Download Why is the Normativity of Logic Based on Rules?

Pietarinen, Ahti-Veikko (2011). "Why is the Normativity of Logic Based on Rules?" in
Cornelis de Waal and Krzysztof Piotr Chris Skowronski (eds.), The Normative
Thought of Charles S. Peirce, Bloomington: Indiana University Press, 150-163.
Why is the Normativity of Logic Based on Rules?
AHTI-VEIKKO PIETARINEN
Abstract
According to Peirce, logic is a normative science. What does this actually mean? In a
nutshell, rules or laws govern self-controlled action, all communication is in signs,
logical thought and habits are self-controlled, and logic is semeiotic. Self-controlled
agents have normative ideals in the mind as they converse upon the meaning of
intellectual signs and purports. Habits are many-world entities that link situations
to actions, and the rules of meaning-constitutive practices and activities provide the
logical and strategic structure for habits. This paper argues that the position which
takes normativity not to be grounded in the rules governing the meaningconstitutive practices is inconsistent. This argument lies in the core of the proof of
pragmaticism. That normativity of logic is grounded in rules governing selfcontrolled action is manifest in the general model-theoretic thinking about logic.
Normativity has to do with rule-governed, meaning-constitutive practices and
activities, because logic as a normative science is, according to Peirce, one of the
“most purely theoretical of purely theoretical sciences” (CP 1.281, c.1902).
1. Introduction: Logic as a Normative Science
According to Peirce, normative sciences are the “most purely theoretical of purely
theoretical sciences” (CP 1.281, c.1902, A Detailed Classification of the Sciences). At
the same time, he takes logic to be a normative science. These two sentences form a
highly interesting pair of assertions. Why is logic among the most purely theoretical
sciences? What does it actually mean that logic is a normative science? In this paper
I will answer these questions by answering to the question of why the normativity
of logic is, as a matter of fact, based on rules.
The statement that logic is a normative science has been routinely taken to
follow from the classification of the sciences that Peirce came up with in 1903, and
termed the “perennial classification” by Kent (1988) (cf. Pietarinen 2006a). Namely,
normative logic is the ‘third’ normative science that depends upon the second or
“mid-normative” science of ethics (a.k.a. practics, anthetics)—or that the second
provides grounds or support for the third—and logic and ethics depend upon the
first normative science, which Peirce spells esthetics. Moreover, normative sciences
as a whole depend upon phenomenology and mathematics, while no normative
science depends in these same senses upon metaphysics or the special sciences
(idioscopy). To show that normative sciences generally need not draw on the special
sciences Peirce first argues that normative sciences have nothing to do with
psychology and linguistics, and then goes on to sketch arguments intended to
extend the case to other branches of science as well.
The first, second and third normative sciences study the three ends of
philosophical inquiry. The purpose of logic is to distinguish truth from falsehood.
The purpose of ethics is to distinguish good conduct from bad conduct. The purpose
of esthetics—a science which Peirce apologies for not having been able to study
150
much of at all—has not so much to do with qualities such as beauty or attraction, let
alone “taste” (CP 1.574, 1906, The Basis of Pragmatism), but with what is desirable
as such, or with what the aim in any fully deliberate line of conduct or thinking in
itself could be, without any special motive or purpose. It is the study of ideals or
standards in themselves. Peirce’s view does not seem to differ much from Aristotle’s
characterization of aesthetics.
In which sense should logic be seen as depending on esthetics? Peirce is not
proposing any straightforward answers. Commentators have been puzzled by the
few of remarks that he has to offer.95 He vaguely states that “I shall not deny that
[logic] depends in some measure, though indirectly for the most part, upon
esthetics” (MS 693, 1904, Reason’s Conscience;96 NEM 4:198; cf. CP 2.199, Why Study
Logic?). Crucial in interpreting these statements is to first do some reconstructive
work on his overall philosophy. For example, the role of logic in his philosophy of
pragmaticism is the core issue that needs to be clarified. Such a reconstruction
forms the gist of my argument that explains why normative logic is “the most purely
theoretical of purely theoretical sciences”. After this clarification, I will observe what
the reconstruction implies to the question of the relationship between logic and
esthetics. I will proceed to the main argument in a moment.
As far as Peirce’s classificationary schemes are concerned, the case that logic
depends on ethics is a little more straightforward to back up. 97 He sees the goal of
reasoners to perform self-controlled thinking, just as good action requires selfcontrolled conduct. “[A]s the reasoning depends upon the virtue”, he writes in
Reason’s Conscience, “so must the theory of the reasoning depend upon the theory of
the virtue” (NEM 4:198). In the version of The Basis of Pragmatism published in the
Collected Papers he continues that “the control of thinking with a view to its
conformity to a standard or ideal is a special case of the control of action to make it
conform to a standard” (CP 1.573, 1906, my emphasis). By reasoning Peirce means
logic in a wide sense, the “theory of deliberate thinking” (CP 1.573). Since deliberate,
inferential thinking is a form of action, logic as self-controlled thought is part of the
theory of self-controlled conduct, and so the general theory of reasoning is part of
the general theory of logic.
