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ICCS 2008 Proceedings
July 27 - 29 ㆍSeoul, korea
An Iconic Logic of Metaphors
Ahti-Veikko Pietarinen
Department of Philosophy, University of Helsinki
P.O. Box 9, FI-00014 University of Helsinki, Finland
[email protected]
dyadic, or so regarded, of the parts of one thing by
analogous relations in their own parts, are diagrams;
those which represent the representative character of a
representamen by representing a parallelism in
something else, are metaphors. (Peirce, 1998)
Abstract
Three theses are defended: (i) that metaphors create
non-literal meaning; (ii) that metaphoric meaning is
a matter of iconic logic; and (iii) that semantics of
metaphors requires modal interpretation. The logic
of metaphors takes similarity considerations to be
central to iconicity. Similarity is a species of
iconicity in the sense of Charles Peirce’s theory of
diagrammatic signs. Consequence is a refutation of
(i) meaning holism, (ii) the language of thought
hypothesis, and (iii) psychologism about
metaphoric meaning.
The logic of images is studied in Pietarinen (to
appear). The logic of diagrams, known as Peirce’s
Existential Graphs (EG), has been studied in
Pietarinen (2006) and Roberts (1973), among
others. My proposal for the logic of metaphors is
built upon the concepts of EGs, such as images as
indecomposable ingredients. Images, diagrams and
metaphors rest in the continuum of increasingly
complexity of iconic signs.
The key phrase in Peirce’s remark about
metaphors is that they represent “by representing a
parallelism in something else”. Because metaphors
are sophisticated, evolving forms of diagrams, I
propose to formulate the logic of metaphors in an
iconic language of diagrammatic logic with a
special modal ingredient. This iconic logic
accomplishes, I submit, the representation of
metaphoric, non-literal meaning.
My approach is logical and non-psychologistic.
It is hence to be preferred over the cognitive
theories of the Lakoff-Johnson-Turner stripe
(Lakoff & Johnson, 1980; Lakoff & Turner, 1989;
Turner & Fauconnier, 1995). They propose
‘blending’, whereas my theory only needs to
account for the composition of concepts.
Introduction
What is a Metaphor? In this paper, I defend
three theses: (i) that metaphors create non-literal
meaning; (ii) that metaphoric meaning is a logical
matter that has to do with iconicity; and (iii) that
such meaning is to be accounted for in terms of a
modal (‘many-world’) interpretation.
The logic of metaphors proposed in this paper
takes similarity considerations to be central to
iconicity. I argue that similarity considerations are
a species of iconicity in the sense of Charles
Peirce’s theory of diagrammatic signs (CP).
According to Peirce, particular kinds of hypoiconic
signs lie at the heart of metaphoric meaning. His
characterisation of metaphoric icons contains an
argument for metaphors as conveying non-literal
meaning. In other words, iconicity enables the
creation of various similarity considerations
essential to non-literal meaning.
The Meaning of Metaphors
Metaphors as Hypoicons The goal of this paper
is to sketch an explanation to Peirce’s succinct
remark about metaphors as the ‘thirdness’ of
hypoicons:
Non-literal Meaning Metaphors communicate
non-literal meaning. In metaphors, representations
are translocated from one medium into another.
This transference, or parallelism of several
representations, is what effects a change in
meaning from linguistic or literal to non-linguistic
or non-literal meaning.
Hypoicons may be roughly divided according to the
mode of Firstness of which they partake. Those which
partake of simple qualities, or First Firstnesses, are
images; those which represent the relations, mainly
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ICCS 2008 Proceedings
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Iconicity is similarity, semblance or likeness of
that which represents with that which is being
represented. Similarity may be qualitative,
structural or functional. Hence it can be abstract
and intellectual, and need not be based only in
closeness in looks or in some visual or sensuous
features.
Figure 1: There is a woman who will commit a
suicide if she fails in business.4
Many-world Interpretation Hintikka & Sandu
(1994) argue that metaphoric meaning is a matter
of possible-worlds semantics, which is extended
with non-standard ‘meaning lines’ between objects
of the domains and the interpretations of predicate
terms across different possible worlds.
I take that modal approach to metaphors to be
essentially correct (see also Engström, 2001). The
key is that to understand a metaphor, we need to
understand its extensions under many kinds of
circumstances besides the actual one. Moreover,
we need mechanisms of drawing meaning lines in
a non-standard fashion.
Non-standard lines are effectuated by
considerations of similarity between the
interpretations of metaphoric terms.
Notable in this graph is that lines of identities
enter the field of modalities. That is, whenever a
line occupies an area covered by a tincture, it
creates a ‘worldline’, a mapping from worlds to
extensions. Worldlines signal identities of objects
across different situations or possible worlds in
which terms and objects are interpreted.
I propose to add a special tincture for
metaphoric meaning. Thus, whatever is interpreted
within such areas by necessity refers to nonstandard domains. Whenever a line occupies an
area tinctured with such metaphoric modality, a
‘meaning line’ is created to signify non-standard
interpretation. The line, connecting various parts
and concepts of the graphs, draws a connection
that is metaphorically interpreted. I propose to
term such non-standard lines of identity lines of
similarity.5
Diagram Logic for Metaphors
Preliminaries Diagrams are icons that reflect
continuous relationships between “rationally
related objects” (Peirce, manuscript 293).
