[lit-ideas] Herbert Paul Peirce

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  • Date: Sun, 29 Mar 2015 07:55:54 -0400

In a message dated 3/28/2015 8:24:34 A.M.  Eastern Daylight Time, 
omarkusto@xxxxxxxxx writes:
I haven't read much of  Hintikka but I have got a positive impression, 
especially as he seems to  understand something of chess as well. For example, 
he speaks of rules of  logical inference on the analogy to rules of chess, 
which are necessary to play  the game but not sufficient to play it well. Good 
reasoning, he thinks, requires  an understanding of strategic rules as 
well. This looks like I might want to  read more of him, if I manage to find 

A student of Hintikka has provided a historical development of the idea of  
a 'language game' and related concepts all the way from Peirce to Hintikka 
and  Grice. Grice gave a series of lectures on Peirce's general theory of 
signs, and  he uses 'interpretant' once in "Logic and Conversation" -- a relic 
of those  lectures.
Peirce had a few things to say about the games that would later become more 
 or less crucial in Grice's idea of seeing conversation as a co-operative  
Peirce‘s conception of logic and pragmaticism is virtually the idea of  
players ―feigned in our makebelieve. Peirce was interested in logic as a theory 
 of normative, conventional, habitual and strategic action. Later Grice 
erected  his theory of conversation on Peircean background. But cooperation is 
a property  of model-building games and an integral part of Peirce‘s method.
First, we need the players, the participants of these games. According to  
Peirce, in logic such parties are
―feigned in our make-believe [MS 280, p.  29, 1906]. 
Peirce‘s logic is not meant to serve as a formal calculus or pasigraphy,  
but to be an ―aid in the analysis of reasoning‖ for which certain procedures 
of  ―imaginary‖ parties are called for [MS 1589].
Thus players are theoretical constructs rather than actual agents partaking 
 in real conversational situations. They are introduced in order to 
articulate  the conceptual workings of one‘s logical systems. 
In Peirce‘s writings – some of the most important of which are still  
unpublished to date – we are able to
gather some significant answers to that  question of who the players of the 
game are.
Second, in Peirce‘s wide notion of logic, there is room for many kinds of  
games and moves that the players entertain. We find not only actions 
pertaining  to the semantics of logic but also the assertoric, definitory, 
interrogative,  deductive and model-building moves.
Peirce‘s logic is grounded on the idea of contemplating there being two  ―
make believeplayers. In Peirce‘s terms, there is the Graphist (the Utterer) 
who  ―scribes the graphs and proposes modifications to them, and
there is the  Interpreter (the Grapheus) who ―authorizes the modifications 
[MS 492,  1903].
Generally, Peirice designates the parties as the Utterer and the  
Interpreter. Sometimes he even used the terms the Attacker and the Defender, as 
case is in dialogue logics. We also find him talking about the ―assertor and 
 critic, ―concurrent and antagonist, ―speaker and hearer, ―addressor and  
addressee, ―Artifex of Nature and Interpreter of Nature, ―symboliser and  
thinker, ―scribe and user, ―affirmer and denier, ―compeller and resister, ―
agent  and patient, ―Me and Against-Me, and so on. 
The truth of the whole graph agrees with the existence of a winning  
strategy for the Graphist, which in Peirce‘s terms is the being of a habit of  
action. It has been alleged that Peirce lacked a notion of game  game theory, 
that of a strategy. However, habits of action are for Peirce  ―generalizing 
tendencies which are of ―a tolerably stable nature [MS 280, p.  32]. (The 
idea of stableness re-emerged in von Neumann‘s work on game theory,  among 
others.) Likewise, falsity is the existence of such habits for the  
Peirce is obviously thinking of the game-theoretic concept of a  "solution" 
(or as I prefer 'resolution' -- cfr. Becket, game end). 
What Peirce terms the sheet of assertion represents everything that is well 
 understood to be taken for granted between the two parties.
Peirce is interested in truthful assertions much more than in the nature of 
In some of the late writings he even suggests that the sheet is one of  
affirmation rather than assertion, because ―whatever state of things you  
represent on this page, you will be understood to affirm as existing somewhere, 
or, at least, consistently to make believe to affirm [MS 650, 1910]. 
In another place he calls it the sheet of assent.
In any event, the emphasis here is on assertions that are binding. 
Utterers are responsible for what they state, scribe or assert. 
Thus on the sheet only true assertions may be scribed. 
Peirce took the notion of the universe of discourse essential to any  
feasible method of logic: ―The different points of this sheet shall represent  
the different possible states of a certain individual subject, it being well  
understood between the drawer and the interpreter of the diagram what this  
subject is. 
"Let this subject be termed the Universe of Discourse" [MS  479,
Peirce conceived its role in logic in predominantly two ways. First,  there 
is the contextualisation: players gain collateral observation and  
experience by virtue of which communication becomes possible. The ―common  
ground‖ –
 again an idea widespread in contemporary pragmatics dating back to  Peirce 
– is built
from an endless series of ―common familiar knowledge [MS  614]. In 
interpreting the non-logical constants the boundaries of language need  to be 