The overall point I wish to make is that explaining normativity solely by
reference to the role a branch of science plays in the classification scheme is
unsatisfactory. I am not saying that there is anything fundamentally out of place in
the classification as such, only that it does not serve as an explanation of why
individual sciences are so classified in that scheme. Taxonomies and classifications
are not scientific explanation.
95
See e.g. Barnouw (1995) for attempted clarification of what Peirce might have meant by
esthetics, emphasizing how markedly his conception differs from the contemporary
study of aesthetics. Pietarinen (2009) is a study of Peirce’s esthetics in the context of
pragmaticism.
96 The full title of this manuscript is Reason’s Conscience: A Practical Treatise on the Theory
of Discovery; Wherein logic is conceived as Semeiotic. The date 1904 is by Carolyn Eisele.
97 Burks (1943) is the early study concerned with this question.
151
Moreover, Peirce did not intend the classification to be a completed
reproduction of the totality of the branches of scientific inquiry, let alone the final
word on the complex relationships that may obtain between evolving compartments
of science. Rather, he meant it as a blueprint for the future state of the sciences. For
one thing, he left open the possibility that the relations between parts, though
superficially represented as hierarchies of partial orders or semi-lattices, may
involve symmetrical relationships.98
What, then, does it mean that logic is a normative science? To tackle this
question I suggest breaking it down to the one of answering why the normativity of
logic is based on rules. This is the problem I will analyze next. After that, I will
consider the main implications of the solution to that key problem.
2. The Argument for Pragmaticism
Let us focus on those intellectual signs that we come across in propositional
contexts. Examples are logical constants, such as ‘and’, ‘or’, ‘exists’ or ‘is equivalent
to’, for which Peirce shows how they can have objects. They can have objects by
virtue of the precepts that guide the actions of the utterers and the interpreters of
propositions. But if such signs can have objects, the meanings of our intellectual
signs supervene on the contributions signs have to those activities, practices and
lines of conducts of the utterers and the interpreters that mediate the ways in which
language, cognition and the world stand in a relationship.
This compact argument can be made precise. I will use game-theoretic
semantics (GTS), which is a nearly exact contemporary rendering of pragmaticism
(Hilpinen 1982; Pietarinen 2006b). According to GTS, the truth of a sentence is the
existence of a winning strategy in a two-player zero-sum game played on that
sentence (Hintikka 1973). But if truth and the existence of a winning strategy are so
related, then the contribution a sentence makes to its truth-conditions is its
contribution to those semantic games that can be played on sentences. Since
semantic games exemplify practices and activities by which we compare sentences
to their models, such contributions to truth-conditions are contributions to those
practices and activities by which we compare sentences to their models.
The argument runs as follows:
1. A is true (resp. false) in (M, w), if and only if the Utterer (resp. the
Interpreter) has a winning strategy in a semantic game G(A, M, w).99
Esthetics and logic provide an example of such a mutual dependence. Take contemporary
artwork which makes heavy use of multi-modal features, for instance. Such forms of art
run the risk of remaining incoherent or hard to comprehend and interpret without the
collecting powers of modes of reasoning provided by logic.
99 M is a model, w a possible world, A an assertion, and G a non-cooperative, two-player,
zero-sum game of perfect information played on A, in M, and in w. Peirce terms the two
parties engaged in such strategic dialogue variously the “utterer-interpreter”, “proponent–
opponent”, “defender–attacker”, “speaker–hearer”, “addressor–addressee”, “assertor–
critic”, “Graphist–Grapheus”, “Artifex of Nature–Interpreter of Nature”, “symboliser–
98
(cont.)
152
2. The Utterer (the Interpreter) has a winning strategy in G(A, M, w), iff there
exists a habit of action associated with A by which we can seek and find
certain objects in certain worlds.
3. Logical constants contribute to the habit of action by giving it form in terms
of the choices that are possible in a given possible world w.
4. Non-logical constants contribute to the habit of action by giving it points of
terminations in w.
5. Thus, A is true in (M, w), iff there exists a habit of action by which we can
seek and find certain objects in w, and the sub-expressions of A contribute to
the habit by giving it form or points of termination in w.
6. Thus, the sub-expressions of A contribute to the truth-conditions by giving
form or points of termination to a habit of action connected with A by which
we can seek and find certain objects in world w, and A has truth-conditions
only if there exists a habit of action for A by which we can seek and find
certain objects in w.
7. If (6), and the truth-conditions of A constitute A’s meaning, the subexpressions of A are meaningful by giving form or points of termination to
the habit of action connected with A in w, and A has a meaning by its
association with a habit of action by which we can seek and find certain
objects in w.
