[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
the
texts.
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
enterprise.
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unpublished to date – we are able to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
the
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
Interpreter.
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
propositions.
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,
1903].
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
fixed.
We observe that these activities correspond to definitory moves of the
game.
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
comes
to decide the truth of atomic expressions.
The Grapheus does this by either ―authorizing or ―refuting the actions
proposed by the Graphist [MS
492].
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
and
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
action.
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
agent
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
factors
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
of
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
the
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
assertion
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
of
'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
the
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
of
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
Interpreter
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
to
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
Opponent).
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
exists.
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
and
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
is
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
by
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
towards
the 'kryptotechnical' whereas Grice, like Hart, were into linguistic
botany, and would never depart MUCH from the 'ordinary language' used to
describe
the situations they were providing conceptual analyses for -- (In this,
the spirit is already in that famous letter that Epicurus wrote to Herodotus).
Cheers,
Speranza
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