We observe that these activities correspond to definitory moves of the  
These activities are followed by model building. Peirce describes it in  
terms of collaborative activities of the Graphist and the Grapheus, the ―
author  of the universe of discourse [MS 450, 1903]: the Graphist ―proposes 
to  decide the truth of atomic expressions. 
The Grapheus does this by either ―authorizing or ―refuting the actions  
proposed by the Graphist [MS
Interestingly, he held that there is no competition in the description of  
such activities. The common aim is to agree first on the relevant aspects of 
the  system to be modelled and its properties.

Concerning the parties undertaking the scribing, authorizing and  
interpreting logical assertions, Peirce assumed that the minds of the Graphist  
the Grapheus (and the minds really are not so much the human minds as what  
he terms the ―quasi-minds‖, anything that can produce and process signs) 
should  be able to control the process as well as to develop the habits of  

This is in line with the idea that the players ought to share the essential 
 ingredients of an intelligent mind:

"Now nothing can be controlled that cannot be observed while it is in  
action. It is therefore requisite that both minds but especially the  
Graphist-mind should have a power of self-observation. Moreover, control  
supposes a 
capacity in that which is to be controlled of acting in accordance  with 
definite general tendencies of a tolerably stable nature, which implies a  
reality in this governing principle. But these habits, so to call them, must be 
capable of being modified according to some ideal in the mind of the 
controlling  agent; and this controlling agent is to be the very same as the 
controlled; the control extending even to the modes of control themselves, 
since  we suppose that the interpreter mind under the guidance of the 
Graphist-mind  discusses the rationale of logic itself. Taking all these 
into account,  we should come to the same conclusion that common-sense would 
have jumped to at  the outset; namely, that the Graphist-mind and 
interpreter-mind must have all  the characters of personal intellects possessed 
moral natures [MS  280].

