Good question. This is how I understand why içeriyi is used instead of içinde. In this sentence, içeriyi is serving as a noun and is the direct object of "görüyor" (to see). Therefore, it is in the accusative case -- içeri + i (plus the buffer "y") = içeriyi. It's a bit strange to me because in English "inside" in a sentence constructed like this would simply be an adverb. I wonder if "Yaşlı kadın içeri görüyor," wouldn't also be an acceptable translation of "The old woman sees inside."
I am also reminded of a couple of other sentences in this lesson:
"İçeriye gel ve çorba iç." [Come (to the) inside and drink soup.][ içeri + buffer y + e (to maintain vowel harmony)]
Dışarıya gel!" [Come (to the) outside.][ Dışarı + buffer y + a (to maintain vowel harmony)]
In the two examples above, "inside" and "outside" are nouns in the dative case because the meaning is slightly different from “The old woman sees inside,” but I thought it might be helpful for you to see the comparison.
You, however, specifically asked, "Why is it not içinde?" so I want to address that. In examples we have been given where içinde is used, it is similar to the English "prepositional phrase." Because the order of such phrases are reversed in Turkish they call them "postpositional phrases." They consist of a postposition (e.g., in/inside, out/outside, behind, under, …) preceded by a noun. It gets a lot more complicated than that, but for now, let's go back and take a look at some examples found in duolingo's lessons.
Şeker kahvenin içinde. (The sugar is in the coffee.)
Çilek şekerin içinde. (The strawberry is in the sugar.)
In both of the sentences above, the postposition içinde (in/inside of) is preceded by the second part of the phrase -- coffee in the first example and sugar in the second. In English we would call these nouns the "object of the preposition." Genitive case is applied to the noun that links to the postposition because içinde is one of the postpositions that uses a postpositional phrase in this way [için (for) , gibi (like), kadar (up to/until), and ile (with) are others]. So, therefore, we get a sentence construction as the one used in the two sentences above. Kahve becomes kahvenin, şeker becomes şekerin.
My source for some of this information is a resource I think is particularly good. It is called Turkish: A Comprehensive Grammar. You can link to it here: https://goo.gl/2pIUhl.
There's been a few posts that kind of touch on this topic, but sometimes more information can just be more confusing. You can click on the "Discussion" tab and search for any topic you'd like there. It helps if you type in the Turkish word, but if you prefer to use English instead, it might help to also type "Turkish" to limit your results to this language. You may already be doing that, and if so, please just disregard my attempt to be helpful, but if not, you might find it useful.
In the grammar book I refer to in this post, the authors have written “the boundaries between noun, adjective, and adverb are somewhat blurred” in Turkish. Somehow having read that makes trying to learn Turkish a bit less frustrating. Knowing is half the battle, right?
Hope this helped in some way.
Glad you appreciated it. Not sure why it was included in this lesson on postpositions. My guess is that someone wanted to show us that a postpositional/prepositional word can also be a noun. I don't think there are a great many of them and in fact, when I go to Tureng's online dictionary, "içeri" as a noun actually means "within."
Be that as it may, I found two other "postpositional" words that also serve as nouns -- beyond and outside. Applying this same example to them, you have
Yaşlı kadın öteyi görüyor. (The old woman sees beyond.)
Yaşlı kadın dışı görüyor. (The old woman sees outside.)
Anyway, thanks again for expressing gratitude and best wishes with your study of Turkish.
Based on the nice and intricate answer above, I am inclined to think that this is one of the beautifully poetic and philosophical phrases that color the Turkish language.. Like, the old woman sees inside - in terms of.. she sees that the inside is more important in a person than the exterior? Which would explain the specification of the woman being old; wisdom comes with age and such?
I'm just guessing here though.
I think that would be a different verb. "Görmek" is seeing; "bakmak" is looking. Really, it's an odd sentence. I always get it wrong because I picture an old lady peeping in someone's windows ("looking inside"), but really she is seeing the inside of something. If I would pay attention to the verb (to see not to look), I would get it right because when you see something it should take the accusative.
But the English sentence is, "The old woman sees inside." Doesn't that indicate she's looking at an x-ray or something? She can't see the guts, but she can see all the ball bearings that dude swallowed. If the old woman were a knife weilding maniac, litterally looking at people's guts, then the English sentence would have been, "The old woman sees the insides." and then inside would go in the accusative.
Oh, I see what you mean (sorry AboAyman if that's what you meant as well and I misunderstood)...
I do like your suggestion that this could be metaphorical... It brings to mind an image of an old woman who sees inside my soul while she's reading my fortune at the bottom of my coffee cup. Haha!
Or it could be more mundane, as in: she sees the inside of her fish tank (because she's finally cleaned the glass).
I completely agree that "looking inside"/"içeriye bakıyor" is more likely to be used in most contexts.... But this could just be Duo's way of introducing us to "içeriyi" as a comparison to "içeriye". :-)
Continuous present verbs in Turkish end with -iyor + personal ending (and the "i" changes for vowel harmony). So "görüyorum" is specifically 1st person ("I am seeing"), and görüyor is 3rd person ("he/she/it is seeing").
However in English, "to see" is usually treated as a stative verb, so we translate it as simple present: "I see", "she sees", etc. If we use continuous present (ex. "I'm seeing things"), it has different connotations, as though what I'm seeing isn't really there (at least where I'm from!)
But neesha64 was pointing out that maybe this difference in connotation isn't as distinct in the UK, which I'm not qualified to comment on :-)