Re: [PEIRCE-L] The formal logic of chemistry and the trichotomy.(Revised) Was Re: The 1911 EGs
List:
> On Jun 8, 2021, at 8:12 AM, Edwina Taborsky wrote:
>
> Jerry, list
>
> This is a very densely packed outline, and therefore, at the moment, I have
> just a few comments.
>
> 1] I note that you wrote: "semiosis of singular (unique) objects, identified
> (termed) “sin-signs” by CSP. "
>
> I am pleased to see that you define a singular object as a sign [in this
> case, a sin-sign]. I have long argued that the Peircean semiosic triad, of
> Object-Representamen-Interpretant, which is irreducible, should be understood
> as a 'singular object', which I understand as a Sign.
>
>
While I appreciate your interpretation, it is not quite the case.
CSP introduced the term “sin-sign”. While this compound word was coined by
CSP, the question was “Why” the semantics of "sin-sign" and not just “sign”?
For the logic of identity of a sign, one must first presuppose the number of
“identities” that the sign represents. Usually, the simple syntax is to assume
one identity and not semantically express the potential of multiple components
(terms). If one supposes multiple terms, then the nature of the conjunctions
among the identities must be addressed for a truth function.
In the chemical sciences, it is essential practice to first ascertain the
singularity of the material form. Otherwise, the multiplicity of indices
provide ambitious truth tables for the molecular formula. Technically, chemists
speak of “isomers” for two "sin-signs" with similar truth tables. Pastuer’s
determination of handedness of crystals from wine bottoms in the 1860 puzzled
CSP greatly, as noted in his texts in the 1880’s or early 1890’s. This
observation is an extremely important constrain on the logic of chemistry and
hence the forms of logic proposed by CSP.
> I note that the major theorist in biosemiotics, Jesper Hoffmeyer, also wrote;
> "Peirce called the triad - the basic relational element in logic - quite
> simply a sign" {1996, 18}.
>
>
Possibly. I suspect, however, that Jasper, a microbial chemist, was referring
to the form of propositions as “subject-copula-predicate.” In other words, he
recognized the need for a richer semantics and syntax than is afforded by
orthodox mathematics of set theory / physics and predicate logic.
> That is - no part of the triad 'exists' or is even pragmatically functional,
> except within that triadic process.
>
> 2] You write: "From these three antecedents, a plethora of many to one and
> one to many semantic mappings emerge as possible propositional sentences"
>
> And this points out how the semiosic logical process, which is triadic,
> enables multi-dimensional networks. As a side note, such multidimensional
> networking is impossible using the dyadic Saussurian framework.
>
>
Yes, I concur.
But, more importantly, the form of semiotic logic needed to grow a semiotic
network obligates conjunctive forms of terms. Hence, the necessity for the
table of elements as logical constants that can copulate (co-operate) to form
semiotic patterns.
3] The above points also acknowledge that semiosis - and singular objects - do
not exist except within the dynamic process of, as you note, a logical process
of 'antecedent and consequent’.
Well, yes and no.
The table of chemical elements is held to exist as a reference source for all
of chemical logic. These logical constants form an order relation.
Any dynamics of interpreting the relevant, relational and illational
propositional (atomic and molecular) forms is a problem created by human being.
This problem is of very recent origin as my references indicated.
Cheers
Jerry
> This puts us 'back' into the analysis of the hylomorphic correlation of
> matter and mind.
>
>
Edwina
>
>
>
> On Mon 07/06/21 11:16 PM , Jerry LR Chandler jerry_lr_chand...@icloud.com
> sent:
>
> (List: Please substitute this edited version of my post earlier today. I
> accidentally submitted the first draft of the post which was extensively
> revised over the week-end with numerous additions and clarifications. JLRC)
>
> List:
>
> This submission addresses the potential connections between category theory,
> formal chemical logic and CSP’s critical constituents of a philosophy of
> pragmaticism such as notions of the trichotomy and existential graphs. At
> issue is the connection, if any, between the vast plethora of modern logics,
> chemical logic and existential graphs.
>
> In particular, it addresses the dictionary of terms deployed in drawing
> conclusions from semiosis of singular (unique) objects, identified (termed)
> “sin-signs” by CSP.
