Cf: Peirce’s 1870 “Logic of Relatives” • Preliminaries
https://inquiryintoinquiry.com/2014/01/27/peirces-1870-logic-of-relatives-p…
All,
I need to return to my study of Peirce’s 1870 Logic of Relatives,
and I thought it might be more pleasant to do that on my blog than
to hermit away on the wiki where I last left off.
Peirce’s 1870 “Logic of Relatives” • Part 1
===========================================
https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1
Peirce’s text employs lower case letters for logical terms of general reference
and upper case letters for logical terms of individual reference. General terms
fall into types, namely, absolute terms, dyadic relative terms, and higher adic
relative terms, and Peirce employs different typefaces to distinguish these.
The following Tables indicate the typefaces used in the text below for Peirce’s
examples of general terms.
Table 1. Absolute Terms (Monadic Relatives)
https://inquiryintoinquiry.files.wordpress.com/2021/11/peirces-1870-lor-e28…
Table 2. Simple Relative Terms (Dyadic Relatives)
https://inquiryintoinquiry.files.wordpress.com/2021/11/peirces-1870-lor-e28…
Table 3. Conjugative Terms (Higher Adic Relatives)
https://inquiryintoinquiry.files.wordpress.com/2021/11/peirces-1870-lor-e28…
Individual terms are taken to denote individual entities falling under
a general term. Peirce uses upper case Roman letters for individual terms,
for example, the individual horses H, H′, H″ falling under the general term h
for horse.
The path to understanding Peirce’s system and its wider implications
for logic can be smoothed by paraphrasing his notations in a variety
of contemporary mathematical formalisms, while preserving the semantics
as much as possible. Remaining faithful to Peirce’s orthography while
adding parallel sets of stylistic conventions will, however, demand close
attention to typography-in-context. Current style sheets for mathematical
texts specify italics for mathematical variables, with upper case letters
for sets and lower case letters for individuals. So we need to keep an
eye out for the difference between the individual X of the genus x and
the element x of the set X as we pass between the two styles of text.
References
==========
• Peirce, C.S. (1870), “Description of a Notation for the Logic of Relatives,
Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic”,
Memoirs of the American Academy of Arts and Sciences 9, 317–378, 26 January 1870.
Reprinted, Collected Papers (CP 3.45–149), Chronological Edition (CE 2, 359–429).
Online:
• https://www.jstor.org/stable/25058006
• https://archive.org/details/jstor-25058006
• https://books.google.com/books?id=fFnWmf5oLaoC
• Peirce, C.S., Collected Papers of Charles Sanders Peirce,
vols. 1–6, Charles Hartshorne and Paul Weiss (eds.),
vols. 7–8, Arthur W. Burks (ed.), Harvard University Press,
Cambridge, MA, 1931–1935, 1958. Cited as (CP volume.paragraph).
• Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition,
Peirce Edition Project (eds.), Indiana University Press, Bloomington and
Indianapolis, IN, 1981–. Cited as (CE volume, page).
Resources
=========
• Peirce’s 1870 Logic of Relatives
https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Overview
Regards,
Jon
Lars,
I added the word 'women' to the subject line because I wanted to mention a
debate in 1958 that was both humorous and enlightening: "The ontological
status of women and abstract entities",
http://jfsowa.com/ontology/church.htm
In 1947, Nelson Goodman and Willard Van Orman Quine published an article on
"Steps toward a constructive nominalism", which systematically avoided
abstract entities. In 1951, Alonzo Church replied with an article on The
need for abstract entities. In 1958, Church continued the debate by
presenting a lecture at Harvard (church.htm is an excerpt).
That article explains the issues in my recent notes in this thread. I don't
know whether it convinced Quine about the importance of abstract entities.
But he eventually admitted that abstract entities (sets, for example) are
necessary to define mathematics, and mathematics is necessary for all
branches of science and engineering. If you're not convinced by church.htm
and the references it cites, there is no point in continuing this thread.
JFS> Perception is more fundamental to all living things than any kind of
human cognition.
Lars> You are right. You are pointing into a direction of cognitive
research that is very notable: The school of perception-action-research.
See the works of Wolfgang Prinz, Max-Plack Institute for Cognitive- and
Neuroscience in Munich, and the late theoretician Odmar Neumann, University
of Bielefeld). They ingeniously researched and theorized on the most basic
forms of action parameterization (called 'direct [perception-to-action]
parameter specification'). It's an old neuronal system/pathway still active
in humans (that was therefore studied in humans). Neumann, by the way, was
my cognitive psychology teacher.
