ONT Re: Toward A Functional Conception Of Quantificational Logic
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i have run into chaos for picking things up out of order before,
so this may be all that i do with the first order stuff for now.
i find various old notes on "doctrines and myths of individuals"
that look like they might be used again at some point in future.
exhibit 2.
Subj: Doctrine Of Individuals
Date: Thu, 30 Nov 2000 13:38:24 -0500
From: Jon Awbrey <jawbrey@oakland.edu>
To: Conceptual Graphs <cg@cs.uah.edu>,
Stand Up Ontology <standard-upper-ontology@ieee.org>
CC: Peirce Subgroup
Re: "Myths Of Individuals" (MOI's)
I would like to go back and do a "slow reading" of Peirce's text now,
and also to unpack some of my more pachydermatic statements about it.
I left you with the thought, last time, that this reflection on
the "doctrine of individuals" (DOI) ought to have a significant
bearing on our best choices for a "theory of quantifiers" (TOQ).
To expand on this point, let me just append this self-quotation,
from a project proposal on "Inquiry & Analogy" that I drafted
for an independent study in my systems engineering programme,
the text created in January and revised in November of 1995.
[Revision of Excerpt]
| Document History:
|
| Subject: Inquiry & Analogy
| Contact: Jon Awbrey <jawbrey@oakland.edu>
| Version: Draft 3.10
| Created: 01 Jan 1995
| Revised: 20 Dec 2001
| Faculty: F. Mili & M.A. Zohdy
| Setting: Oakland University, Rochester, Michigan, USA
| Excerpt: Abstract, Section 2 (Higher Order Propositional Expressions)
| Exceprt: Subsection 2.1 (A Functional Conception of Quantification Theory)
Inquiry & Analogy
Abstract
This report discusses C.S. Peirce's treatment of analogy,
placing it in relation to his overall theory of inquiry.
The first order of business is to introduce the three
fundamental types of reasoning that Peirce adopted
from classical logic. In Peirce's analysis both
inquiry and analogy are complex programs of
reasoning which develop through stages of
these three types, although normally in
different orders.
1. Three Types of Reasoning
1.1 Types of Reasoning in Aristotle
1.2 Types of Reasoning in C.S. Peirce
1.3 Comparison of the Analyses
1.4 Aristotle's "Apagogy": Abductive Reasoning as Problem Reduction
1.5 Aristotle's "Paradigm": Reasoning by Analogy or Example
1.6 Peirce's Formulation of Analogy
1.7 Dewey's "Sign of Rain": An Example of Inquiry
2. Higher Order Propositional Expressions
2.1 A Functional Conception of Quantification Theory
Up till now quantification theory has been based on the assumption of
individual variables ranging over universal collections of perfectly
determinate elements. Merely to write down quatified notations like
"(For All)_(x in X) F(x)" and "(For Some)_(x in X) F(x)" involves a
subscription to notions of this order, as certified in the membership
relations that are exhibited in their indices. Reflected on pragmatic
insights and constructive principles, however, these ideas begin to
appear as problematic hypotheses whose warrants to be admitted are
not beyond question, as projects of exhaustive determination that
overreach the powers of finite information and control to manage.
Therefore, it is worth considering how we might opt to shift the
foundations of quantification theory closer to familiar ground,
namely, toward the predicates themselves that represent our
continuing acquaintance with phenomena.
Jon Awbrey
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