>
> The first row of the trichotomy proposes that the representation of pragmatic
> objects as signs - qualisigns, sin-signs and legisigns. Presumably, these
> three terms are pragmatically coherent, that is, all refer to the same
> object. Presumably, all three terms could refer to a multitude of scientific
> object
Re: [PEIRCE-L] Logical Graphs, Truth Tables, Venn Diagrams
Cf: Logical Graphs, Truth Tables, Venn Diagrams • 8 https://inquiryintoinquiry.com/2021/06/08/logical-graphs-truth-tables-venn-diagrams-8/ Re: Logical Graphs, Truth Tables, Venn Diagrams https://inquiryintoinquiry.com/2021/05/29/logical-graphs-truth-tables-venn-diagrams-2/ https://inquiryintoinquiry.com/2021/05/30/logical-graphs-truth-tables-venn-diagrams-3/ All, Looking to the day we can make our ascent on logical graphs with increasing numbers of variables, I'd like to flag the following points of discussion for further development. JM: Most of the recent discussion is about two-variable logic forms where there is a logical relation between two logical variables. I want to bring up the subject of three-variable logic which I think is very rich but not much discussed. JA: One of the biggest advantages of the systems of graphical forms derived from C.S. Peirce's logical graphs and Spencer Brown's calculus of indications is precisely the conceptual and computational efficiencies they afford us in dealing with propositional forms and boolean functions of many variables. JA: As it happens, I did once write out all 256 boolean functions on three variables in cactus syntax several years ago — pursuant to discussions in Stephen Wolfram's New Kind of Science (NKS) Forum regarding Elementary Cellular Automaton Rules (ECARs), which are in effect just that set of boolean functions. I'll have to dig up a passel of ancient links from the WayBack Machine, but see the following archive page for a hint of how it went. • Cactus Rules (NKS Forum) https://web.archive.org/web/20041025093703/http://forum.wolframscience.com/archive/topic/256-1.html There is now a copy of the above content at the following location and I'll be working to improve the formatting and graphics as time goes on. • Cactus Rules https://oeis.org/wiki/User:Jon_Awbrey/Cactus_Rules • Propositional Forms on Three Variables https://oeis.org/wiki/User:Jon_Awbrey/Cactus_Rules#Propositional_Forms_on_Three_Variables Regards, Jon _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] The formal logic of chemistry and the trichotomy.(Revised) Was Re: The 1911 EGs
Jerry, list
This is a very densely packed outline, and therefore, at the moment,
I have just a few comments.
1] I note that you wrote: "semiosis of singular (unique) objects,
identified (termed) “sin-signs” by CSP. "
I am pleased to see that you define a singular object as a sign [in
this case, a sin-sign]. I have long argued that the Peircean semiosic
triad, of Object-Representamen-Interpretant, which is irreducible,
should be understood as a 'singular object', which I understand as a
Sign.
I note that the major theorist in biosemiotics, Jesper Hoffmeyer,
also wrote; "Peirce called the triad - the basic relational element
in logic - quite simply a sign" {1996, 18}.
That is - no part of the triad 'exists' or is even pragmatically
functional, except within that triadic process.
2] You write: "From these three antecedents, a plethora of many to
one and one to many semantic mappings emerge as possible
propositional sentences"
And this points out how the semiosic logical process, which is
triadic, enables multi-dimensional networks. As a side note, such
multidimensional networking is impossible using the dyadic Saussurian
framework.
3] The above points also acknowledge that semiosis - and singular
objects - do not exist except within the dynamic process of, as you
note, a logical process of 'antecedent and consequent'.
This puts us 'back' into the analysis of the hylomorphic correlation
of matter and mind.
Edwina
On Mon 07/06/21 11:16 PM , Jerry LR Chandler
jerry_lr_chand...@icloud.com sent:
(List: Please substitute this edited version of my post earlier
today. I accidentally submitted the first draft of the post which
was extensively revised over the week-end with numerous additions and
clarifications. JLRC)
List:
This submission addresses the potential connections between category
theory, formal chemical logic and CSP’s critical constituents of a
philosophy of pragmaticism such as notions of the trichotomy and
existential graphs. At issue is the connection, if any, between the
vast plethora of modern logics, chemical logic and existential
graphs.
In particular, it addresses the dictionary of terms deployed in
drawing conclusions from semiosis of singular (unique) objects,
identified (termed) “sin-signs” by CSP.
The first row of the trichotomy proposes that the representation of
pragmatic objects as signs - qualisigns, sin-signs and legisigns.
Presumably, these three terms are pragmatically coherent, that is,
all refer to the same object. Presumably, all three terms could
refer to a multitude of scientific objects and sematic terms for any
particular “sin-sign” that are relevant to pragmatic inquiry.
The second row of the trichotomy proposes three identifiable
constraints on the meaning of signs - icons, indices, and symbols.
Again, presumably, each of these semantic terms could refer to a vast
multitude of scientific terms that represent the unique object of the
designated (existent) sin-sign. Of particular importance to the
logic of chemistry is the term “index.” This term has
implications for measurements, counting, listing, illations,
relations, categorizing, organizing, and (critically) the artificial
name assigned to the singularity. Again, presumably, each of the
semantic terms associated with the indices of a sin-sign are relevant
to the sin-signand also can be symbolized (and also vaguely iconized).
The third row of the trichotomy proposes that a proposition can be
categorically composed from the relevant terms of the second row that
describe the interpretations of the semiosis of the interpreter.
Again, presumably each of the three terms could be composed from the
potential logical implications of the plethora of terms emanating
from the first and second rows of the trichotomy, CSP’s personal
weltanschaung. Further, CSP used symbolic arrows to express
implications from the third row to the second and first rows.
