I've noticed that the shorthand notations for chemical elements, such as C for carbon, are called symbols, not abbreviations. This also seems to be the case in several other scientific contexts, such as physical constants.
What special meaning does the term symbol carry in these contexts? How is a symbol distinct from an abbreviation?
An abbreviation is a shortening of a word. An example of an abbreviation would be "intro." instead of "introduction". Another example would be the use of "Mr." for the word "Mister". In Medicine, "pre-op." is an abbreviation for pre-operative. Note that abbreviations are followed by periods.
On the other hand, the word for the characters representing Chemical elements, and certain physical constants is "symbol". One reason for this is that while a some elements, such as Neon (NE), Nitogen (N), Carbon (C), and Oxygen (O) look like abbreviations, they are not written with periods (unless at the end of a sentence), and in some cases the symbol is not an abbreviation of the English name. The symbol for the element iron, for example, is Fe. Also, note that the symbol is universal. The symbol for iron in a scientific paper written in English is FE; so is the symbol in a scientific paper written in Spanish, where the word for iron is "Hiero", and in a scientific paper written in German, where the word for iron is "Eisen". Other common symbols which do not appear to be abbreviations in English are those for lead (Pb), and for Tin (Sn), and there are cases where the symbol that appears to be an abbreviation in English, like "O" for oxygen, would not appear to be an abbreviation. For example, the German word for Oxygen is "Sauerstoff".
Similarly with symbols for physical and mathematical constants. KN is universally known as a kilonewton, and R is universally known as the Gas constant.
[Too long for a comment, but might be useful nonetheless]
The chemical symbols are symbols because they are universal, as brasshat has stated in his answer.
However, they were originally derived as abbreviations — often from Latin. Fe for iron comes from ferrum; Pb for lead comes from plumbum (think plumbing); Sn for tin from stannum; C for carbon from carbo "coal"; there are many more examples.
H is an abbreviation of Lavoiser's French name for the element, which he derived from Greek.
Tungsten's symbol W is unusual though. Tungsten is a Swedish word, but its other name wolfram is derived from wolframite, tungsten's principal ore. Wikipedia has
The name "tungsten" (from the Swedish tung sten, "heavy stone") is used in English, French, and many other languages as the name of the element, but not in the Nordic countries. Tungsten was the old Swedish name for the mineral scheelite. The other name "wolfram" (or "volfram"), is used in most European (especially Germanic and Slavic) languages, and is derived from the mineral wolframite, which is the origin of its chemical symbol, W. The name "wolframite" is derived from German "wolf rahm" ("wolf soot" or "wolf cream"), the name given to tungsten by Johan Gottschalk Wallerius in 1747. This, in turn, derives from "Lupi spuma", the name Georg Agricola used for the element in 1546, which translates into English as "wolf's froth", and is a reference to the large amounts of tin consumed by the mineral during its extraction.
The same has happened for SI units: the unit of energy is the joule, named after the English physicist James Joule; its symbol, derived from his name, is J.
Even the gas constant R mentioned by brasshat might be originally an abbreviation, or at least derived from a name. Wikipedia again:
Some have suggested that it might be appropriate to name the symbol R the Regnault constant in honour of the French chemist Henri Victor Regnault, whose accurate experimental data was used to calculate the early value of the constant; however, the exact reason for the original representation of the constant by the letter R is elusive.
Thus although the letters are symbols (because they are universal), they had to come from somewhere. The particular choice of which letter to use is at least guided by some name relevant to the element or quantity, but it's not strictly an abbreviation.
The term C for carbon symbolises carbon and can be used as a shorthand for carbon in a sentence. It's definitely an abbreviation but technically given the term symbol.
Symbol in chemistry == Abbreviation in English
