זכור את יום השבת לקדשו - Chazal say: Remember Shabbos when it comes in and goes out. Kiddush and Havdala. What is the הגדרה of Havdala? What is it's essence? Kiddush is already Havdala. By sanctifying we are separating! So once we say Kiddush we don't need Havdala as they are two sides of the same coin. When you say הרי את מקודשת לי you are both making her special for you and separating her from the rest of the world - דאסר לה אכולי עלמא כהקדש.
Not only that but Havdala in the Kedusha of time is different than other ways of separating. When we sanctify the animal Bechor - it is already holy. We just add our קדושה בפה. Similarly, when we sanctify Shabbos with Kiddush - it is already holy and we are just adding our קדושה בפה. But when we say הבדלה we are creating a new Halachic reality. Until Havdala it is forbidden to do Melacha. Interesting.
The words בין קודש לחול are the עיקר of Havdala even more than בין יום השביעי לששת ימי המעשה [Pesachim 103/104]. Why is that?
So what is Havdala all about???
We would like to explain a principle in the קדושת הזמנים:
Mussaf is a verbalization of the מצוה דואורייתא of Koban Mussaf [ונשלמה פרים שפתינו]. Yet we say מענגיה לעלם כבוד ינחלו. Now Oneg Shabbos is only מדברי קבלה from the נביא so what is it doing in Mussaf??
A Yesod from the Gaon R' Yehoshua Leib Diskin זצ"ל which can be used as an illustration of our issue. The Rosh cites the Maharam of Rottenberg that the דין of פיקוח נפש is a דין of דחויה - pushing away [but not permitting] the aveira. But when it comes to Shabbos פיקוח נפש is completely הותרה and permits the aveirah.
This is built on the foundation of the derivation of פיקוח נפש דוחה שבת from the pasuk of קדש היא לכם which is taken to mean - שבת מסורה בידכם ואין אתם מסורים בידה - Shabbos is given over to you and and you are not given over to it [Yoma 82b]. Another opinion: It is derived from the pasuk וחי בהם - ולא שימות בהם - Live by them and don't die by them. So פיקוח נפש wins. On the first opinion there is a question that if the source is קדש היא לכם then it would not apply in a case of doubt and one would not be allowed to be מחלל שבת in a case of doubtful פיקוח נפש. But if the source is וחי בהם then even in a case of doubt we would be מחלל שבת to save a life. For וחי בהם means to make sure that no matter what the person lives. On this comments R' Yehoshua Leib that the first source of קדש היא לכם has not been completely rejected. If it is a case of DEFINITE פיקוח נפש then we fall back on the source of קדש היא לכם and thus שבת מסורה בכם ואין אתם מסורים בידה. Shabbos is completely in your hands [in a case of פיקוח נפש] meaning הותרה and not merely דחויה. Other Mitzvos however are דחויה b/c they don't have this source.
To be continued... hopefully!