From these three antecedents, a plethora of many to one and one to
many semantic mappings emerge as possible propositional sentences.
(In special cases,matheamtical mappings are also necessary, e.g.
chemical structures). The logical terms of each possible
propositional sentence is constrained to the relevant indices of the
sin-sign . That is, the attributes of sin-sign are necessary terms in
the argument if the sin-sign is be logically coherent with the
relevant qualities and quantities and the name (legisign) of the
emanating sign-generator.
One very very special case of trichotomistic reasoning is the formal
logic of chemistry which is based on atomic and molecular sentences
(Russell/Whitehead). Each symbol for a chemical element represents a
triad, an informed logical constant, an atomic number, an informed
integer. That is, a symbol, an index and an icon.
The perplexity of table of chemical elements was well-known to
CSP; in his earlier writ
[PEIRCE-L] The formal logic of chemistry and the trichotomy.(Revised) Was Re: The 1911 EGs
(List: Please substitute this edited version of my post earlier today. I accidentally submitted the first draft of the post which was extensively revised over the week-end with numerous additions and clarifications. JLRC) List: This submission addresses the potential connections between category theory, formal chemical logic and CSP’s critical constituents of a philosophy of pragmaticism such as notions of the trichotomy and existential graphs. At issue is the connection, if any, between the vast plethora of modern logics, chemical logic and existential graphs. In particular, it addresses the dictionary of terms deployed in drawing conclusions from semiosis of singular (unique) objects, identified (termed) “sin-signs” by CSP. The first row of the trichotomy proposes that the representation of pragmatic objects as signs - qualisigns, sin-signs and legisigns. Presumably, these three terms are pragmatically coherent, that is, all refer to the same object. Presumably, all three terms could refer to a multitude of scientific objects and sematic terms for any particular “sin-sign” that are relevant to pragmatic inquiry. The second row of the trichotomy proposes three identifiable constraints on the meaning of signs - icons, indices, and symbols. Again, presumably, each of these semantic terms could refer to a vast multitude of scientific terms that represent the unique object of the designated (existent) sin-sign. Of particular importance to the logic of chemistry is the term “index.” This term has implications for measurements, counting, listing, illations, relations, categorizing, organizing, and (critically) the artificial name assigned to the singularity. Again, presumably, each of the semantic terms associated with the indices of a sin-sign are relevant to the sin-sign and also can be symbolized (and also vaguely iconized). The third row of the trichotomy proposes that a proposition can be categorically composed from the relevant terms of the second row that describe the interpretations of the semiosis of the interpreter. Again, presumably each of the three terms could be composed from the potential logical implications of the plethora of terms emanating from the first and second rows of the trichotomy, CSP’s personal weltanschaung. Further, CSP used symbolic arrows to express implications from the third row to the second and first rows. >From these three antecedents, a plethora of many to one and one to many >semantic mappings emerge as possible propositional sentences. (In special >cases,matheamtical mappings are also necessary, e.g. chemical structures). >The logical terms of each possible propositional sentence is constrained to >the relevant indices of the sin-sign . That is, the attributes of sin-sign are >necessary terms in the argument if the sin-sign is be logically coherent with >the relevant qualities and quantities and the name (legisign) of the emanating >sign-generator. One very very special case of trichotomistic reasoning is the formal logic of chemistry which is based on atomic and molecular sentences (Russell/Whitehead). Each symbol for a chemical element represents a triad, an informed logical constant, an atomic number, an informed integer. That is, a symbol, an index and an icon. The perplexity of table of chemical elements was well-known to CSP; in his earlier writings, be often gives exact chemical descriptions to his examples of logical reasoning. Later, after the discovery of unique parts of atoms (electrons, JJ Tompson, 1897), the chemical examples faded from his writings. The mystical nature of the plethora of electrical forms does not rest comfortably in this semantic milieu. The formal inquiries of chemistry are referenced to and indexed by the chemical table of elements (which CSP acknowledged as the bedrock of his reasoning.) A formal logic of the chemical sciences is based on five indices. These five indices are the molecular weight, the molecular formula, the molecular number, the molecular structure, and the handedness. By convention, the name of a chemical molecule is commensurable with exactly one permutation group that matches these quali-signs. The molecular permutation group matches the index with the sin-sign. The indices of the permutation group also match the existential bipolar graphs representing atomic and molecular sentences as well as metabolic graphs. The formal logic of chemistry matches the meanings of these terms with the signs emanating from the sin-sign. The one to many and many to one mappings unconcealed (Wittgenstein, Heidegger, Whitehead) by the quali-signs reveal the composition of the identity of the object. The proof of the validity of the matchings of numerical terms is valided by the adjunctive synthesis of the object designated by the sin-sign. The antecedent and consequent are related by analysis and synthesis. Metaphorically, one can propose a