8. The sub-expressions of A are meaningful by giving form or points of
termination to the habit of action connected with A in w, and A has a
meaning by its association with a habit of action by which we can seek and
find certain objects in w.
This argument establishes that intellectual signs have a meaning by virtue of
the habit of action by which we compare signs with their models and the world.
Signs are here assumed to be sentential expressions that have propositional content.
In the simplest and perhaps most typical case, they are declarative assertions of
subject-predicate sentences. The logical structure of these sentences is constituted
by logical and non-logical constants. The domain of the applicability of GTS can be
extended to cover other classes of sentential expressions as well.
Elsewhere, we have argued that this reconstruction of the key features of
Peirce’s pragmaticism in terms of the framework of GTS serves as a conclusive
argument for Peirce’s middle proof of pragmaticism (Pietarinen & Snellman 2006;
Pietarinen 2011b). His “proof” is therefore not merely a “seductive persuasion” for
the truth of pragmaticism as he himself tended to state but a logical demonstration
of its validity.
Now we are ready to proceed to the argument according to which this
demonstration also serves to establish the fundamental connection between
pragmaticism and logic as a normative science.
thinker”,
“scribe–user”,
“affirmer–denier”,
“ego–non-ego”,
“quasi-utterer–quasiinterpreter”, “delineator–interpreter”, “concurrent–antagonist”, “compeller–resister”,
“agent–patient”, “putter forth–auditor”, “writer–reader”, “Me–Against-Me”, and
“interlocutor–receiver”. These pairs are feigned in our “make believe”, yet they must have
the qualities of “intelligent agents” (MS 280: 29; MS 3).
153
3. Meaning is Rule Governed
Habits are many-world entities which inhabit not only our actual world. Think of the
habit of greeting a friend: we act according to this habit if, and only if, in any
situation in which we may meet a friend we normally and typically greet him. Habits
connect possible situations and scenarios with acting according to, or being guided
by, the habit. More precisely, what corresponds to such a habit is a mapping from
possible worlds or situations to actions. The range of those mappings is defined by
the acts that are permitted (or determined) by the habits in whatever kind of world
or situation.100
Semantic games work by way of two kinds of rules: defining rules and
strategic rules. A rule is defining if, and only if, an action is a move in a game and the
action is permitted by the rule. A rule is strategic if, and only if, an action maximises
the expected payoff and is permitted by the rule.101 Which habits qualify for the
‘language games of seeking and finding’ (cf. item 5 above) is given gametheoretically and is based on the characteristics of the defining rules, because
defining rules constitute the actions that are correct or legitimate as soon as the
model and its domains have been given. Likewise, since the defining rules constitute
both the various plays of the game (game histories) as well as the rules for winning
the plays of the game, they also constitute which strategic rules and plans of actions
are correct as soon as the model and its domain is given (since every value of a
strategic rule is also a value of a defining rule). Since the defining rules give the
winning conditions as well as all the available choices for all the possible
continuations of the game, and strategic rules give the right choices in every
situation that has more than one available choice, rules provide the logical and
strategic structure to the habit of action by which we seek and find objects and
possible continuations of events within classes of models that are evoked in our
logical (semeiotic) inquiries.
Consequently, our intellectual signs and purports have a logical role in these
strategic activities according to the game-theoretic rules. Our individual acts are
By a mapping we mean generalizations of an ordinary concept of a function to
accommodate, for example, non-deterministic and intensional forms of mappings. By
model theory we mean its wide sense that takes into account possible-worlds semantics
and intensional concepts. Ordinary notions of a function or a model theory do not cover
such extensions. The broader conception of model theory comes close to what Peirce’s
intention was in regarding formal semantics/pragmatics as the logical theory of
semeiotics (see Pietarinen 2006b, 2006c).
101 This vague definition of strategic rules may well need to be qualified in several ways. But
nothing in the argument depends on the details of those qualifications. Recent literature
in game theory is rife with suggestions about the ways in which ‘the maximization of
expected utilities’ could or should be replaced with goals and ends that make less-thanideal assumptions concerning, for instance, the rationality of the players (Gintis 2009;
Rubinstein 1998).
100
154
made in accordance with the habits, or are being guided by them if, and only if, they
are made in accordance with, or are guided by, the rules of the game.
Now suppose, for the sake of argument, that the meaning of our intellectual
signs is not based on rules in the manner just described. This would require showing
that the normativity of these semantic games is not based on rules, since strategic
rules determine what the right choices are in every non-terminal contingency, no
matter how improbable they are.102
However, the assertion that the normativity of games is not based on rules is
inconsistent. The reductio goes as follows. If the normativity of games is not based
on the rules of the game, it is based on what our actions in fact are in those plays of
the game that are actually played. However, our actions are those that we in fact do.
