What is an Element?
Elements are defined as minimum parts that cannot be divided any more. Are elements of material systems atoms and those of information systems bits?
1. material and non-material elements
Scientists consider atoms composed of elementary particles and some of the elementary particles (hadrons) composed of quarks. The classical question as to whether materials can be divided infinitely or not is still in dispute.
On the other hand, the element of information system seems logically clear: bit. Bit is an abbreviation for binary digit, which is consisting of 0 and 1.
You can get two raised to nth combinations out of the following conjunction:
(0 or 1) and (0 or 1) and (0 or 1) and (0 or 1) and …
ASCII, American Standard Code for Information Interchange, is seven bit code, and can express the two raised to seventh power =128 characters.
It is, however, not the signified (signifie) but the signifying (signifiant) that is composed of bits. What is the element of the signified?
2. The element of propositon
Logicians often draw a distinction between atomic propositions and molecular propositions. For example, a molecular proposition "If you sing before breakfast, you’ll cry before night." is composed of two atomic propositions "you sing before breakfast" and "you’ll cry before night" connected by means of the conditional "if".
But the atomic propositions are no more the most fundamental elements than material atoms are. For example, the sentence "The present king of France is bald-headed" seems to be an atomic proposition including one subject, one verb and one predicate. This famous proposition has a problem that neither its affirmative
"The present king of France is bald-headed"
nor its negative
"The present king of France is not bald-headed"
is true, because there are no kings in France at present. If you decompose it into two atomic propositions: "There is a king of France at present" and "The king is bald-headed", you can get the true molecular proposition by negating the former proposition.
Is the proposition "There is a king of France at present" really atomic and elementally? This one also can be decomposed into two: "There is a king of a certain country at present" and "The country is France." You can decompose any propositions, as you like.
3. The essence of elemets is obviousness
What is the criterion for element, then? I would like to work out a pragmatic answer: elements are what are self-evident. The motive for decomposition is to explain an unintelligible whole in terms of intelligible parts. If something is self-evident, you can regard it as an element to begin with. If the self-evidence fluctuates, then you can decompose it into self-evident elements. The same applies to material elements.