Re: [PEIRCE-L] Triadic and Tetradic relations

[Jon Alan Schmidt]

Jeff, List:

JD:  On my interpretation of the text, the law of inertia functions as the
third correlate in the triadic relation.


Are there any passages in Peirce's writings where he *explicitly *presents
a triadic relation that has a law as one of its correlates?

JD:  We can analyze the relation in a number of ways, here is a simple
version:  A determines B to accelerate in accord with LI.


How would you diagram this as an Existential Graph?

JD:  A fuller analysis would involve a closer look at LI.  Newton's account
of this law takes the following form:  Force of inertia=mass*acceleration.


A mathematical equation is a diagram of a *hypothetical *state of things.
We effectively *define *force and mass in accordance with this equation,
which is why it includes no arbitrary constants.  The equation for the
force due to gravity *requires *such a constant in order to make it *compatible
*with this one, and the *value *of that constant must be determined
*empirically*.  It seems to me that *this *is why the one "is taken to be
unchanging in its form," while the other "might be evolving"; we have to
keep checking the calculations to confirm that the constant is *really *
constant.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Tue, May 14, 2019 at 2:29 PM Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Jon S, Gary F, John S, List,
>
> Let me offer a brief response to the objection Jon S. raised earlier.
>
> JD:  I take the expression of the conditional (i.e., expressed in the EGs
> by a scroll)  to involve a genuinely triadic relation because there is a
> law that governs the relation.
>
> Jon S:  What is the warrant for taking *every *relation that is governed
> by a law to be *genuinely triadic* on that sole basis?  On the contrary,
> most (if not all) *dyadic *relations that we encounter in experience are
> governed by laws in some way, but we still classify them as dyadic because
> they have *exactly two* correlates; the law itself is *not *a third
> correlate.
>
> CSP:  Any dynamic action--say, the attraction by one particle of
> another--is in itself *dyadic*. It is governed by a law; but that law no
> more furnishes a correlate to the relation than the vote of a legislator
> which insures a bill's becoming a statute makes him a participator in the
> blow of the swordsman who, in obedience to the warrant issued after
> conviction according to that statute, strikes off the head of a condemned
> man. (CP 6.330; 1908)
>
> Jon S: Even a *degenerate *dyadic relation is governed by a law; e.g.,
> the hardness of a diamond consists in the truth of the conditional
> proposition that if it *were *to be rubbed with another substance, it
> *would *resist scratching.  Are there any passages in Peirce's writings
> where he characterized a relation with *exactly two* correlates as
> triadic?
>
> Jeff D:  Most of the relations that we encounter in experience are rich
> and complex. Consider the experience of one billiard ball A colliding
> with another B in accordance with the law of inertia LI. We can abstract
> from the law of inertia and attend solely to the dynamical relation
> between A and B as existing individuals. There is a fact about each. A is
> in motion, and then it collides with B, which was stationary. As a
> result, B moves. That can be treated as a dynamical dyadic relation that
> is formally ordered such that A is agent and B is patient. Considered in
> this way, we treat the dyadic relation between them as a mere matter of
> brute force.
>
> Alternately, we can consider the relation between the fact that A was
> moving and B was stationary, and then the later fact that B was put into
> motion as a result of the collision as being governed by the law of inertia
> (LI). According to Peirce's classification of relations in "The Logic of
> Mathematics,...), this is a genuinely triadic relation of fact. All such
> genuinely triadic relations of fact are governed by some kind of law. On my
> interpretation of the text, the law of inertia functions as the third
> correlate in the triadic relation. We can analyze the relation in a number
> of ways, here is a simple version:  A determines B to accelerate in accord
> with LI.
>
> A fuller analysis would involve a closer look at LI.  Newton's account of
> this law takes the following form:  Force of inertia=mass*acceleration.
> How does the law of inertia govern the relations between the facts
> concerning A and B? The first fact attributes qualities to each (i.e., each
> billiard ball has a position at the first time, such that A is in motion
> heading towards the other ball and B is not in motion). The second fact
> attributes a different set of qualities to each. The law governs the
> changes in those facts so that there is a general regularity that governs
> other possible interactions between any masses of this 

Re: [PEIRCE-L] Triadic and Tetradic relations

[Jeffrey Brian Downard]

hat I see between the law of inertia and the law of 
gravity is that, on Peirce's account, the former is governed by (if you will) a 
logical law of deductive demonstration. As such, the law is taken to be 
unchanging in its form.

The law of gravity, on the other hand, might very well continue to evolve. For 
instance, gravitational "constant" in Newton's version of the law might be 
evolving. Furthermore, it's being an inverse square law and not an inverse of a 
2.1 power might not be fixed. Rather, the inverse power relation (as a function 
of distance) might be evolving.

The fundamental law governing the evolution of the law of gravity is, on 
Peirce's account, the one law of mind. On my reading of this text, we can 
understand that law to be an objective manifestation of the one law of logic. 
In this case, the third clause that is governing the law of gravity is not one 
of deductive demonstration. Rather, it is one that brings abductive and 
inductive patterns of inference to bear on the ongoing formation of the spatial 
and temporal habits in their relations to the distribution of mass both locally 
and globally (e.g., understood in terms of the paths that are possible through 
a given space).

There appears to be a difference between the operation of these laws. The law 
of inertia is, at this point in the history of the universe, relatively static 
and dead. For the most part, it operates in an efficient, mechanical, linear, 
conservative manner. The law of gravity, on the other hand, continues to 
evolve. As a law, it appears to have some sort of life.

Is the claim that the law of inertia seems to govern the motions of masses in a 
manner that is akin to a form of logical demonstration, while the law of 
gravity seems to govern the relations between space and mass in a manner that 
is akin to a form of logical abduction and/or induction testable as a 
hypothesis? My hunch is that it is a testable hypothesis.

Yours,

Jeff




Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354



From: Jon Alan Schmidt 
Sent: Sunday, May 12, 2019 11:57 AM
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Triadic and Tetradic relations

Jeff, List:

JD:  I take the expression of the conditional to involve a genuinely triadic 
relation because there is a law that governs the relation.

What is the warrant for taking every relation that is governed by a law to be 
genuinely triadic on that sole basis?  On the contrary, most (if not all) 
dyadic relations that we encounter in experience are governed by laws in some 
way, but we still classify them as dyadic because they have exactly two 
correlates; the law itself is not a third correlate.

CSP:  Any dynamic action--say, the attraction by one particle of another--is in 
itself dyadic. It is governed by a law; but that law no more furnishes a 
correlate to the relation than the vote of a legislator which insures a bill's 
becoming a statute makes him a participator in the blow of the swordsman who, 
in obedience to the warrant issued after conviction according to that statute, 
strikes off the head of a condemned man. (CP 6.330; 1908)

Even a degenerate dyadic relation is governed by a law; e.g., the hardness of a 
diamond consists in the truth of the conditional proposition that if it were to 
be rubbed with another substance, it would resist scratching.  Are there any 
passages in Peirce's writings where he characterized a relation with exactly 
two correlates as triadic?

JD:  I take the EGs to be topological in character. As a formal system, they 
are based on the notion of relations of composition and transformation that 
hold between areas on a sheet of assertion that is, itself, continuous. Various 
discontinuities are introduced onto the sheet to represent what is existing and 
discrete as individuals, but the continuity of this type of logical system is 
central and not peripheral.