But if that is the case, then only one world, namely this current, actual world of ours,
is relevant to the formation of habits that constitute the meaning of our intellectual
signs. If only one world is relevant to the formation of habits that constitute the
meaning of our signs, in applying the sign or expression to something we affect or
change the ways in which situations are mapped to actions. And as argued, these
mappings correspond to habits. But if so, then all action constitutes meaning, and
hence language could not be misused and all sentences would be true: all
communication would be impossible.
Since there is communication (and for the sake of sanity and non-solipsism we
must take this for granted), this conclusion is absurd. The above argument thus
establishes the following three conclusions. First, the actual world is not the
sufficient ‘thing’ for the formation of meaning-constitutive habits. Second, it is
inconsistent and hence not true to take the meaning of our intellectual signs not to
be based on rules. Third, it is not true that the normativity of semantic games, the
habits of which constitute the meaning of our intellectual signs, is not governed by
rules.
I have argued in this section that logic, in its wide sense,103 is the general
theory of the meaning of intellectual signs, in other words pragmaticism, and in
section 2 I associated that theory with the theory of semantic games. We can thus
see the reason why the normativity of logic is, and has to be, based on rules.104
This is really how strategies are conceived both in Peirce’s sense and in contemporary
game theory. Knock-down evidence comes from Peirce’s 1893 marginal addition to his
revision of How to Make Our Ideas Clear, where he writes, next to his definition of the
identity of a habit as leading us to action under any possible (even zero-probability)
circumstance: “No matter if contrary to all experience” (CP 5.400).
103 On Peirce’s notion of logic conceived in its broad and narrow senses, as well as their
relations to normative sciences, see Bergman (2007).
104 It might help one to savor this conclusion by thinking of rules as very complex entities: in
addition to being non-deterministic and intensional functions and mappings, they can
come in the forms of conditionals, subjunctives and counterfactuals, among others. Or
rules can have antecedents whose falsity calls for demonstration by abductive reasoning.
It is by no means the case that rules in question are static, indefeasible entities or canons
that restrict or constrain our actions. Instead of rules, one might think of habits as laws,
including statistical laws, but this is problematic since such terminology suggests a
102
(cont.)
155
4. Habits, Ethics and Ideals
That normativity is based on rules of the game-theoretic kind is something Peirce
struggled to establish. His terminology of course differs from ours, but the
motivations and goals are the same, and they are best expounded in the
contemporary frameworks provided by logical semantics, pragmatics, and the
theory of games, all of which can be taken to pertain to normative sciences.105 One of
the most acute struggles to articulate these frameworks takes place in the
unpublished MS 280 The Basis of Pragmaticism from 1905:
A critical analysis of the nature of a sign would show that the action
requires a source of concepts to be conveyed, and therefore in some sense
a mind from which the ideas and [concepts,] propositions, and arguments
are conveyed to the mind of the interpreter; and the two minds must be
capable of coming to an understanding and of observing it when it is
reached. This supposes a power of deliberate self-controlled thinking. Now
nothing can be controlled that cannot be observed while it is in action. It is
therefore requisite that both minds but especially that of 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 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, in a way that can here only be
suggested, 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
endowed with possessed of moral natures. But let us not to be forgotten that
the Graphist, whom we now speak of as a person, is such a person that the
truth and being of the things that are objects of thought, consist in his
assent to their being. (MS 280: 30-33, 1905, emphases and paragraph skip
added)
This is what it all comes down to. The relationship between pragmaticism and
semantic games is, in a nutshell, as follows. “The two minds” are the two players of
the game, the Graphist (the Utterer) and the Interpreter (the Grapheus). The two
minds undertake to show the material truth or the falsity of the given assertion.
naturalistic interpretation of habits which is alien to Peirce’s own argument about their
identity.
105 Admittedly, there is considerable disagreement among game theorists on whether what
the study is to be conceived as a normative, descriptive or prescriptive science (see
Osborne & Rubinstein 1994; Pietarinen 2003).
156
What “capable of coming to an understanding and of observing it” means is that the
payoffs, determined at the terminal histories of each play of the game, are known,
and commonly known to be known, by the players. Common knowledge of payoffs is
a standard assumption in game theory in so far as the class of complete information
games is concerned. The “power of deliberate self-controlled thinking” and the
“power of self-observation” refer to strategic thinking and planning. As any game
theorist is quick to confirm, our plans need to be able to accommodate and undergo
changes that reflect the expectations we formulate about the actions of our fellow
contestants. Peirce’s self-control, expressed here in terms of the “definite tendencies
of a tolerably stable nature”, refers to the fact that the existence of certain winning
strategies, or habits of acting for a purpose, is eventually guaranteed. Such stable
tendencies and acting for a purpose are the essence of reaching the equilibrium
points. They can be likened to the ways solution concepts behave for a wide variety
of games.
