meant that all along’, or if the speaker was ex­tend­ing the defi­ni­tion to a new situ­a­tion.

Back to linguistics

There are some ways we might be able to dis­t­in­guish whether “gav­a­gai” means “rab­bit” or “un­de­tached rab­bit-part”, even if u and r can­not be dis­t­in­guished in prac­tice. It’s plau­si­ble that there might be an in­ter­nal vari­able in the speaker that cor­re­sponds to “part of an an­i­mal”, and an in­ter­nal that cor­re­ponds to “un­de­tached” (ver­sus de­tached).

Then, when is ac­ti­vated, we might ask whether and are also ac­ti­vated, or not. You can see this as the in­ter­nal web of con­no­ta­tions amongst the vari­ables in the hu­man brain. It seems peo­ple with differ­ent lan­guages have differ­ent in­ter­nal webs, differ­ent ways of con­nect­ing words and con­cepts to­gether.

This does not, how­ever, af­fect the con­nec­tion be­tween and ex­ter­nal vari­ables.

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