The comfortable middle
Measured at noon in every year from 1930 to 2035, the Sun on 4 December has fallen between about eleven and two fifths and twelve and four fifths degrees of Sagittarius. The nearest sign boundary behind is the Scorpio ingress, a fortnight back, and the nearest ahead is Capricorn, more than a fortnight forward.
The decan boundaries are closer but still not close. The middle face of the sign runs from ten to twenty degrees, and this position sits with a degree and a half of margin behind it and seven degrees of margin ahead.
So there is no argument to have. The value of stating the degree here is not that it resolves a dispute but that it is the number the rest of a chart reading is built on.
What the degree is actually used for
Aspects are measured in degrees, not in signs. Whether the Sun is square a planet or merely near it depends on how many degrees separate them, and the difference between a tight aspect and a loose one is a few degrees either way. A sun sign cannot supply that; a solar longitude can.
House placement works the same way. Once a birth time gives the Ascendant, the houses are laid out in degrees, and a Sun at twelve degrees of Sagittarius can sit near the start of one house or near the end of another depending on where the cusps land.
This is the ordinary working use of a solar degree, and it is why the number is more useful than the adjectives that usually accompany a birthday. It feeds into calculations rather than into descriptions.
Why the number stays put
The band above is a little over a degree wide for a reason that has nothing to do with astrology. A tropical year exceeds a common calendar year by close to a quarter of a day, so the Sun reaches a given longitude about six hours later against the calendar each year, and every fourth year a leap day pulls it back by nearly a whole day.
The result is a sawtooth that repeats rather than accumulates, which is exactly what a calendar is supposed to produce. A residual drift of about a day per century survives it, and the Gregorian rule about century years keeps that from building up.
The middle face of Sagittarius, where this position sits, is assigned to the Moon by the Chaldean order and to Aries, and so to Mars, by the triplicity scheme. Tradition reads one as attachment to familiar ground and the other as views taken up and defended at once. Both are interpretation, as marked.
The placements the date leaves open
The Moon travels about thirteen degrees a day and changes sign roughly every couple of days, so on 4 December it may be in either of two signs and the hour of birth decides. That is the placement the tradition ties most closely to need and to temperament, and a date narrows it only halfway.
The Ascendant is worse served. The whole zodiac passes the eastern horizon in a day, so the rising degree moves by about a degree every four minutes and two births on this date a few hours apart share nothing in the house layout.
The widget above computes your exact solar degree from your own year and birthplace, and reports how far you were born from the nearest sign boundary. On this date the boundary distance will be large and the degree will still be worth keeping, because it is the input everything else uses.
Questions people ask about this
Is 4 December always Sagittarius?
Yes, at any hour and in any year on record. The Sun is around twelve degrees into the sign, which is roughly a fortnight from either boundary.
What decan is a 4 December birthday?
The second decan of Sagittarius, ruled by the Moon in the Chaldean order and by Mars, through Aries, under the triplicity scheme.
Why does the exact degree matter if the sign is obvious?
Because aspects and house cusps are measured in degrees. The sign tells you very little that a calculation would use; the longitude tells you a great deal.
How much does my birth time change the degree?
By up to about half a degree either side of the noon figure, since the Sun covers a little under a degree a day. That is enough to matter for a tight aspect.
Can I get my Moon sign from the date alone?
Only to within two possibilities. The Moon changes sign every couple of days, so the hour of birth decides which one applies.
What should I look up next?
Your birth time, if you can find it. Without it the Ascendant is unavailable and the houses cannot be drawn, which is where a reading stops being generic.