A number of solution concepts have been proposed in game theory. A central
issue has been how to choose among them. One candidate I would like to suggest as
the solution concept of a Peircean stripe of game theoretic action is Reinhard
Selten’s trembling-hand perfect equilibrium (Selten 1975). According to it, players
may sometimes, though very rarely, play unintended moves and thus slightly
deviate from optimal strategies. Trembling hands are also closely related to
evolutionary stability. We can in fact add evolutionary superstructure to our
semantic games, thus taking a step closer to (i) Peirce’s own understanding of
various levels of self-control as not assuming full rationality (Pietarinen 2005a), (ii)
that faculty of logical reasoning (logica utens) which according to Peirce is based on
“instinctive” reasoning (see De Waal’s chapter in this book and Pietarinen 2005b),
and (iii) evolutionary stable strategies which unlike classical game theory do not
assume full rationality and hence not full but fallible and self-corrective self-control.
Evolutionary stable strategies in fact come close to revealing the mechanisms that
would explain what Peirce’s evolutionary cosmology struggles to be.
Equally interesting is the latter paragraph of the quotation, in which Peirce
reveals that the two minds “must have all the characters of personal intellects
possessed of moral natures”. He is not saying that they are morally acting personal
intellects. On another occasion he makes the well-known allusion to ‘sops thrown to
Cerberus’ in order to make his view that a sign “determines an effect upon a person”
(SS 80-81, 1908, Letter to Welby; Pietarinen 2006b) better understood. Those
“agents” who “discuss the rationale of logic itself” are theoretical constructs which
nevertheless need to possess the same characteristics as personal intellects do.
In explaining the fundaments of the philosophy of his later diagrammatic logic,
“the dyadics”, Peirce repeatedly tells that these minds, in other words the
participants in the logical dialogue taking place in thought, are “intelligent agents”
(MS 3, c.1903, On Dyadics: the Simplest Possible Mathematics).
In other words, our theories of logic must be able to incorporate the theory of
the characteristics of intelligent agents into the concept of the logical agenthood. Or,
alternatively, since GTS is a theory of logical semantics, they must be able to
157
incorporate those characteristics into the concept of the player of a semantic
game.106
This I take to be the impact of Peirce’s assertion that logic as a normative
science is among the “most purely theoretical of purely theoretical sciences”. The
agents, endowed with the characteristics equal to personal intellects and capable of
discussing “the rationale of logic itself” as they according to Peirce are prescribed to
do, are the key theoretical constructs indispensable in what pragmaticism
ultimately is calculated to achieve.107
I believe what was just said explains what it means that logic depends on
ethics, or that ethics provides grounds or support for logic. But what is more,
contained is the previous remarks are also intriguing hints as to the senses in which
logic could be taken to hinge on esthetics. Peirce’s well-known remark concerning
ideals read as follows: “If conduct is to be thoroughly deliberate, the ideal must be a
habit of feeling which has grown up under the influence of a course of self-criticism
and of hetero-criticism” (CP 1.574, 1906).108 From this, he goes on to define
esthetics, pretty non-standardly, as “the theory of the deliberate formation of such
habits of feeling” (CP 1.574).109 Recall that in the long quotation from MS 280 above,
Peirce states that “habits [of action], so to call them, must be capable of being
The notion of agenthood that could be gleaned from the structure and dynamics of
games is a prominent topic in the game and decision-theoretic literature.
107 Peirce’s late proof involves the establishment of habits as logical interpretants by
exclusion of other propositional attitudes such as conceptions, desires and expectations
(MS 318; Pietarinen & Snellman 2006). The logical interpretant “can only be a Habit”, he
writes to Giovanni Papini in 1907, “which consists in a conditional future; namely that,
with a given motive, a man, under given circumstances, would rationally behave in a
certain way” (Letter to Papini, p. 7, 10 April 1907). In a little treatise Logic and the Basis
of Ethics (1949: 75) Arthur Prior, who was paying special attention to Scottish moral
philosophers and seeking to ground the normative aspect of logic in ethics and at the
same time avoiding lapses into psychologism, goes on to assimilate habits with desires.
Prior was much influenced by Peirce’s writings since early in his career, but his notion of
a habit is more narrowly conceived than Peirce’s. I believe the key reason for this is
Prior’s universalistic presupposition concerning the theory of logic. It was quite
commonplace thing to have in the wake of Russell, Quine, and the formalistic
restructuring of symbolic logic. And the book was written just prior to the emergence of
model-theoretic approaches.
108 The notion of control (both in the sense of “self-control” and “hetero-control”) is a metalogical principle in operation in Peirce’s logic. Game-theoretically, control presupposes
that the agents know their own types as well as the other players’ types, including
knowledge and common knowledge of the payoff distributions in the game. In the
nomenclature of game theory these standard epistemological assumptions refer to the
class of games that have complete information. MS 280 refers to the agents’ capabilities
of “coming to an understanding and of observing it”, which from the game-theoretic
point of view interestingly expresses one side of the principle of complete information:
players’ knowledge of their own types.
109 This definition was written around the same time, in 1905, as the manuscript 280 from
which the key quotation is taken.
106
158
modified according to some ideal in the mind of the controlling agent”. Now such
habits are rules for thinking about, and thus rules for proper conduct concerning,
the meaning of signs. Habits are modified or changed with reference to the purpose
or ideal that an agent has in mind. But an ideal is also a controlled habit, a habit that
has to do with feeling and not only with thinking or action.
Therefore, in the senses given both in his 1905 definition of esthetics and in
the central passages from MS 280 written in the same year, Peirce is implanting the
‘first’ of the normative science into the very core of logic. For these reasons, he is
justified in regarding logic as the general theory of the meaning of all intellectual
signs, thoughts, generalities, concepts and purports.
5. The Normativity of Esthetics and Its Implications to Logical Theory
Since esthetics for Peirce has to do with controlled habits and not merely qualities of
feelings, it should not be regarded only as the most fundamental of the normative
sciences. Also, the question of why the normativity of esthetics is based on rules
falls, mutatis mutandis, from the argument for the normativity of logic. The only
issue that needs to be separately considered is whether habits of feelings are manyworld entities just as are habits of thinking and action. It turns out that, analogously
to habits of thinking and action being many-world entities, to confine the formation
and application of habits of feeling to the actual world is liable to lead to an
inconsistent position in semeiotic, that is, aesthetic relativism.
In comparison to the habits of reasoning and action it is, however, a
considerably mightier question to address what kinds of rules or laws there are that
give habits of feelings their form or their points of termination. Suffice it to remark
here that this question should be discussed in connection with phenomenology
(phaneroscopy), the first compartment of philosophy immediately preceding the
normative science of esthetics. Second, if we are to regard habits as having to do
with game-theoretic actions of ‘seeking and finding’, then the question boils down to
what is it that in fact constitutes the universes of discourses concerning our habitual
activities of feeling.
My suggestion as to this latter question goes along the following lines. (i) For
logic and its habits of reasoning and self-controlled thinking, the universes of the
model consist of objects and possible states of affairs. Objects can be of very varied
kinds and refer to “special kinds of universes”, such as times, fictions, limits,
collections, continuities or different kinds of modalities (MS 1632, Logic Notebook
639, 1909). (ii) For practics and its habits of acting and self-controlled conduct, the
domains of discourse are characterized by those parts of the world which we
actually inhabit.110 (iii) For esthetics and its habits of feeling and controlled ideas, it
is the Phaneron, “the total content of any one consciousness” and “the sum of all we
110
And so in metaethical terms Peirce would agree with cognitivism, that ethical statements
have propositional content and that they can be evaluated by virtue of that content. A
necessary qualification is that his understanding of propositional content (the content of
dicisigns) is somewhat broader than what normally is accepted in contemporary
philosophy of language.
159
have in mind in any way whatever, regardless of its cognitive value”(EP 2:362, The
Basis of Pragmaticism in Phaneroscopy), as Peirce remarks in that annus mirabilis of
his, 1905.
Therefore, the universe of our habitual activities of feeling in a certain way in
certain kinds of aesthetic or artistic situations is constituted by the totality of the
content of a mind.
It is noteworthy that phaneroscopy is the locus in which Peirce’s logical theory
of Existential Graphs is really set in motion. The sheet of assertion (MS 298, 1905,
Phaneroscopy) upon which logical graphs are scribed contains all the conceivable
mind-like qualities that the interpreter may come across. The sheet of assertion
“represents the state of mind of the interpreter” (MS 280: 22). The question of what
it is that the agents seek and find in the Phaneron is thus related to the question of
what the rules are that govern the interpretations of those simple qualities scribed
upon the sheets of assertion. And such simple qualities, denoted as certain bounded
regions of space differing in quality from other regions of the space, constitute the
meaning of the diagrammatic correlates to predicate and relation terms. Such
simple qualities are thus the building blocks of logical propositions (expressed in
the graphical language of iconic logic) and hence contribute to the habits of action
by providing them with points of termination.
The rules or laws that govern the interpretation of these simple qualities are,
however, quite different from the rules or laws that govern the interpretation of
logical propositions. The former are analogous to the interpretation of non-logical
constants of our vocabularies (Pietarinen 2011a). Thus, such rules have to do with
the processes of constructing the models to which propositions are compared in the
first place, and not with the semantic processes of interpreting the assertions in the
models. In that sense they precede the rules governing the interpretation of
propositional signs.
