If someone wants to make a prohibition on himself from eating apples and has some apples in front of him and uses a language of "konem" in his neder and says "these apples" then they become forbidden (Shulchan Aruch YD 216:1). What about if the person says something along the lines of "konem alei" (it should be forbidden to me) the "thing that I know" and has in his mind at that moment apples (even though he doesn't speak this out specifically in the language of the neder.) Are the apples still forbidden?
We have a concept that if he merely indicates a Neder, and it is Not clear because it is lacking both verbal expression, and visual indication, is not a Neder.
Source Nedarim 6a; where the Ran says on that Gemoro.קיימא לן כרבא: ידיים שאין מוכיחות לא הוויין ידיים we hold like Rovo that an indication of a Neder which has no clear meaning to other people is not a neder.
The Gemoro in Kiddushin 5b says (with explanation of the Ran): (קידושין ה ב) אמר שמואל האומר לאשה, "הרי את מקודשת", "הרי את מאורסת", הרי זו מקודשת. וכן בגרושין, "הרי את מגורשת", "הרי את מותרת לכל אדם", הרי זו מגורשת.
ומקשינן התם: "למימרא דסבר שמואל ידיים שאין מוכיחות הויין ידיים"? כלומר: מדקאמר הרי זו מקודשת אף על גב דלא אמר "לי".Says Shmuel: Someone who says to a woman "You are betrothed"(with money) she is betrothed to him, and when he divorces and says to his wife "you are divorced," she is divorced from him (with a get). The Gemora asks: Surely Shmuel Holds that a Yad Sheeino Mochiach (indication which is unclear), is not a Yad? i.e He never mentioned that the woman was betrothed or divorced "to/from me." This is a lack of indication.
ומשני, הכא במאי עסקינן, דאמר לה "לי". אלמא שמואל גופיה סבירא ליה דידיים שאין מוכיחות לא הויין ידיים. The Gemora answers that Shmuel meant that when he is betrothing/divorcing his wife, he says: "you are betrothed divorced To/from me" which is a clear Kiddushin/geirushin. Therefore a Yad Sheeino Mochiach (indication which is unclear) is not valid(for a Kiddushin/get) or binding (for a neder)
We see that its considered a "Yad Sheeino Mochiach" (indication which is unclear) even with the mention of "Kiddushin" or "Geirushin," and She is not married/divorced to/from him, because He never said "You are Betrothed/divorced to/from me"
So too in our case where he says Konam alai and merely thinks about what he wants to prohibit on himself, even though he Mentioned "Konam," since he didn't indicate at all what he is referring to, it is called a Yad Sheeino Mochiach (indication which is unclear), and the Neder would not be binding.
However lets say apples were in front of him (I'm not sure if the questioner is talking about this situation), and he said "Konam alai", if the people around see that he is clearly referring to the apples e.g there is no other fruit in front of him, even though his words have no clear indication by themselves, the fact that an exterior factor (i.e the apples in front of him) indicates clearly what he means, this would be considered a Yad Mochiach (clear indication) and the Neder will be binding.
This is clear from the continuation of the Gemoro kiddushin 5b: והתנן: האומר "אהא", הרי זה נזיר. והוינן בה: ודילמא אהא בתענית קאמר? ואמר שמואל: כשהיה נזיר עובר לפניו; דמשמע דהא לאו הכי, הוו להו ידיים שאין מוכיחות ולא הויין ידיים. We have a Mishna That say :A person who says "I will be" He becomes a Nazir , But surely this is a Yad Sheeino Mochiach (indication which is unclear), since "i will be" could be referring to "I will be fasting." Therefore Shmuel explains in this case, he is saying "I will be," whilst a Nazir is walking in front of him. Therefore it is clear to everyone he wants to be a Nazir (and he doesn't want to fast).