EGs represent the relations of (ter)coexistence and (ter)identity as 
continuous--we can always add another Graph to the Sheet of Assertion, and we 
can always add another branch to any Line of Identity--but they do not 
represent the process of semeiosis as continuous.  Instead, they represent a 
hypothetical instantaneous state of an Argument, and the transformation to a 
subsequent state is always by means of discrete steps.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt<http://www.LinkedIn.com/in/JonAlanSchmidt> - 
twitter.com/JonAlanSchmidt<http://twitter.com/JonAlanSchmidt>

On Sat, May 11, 2019 at 10:22 PM Jeffrey Brian Downard 
mailto:jeffrey.down...@nau.edu>> wrote:

Jon S, List,

JD:  In the Prolegomena, Peirce uses the modal tincture of Fur as a means of 
expressing intentions in the gamma system. The pattern of ermine (or the color 
yellow), is used to r

Re: [PEIRCE-L] Triadic and Tetradic relations

[Jon Alan Schmidt]

Jeff, List:

JD:  I take the expression of the conditional to involve a genuinely
triadic relation because there is a law that governs the relation.


What is the warrant for taking *every *relation that is governed by a law
to be *genuinely triadic* on that sole basis?  On the contrary, most (if
not all) *dyadic *relations that we encounter in experience are governed by
laws in some way, but we still classify them as dyadic because they
have *exactly
two* correlates; the law itself is *not *a third correlate.

CSP:  Any dynamic action--say, the attraction by one particle of
another--is in itself *dyadic*. It is governed by a law; but that law no
more furnishes a correlate to the relation than the vote of a legislator
which insures a bill's becoming a statute makes him a participator in the
blow of the swordsman who, in obedience to the warrant issued after
conviction according to that statute, strikes off the head of a condemned
man. (CP 6.330; 1908)


Even a *degenerate *dyadic relation is governed by a law; e.g., the
hardness of a diamond consists in the truth of the conditional proposition
that if it *were *to be rubbed with another substance, it *would *resist
scratching.  Are there any passages in Peirce's writings where he
characterized a relation with *exactly two* correlates as triadic?

JD:  I take the EGs to be topological in character. As a formal system,
they are based on the notion of relations of composition and transformation
that hold between areas on a sheet of assertion that is, itself,
continuous. Various discontinuities are introduced onto the sheet to
represent what is existing and discrete as individuals, but the continuity
of this type of logical system is central and not peripheral.


EGs represent the relations of (ter)coexistence and (ter)identity as
continuous--we can always add another Graph to the Sheet of Assertion, and
we can always add another branch to any Line of Identity--but they do not
represent the *process of semeiosis* as continuous.  Instead, they
represent a hypothetical *instantaneous *state of an Argument, and the
transformation to a subsequent state is always by means of *discrete *steps.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Sat, May 11, 2019 at 10:22 PM Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Jon S, List,
>
> JD:  In the Prolegomena, Peirce uses the modal tincture of Fur as a means
> of expressing intentions in the gamma system. The pattern of ermine (or the
> color yellow), is used to represent iconically that the area shaded
> expresses an intention on the part of the agent (see Don Roberts, 92-102).
>
>
> JS:  Yes, but the attachment of any EG to the *surface *on which it is
> scribed does not constitute an increase of its valency.  "A surrenders B"
> and "A acquires D" are *dyadic *relations, whether their EGs appear on
> Metal (actuality) or Fur (intention).  A *triadic *relation is one that
> requires a Spot with *three *Pegs to represent it.  Again, what third
> correlate would you identify in order to treat these relations as triadic?
>
>
> JD:  The EGs are formal systems of mathematical logic. Taken alone, the
> systems do not provide adequate answers to the philosophical questions we
> are asking. Rather, they can be used as toolsets. Peirce is trying to
> improve these toolsets for the sake of doing philosophy with the aim of
> ensuring that they do not misrepresent what we seek to clarify. I take
> myself to be starting with a question about some phenomena drawn from
> common experience. Such data are the proper starting point, Peirce
> suggests, for all philosophical inquiries. Consider a case of somebody
> giving something to another person. That is pretty common. Other
> philosophers have made much of these sorts of experiences. Witness the
> essay written by Emerson on the topic.
>
> In the phenomenological analysis of the experience of such activities,
> what kinds of relations are involved? This, I think, is prior to and
> different in some respects from asking the question of what kinds of
> *logical* relations are involved in our general conception of giving.  In
> the cases we've been considering of giving, exchanging and selling, I take
> Peirce to be starting with a more or less particular case in mind--and he
> is filling in the details of that case as he goes. You seem to be
> suggesting that the details don't matter. My reply is that they do for the
> sake of the phenomenological analysis.
>
> We can apply the EGs--considered as mathematical toolsets--in the
> phenomenological analysis of features drawn from our common experience and
> in the logical analysis of common conceptions. It may be more at home in
> the latter case than in the former, but it appears to be useful in both
> areas of inquiry.
>
> Consider the converse way of looking at the relations between the EGs and

Re: [PEIRCE-L] Triadic and Tetradic relations

[John F Sowa]

Jeff, Mike, and Jon,

Mathematics is diagrammatic reasoning, and EGs are a version of
logic that uses a more flexible and versatile system of diagrams
than Peirce's algebra of 1885 or any algebra since then.

But the diagrams are fundamental.  Any words used to describe
the diagrams are useful *only* in teaching and explaining the
diagrams.  Mathematicians, especially Peirce, always think in
terms of the diagrams, not the words that describe the diagrams.

I agree with Jeff's comments and Mike's emphasis of what Jeff said:
MS quoting JD:

I take the EGs to be topological in character. As a formal system,
they are based on the notion of relations of composition and
transformation that hold between areas on a sheet of assertion that
is, itself, continuous. Various discontinuities are introduced onto
the sheet to represent what is existing and discrete as individuals,
but the continuity of this type of logical system is central and not
peripheral.


As an example, I drew the attached diagram EGgiving.png.  It shows
four different EGs for the sentence "Sue gives a child a book."

 1. The EG on the upper left is the simplest.  The relation named
Gives is a triad with three subjects:  Sue, Child, and Book.

 2. The EG on the upper right is transformed from #1 in two ways:

(a) The verb 'gives' may be nominalized to the gerund Giving
by hypostatic abstraction.  That creates a tetra-identity.

(b) Three dyads, named Agent, Recipient, and Theme, are linked to
the three subjects of Give or the gerund Giving.  In linguistics,
those dyads are called case relations or thematic roles.

 3. The EG on the lower left shows that the tetra-identity in #2
may be replaced by two teridentities.  It has no effect on
the semantics of the EG or its translation to the algebra.

 4. The EG on the lower right replaces the triad Gives in #1
with the tetrad Covenant.  It shows that Covenant is linked
to Child by two different dyads:  Co-agent and Recipient.

These examples show how a single EG can replace a vague cloud
of verbiage with a clear and precise diagram.  Since diagrams are
Peirce's natural way of thinking, especially about math & logic,
the diagrams must always take precedence over the words.

During the past century, there have been many new developments in
linguistics, logic, and the many branches of cognitive science.
For example, the labels for thematic roles are very convenient for
highlighting the relationships.  Compare EG #4 in EGgiving.png to
Peirce's explanation:

CSP

Thus, A gives B to C becomes A makes the covenant D with C
and the covenant D gives B to C.  (CP 1.474)


EG #4 shows that Covenant is a tetrad, and the labels Agent,
Co-agent, Recipient, and Theme show how the covenant is related
to each of the three participants.  The EG also shows that the
covenant is related to the child in two distinct ways.

JAS

My purpose (as usual) is to interpret Peirce by attempting to
harmonize each passage that I encounter with his corpus taken
as a whole, in accordance with my systematizing and regularizing
tendencies.


But the diagrams are fundamental and *permanent*.  For first-order
logic, the linear diagrams of 1885 and the 2D diagrams of EGs
have *identical semantics*.  That semantics is also identical to
Frege's version of 1879 and to *every* version of classical FOL
for the past 140 years.