*
*
*
I would like to emphasize in conclusion one distinctive feature of such
Peircean model-construction game activities: they are cooperative rather than
competitive. The sheet of assertion represents “everything that is well understood to
be taken for granted between the two parties”, and Peirce goes on to insist that “the
two must come to an agreement of convention” (MS 280)—otherwise all
communication is impossible.111
111
Recall David Lewis’s (1969) argument how the establishment of conventions appears to
follow certain simple cooperative signalling games. Like Lewis, Peirce presupposes the
common ground between communicants and analyses its constitution in terms of an
infinitary construction of common knowledge (MS 614; Pietarinen 2006b). However,
despite its name, Peirce would regard Lewis’s modal realism an unacceptable form of
nominalism because of its commitment to actuality and indexicality only. Modal realism
does not take real unactualised possibilities seriously.
160
These activities seem to concern actual communicative practices and
discourse rather than non-cooperative games that mediate the semantics of
propositions. The former, it seems, have to do with the issues which we may in
Peirce’s terms consider to fall within the realm of speculative rhetoric.112
However, there is an important result that needs to be taken into
consideration as to the presumption that the classes of games that describe the two
kinds of activities are different. For one thing, it needs to be asked whether “the two
parties” engaged, on the one hand, in cooperative model-building communicative
activities and, on the other, in non-cooperative meaning-constitutive activities, are
fundamentally different entities. We might indeed be led to think, sight unseen, that
in the former, model-building activities, they are the actual participants in actual
conversational situations, and in the latter they are the theoretical agents that are
real but which subsist, as Peirce remarks, in our “make believe”.113
However, the contrary is, at the end, the case. For one thing, Peirce’s writings
do not support the distinction between agents of these two kinds of activities
pertaining to altogether different categories (Pietarinen 2007b). Cooperative modelbuilding resorts to same theoretical constructs of the make-believe agents as the
strictly competitive semantic activities do. Secondly, we can bring forth a technical
result supporting this unanimity: what the two minds practice are not
fundamentally separate activities after all.114 The two kinds of games, the semantic
and model-construction games, are two sides of the same conceptual coin.
Cooperation and competition can peacefully coexist.
The fundamental correlation or intermingling of cooperation and competition
has some significant implications. Let me mention one, namely that any hard and
fast division between Peirce’s second division of normative logic, logic proper
(critic), and the third division, that of speculative rhetoric, is liable to be an illusion
and be in the name only. And this was, I believe, also Peirce’s aim to be able to
establish. Nowadays we can bring the same argument to bear on the much-debated
distinctions and interfaces between the study of semantics and the study of
pragmatics. I have argued in Pietarinen (2007a) that from the game-theoretic point
of view, the semantics/pragmatics distinction is an epistemological one and has to
do with the players’ knowledge of the content of their strategies. If we need not be
concerned with that kind of knowledge as we normally do not, the distinction
Liszka’s and Redondo’s chapters in the present book characterize speculative rhetoric.
“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” (MS 280).
114 To prove this connection, we show the following. From the winning strategies of the
model-construction games we can construe a model set that guarantees the existence of
witness individuals and witness predicates in the semantic game correlated with a
sentence A. There exists a habit of choosing these witness individuals and predicates if,
and only if, there exists a winning strategy in the semantic game correlated with A.
Conversely, if there exists a winning strategy in the semantic game correlated with A, we
can construe a model set from which we get a model for A by playing through all the
positions allowed by the model set in question.
112
113
161
simply is not there. Separating pragmatics from semantics is not something that
general theories of meaning such as pragmaticism need to be concerned with. In this
very concrete sense the divide between semantics and pragmatics is artificial and
has little philosophical support. It also means that Charles Morris’s suggestion that
the studies of semantics and pragmatics be grouped with critic and speculative
rhetoric, respectively, is not correct.
University of Helsinki
[email protected]
Acknowledgments
Supported by the University of Helsinki Excellence in Research Grant (Peirce’s
Pragmatistic Philosphy and Its Applications, 2006-2008, project 2104027, Principal
Investigator A.-V. Pietarinen). My thanks to the organizers and participants of
Charles S. Peirce’s Normative Thought: International Conference in Philosophy held in
Opole, Poland in June 2007. Mats Bergman, Vincent Colapietro, Nathan Houser, Dan
Nesher, Mateusz W. Oleksy, Helmut Pape and Sami Pihlström merit an individual
mention for their comments and criticism concerning earlier versions. Lauri
Snellman deserves special credit for participating in the formulation and contesting
of the key arguments of Sections 3 and 4. This paper is dedicated to the memory of
Mateusz W. Oleksy, with who I exchanged thoughts on our papers during that
conference.
REFERENCES
Bergman, Mats (2007). ―Is logic in the broad sense normative?‖, manuscript.
Barnouw, Jeffrey (1995). ―The place of Peirce‘s ‗Esthetic‘ in his thought and in the
tradition of esthetics‖. In: Herman Parret (ed.), Peirce and Value Theory: On
Peircean Ethics and Aesthetics, Amsterdam: John Benjamins, 155-178.