Diagrammatic logic of EGs is a system of logical
description and reasoning build up from
diagrammatic expressions that function as iconic
counterparts of logical constants familiar from
symbolic logic.
Similarity Comparisons
The meaning of metaphors is thus based on
considerations of similarity between different parts
of logical diagrams. Typically, these parts refer to
different universes of discourse.
However, similarity per se is a vague notion. It
must be preceded by ways of composing terms and
expressions, including metaphoric ones.6
Modality Since metaphor is a matter of a manyworld interpretation, the modal dimension is
essential in diagrams. This can be achieved by
adding to logical diagrams ‘tinctures’ or colours
that represent different modes of interpretation of
objects and terms.
Peirce did not consider such possibility to
capture metaphoric meaning. But he suggested
diagrammatic modal logics for various other kinds
of modalities, including epistemic, deontic,
intentional and non-declarative moods (Pietarinen,
2008; Roberts, 1973). An example involves logical
modality:
Composition of Concepts Take, for instance, the
sentence The surgeon is a butcher. The two
concepts (is a surgeon and is a butcher) are
indeterminate. How metaphor is created is a
question of the composition of the two concepts.
4
The example belongs to the famous “Peirce’s
Puzzle” concerning material implication and
equivalence in first-order logic.
5
Think of metaphoric modality effectuating a change
of what is the originally a line of identity into that of
similarity.
6
As such, composition of concepts is an old problem
in logic and philosophy antedating cognitive sciences.
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How do we put together two indeterminate
expressions to create non-literal meaning?
The problem concerns the indeterminacy of the
word for being. Such indeterminacy is, I propose,
considerably greater for metaphoric than for nonmetaphoric, literal interpretations of predicates.
The composition nevertheless succeeds as soon
as a sufficient number of connections are found
between different meanings of “is a butcher” and
according to which the copula is intended to
transmit between the two concepts.
Diagrammatically:
Figure 5: Words decay, will not stay in place,
will not stay still.
Likewise, the interpretation of objects is, in
addition to the continuity of non-metaphoric
objects, world dependent and based on similarity
considerations. Similarity considerations at the
level of the interpretation of metaphoric objects
exemplify iconic relationships.
Figure 2: The surgeon is a butcher.
Such connections are no more and no less
objective as being of the character of associations
of mental facts (CP 7.464).
Similarity has to be taken in a loose and wide
sense; also contraries can be joined. And similarity
need not be symmetric: the direction of the
interpretation of graphs is from outside in.
The proposed mechanism implies that the more
poetic or creative a metaphor is the more
indeterminacy there is to be taken into account in
composing the predicates. Hence, poetic
metaphors engage in considerable referential
multiplicity.
Parallelism Thus the explanation falls neatly
within Peirce’s classification of metaphors as the
‘thirdness’ of hypoicons (the first being the images
and the second the diagrams). Since the basic
constituents of diagrams are images, it is only to
be expected that representations of metaphors are
built up from diagrams whose terms acquire
multiply referential interpretations.
This is, in a nutshell, what it means that
metaphors are able to represent “a parallelism in
something else” (Peirce, 1998).
Moreover, the “materiality” (Anderson, 1984)
of metaphors is found in the fact that meanings are
always grounded in the actual world or in one of
the possible worlds, including worlds of fiction.
Hence the reason why metaphors can be either true
or false.
Examples and Illustrations The interpretation of
predicates that fall within metaphorically modal
areas of the sheet of assertion is world dependent.
Thus, complex forms of metaphors can be
diagrammatically represented:
Implications
No Meaning Holism The iconic-logical theory of
metaphors provides a refutation of meaning holism.
Lakoff & Johnson (1980) argue that metaphors
affect the way an entire network of interconnected
words behaves. But not all action concerning the
ways of interpreting metaphoric words can
contribute to how the similarities between objects
of metaphors are drawn and conceived. For
otherwise, there could be no false metaphors.
Figure 3: My cup overflows.
Figure 4: Chicago, the windy city.
No Language of Thought The word for being in
metaphoric statements, represented iconically by
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the line of similarity, is made unambiguous by the
particular, tinctured mode of representation in
graphs. Thus there is no need for ‘the language of
thought’ determining the correct interpretation.
References
Anderson, D. (1984) Peirce and Metaphor.
Transactions of the Charles S. Peirce Society
20, 453-468.
Engström, A. (2001) Hintikka and Sandu on
Metaphor. Philosophia 28, 391-410.
Hintikka, J. & Sandu, G. (1994) Metaphor and
Other Kinds of Nonliteral Meaning. In J.
Hintikka (Ed.). Aspects of Metaphor. Dodrecht:
Kluwer, 151-189.
Lakoff, G. & Johnson, M. (1980) Metaphors We
Live By. Chicago: The University of Chicago
Press.
Lakoff, G. & Turner, M. (1989) More than Cool
Reason: A Field Guide to Poetic Metaphor.
Chicago: University of Chicago Press.
Pietarinen, A.-V. (2006) Signs of Logic: Peircean
Themes on the Philosophy of Language,
Games and Communication. Dordrecht:
Springer.
Pietarinen, A.-V. (2007) Getting Closer to Iconic
Logic. In G. Dodig-Crnkovic & S. