[Inquiry] Simple Meanings In Limnal Expressions -- Commentary

[Jon Awbrey]

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SMILE.  Commentary Note 1

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Re: SMILE 4.  http://stderr.org/pipermail/inquiry/2005-November/003166.html
In: SMILE.    http://stderr.org/pipermail/inquiry/2005-November/thread.html#3166

Peirce List,

The paragraph that leads off "The Simplest Branch of Mathematics"
(CP 4.250) is very important, so let's go through it line by line.

| 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!.

It's good to observe that Peirce begins with inquiry, inquiring into the
minimal conditions for the possibility of asking a sensible question and
receiving a sensible answer.  It all begins casually, disarmingly enough,
in the "niche of inquiry's sensible evolution" (NOISE), which is to say
in a state of uncertainty that makes a question necessary and possible,
in effect, a state of uncertainty that 'is' the question.  And Peirce
notes that the niche of inquiry is at its narrowest a space that has
just two "objects", or constant values, here dubbed !v! and !f!.
With those humble beginnings, it becomes possible to enumerate
a few of the simplest sorts of inquiries or problems that
are able to arise on this basis.

| 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!.

In the simplest kind of inquiry that is contemplated here,
the matter at issue is naturally expressed by adding to the
concept of constant objects or constant values the concept of
unknown objects or unknown values, that is, objects and values
that remain to be determined by the data that is accumulated as
the inquiry proceeds.  As signs of unknown things, one normally
uses signs like "'x'", and so the answer to the problem can be
expressed by saying that the sign "'x'" comes to be assigned
a value in the set {!v!, !f!}.  One might also say that the
sign "'x'" comes to denote an object in the set {!v!, !f!}.

To be continued ...

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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