That must be the foundation for any kind of harmonizing,
systematizing, and regularizing.  It is also a solid foundation
for teaching Peirce's logic, semeiotic, and philosophy to any
students and professors who began their education with any other
kind of notation or terminology.

Remember that Peirce admitted that his "left-handed brain" made
it difficult for him to translate his thoughts into words.  That
means that the diagrams are the primary evidence for what he was
thinking, and the words are secondary.

In EG #4, for example, the word 'covenant' has several senses.
Google, for example, lists the following synonyms:  contract,
compact, treaty, pact, accord, deal, bargain, settlement, concordat,
protocol, entente, agreement, arrangement, understanding, pledge,
promise, bond, indenture, guarantee, warrant; undertaking, commitment.

But EG #4 shows that the covenant is an agreement or commitment
by the agent with or to the co-agent that the co-agent would be
the recipient of the book.  That pattern of relationships can
be seen at a glance from EG #4.  There is no need for Googling.

When in doubt, draw a diagram.  That's what Peirce would do.

John

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Re: [PEIRCE-L] Triadic and Tetradic relations

[Mike Bergman]

On 5/11/2019 10:22 PM, Jeffrey Brian Downard wrote:
JD:  I take the EGs to be topological in character. As a 
formal system, they are based on the notion of relations of 
composition and transformation that hold between areas on a sheet of 
assertion that is, itself, continuous. Various discontinuities are 
introduced onto the sheet to represent what is existing and discrete 
as individuals, but the continuity of this type of logical system is 
central and not peripheral.


--
__

Michael K. Bergman
Cognonto Corporation
319.621.5225
skype:michaelkbergman
http://cognonto.com
http://mkbergman.com
http://www.linkedin.com/in/mkbergman
__


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Re: [PEIRCE-L] Triadic and Tetradic relations

[Jeffrey Brian Downard]

Jon S, List,

JD:  In the Prolegomena, Peirce uses the modal tincture of Fur as a means of 
expressing intentions in the gamma system. The pattern of ermine (or the color 
yellow), is used to represent iconically that the area shaded expresses an 
intention on the part of the agent (see Don Roberts, 92-102).

JS:  Yes, but the attachment of any EG to the surface on which it is scribed 
does not constitute an increase of its valency.  "A surrenders B" and "A 
acquires D" are dyadic relations, whether their EGs appear on Metal (actuality) 
or Fur (intention).  A triadic relation is one that requires a Spot with three 
Pegs to represent it.  Again, what third correlate would you identify in order 
to treat these relations as triadic?

JD:  The EGs are formal systems of mathematical logic. Taken alone, the systems 
do not provide adequate answers to the philosophical questions we are asking. 
Rather, they can be used as toolsets. Peirce is trying to improve these 
toolsets for the sake of doing philosophy with the aim of ensuring that they do 
not misrepresent what we seek to clarify. I take myself to be starting with a 
question about some phenomena drawn from common experience. Such data are the 
proper starting point, Peirce suggests, for all philosophical inquiries. 
Consider a case of somebody giving something to another person. That is pretty 
common. Other philosophers have made much of these sorts of experiences. 
Witness the essay written by Emerson on the topic.

In the phenomenological analysis of the experience of such activities, what 
kinds of relations are involved? This, I think, is prior to and different in 
some respects from asking the question of what kinds of logical relations are 
involved in our general conception of giving.  In the cases we've been 
considering of giving, exchanging and selling, I take Peirce to be starting 
with a more or less particular case in mind--and he is filling in the details 
of that case as he goes. You seem to be suggesting that the details don't 
matter. My reply is that they do for the sake of the phenomenological analysis.

We can apply the EGs--considered as mathematical toolsets--in the 
phenomenological analysis of features drawn from our common experience and in 
the logical analysis of common conceptions. It may be more at home in the 
latter case than in the former, but it appears to be useful in both areas of 
inquiry.

Consider the converse way of looking at the relations between the EGs and 
phenomenology. Peirce often is drawing on the phenomenological analysis of 
common experience as he develops and refines the EGs. He explicitly says that 
the analysis of common phenomena such as the practice of counting and the 
activity of moving a particle from a point on a piece of paper are guiding the 
formulation of the postulates for mathematical systems of number theory, 
topology. The same is true in the development of the conventions (i.e., 
permissions, precepts and postulates) of the EGs.

You claim that "the attachment of any EG to the surface on which it is scribed 
does not constitute an increase of its valency." The question, I take it, was 
whether the EGs represent different kinds of relations in the case of "A gives 
up B" (as scribed in the beta system) as compared "A intends to give up B" (as 
scribed in the gamma system). In the gamma system, the intention of A giving up 
B is represented in an area of that is colored yellow to represent its modal 
character as something that is or was intended.

On my interpretation of such a graph in the gamma system, the differently 
colored areas of the sheet represent different kinds of relations as compared 
to an existential dyadic relation that is represented by spots and lines of 
identity in the beta system. In addition to the relations between the different 
shaded areas that are represented on one side of the SA, there are also the 
relations to what is represented on the other side and/or on other deeper 
sheets in a book with different modal characteristics. My assumption is that, 
just as a cut may take us from one sheet to another that is deeper, the shading 
may also represent relations that penetrate down into those sheets that lie 
below. My approach to interpreting these different sheets is to think of them 
as 2-dimensional slices through a multidimensional topological space. I'll 
leave the implications of such a reading to the side.

JD:  You say: "'A surrenders B' and 'A acquires D' are dyadic relations, 
whether their EGs appear on Metal (actuality) or Fur (intention).  A triadic 
relation is one that requires a Spot with three Pegs to represent it." As you 
can tell, I see things differently. One does not need to consider the 
intricacies of the gamma system to understand the main point I am trying to 
make. Compare these two assertions:  "A shot B in the heart and he died" and 
"If A shoots B in the heart, then B will die." What is the upshot of scribing 
both in the beta 

Re: [PEIRCE-L] Triadic and Tetradic relations

[Jon Alan Schmidt]

Jeff, List:

My purpose (as usual) is to interpret Peirce by attempting to harmonize
each passage that I encounter with his corpus taken as a whole, in
accordance with my systematizing and regularizing tendencies.  In this
case, I am mainly just calling attention to the incongruity of treating the
relations of surrendering and acquiring as triadic, rather than dyadic.
If, in fact, Peirce was incorrect to do so in this particular manuscript,
then that obviously casts doubt on its usefulness for understanding what he
said elsewhere.

I would also like to point out that as far as I can tell, the concept of a
"thoroughly genuine triadic relation" appears *only *in "The Logic of
Mathematics" (c. 1896), and not in any of Peirce's subsequent writings,
with one notable exception.

CSP:  It may here be remarked that Combination is a triadic relation
between the two elements (for every Combination results from successive
couplings) and the result, and is in so far genuine that it cannot be
analyzed into any Combination of dyadic relations. But Combination is not a
thoroughly genuine triadic relation, since the different elements, the
Combinants, are (as far as the mere relation of combination goes) in
precisely the same relation to the result, the Combinate. (EP 2:391; 1906
Jan)


With all of that said, far be it from me to block the way of inquiry--if
you are finding it fruitful to continue down the road that you are
pursuing, by all means keep going.

Thanks,

Jon S.