Burks, Arthur W. (1943). ―Peirce‘s conception of logic as a normative science‖, The
Philosophical Review 52, 187-193.
Gintis, Herbert (2009). The Bounds of Reason: Game Theory and the Unification of the
Behavioral Sciences. Princeton: Princeton University Press.
Hilpinen, Risto (1982). ―On C. S. Peirce‘s theory of the proposition: Peirce as a precursor
of game-theoretical semantics‖. The Monist 65, 182-188.
Hintikka, Jaakko (1973). ―Language-games for quantifiers‖. In: Jaakko Hintikka, Logic,
Language-Games and Information. London: Oxford University Press, 53-83.
Kent, Beverley (1988). Charles S. Peirce: Logic and the Classification of the Sciences.
Kingston: McGill-Queen.
Lewis, David (1969). Convention: A Philosophical Study. Cambridge, Mass.: Harvard
University Press.
Osborne, Martin J. and Rubinstein, Ariel (1994). A Course in Game Theory. Cambridge,
Mass.: MIT Press.
Peirce, Charles S. (1931-58). (CP) Collected Papers of Charles Sanders Peirce. 8 vols.,
ed. by Charles Hartshorne, Paul Weiss, and Arthur W. Burks. Cambridge, Mass.:
Harvard University Press.
———. (1967). (MS) Manuscripts in the Houghton Library of Harvard University, as
identified by Richard Robin, Annotated Catalogue of the Papers of Charles S. Peirce
162
(Amherst: University of Massachusetts Press, 1967), and in The Peirce Papers: A
supplementary catalogue, Transactions of the C. S. Peirce Society 7 (1971), 37-57.
———. (1976). (NEM) The New Elements of Mathematics, Edited by Carolyn Eisele,
The Hague: Mouton Publishers.
———. (1977). (SS) Semiotic and Significs: The Correspondence Between Charles S.
Peirce and Victoria Lady Welby. Edited by Charles S. Hardwick and J. Cook,
Bloomington: Indiana University Press.
———. (1998). (EP) The Essential Peirce 2. Peirce Edition Project, Bloomington:
Indiana University Press.
Pietarinen, Ahti-Veikko (2003). ―Games as formal tools versus games as explanations in
logic and science‖, Foundations of Science 8, 317-364.
——— (2005a). ―Evolutionary game-theoretic semantics and its foundational status‖, in
N. Gontier, J. P. Van Bendegem and D. Aerts, (eds), Evolutionary Epistemology,
Language and Culture: A Nonadaptationist Systems-theoretical Approach,
Dordrecht: Springer, 429-452.
——— (2005b). ―Cultivating habits of reason: Peirce and the logica utens vs. logic
docens distinction‖, History of Philosophy Quarterly 22, 357-372.
——— (2006a). ―Interdisciplinarity and Peirce‘s classification of the sciences: a
centennial reassessment‖, Perspectives on Science 14, 127-152.
——— (2006b). Signs of Logic: Peircean Themes on the Philosophy of Language,
Games, and Communication (Synthese Library 329). Dordrecht: Springer.
——— (2006c). ―Peirce‘s contributions to possible-worlds semantics‖, Studia Logica 82,
345-369.
——— (ed.) (2007a). ‖The semantics/pragmatics distinction from the game-theoretic
point of view‖, in Pietarinen, Ahti-Veikko (ed.),Game Theory and Linguistic
Meaning (Current Research in the Semantics/Pragmatics Interface 18), Oxford:
Elsevier, 229-242.
——— (2007b). ―To Peirce Hintikka‘s thoughts‖, The Epistemology and Methodology of
Jaakko Hintikka, The Carlsberg Academy, to appear.
——— (2008). ―Esthetic interpretants: Pragmatism, semiotics, and the meaning of art‖,
Chinese Semiotic Studies: Journal of the International Institute for Semiotic
Studies. Nanjing: Nanjing Normal University Press, 223-229.
——— (2011a). ―Peirce and the logic of image‖, to appear in Semiotica.
——— (2011b). ―Moving pictures of thought II: Graphs, games, and pragmaticism‘s
proof‖, to appear in Semiotica.
Pietarinen, Ahti-Veikko and Lauri Snellman (2006). ‖On Peirce‘s late proof of
pragmaticism‖. In: Tuomo Aho and Ahti-Veikko Pietarinen (eds), Truth and Games,
Helsinki: Acta Philosophica Fennica, 275-288.
Prior, Arthur N. (1949). Logic and the Basis of Ethics, Oxford: Clarendon Press.
Rubintein, Ariel (1998). Modeling Bounded Rationality. Cambridge, Mass.: MIT Press.
Selten, Reinhard (1975). ―A reexamination of the perfectness concept for equilibrium
points in extensive games‖, International Journal of Game Theory 4, 25-55.
163