Kirsti and Gary F,
K
Euclid introduced the word SEMEION, and defined it as that which
has no parts, and his followers started to that word instead of
the earlier STIGME .
GF
By the way, according to my sources, Aristotle used the word σημεῖον
for point before Euclid. [And from web site] According to the Liddell
and Scott lexicon, the word σημεῖον (the usual Greek word for sign
and root of semeiotic) was also used by Aristotle for a mathematical
point, or a point in time. In this sense it was synonymous with
στιγμή (stigma).
I checked Liddell & Scott, Chantraine's dictionnaire étymologique,
and Heath's translation and commentary on Euclid.
The base word is the verb 'stigo', which means to mark something;
for example, as a sign of ownership. From that, the word 'stigma'
(ending in alpha instead of eta) meant the mark caused by a pointed
instrument. The word 'stigme' originally meant a spot in a bird's
plumage; then it came to mean any spot, a small mark, or an instant.
Aristotle explicitly said that a point was a marker on a line,
not a part of the line. Heath said that Euclid generally followed
Aristotle. But in vol. 1, p. 156, he said that 'semeion' was
probably "considered more suitable than 'stigme' (a puncture)
which might claim to have more reality than a point."
In summary, all three words (stigma, stigme, and semeion) could refer
to a mark, but semeion is more abstract and general than the others.
K
Does a sign have parts? - How about meaning?
The word 'semeion' could be used to refer to any kind of mark.
Euclid used it for just one particular kind. For that use in
geometry, the thing it refers to has no parts.
K
the Romans & later Boethius changed it to PUNCTUM in their commentaries.
I believe that it was good idea to have two distinct words:
'signum' for sign, and 'punctum' for point.
John
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