On Sat, May 11, 2019 at 8:17 PM Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Jon S,
>
> If I understand you correctly, then it appears that we are guided--at
> least in part--by different purposes.
>
> I am trying to interpret Peirce's account triadic relations and square it
> with what he says about tetradic and higher ordered relations. You, on the
> other hand, don't accept some of the claims he is making, and you are
> asking me for demonstrations that Peirce's analyses of these relations are
> correct.
>
> Given the fact that I don't take myself to understand what he is saying in
> these puzzles passages in the 1905 letter to Lady Welby, it seems a bit
> premature to ask me for demonstrations that his assertions are correct. I'm
> just trying to work out some interpretative hypotheses and then see if they
> square with--and perhaps even shed some light on--what he says about the
> living character of thoroughly genuine triadic relations. My primary
> interest is in explaining the living character of these relations, and I'm
> looking at puzzling passages as a way of testing the general approach I've
> been exploring.
>
> It is good, I think, to be clear about one's purpose in making a post. As
> such, I'm making mine more explicit now.
>
> Yours,
>
> Jeff
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354
>
> ----------
> *From:* Jon Alan Schmidt 
> *Sent:* Saturday, May 11, 2019 6:02 PM
> *To:* peirce-l@list.iupui.edu
> *Subject:* Re: [PEIRCE-L] Triadic and Tetradic relations
>
> John, List:
>
> JFS:  To clarify these issues, search CP for every occurrence of "A gives
> B".
>
>
> I did exactly that last night, and what I found has influenced my
> responses accordingly.
>
> CSP;  ... every dyad by a particularization evolves a dyadic triad. Thus,
> A murders B is a generalization of A shoots that bullet, and the bullet
> fatally wounds B. (CP 1.474; c. 1896)
>
> JFS:  By the same analysis, 'surrender' and 'acquisition' would be dyadic
> triads ...
>
>
> What replaces the bullet as the third correlate if we evolve "A surrenders
> B" or "A acquires D" into a dyadic triad?
>
> Incidentally, there are various circumstances when "A murders B" is *not *
> an accurate generalization of "A shoots that bullet" and "that bullet
> fatally woulds B"--e.g., if A and B are soldiers for opposing armies during
> a battle, or if A is acting in self-defense, or if B is not a human being,
> or if the shooting is accidental.
>
> Regards,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Professional Engineer, Amateur Philosopher, Lutheran Layman
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>
> On Sat, May 11, 2019 at 1:26 PM John F Sowa  wrote:
>
>> Jeff and Jon,
>>
>> To clarify these issues, search CP for every occurrence of
>> "A gives B".  Peirce states the issues in different ways,
>> but the following example illustrates the general principle:
>>
>> > A triad may be explicated into a triadic tetrad. Thus, A gives B
>> > to C becomes A makes the covenant D with C and the covenant D
&

Re: [PEIRCE-L] Triadic and Tetradic relations

[Jon Alan Schmidt]

Jeff, List:

JD:  Insofar as there is a mental component involved in each, both are
genuinely triadic in their character because the existential facts are now
considered to be governed by general habits of thought.


In the quoted passage (CP 8.331; 1904 Oct 12), Peirce did not say that
having a mental component makes a relation *genuinely *triadic.  On the
contrary, he stated at the end of the text that you omitted at the first
ellipsis, "If you take any *ordinary *triadic relation, you will *always *find
a mental element in it. Brute action is secondness, *any* mentality
involves thirdness" (emphases added).  His subsequent example demonstrates
this.

CSP:  But now suppose that giving *did *consist merely in A's laying down
the B which C subsequently picks up. That would be a degenerate form of
Thirdness in which the thirdness is externally appended. In A's putting
away B, there is no thirdness. In C's taking B, there is no thirdness. But
if you say that these two acts constitute a single operation by virtue of
the identity of the B, you transcend the mere brute fact, you introduce a
mental element."


Even a *degenerate *triadic relation, in which one correlate is in dyadic
relations with two other correlates such that those two acts constitute a
single operation, has a mental element.  Therefore, introducing the mental
element of *intention *into the dyadic relations of surrendering and
acquiring does not somehow turn them into *genuine *triadic relations;
rather, a dyadic triad is always a *degenerate *triadic relation.
Moreover, it still requires a *third *correlate in order to be a
*triadic *relation
at all, like the bullet in Peirce's (corrected) example of "A kills B"
evolving into "A shoots that bullet" and "that bullet fatally wounds B."
If we cannot identify a *third *correlate in the relations of surrendering
and acquiring, then I do not see how we can legitimately treat them as *triadic
*relations.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Sat, May 11, 2019 at 4:59 PM Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> John S, Jon S, List,
>
> JohnS:  To clarify these issues, search CP for every occurrence of
>
> "A gives B".
>
>
> Jeff D: Here is one passage that is particularly germane to the question
> at hand. When Peirce claims that giving is a genuinely triadic relation,
> I take note of the fact that in the "Logic of Mathematics, an attempt to
> develop my categories from within" the intentional act of one person giving
> something to another person under a law is classified, on my reading of
> the text, as a paradigmatic example of *thoroughly* genuine triadic
> relation.
>
> Consider the following passage:
>
> I now come to Thirdness. To me, who have for forty years considered the matter
> from every point of view that I could discover, the inadequacy of Secondness 
> to
> cover all that is in our minds is so evident that I scarce know how to
> begin to persuade any person of it who is not already convinced of it.
> ... Analyze for instance the relation involved in 'A gives B to C.' Now
> what is giving? It does not consist [in] A's putting B away from him and
> C's subsequently taking B up. It is not necessary that any material
> transfer should take place. It consists in A's making C the possessor 
> according
> to * Law. *There must be some kind of law before there can be any kind of 
> giving,
> -- be it but the law of the strongest. But now suppose that giving *did *
> consist merely in A's laying down the B which C subsequently picks up.
> That would be a degenerate form of Thirdness in which the thirdness is
> externally appended. In A's putting away B, there is no thirdness. In C's
> taking B, there is no thirdness. But if you say that these two acts
> constitute a single operation by virtue of the identity of the B, you
> transcend the mere brute fact, you introduce a mental element . . . . The
> criticism which I make on [my] algebra of dyadic relations, with which I
> am by no means in love, though I think it is a pretty thing, is that the
> very triadic relations which it does not recognize, it does itself
> employ. For every combination of relatives to make a new relative is a
> triadic relation irreducible to dyadic relations. Its *inadequacy *is
> shown in other ways, but in this way it is in a conflict with itself *if
> it be regarded, *as I never did regard it, * as sufficient for the
> expression of all relations. *My universal algebra of relations, with the
> subjacent indices and and, is susceptible of being enlarged so as to
> comprise everything; and so, still better, though not to ideal perfection,
> is the system of * existential graphs. *CP 8.331
>
>
> In this passage, Peirce says that the relation of giving does not consist 
> merely
> in the following two facts:
>
>
>
>1. A's putting B away from him, and
>2. 

Re: [PEIRCE-L] Triadic and Tetradic relations

[Jeffrey Brian Downard]

Jon S,


If I understand you correctly, then it appears that we are guided--at least in 
part--by different purposes.


I am trying to interpret Peirce's account triadic relations and square it with 
what he says about tetradic and higher ordered relations. You, on the other 
hand, don't accept some of the claims he is making, and you are asking me for 
demonstrations that Peirce's analyses of these relations are correct.


Given the fact that I don't take myself to understand what he is saying in 
these puzzles passages in the 1905 letter to Lady Welby, it seems a bit 
premature to ask me for demonstrations that his assertions are correct. I'm 
just trying to work out some interpretative hypotheses and then see if they 
square with--and perhaps even shed some light on--what he says about the living 
character of thoroughly genuine triadic relations. My primary interest is in 
explaining the living character of these relations, and I'm looking at puzzling 
passages as a way of testing the general approach I've been exploring.