JFS> I agree with that point. See my review of neuroscience and its
implications for AI: "The virtual reality of the mind",
http://jfsowa.com/talks/vrmind.pdf
My contribution to vrmind.pdf is in the selection and summary of research
by other people, whom I cite with URLs in nearly every slide.
John
Lars> I think we revolve around the same basic problem: is there anything
called 'abstraction' beyond instances of abstract cognition?
Yes. Those things are called "patterns". And the formal study of
patterns is called "mathematics". And the foundation for cognition in
every living thing from bacteria to humans is the perception of patterns.
And a pattern is a simplified image with some of the detail omitted. Those
simplifications are called "diagrams". The simplest diagrams are called
"graphs".
Lars> I wouldn't (and nobody could) know what this would be, as anytime
one or any assumed alien looks or thinks about it, it would just be an
instance of their cognition, or an instance of a mneme (if you think in
terms of memory/thought processes).
No to the first part of that sentence. And yes to the second part.
There is something fundamental that is common to all forms of cognition on
planet earth: simplified perception. Since aliens that evolved on any
planet in any galaxy in the universe would also need some form of
perception, a reasonable assumption is that their cognition is based on a
simplified version of their perception.
Since everything in our universe is based on the same physics and
chemistry, it's very likely that any kind of biology and any kinds of
patterns the aliens may encounter would have some similarities in the
patterns they perceive. Therefore, their cognition is likely to be based
on simplified patterns that have some similarity to the patterns that
scientists have observed on earth, our solar system, and our galaxy.
Lars> In the cognitive sciences (as I explain in my book), scientists more
and more start studying the workings of cognitive development and evolution
instead of thinking of language and logic...
That's a good start. But I suggest that you go to a more fundamental
level. Perception is more fundamental to all living things than any kind
of human cognition. Images are a good start for anything that has eyes.
But structures are more fundamental for sentient beings without eyes. And
chemical distributions are more fundamental for single-celled beings.
For bacteria, a important feature of their perception enables them to swim
upstream in a glucose gradient. that implies that chemistry plus plus a
spatial direction is the most primitive form. And that can be mapped to a
simple kind of pattern.
Conclusion: patterns are fundamental to perception, and the simplest
patterns are directed graphs with labels that indicate good or bad
directions. That would be the simplest and most universal basis for
cognition.
Can anyone think of anything simpler or more fundamental?
John
Barry> Landgrebe and I have been working on a BFO physics Ontology and on
a mathematics Ontology, separate from BFO.
I'm glad to hear that you're finally developing an ontology for
mathematics and that it's independent of the current BFO.
Since it's impossible to do modern physics without a huge amount of
mathematics, I suggest that you combine your math ontology with BFO in
order to support physics.
There are three ways to combine an ontology of actual entities with a math
ontology:
1. Platonic: The mathematical forms are really real, and the physical
stuff is a degenerate approximation to reality.
2. Aristotelian: The physical entities are the real existents and the
forms exist only when they are embodied in physical stuff.
3. Peirce's update to Aristotle: All mathematical forms exist as real
possibilities, which may be used to describe or characterize anything that
exists in actuality or in any kind of imagined, planned, intended, hoped,
feared, described, communicated, or hypothesized aspect of reality.
Peirce's version implies that pure mathematicians can talk and act like
Platonists (which they frequently do), but applied mathematicians can focus
on the actual universe while having an infinite book of mathematical forms
to use as they wish when they're doing any kind of engineering, virtual
reality, or plans for future things that do not yet exist.
Option 3 also supports every kind of pattern on paper, in anyone's
imagination, implicit in any spoken or written language or notation,
implicit in anybody's knowledge, or implicit in any data structures in any
computer or collection of computers anywhere in the universe.
In short, Peirce's option #3 supports common sense, the most advanced
sciences, and every form of artistic endeavor in any culture in the world
-- or even in any alien life anywhere in the universe.
I recommend it,
John
Azamat,
The words 'data' and 'information' represent special cases of signs.
The word 'data' is Latin for "that which has been given" and the word
'information' is an English word, derived from Latin, for that which
informs. But the word 'sign' is the general term that includes signs from
any source for any purpose. It includes all the signs that have been given
(the data) and all the signs that have been used to inform (the
information), and all the signs that any living thing from bacteria on up
receive, perceive, process, generate, store, and communicate.
AA: Data denotes the information conveyed in the sign, symbol or
signal. Data could be coded and represented, measured and reported,
analyzed and visualized, collected and stored, processed and communicated.
As a general concept, it could cover information and knowledge, facts and
statistics, values and variables, patterns and rules.
