[Inquiry] Re: Simple Meanings In Limnal Expressions

[Jon Awbrey]

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SMILE.  Note 4

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Peirce List,

I may need, eventually, to go back and pick up some of
the earlier material from of "The Simplest Mathematics",
but for the time being I'll just copy out the more salient
passages that I noted as having some relevance to this theme.
I use !v! and !f! for Peirce's boldface letters, 'x', 'y', 'z',
etc. for his italic symbols, and also break up the paragraphs as
may be convenient for the sake of facilating study and discussion.

Jon Awbrey

| Minute Logic (January-February 1902)
|
| 3.  The Simplest Mathematics
|
| 3.3.  The Simplest Branch of Mathematics
|
| Were nothing at all supposed, mathematics would have no ground at all
| to go upon.  Were the hypothesis merely that there was nothing but
| one unit, there would not be a possibility of a question, since
| only one answer would be possible.  Consequently, the simplest
| possible hypothesis is that there are two objects, which we
| may denote by !v! and !f!.
|
| Then the first kind of problem of this algebra will be,
| given certain data concerning an unknown object, 'x',
| required to know whether it is !v! or !f!.
|
| Or similar problems may arise concerning several unknowns,
| 'x', 'y', etc.
|
| Or when the last problem cannot be resolved, we may ask
| whether, supposing 'x' to be !v!, will 'y' be !v! or !f!?
| And similarly, supposing 'x' to be !f!.
|
| Again, given certain data concerning 'x', we may ask,
| what else needs to be known in order to compel 'x'
| to be !v! or to be !f!.
|
| Or again, given certain information about 'x', 'y', and 'z',
| what relations between 'x' and 'z' remain unchanged whether
| 'y' be !v! or !f!?
|
| C.S. Peirce, 'Collected Papers', CP 4.250
|
| C.S. Peirce, 'Collected Papers of Charles Sanders Peirce, Volume 4,
| The Simplest Mathematics', Charles Hartshorne and Paul Weiss (eds.),
| Belknap Press of Harvard University Press, Cambridge, MA, 1933, 1961.

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