[Inquiry] Question About CP 1.339

Jon Awbrey jawbrey at att.net
Wed Sep 8 19:22:17 CDT 2010

[Query to Irving Anellis, 02 Sep 2010]

| I've had numerous occasions over the last 10 years
| to refer to Peirce's "Lo, another infinite series"
| passage at CP 1.339, most recently in this context:
| http://ontolog.cim3.net/forum/ontolog-forum/2010-08/msg00272.html
| The editors of CP note this as being from an "unidentified fragment"
| and don't give any date.  I was wondering if you had a more definite
| date for it or any additional information about it.

[Reply from Irving Anellis, 05 Sep 2010]

| As you probably know, the mathematical concept of an infinite series
| was expressed in those terms in the 17th century.  Thus, for example,
| in his Algebra (in his own English translation of 1685), Wallis wrote:
| "Now (to return where we left off:) Those Approximations
| (in the Arithmetick of Infinites) above mentioned, (for the
| Circle or Ellipse, and the Hyperbola;) have given occasion to
| others (as is before intimated,) to make further inquiry into
| that subject; and seek out other the like Approximations, (or
| continual approaches) in other cases.  Which are now wont to
| be called by the name of Infinite Series, or Converging Series,
| or other names of like import,"
| and in 1777 Francis Maseres talks about "A Method of finding
| the Value of an infinite Series of decreasing Quantities of
| a certain Form," by in the Philosophical Transactions of
| the Royal Society vol. 6.
| However, CSP in the citation you give, is apparently discussing
| Bradley's infinite relational regress, which, I understand, can
| first be found in Bradley's Appearance and Reality of 1893, at
| pp. 17-28.
| If so, then perhaps it is to this that CSP might be referring.
| I do not, off hand, know whether, and if so, when, CSP might
| have read Bradley.


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