Here we note the strategic aspects of reasoning of the two agents –  stable 
general tendencies, modifications of habits of actions, and the  
meta-logical principle of self-control.
Peirce‘s note that the parties, though created in our make-believe,  
nevertheless share ―all the characters of personal intellects‖, which assumes  
that they are capable not only of controlling their own reasoning but also of  
entertaining normative ideals in their ―quasi-minds.
Peirce describes the interaction between the two parties as follows: ―The  
grapheus communicates to the graphist from time to time his determinations 
in  regard to the character of the universe. Each such communication 
authorizes the  graphist to express it‖ [MS 492, 1903]. This is consonant with 
idea of  interrogating Nature. The commonplace idea of putting questions to 
nature is  here put in the outfit of communication concerning the 
determinations of some  fact or a law that authorises the interpreter, who 
perhaps is 
the scientist, to  assert the content of that determination in terms of his 
or her favourite system  of representation. The overall methodological value 
of thinking in the terms of  putting questions to Nature‘ was familiar to 
Peirce though he did not go on to  systematise the idea beyond what is 
expressed in these couple of pages.
Interestingly, though, Peirce continues the previous passage by stating  
that ―an authorization once given is irrevocable: this constitutes the 
universe  to be perfectly definite. Being perfectly definite and perfectly 
determinate are  not the same thing, however: ―Should the graphist risk an 
without  authorization, he must hope to receive an authorization later; for 
what never  will be authorized is forbidden: this constitutes the universe 
to be perfectly  determinate [MS 492]. If it so happens that a modification 
needs to be made to  the asserted graph, it has to be made according to the 
illative permissions of  the system. The modifications that may be made to 
the assertions once scribed on  the sheet of assertion proceed by way of the 
given sound rules of  transformation, that is, they describe the deductive 
moves of the given logic.  Peirce then refers to the Graphist as the one who 
does all the scribing: In our  make believe, two parties are feigned to be 
concerned in all scribing of graphs;  the one called the Graphist, the other 
the interpreter. Although the sheet that  is actually employed may be quite 
small, we make believe that the so-called  sheet of assertion is only a 
particular region or area of an immense surface,  namely that it is the field 
'distinct vision‘ of the interpreter. It is only  the Graphist who has the 
power to scribe a graph, and the graphs that he scribes  are true, because 
the truth of the true consists in his being satisfied with it.  The 
interpreter, for his part, has the power, with more or less effort, to move  
graph-instances over the sheet, out of his field of distinct vision or into  it 
if they are not quite out of his sight [MS 280].
What is the reasonable interpretation of the key idea of what Peirce is  
attempting to illustrate here? It is a little hard to see what kinds of moves 
at  the end are involved here, as his way of setting up the numerous 
conventions for  his systems of logic is far from customary compared to logics 
the past  century, but one suggestion is that at the end, these processes 
strive to  describe model construction over and above other kinds of moves. The 
former  operate by way of the Utterer (the Graphist) putting forth an 
assertion by  scribing it on the sheet of assertion, followed by the 
either  refuting (that is, moving the instance thus asserted out of the 
field of  distinct vision) or accepting it (that is, keeping it in the field of 
such  vision).
To check the consistency of the assertion is to perform a satisfiability  
check, which means building a
model for it. Peirce‘s notion comes in terms of  the Grapheus ―being 
satisfied with the graphs the Graphist scribes. Such methods  introduce a 
competitive element in that a set of assertions having a model is  tantamount 
the existence of a winning strategy for the Graphist (or the  Builder or the 
Proponent), while the negation of an assertion is tantamount to  the 
existence of the winning strategy for the Grapheus (or the Critic or the  
What the Grapheus is doing is to search for counterexamples that  would 
demonstrate the
invalidity of the initial assertions. Peirce‘s games  evoke the Graphist, 
the Utterer of the assertion, to propose
modifications to  the initially blank sheet of assertion on which logical 
graphs come to be  scribed. As Peirce aptly recognizes, any one graph 
represents ―one possible  state of the universe [CP 4.431]. Thus its model 
The Grapheus, on the  other hand, determines the characters of the universe 
as he pleases. This brings  to mind how the interpretations of the 
underlying language become determined.  What Peirce is aiming at with these 
descriptions is thus not far from how the  processes of building models may be 
accounted for.
As a technical point,  these processes leave no room for partial 
interpretations, since ―the blank of  the blank sheet…as expressing that the 
universe, in [a] process of creation by  the grapheus, is perfectly definite 
entirely determinate [CP 4.431; cf. MS  492, 1903]. Later Peirce came to 
present a number of systems of triadic logic in  which the requirement of 
determinateness is given up.

Peirce‘s idea is that the Graphist and the Grapheus ―collaborate‖ [CP  
4.552] in the building of what he calls a ―Pheme‖, that is, a model for the  
assertions of the system [CP 4.538; CP 4.552]. In such a game, the Graphist  ―
proposes modifications to the graphs‖ while the Grapheus ―creates the 
universe‖  and decides upon its ―determinations. These determinations are the  
interpretations by way of authorizing or refuting the actions of the 
Graphist  [CP 4.538; CP 4.552]. The model-building proceeds by way of mutual 
consent.  Another way of looking at what Peirce is striving to articulate here 
to take  these activities to represent what much later were named as the 
'cut-and-choose‘  strategies in game theory and in stability theory. After the 
building phase that  has to do with scribing tentative graphs subject to 
criticism, acceptance or  refutation, competitive semantic games on the 
accepted assertions commence.  Secondly, then, logical graphs are interpreted 
sequences of competitive plays  between the Graphist who proposed the 
assertion that any graph thus created  represents, and the Grapheus, now 
playing the 
role of the Interpreter or Nature,  who had created the universe and has an 
antagonist aim.
Grice was fascinated by Peirce, and apparently the students who attended  
his class (as university lecturer at Oxford) on Peirce's general theory of  
signs were, too. But let us be reminded that Peirce is just one of the MANY  
influences that the genial Grice combined in what transpired as a grand 
scheme  for the philosophical grounds of rationality based on intentions, 
categories,  and ends -- to include such trivial stuff as 'over the garden' 
colloquial chat!  (One big disagreement is that Grice found Peirce tended 
the  'kryptotechnical' whereas Grice, like Hart, were into linguistic 
botany, and  would never depart MUCH from the 'ordinary language' used to 
the  situations they were providing conceptual analyses for -- (In this, 
the spirit  is already in that famous letter that Epicurus wrote to Herodotus).
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