It is good, I think, to be clear about one's purpose in making a post. As such, 
I'm making mine more explicit now.


Yours,


Jeff


Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354



From: Jon Alan Schmidt 
Sent: Saturday, May 11, 2019 6:02 PM
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Triadic and Tetradic relations

John, List:

JFS:  To clarify these issues, search CP for every occurrence of "A gives B".

I did exactly that last night, and what I found has influenced my responses 
accordingly.

CSP;  ... every dyad by a particularization evolves a dyadic triad. Thus, A 
murders B is a generalization of A shoots that bullet, and the bullet fatally 
wounds B. (CP 1.474; c. 1896)
JFS:  By the same analysis, 'surrender' and 'acquisition' would be dyadic 
triads ...

What replaces the bullet as the third correlate if we evolve "A surrenders B" 
or "A acquires D" into a dyadic triad?

Incidentally, there are various circumstances when "A murders B" is not an 
accurate generalization of "A shoots that bullet" and "that bullet fatally 
woulds B"--e.g., if A and B are soldiers for opposing armies during a battle, 
or if A is acting in self-defense, or if B is not a human being, or if the 
shooting is accidental.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt<http://www.LinkedIn.com/in/JonAlanSchmidt> - 
twitter.com/JonAlanSchmidt<http://twitter.com/JonAlanSchmidt>

On Sat, May 11, 2019 at 1:26 PM John F Sowa 
mailto:s...@bestweb.net>> wrote:
Jeff and Jon,

To clarify these issues, search CP for every occurrence of
"A gives B".  Peirce states the issues in different ways,
but the following example illustrates the general principle:

> A triad may be explicated into a triadic tetrad. Thus, A gives B
> to C becomes A makes the covenant D with C and the covenant D
> gives B to C.  (CP 1.474)

By this analysis, Peirce used hypostatic abstraction to convert
'gives' into a covenant D that relates A, B, and C.  But that
tetrad is "degenerate" in the sense that it is derived from
a triad.

Earlier in paragraph 1.474, he writes
> every dyad by a particularization evolves a dyadic triad. Thus,
> A murders B is a generalization of A shoots that bullet, and the
> bullet fatally wounds B.

By the same analysis, 'surrender' and 'acquisition' would
be dyadic triads in
> d.  μ is the surrender by A of B
> e.  m is the surrender by C of D
> g.  ν is the acquisition by A of D
> h.  η is the acquisition by C of B

John

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Re: [PEIRCE-L] Triadic and Tetradic relations

[Jon Alan Schmidt]

John, List:

JFS:  To clarify these issues, search CP for every occurrence of "A gives
B".


I did exactly that last night, and what I found has influenced my responses
accordingly.

CSP;  ... every dyad by a particularization evolves a dyadic triad. Thus, A
murders B is a generalization of A shoots that bullet, and the bullet
fatally wounds B. (CP 1.474; c. 1896)

JFS:  By the same analysis, 'surrender' and 'acquisition' would be dyadic
triads ...


What replaces the bullet as the third correlate if we evolve "A surrenders
B" or "A acquires D" into a dyadic triad?

Incidentally, there are various circumstances when "A murders B" is *not *an
accurate generalization of "A shoots that bullet" and "that bullet fatally
woulds B"--e.g., if A and B are soldiers for opposing armies during a
battle, or if A is acting in self-defense, or if B is not a human being, or
if the shooting is accidental.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Sat, May 11, 2019 at 1:26 PM John F Sowa  wrote:

> Jeff and Jon,
>
> To clarify these issues, search CP for every occurrence of
> "A gives B".  Peirce states the issues in different ways,
> but the following example illustrates the general principle:
>
> > A triad may be explicated into a triadic tetrad. Thus, A gives B
> > to C becomes A makes the covenant D with C and the covenant D
> > gives B to C.  (CP 1.474)
>
> By this analysis, Peirce used hypostatic abstraction to convert
> 'gives' into a covenant D that relates A, B, and C.  But that
> tetrad is "degenerate" in the sense that it is derived from
> a triad.
>
> Earlier in paragraph 1.474, he writes
> > every dyad by a particularization evolves a dyadic triad. Thus,
> > A murders B is a generalization of A shoots that bullet, and the
> > bullet fatally wounds B.
>
> By the same analysis, 'surrender' and 'acquisition' would
> be dyadic triads in
> > d.  μ is the surrender by A of B
> > e.  m is the surrender by C of D
> > g.  ν is the acquisition by A of D
> > h.  η is the acquisition by C of B
>
> John
>

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Re: [PEIRCE-L] Triadic and Tetradic relations

[Jon Alan Schmidt]

Jeff, List:

JD:  In the Prolegomena, Peirce uses the modal tincture of Fur as a means
of expressing intentions in the gamma system. The pattern of ermine (or the
color yellow), is used to represent iconically that the area shaded
expresses an intention on the part of the agent (see Don Roberts, 92-102).


Yes, but the attachment of any EG to the *surface *on which it is scribed
does not constitute an increase of its valency.  "A surrenders B" and "A
acquires D" are *dyadic *relations, whether their EGs appear on Metal
(actuality) or Fur (intention).  A *triadic *relation is one that requires
a Spot with *three *Pegs to represent it.  Again, what third correlate
would you identify in order to treat these relations as triadic?

JD:  The analysis he provides shows that Peirce was thinking of a transfer
involving money and a contract, which means that the transfer was not
simultaneous. Barter, as a form of exchange, is often simultaneous. When it
is, that makes the exchange considerably simpler in character.


A contract is not *essential *to the relation of selling, and my
understanding is that time has no bearing on *logical *relations.  I still
have a hard time seeing how bartering is any *simpler *than selling, other
than the peculiar aspect of money being transferred rather than another
item.

JD:  It does not follow from the simple fact that the analyses involve *entia
rationis* that such creations of the mind may not represent something real.


I did not suggest otherwise.  My point was that the *number *of different
relations that we obtain from analysis is *arbitrary *to some degree,
because we are using something *discrete *to represent something that in
itself is *continuous*.

JD:  Notice how Peirce puts the point. In a tetradic relation, there are at
most 10 triadic relations involved, whereas in a pentadic relation, there
are at most 100 triadic relations involved.


Peirce *asserted *these claims, but he certainly did not *demonstrate *either
of them.  If introducing the *non-essential* element of a contract is
necessary in order to analyze the tetradic relation of selling into six
triadic relations, what prevents us from introducing any number of *additional
*non-essential elements in order to analyze it into more than ten?  On the
other hand, I ask yet again--what *essential *element is omitted by
analyzing selling into *only four* triadic relations, two of giving and two
of exchanging?

