1) ONE WHO REMEMBERS SHABBOS BUT FORGETS ALL THE MELACHOS
QUESTION: The Gemara says that it is not possible to forget every Melachah of Shabbos and still know that it is Shabbos. Why is it not possible? One can remember the Mitzvah to recite Kidush and Havdalah, or the Mitzvah of Oneg Shabbos, or he can remember the Mitzvas Aseh to rest on Shabbos ("Shabason," see end of 24b). In that way, he remembers Shabbos but forgets the Melachos.
(a) The RITVA explains that the Mitzvos of Oneg and the recitation of Kidush and Havdalah are not the essence of Shabbos. Rather, the purpose of those Mitzvos is to remind us of the prohibition of Melachah on Shabbos. Therefore, when one remembers those Mitzvos but does not remember the Melachos, he is not considered to have remembered Shabbos at all.
This explanation does not answer why one who remembers the Mitzvas Aseh to rest on Shabbos is not considered to have remembered Shabbos. (TOSFOS (DH d'Yada) leaves this question unanswered.)
(b) The Ritva answers further that Reish Lakish maintains that just as one's transgression of Shabbos is not considered b'Shogeg (unintentional) when he has knowledge that Melachah on Shabbos is prohibited by a Lav (even though he does not know that it is also prohibited because of Kares), so, too, when a person knows that there is an Isur Aseh not to do Melachah on Shabbos (a Mitzvas Aseh which manifests itself as a prohibition), he is also considered as one who transgresses willfully. Since the Gemara is looking for a case which even Reish Lakish will consider a case of Shogeg, it must be that the person does not know that there is any prohibition of Melachah on Shabbos, even a Mitzvas Aseh.
(Tosfos and the other Rishonim who do not suggest this answer apparently disagree with the Ritva's assumptions.)
2) STRANDED IN THE DESERT
QUESTIONS: The Gemara concludes that a person who loses track of the days of the week while wandering in the desert must count six days and observe the seventh as Shabbos. However, since every day of the seven days that he counts might be Shabbos, on each day he is permitted to perform only Melachos that are necessary to keep himself alive. The seventh day of his count is unique only in that he recites Kidush and Havdalah on that day.
The VILNA GA'ON finds a hint to this Halachah in the verses of the Aseres ha'Dibros regarding the Mitzvah to observe Shabbos. The verses state, "Six days you shall work, and you shall do all of your work, and on the seventh day you shall rest for Hash-m your G-d; you shall not do any work..." (Shemos 20:9-10).
The Vilna Ga'on asks three questions on these verses:
Why does the Torah need to tell us not only to rest on the seventh day, but also to work on six days?
Why does the Torah stress that during the week we must do "all" of our work?
Why does the Torah stress that on Shabbos we must not do "any" work?
ANSWER: The Vilna Ga'on explains that these verses teach more than the commandment to "observe" Shabbos. They also command us to remember ("Zachor") what day is Shabbos.
Accordingly, when we remember what day is Shabbos, we will be able to perform all of our work, and not just the bare minimum necessary for life.
Similarly, when we remember what day is Shabbos, on that day we will be able to rest from all forms of work and will not have to do any work, not even work necessary for life. (KOL ELIYAHU, Parshas Yisro, #63)
3) RECITING BLESSINGS ON A DAY WHICH IS IN DOUBT
QUESTION: The Gemara says that a person who does not know what day is Shabbos should not do any Melachah on any day, except for Melachah which is absolutely necessary for his survival. He should count six days, and on every seventh day, he should recite Kidush and Havdalah in order to remind himself of the concept of a seventh day being designated unique as Shabbos.
However, if that day is not really Shabbos, why is he permitted to recite the blessings of Kidush and Havdalah?
(a) The RITVA first explains that when the Gemara says that one should recite these blessings, it means that one should recite them without Hash-m's name.
(b) In his second answer, the Ritva says that since the Isur of Berachah l'Vatalah, reciting a blessing in vain, is prohibited mid'Rabanan, in this situation the Rabanan permitted it for Kavod Shabbos.
(c) The RADVAZ (1:76) says that when the Torah commands us to observe Shabbos, the Torah requires only that we observe one day out of seven as Shabbos. That day does not necessarily have to be "Saturday." However, since the people in any given area have accepted upon themselves a certain day to be observed as Shabbos, that day becomes Shabbos in that place, and thus a person who does not observe Shabbos on that day would be Chayav Sekilah. In a desert, no day has been established as Shabbos, and thus one who forgets what day is Shabbos may keep his seventh day (with certain conditions, as the Radvaz there explains).
According to the Radvaz, the prohibition for such a person to do Melachah on the other six days is only a stringency that the Rabanan enacted (and not a result of a real doubt when Shabbos is), and the seventh day that he chooses to observe is the genuine day of Shabbos for him. (The Radvaz proposes this novel approach in response to the question of what day to observe as Shabbos past the International Dateline. See Parasha Page, Emor 5756.)