SUO: Building Ontologies Through Signs And Inquires (BOTAI)
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| Mark how readily each pliant string
| Prepares itself and as an off'ring
| The tribute of some gentle sound does bring.
| Then altogether in harmonious lays
| To the sublimest pitch themselves they raise,
| And loudly celebrate their Master's praise.
|
| Henry Purcell, 1685
I approach this task of building tools for building ontologies
the way I would any programming problem. All programs are codes
for recursive functions, that is, they are formed like proofs by
mathematical induction, achieving their remarkable elegance and
efficiency by marking out a base of arbitrated value settings
and a set of steps of constant resort for computing the rest.
I always find that it helps to have a stock
of concrete examples and exercises, pitched
at widely varying levels of task complexity.
Here is an excerpt from a paper that I wrote a few years ago
on some relationships that exist between inquiry and analogy
in Peirce's way of analyzing their component phases over the
three types of inference. Specifically, in a first approach,
he treats reasoning by analogy, just as Aristotle before him,
as a combination of deduction and induction, while the first
two stages of the inquiry process are tantamount to the dual
of this link-up, bringing into train abduction and deduction.
In this excerpt I consider the "Example of the Three Wisdoms"
from CSP's Harvard Lectures "On the Logic of Science" (1865),
the quote that I recently gave on the "Determination" thread:
http://suo.ieee.org/email/msg05056.html
| Document History:
|
| Project: Intelligent Systems
| Subject: Inquiry and Analogy
| Contact: Jon Awbrey <jawbrey@oakland.edu>
| Version: Draft 3.0
| Created: 1995 Feb 11
| Revised: 2001 May 20
| Faculty: F. Mili & M.A. Zohdy
| Setting: Oakland University, Rochester, Michigan
| Excerpt: Pages 3-4. Types of Reasoning in C.S. Peirce
Types of Reasoning in C.S. Peirce
Here we present one of Peirce's earliest treatments of
the three types of reasoning, from his Harvard Lectures
of 1865 "On the Logic of Science". It illustrates how
one and the same proposition might be reached from three
different directions, as the end result of an inference
in each of the three modes.
| We have then three different kinds of inference:
|
| Deduction or inference 'à priori',
|
| Induction or inference 'à particularis',
|
| Hypothesis or inference 'à posteriori'.
|
| CSP, CE 1, page 267.
| If I reason that certain conduct is wise
| because it has a character which belongs
| 'only' to wise things, I reason 'à priori'.
|
| If I think it is wise because it once turned out
| to be wise, that is, if I infer that it is wise on
| this occasion because it was wise on that occasion,
| I reason inductively ['à particularis'].
|
| But if I think it is wise because a wise man does it,
| I then make the pure hypothesis that he does it
| because he is wise, and I reason 'à posteriori'.
|
| CSP, CE 1, page 180.
|
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science' (1865)",
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
Suppose we make the following assignments:
A = "Wisdom",
B = "a certain character",
C = "a certain conduct",
D = "done by a wise man",
E = "a certain occasion".
Recognizing that a little more concreteness will aid the understanding,
let us make the following substitutions in Peirce's example:
B = "Benevolence", a certain character,
C = "Contributes to Charity", a certain conduct,
E = "Earlier today", a certain occasion.
The converging operation of all three reasonings is shown in Figure 1.
| D ("done by a wise man")
| o
| \*
| \ *
| \ *
| \ *
| \ *
| \ *
| \ * A ("a wise act")
| \ o
| \ /| *
| \ / | *
| \ / | *
| . | o B ("benevolence", a certain character)
| / \ | *
| / \ | *
| / \| *
| / o
| / * C ("contributes to charity", a certain conduct)
| / *
| / *
| / *
| / *
| / *
| /*
| o
| E ("earlier today", a certain occasion)
|
| Figure 1. A Thrice Wise Act
The common proposition that concludes each argument
is AC, to wit, "contributing to charity is wise".
Deduction could have obtained the Fact AC from
the Rule AB, "benevolence is wisdom", along with
the Case BC, "contributing to charity is benevolent".
Induction could have gathered the Rule AC, after a manner of
saying that "contributing to charity is exemplary of wisdom",
from the Fact AE, "the act of earlier today is wise", along
with the Case CE, "the act of earlier today was an instance
of contributing to charity".
Abduction could have guessed the Case AC, in a style of expression
stating that "contributing to charity is explained by wisdom", from
the Fact DC, "contributing to charity is done by this wise man", and
the Rule DA, "everything that is wise is done by this wise man". Thus,
a wise man, who happens to do all of the wise things that there are to do,
may nevertheless contribute to charity for no good reason, and even be known
to be charitable to a fault. But on seeing the wise man contribute to charity
we may find it natural to conjecture, in effect, to consider it as a possibility
worth examining further, that charity is in deed a mark of his wisdom, not just
an accidental trait or an immaterial peculiarity -- in essence, that wisdom is
the 'reason' he contributes to charity.
Jon Awbrey
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