No. The word 'data' is more specialized than the word 'sign'. It does
not include knowledge, since knowledge represents signs that are known.
And the signs of knowledge may have been derived directly from perception
(a process of interpreting signs derived by the senses). The signs of
knowledge may have been given by somebody as information, but more likely
some sentient being obtained them through an interpretation of signs from
the sense organs. (And sentient beings include everything from bacteria on
up.) Viruses are not sentient beings. They are signs that are interpreted
by the cells of living things.)
AA: data is the new oil and gas, money and and any valuable assets of the
digital age
There is nothing new about data, since computing devices have been given
data since the punched card machines that processed the 1890 census. The
amount of data has been growing exponentially for the past 140 years. That
exp9nential increase has made a qualitative increase in the kinds of ways
that machines can process the data.
But it's important to remember that the human brain has about 90 billion
neurons, and each neuron can store an immense amount of bits internally and
can be connected to a large number of other neurons in a large variety of
ways. The product of all those numbers is immense compared to the WWW.
Neuroscientists are just beginning to explore the potential for
representing and processing that immensity. Today's computer system are
just beginning to catch up with the storage capacity of a small animal
brain, but the current computational mechanisms are primitive compared to
the complex connectivity of the neurons and their interconnections in the
brain of a fruit fly.
As for ontology, I strongly recommend sli de 30 of
http://jfsowa.com/talks/patolog4.pdf (and the other slides before and after
plus all the references in the slides and at the end).
John
BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px;
}John - I quibble with your 'hidden' definition of the Sign.You say
that: .."That term includes every kind of language, logic, patterns,
notations, books, documents, web pages, representations, images,
diagrams, virtual reality."..
I consider that the above definition refers only to the mediative
site, the Representamen, which holds the logic, patterns, etc, that
transform raw input sensate data into an Interpretant of that raw
data. This function of mediation is termed by Peirce, both as 'sign'
and as 'representamen'. I consider this confusing, since this nodal
site does not exist 'per se' but only within an irreducible triadic
process of Object-Representamen-Interpretant.
I consider the full triad as the Sign in that it is an existential
entity [whether a word, a thought, a cell, a molecule] made up of
these three nodal sites in constant processing/interpretation of
input data.
Data itself is a triadic Sign - whether it be a chemical molecule
moving into an organism or... And it includes its own pattern of
organization..
Edwina
On Mon 06/12/21 11:59 AM , "John F Sowa" sowa(a)bestweb.net sent:
Azamat> I have an impression that many big problems in science and
technology could be solved by recognizing Data as a Prime Ontological
Category Yes, of course. That is absolutely true!!!! The failure to
recognize and emphasize that point is the primary reason why the ISO
standard for ontology is hopelessly obsolete. But instead of the
word "Data", I recommend the more general word "Signs". That term
includes every kind of language, logic, patterns, notations, books,
documents, web pages, representations, images, diagrams, virtual
reality... independent of any media, substrate, or equipment on which
the signs may be stored, displayed, processed, or transmitted. In
fact, an ontology that does not include signs as a fundamental
category is incapable of representing or talking about itself. Every
theory of mathematics and logic is a formal system of signs that are
related by formal signs called axioms and rules of inference. For
an ontology that has a two-way split at the top (Signs and Physics),
see slide 30 of http://www.jfsowa.com/talks/patolog4.pdf [1] Those
are the slides for day 4 of a short course on Patterns of Logic and
Ontology. For the slides of the other days, see patlog1, 2, 3, and
5. John
Links:
------
[1] http://www.jfsowa.com/talks/patolog4.pdf
Azamat> I have an impression that many big problems in science and
technology could be solved by recognizing Data as a Prime Ontological
Category
Yes, of course. That is absolutely true!!!! The failure to recognize and
emphasize that point is the primary reason why the ISO standard for
ontology is hopelessly obsolete.
But instead of the word "Data", I recommend the more general word "Signs".
That term includes every kind of language, logic, patterns, notations,
books, documents, web pages, representations, images, diagrams, virtual
reality... independent of any media, substrate, or equipment on which the
signs may be stored, displayed, processed, or transmitted.
In fact, an ontology that does not include signs as a fundamental category
is incapable of representing or talking about itself. Every theory of
mathematics and logic is a formal system of signs that are related by
formal signs called axioms and rules of inference.
For an ontology that has a two-way split at the top (Signs and Physics),
see slide 30 of http://www.jfsowa.com/talks/patolog4.pdf
Those are the slides for day 4 of a short course on Patterns of Logic and
Ontology. For the slides of the other days, see patlog1, 2, 3, and 5.
John