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Sat, May 11, 2019 at 12:42 PM Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Jon S, List,
>
> JD:  In order to interpret "μ is the surrender by A of B" and "ν is the
> acquisition by A of D" as triadic and not merely dyadic relations, my hunch
> is that he is considering these actions as intentional in character.
>
>
> JS:  Maybe, but then how would you restate them as *explicitly *having
> three correlates, perhaps by presenting each as an EG?  And would they then
> be *genuine *or *degenerate* triadic relations?
>
>
> JD: The relation of surrendering, considered as formally ordered dynamical
> dyadic relation, is a relation that can be expressed in the beta system of
> the EG. If μ is understood to involve an intention on the part of A, then
> it can't be expressed in those terms. In the Prolegomena, Peirce uses the
> modal tincture of Fur as a means of expressing intentions in the gamma
> system. The pattern of ermine (or the color yellow), is used to represent
> iconically that the area shaded expresses an intention on the part of the
> agent (see Don Roberts, 92-102). Understanding the character of the
> triadic relations that hold between the areas that are patterned
> or shaded one way to the other areas of the graph is not a simple matter.
> Hence the difficulties of sorting out the modal relations using the
> tinctures (or colors). In his monograph, Don Roberts attempts to revise the
> tinctures in order to overcome some of the concerns that Peirce raised
> about this manner of expressing modal relations in the gamma system. Given
> the complexities involved, I won't try to answer the question of whether
> the triadic relations involved are genuine or degenerate in some
> respects.
>
> JD:  The case that you cite of an object being sold involves a transfer of
> money and a contract. The simpler case of exchange as barter with no
> contract is illustrative of how other kinds of relations may be involved
> when more general things, such as property laws and legal systems, are
> governing the intentional acts.
>
>
> JS: There is no reference to a contract in the initial proposition, "S
> sells T to B for M"; and it is *isomorphic *with the allegedly simpler
> case, "A gives up B to C in exchange for D."  In other words, it seems to
> me that "sells X for Y" is *logically *the same relation as "gives up X
> in 

Re: [PEIRCE-L] Triadic and Tetradic relations

[Jeffrey Brian Downard]

John S, Jon S, List,


JohnS:  To clarify these issues, search CP for every occurrence of
"A gives B".

Jeff D: Here is one passage that is particularly germane to the question at 
hand. When Peirce claims that giving is a genuinely triadic relation, I take 
note of the fact that in the "Logic of Mathematics, an attempt to develop my 
categories from within" the intentional act of one person giving something to 
another person under a law is classified, on my reading of the text, as a 
paradigmatic example of thoroughly genuine triadic relation.

Consider the following passage:


I now come to Thirdness. To me, who have for forty years considered the matter 
from every point of view that I could discover, the inadequacy of Secondness to 
cover all that is in our minds is so evident that I scarce know how to begin to 
persuade any person of it who is not already convinced of it. ... Analyze for 
instance the relation involved in 'A gives B to C.' Now what is giving? It does 
not consist [in] A's putting B away from him and C's subsequently taking B up. 
It is not necessary that any material transfer should take place. It consists 
in A's making C the possessor according to Law. There must be some kind of law 
before there can be any kind of giving, -- be it but the law of the strongest. 
But now suppose that giving did consist merely in A's laying down the B which C 
subsequently picks up. That would be a degenerate form of Thirdness in which 
the thirdness is externally appended. In A's putting away B, there is no 
thirdness. In C's taking B, there is no thirdness. But if you say that these 
two acts constitute a single operation by virtue of the identity of the B, you 
transcend the mere brute fact, you introduce a mental element . . . . The 
criticism which I make on [my] algebra of dyadic relations, with which I am by 
no means in love, though I think it is a pretty thing, is that the very triadic 
relations which it does not recognize, it does itself employ. For every 
combination of relatives to make a new relative is a triadic relation 
irreducible to dyadic relations. Its inadequacy is shown in other ways, but in 
this way it is in a conflict with itself if it be regarded, as I never did 
regard it, as sufficient for the expression of all relations. My universal 
algebra of relations, with the subjacent indices and and, is susceptible of 
being enlarged so as to comprise everything; and so, still better, though not 
to ideal perfection, is the system of existential graphs. CP 8.331


In this passage, Peirce says that the relation of giving does not consist 
merely in the following two facts:


  1.  A's putting B away from him, and
  2.  C's subsequently taking B up.

On the analysis offered at CP 1.474, I agree that both of these 
facts--considered as individual facts about existing objects--are dyadic in 
character. Both facts may, by particularization, be evolved into a dyadic 
triad. Note that the particularization requires a further evolution of the 
dyadic relations involved in each fact into a dyadic triad.

Those same facts can also be analyzed as being parts of intentional actions. 
Insofar as there is a mental component involved in each, both are genuinely 
triadic in their character because the existential facts are now considered to 
be governed by general habits of thought. What is more, Peirce notes that B 
does need not be an existing object. It might, for instance, be a piece of 
intellectual property, such as the rights of ownership to a patented invention.

As such, I believe that this passage provides a basis for analyzing some acts 
of giving as involving three genuinely triadic relations.


  1.  The intentional action μ which consists in A surrendering B
  2.  The intentional action η which consists in C acquiring B
  3.  Μ is the performance of μ with the 
intent of bringing about η under a Law of some kind.

In offering this analysis, I accept the general point that a genuinely triadic 
relation a combination of two or more individual facts concerning existential 
objects under some genuine third that, as a general, governs the interaction of 
the two.

My suggestion is that a thoroughly genuine triadic relation also involves three 
genuinely triadic relations that are brought together by a genuinely triadic 
relation. What is special about representations, Peirce says, is that they are 
not governed by mere laws of fact.

Peirce says:


Genuine triads are of three kinds. For while a triad if genuine cannot be in 
the world of quality nor in that of fact, yet it may be a mere law, or 
regularity, of quality or of fact. But a thoroughly genuine triad is separated 
entirely from those worlds and exists in the universe of representations. 
Indeed, representation necessarily involves a genuine triad. For it involves a 
sign, or representamen, of some kind, outward or inward, mediating between an 
object and an interpreting thought. Now this 

Re: [PEIRCE-L] Triadic and Tetradic relations

[John F Sowa]

Jeff and Jon,

To clarify these issues, search CP for every occurrence of
"A gives B".  Peirce states the issues in different ways,
but the following example illustrates the general principle:


A triad may be explicated into a triadic tetrad. Thus, A gives B
to C becomes A makes the covenant D with C and the covenant D
gives B to C.  (CP 1.474)


By this analysis, Peirce used hypostatic abstraction to convert
'gives' into a covenant D that relates A, B, and C.  But that
tetrad is "degenerate" in the sense that it is derived from
a triad.

Earlier in paragraph 1.474, he writes

every dyad by a particularization evolves a dyadic triad. Thus,
A murders B is a generalization of A shoots that bullet, and the
bullet fatally wounds B.


By the same analysis, 'surrender' and 'acquisition' would
be dyadic triads in

d.  μ is the surrender by A of B
e.  m is the surrender by C of D
g.  ν is the acquisition by A of D
h.  η is the acquisition by C of B


John

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Re: [PEIRCE-L] Triadic and Tetradic relations

[Jeffrey Brian Downard]

Jon S, List,

JD:  In order to interpret "μ is the surrender by A of B" and "ν is the 
acquisition by A of D" as triadic and not merely dyadic relations, my hunch is 
that he is considering these actions as intentional in character.

JS:  Maybe, but then how would you restate them as explicitly having three 
correlates, perhaps by presenting each as an EG?  And would they then be 
genuine or degenerate triadic relations?

JD: The relation of surrendering, considered as formally ordered dynamical 
dyadic relation, is a relation that can be expressed in the beta system of the 
EG. If μ is understood to involve an intention on the part of A, then it can't 
be expressed in those terms. In the Prolegomena, Peirce uses the modal tincture 
of Fur as a means of expressing intentions in the gamma system. The pattern of 
ermine (or the color yellow), is used to represent iconically that the area 
shaded expresses an intention on the part of the agent (see Don Roberts, 
92-102). Understanding the character of the triadic relations that hold between 
the areas that are patterned or shaded one way to the other areas of the graph 
is not a simple matter. Hence the difficulties of sorting out the modal 
relations using the tinctures (or colors). In his monograph, Don Roberts 
attempts to revise the tinctures in order to overcome some of the concerns that 
Peirce raised about this manner of expressing modal relations in the gamma 
system. Given the complexities involved, I won't try to answer the question of 
whether the triadic relations involved are genuine or degenerate in some 
respects.

JD:  The case that you cite of an object being sold involves a transfer of 
money and a contract. The simpler case of exchange as barter with no contract 
is illustrative of how other kinds of relations may be involved when more 
general things, such as property laws and legal systems, are governing the 
intentional acts.

JS: There is no reference to a contract in the initial proposition, "S sells T 
to B for M"; and it is isomorphic with the allegedly simpler case, "A gives up 
B to C in exchange for D."  In other words, it seems to me that "sells X for Y" 
is logically the same relation as "gives up X in exchange for Y."  Do you 
disagree?  Again, is an essential element somehow omitted if we analyze the 
tetradic relation of selling (or bartering) as a combination of only four 
triadic relations, two of giving (genuine) and two of exchanging (degenerate)?

JD: The initial description is underdetermined. The analysis he provides shows 
that Peirce was thinking of a transfer involving money and a contract, which 
means that the transfer was not simultaneous. Barter, as a form of exchange, is 
often simultaneous. When it is, that makes the exchange considerably simpler in 
character. That is one reason that exchange by barter may have preceded the 
development of formal systems of law.

JD:  How many triadic relations are involved in this process of a young child 
learning? Well, it appears to grow according to a power law. As such, it grows 
into a multitude that exceeds any system of numbers that is numerable or even 
any system that is abnumerable.

JS: Of course it does, because real semeiosis is continuous--it is not composed 
of discrete relations (prescinded predicates) and their discrete correlates 
(abstracted subjects) as expressed in definite propositions; those are all 
artificial creations of thought for the purposes of description and analysis.

JD:  It does not follow from the simple fact that the analyses involve entia 
rationis that such creations of the mind may not represent something real. 
Notice how Peirce puts the point. In a tetradic relation, there are at most 10 
triadic relations involved, whereas in a pentadic relation, there are at most 
100 triadic relations involved. It does not follow from the claim that semiosis 
is continuous that there are, somehow, an unlimited number of triadic relations 
involved. Inserting a real triadic relation where, before, one was only a 
potentiality, can be done any number of times. In doing so, however, you've 
made a new relation.

Yours,

Jeff


On Fri, May 10, 2019 at 10:44 PM Jeffrey Brian Downard 
mailto:jeffrey.down...@nau.edu>> wrote:

Jon S., List,

My strategy for interpreting these passages is to take Peirce at his word when 
he refers to the triadic relations that are involved. In order to interpret "μ 
is the surrender by A of B" and "ν is the acquisition by A of D" as triadic and 
not merely dyadic relations, my hunch is that he is considering these actions 
as intentional in character. The object surrendered and the agent who 
surrenders it are existing individuals in the relation of agent and patient, 
but that existential description of the individuals is part of an intentional 
action by A. As a general sort of thing, the intention makes the action of 
surrendering triadic in character--and so too with the action of A 

Re: [PEIRCE-L] Triadic and Tetradic relations

[Jon Alan Schmidt]

Jeff, List:

JD:  My strategy for interpreting these passages is to take Peirce at his
word when he refers to the triadic relations that are involved.


Normally I would do likewise, which is why I find them so problematic.

JD:  In order to interpret "μ is the surrender by A of B" and "ν is the
acquisition by A of D" as triadic and not merely dyadic relations, my hunch
is that he is considering these actions as intentional in character.


Maybe, but then how would you restate them as *explicitly *having three
correlates, perhaps by presenting each as an EG?  And would they then
be *genuine
*or *degenerate* triadic relations?

JD:  The case that you cite of an object being sold involves a transfer of
money and a contract. The simpler case of exchange as barter with no
contract is illustrative of how other kinds of relations may be involved
when more general things, such as property laws and legal systems, are
governing the intentional acts.


There is no reference to a contract in the initial proposition, "S sells T
to B for M"; and it is *isomorphic *with the allegedly simpler case, "A
gives up B to C in exchange for D."  In other words, it seems to me that
"sells X for Y" is *logically *the same relation as "gives up X in exchange
for Y."  Do you disagree?  Again, is an essential element somehow omitted
if we analyze the tetradic relation of selling (or bartering) as a
combination of only four triadic relations, two of giving (genuine) and two
of exchanging (degenerate)?

JD:  How many triadic relations are involved in this process of a young
child learning? Well, it appears to grow according to a power law. As such,
it grows into a multitude that exceeds any system of numbers that is
numerable or even any system that is abnumerable.


Of course it does, because *real *semeiosis is *continuous*--it is not
*composed
*of discrete relations (prescinded predicates) and their discrete
correlates (abstracted subjects) as expressed in definite propositions;
those are all *artificial *creations of thought for the purposes of
description and analysis.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Fri, May 10, 2019 at 10:44 PM Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Jon S., List,
>
> My strategy for interpreting these passages is to take Peirce at his word
> when he refers to the triadic relations that are involved. In order to
> interpret "μ is the surrender by A of B" and "ν is the acquisition by A
> of D" as triadic and not merely dyadic relations, my hunch is that he is
> considering these actions as intentional in character. The object
> surrendered and the agent who surrenders it are existing individuals in the
> relation of agent and patient, but that existential description of the
> individuals is part of an intentional action by A. As a general sort of
> thing, the intention makes the action of surrendering triadic in
> character--and so too with the action of A acquiring object D.
>
> The case that you cite of an object being sold involves a transfer of
> money and a contract. The simpler case of exchange as barter with no
> contract is illustrative of how other kinds of relations may be involved
> when more general things, such as property laws and legal systems, are
> governing the intentional acts. As a historical point, it is reasonable to
> suppose that social conventions governing exchanges by barter developed
> prior to any contracts or legal systems. Consequently, I think that the
> proper analysis of every genuine triadic relation involves a correlate
> that, itself, has the character of a general rule. As a correlate, that
> intention, or property law, or what have you, may involve a general rule
> that is part of a larger system of rules (such as a legal system).
>
> Having said that, the reason the number of triadic relations involved in
> tetradic, pentadic and higher order relations goes up by a power of 10 is
> not obvious to me.  While it isn't obvious, here is a conjecture:  Peirce
> may be thinking about the operation of general laws and intentions as
> conforming to a general model that applies to all genuinely triadic
> relations.
>
> One such model is articulated in "The Logic of Mathematics, an attempt to
> develop my categories from within". In that account of genuinely triadic
> relations, the law of quality and most general laws of fact each involves
> three clauses. The first clause governs each correlate considered in
> itself. The second clause governs the dyadic relations between pairs of
> correlates. The third clause governs the triadic relations between the three
> correlates. It is possible that the operation of the three clauses involved
> in such law might multiply the number of relations that may be involved in
> tetradic, pentadic, sextadic (etc.) relations by a power of ten in each
> case. The long explanations that 

Re: [PEIRCE-L] Triadic and Tetradic relations

[Jeffrey Brian Downard]

a child learning how to engage more or less 
self-controlled patterns of logical reasoning. My assumption is that the child 
was already capable of thinking in a manner that conformed to the laws of logic 
from an early age. The instinctive patterns of inference were not subject to 
much self-control at the ages of 1 and 2, but the child was learning how to use 
a conventional system of symbols (i.e., a natural language) as a matter of 
habit. In time, what the child learned was how to represent those laws to 
himself as principles. In turn, the child learned to recognise what those 
principles, functioning as imperatives, might require of him in terms of the 
future conduct of his inquiry.


How many triadic relations are involved in this process of a young child 
learning? Well, it appears to grow according to a power law. As such, it grows 
into a multitude that exceeds any system of numbers that is numerable or even 
any system that is abnumerable. The upshot of what I am suggesting is that 
Peirce's observation that there may be a power law involved in richer relations 
would explain his earlier assertions about the sort of infinity and resulting 
continuity that is involved in the growth of our cognitions.


Yours,


Jeff



Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354



From: Jon Alan Schmidt 
Sent: Friday, May 10, 2019 6:40 PM
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Triadic and Tetradic relations

Jeff, List:

That passage by Peirce is quite a head-scratcher.  For one thing, the relations 
of surrendering and acquiring are clearly dyadic, rather than triadic.  For 
another, it seems obvious that just as any triadic relation involves exactly 
three dyadic relations, likewise any tetradic relation involves exactly four 
triadic relations.  In the case of "A gives up B to C in exchange for D," they 
would be "A gives B to C," "C gives D to A," "A exchanges B for D," and "C 
exchanges D for B."  The difference is that a tetradic relation is always 
reducible to the combination of its constituent triadic relations, while a 
genuine triadic relation is irreducible.  Of course, "A gives B to C" is a 
paradigmatic example of a genuine triadic relation; so it is irreducible to the 
combination of its constituent dyadic relations--"A surrenders B," "C acquires 
B," and "A benefits C" (cf. CP 6.323; 1908).

I wonder if what Peirce had in mind as the result of analyzing a tetradic 
relation were not ten triadic relations, but ten relations of any lower 
adicity.  Besides the four triadic relations, there are six dyadic relations 
involved in any tetradic relation--e.g., "A surrenders B," "C surrenders D," "A 
acquires D," "C acquires B,"  "A trades with C," and "B is traded for D."  
However, such an approach would still not translate to the alleged "power law" 
for relations of increasing adicity--a pentadic relation involves five 
tetradic, ten triadic, and ten dyadic relations for 25 total relations, rather 
than 100; a hexadic relation involves 6+15+20+15=56 relations, rather than 
1,000; and an enneadic relation involves 9+36+84+126+126+84+36=501 relations, 
rather than 1,000,000.

By the way, Peirce elsewhere gave a different but (in my view) equally puzzling 
analysis of what amounts to the very same tetradic relation.

CSP:  Suppose a seller, S, sells a thing, T, to a buyer, B, for a sum of money, 
M. This sale is a tetradic relation. But if we define precisely what it 
consists in, we shall find it to be a compound of six triadic relations, as 
follows:
1st, S is the subject of a certain receipt of money, R, in return for the 
performance of a certain act As;
2nd, This performance of the act As effects a certain delivery, D, according to 
a certain contract, or agreement, C;
3rd, B is the subject of a certain acquisition of good, G, in return for the 
performance of a certain act, Ab;
4th, This performance of the act Ab effects a certain payment, P, according to 
the aforesaid contract C;
5th, The delivery, D, renders T the object of the acquisition of good G;
6th, The payment, P, renders M the object of the receipt of money, R. (CP 
7.537; no date)

Why introduce so many additional subjects, rather than sticking with the four 
in the initial proposition?  Is an essential element somehow omitted if we 
simply analyze selling as a combination of giving and exchanging?

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt<http://www.LinkedIn.com/in/JonAlanSchmidt> - 
twitter.com/JonAlanSchmidt<http://twitter.com/JonAlanSchmidt>

On Fri, May 10, 2019 at 4:05 PM Jeffrey Brian Downard 
mailto:jeffrey.down...@nau.edu>> wrote:

List,

I

Re: [PEIRCE-L] Triadic and Tetradic relations

[Jon Alan Schmidt]

Jeff, List:

That passage by Peirce is quite a head-scratcher.  For one thing, the
relations of surrendering and acquiring are clearly *dyadic*, rather than
triadic.  For another, it seems obvious that just as any triadic relation
involves *exactly three* dyadic relations, likewise any tetradic relation
involves *exactly four* triadic relations.  In the case of "A gives up B to
C in exchange for D," they would be "A gives B to C," "C gives D to A," "A
exchanges B for D," and "C exchanges D for B."  The difference is that a
tetradic relation is *always reducible *to the combination of its
constituent triadic relations, while a *genuine *triadic relation is
*irreducible*.  Of course, "A gives B to C" is a *paradigmatic example* of
a genuine triadic relation; so it is *irreducible *to the combination of
its constituent dyadic relations--"A surrenders B," "C acquires B," and "A
benefits C" (cf. CP 6.323; 1908).

I wonder if what Peirce had in mind as the result of analyzing a tetradic
relation were not ten *triadic *relations, but ten relations of *any *lower
adicity.  Besides the four triadic relations, there are six dyadic
relations involved in any tetradic relation--e.g., "A surrenders B," "C
surrenders D," "A acquires D," "C acquires B,"  "A trades with C," and "B
is traded for D."  However, such an approach would still not translate to
the alleged "power law" for relations of increasing adicity--a pentadic
relation involves five tetradic, ten triadic, and ten dyadic relations for
25 total relations, rather than 100; a hexadic relation involves
6+15+20+15=56 relations, rather than 1,000; and an enneadic relation
involves 9+36+84+126+126+84+36=501 relations, rather than 1,000,000.

By the way, Peirce elsewhere gave a different but (in my view) equally
puzzling analysis of what amounts to the very same tetradic relation.

CSP:  Suppose a seller, S, sells a thing, T, to a buyer, B, for a sum of
money, M. This sale is a tetradic relation. But if we define precisely what
it consists in, we shall find it to be a compound of six triadic relations,
as follows:
1st, S is the subject of a certain receipt of money, R, in return for the
performance of a certain act As;
2nd, This performance of the act As effects a certain delivery, D,
according to a certain contract, or agreement, C;
3rd, B is the subject of a certain acquisition of good, G, in return for
the performance of a certain act, Ab;
4th, This performance of the act Ab effects a certain payment, P, according
to the aforesaid contract C;
5th, The delivery, D, renders T the object of the acquisition of good G;
6th, The payment, P, renders M the object of the receipt of money, R. (CP
7.537; no date)


Why introduce so many additional subjects, rather than sticking with the
four in the initial proposition?  Is an essential element somehow omitted
if we simply analyze selling as a combination of giving and exchanging?

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Fri, May 10, 2019 at 4:05 PM Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> List,
>
> In a draft of a 1905 letter to Lady Welby, Peirce analyzes the tetradic
> relationship of A gives up B to C in exchange for D (Semiotic and
> Significs, 190). I am interested in his remarks about the exchange of
> goods for the sake of better understanding his account of the relations
> that hold between signs, objects and interpretants.
>
> Peirce argues that any tetradic or higher order relationship (i.e.,
> valency >3) is complex and can be analyzed into elementary monadic, dyadic
> and triadic relations. Here is the upshot of his analysis of exchanging
> goods:
>
>
>
> The tetradic relationship is reducible to, at most, 10 elementary triadic
> relations.  Here they are:
>
>
> a. λ is an exchange of property (B and D) between A and C
>
> b. ι is a transposition of ownership of B and D
>
> c. L is an accomplishment of λ through ι
>
> d. μ is the surrender by A of B
>
> e. m is the surrender by C of D
>
> f.  Μ  is the performance of μ
> in reciprocal consideration of m (Note the error in the transcription,
> which has M instead of m at the end.)
>
> g. ν is the acquisition by A of D
>
> h. η is the acquisition by C of B
>
> i.  Ν  is the performance of μ
> in reciprocal consideration of η (Note the error in the transcription,
> which has N instead of η at the end.)
>
> j.  L is carried out by the union of M and N.
>
>
>
> On the basis of this type of analysis, Peirce generalizes to relationships
> of higher adicity. He claims there is a power law that holds for relations
> of adicity four or greater.
>
>
> 1. Tetradic relations such as exchanging appear to be reducible to,
> at most, 10 triadic relations.
>
> 2.  Pentadic relations are reducible to, at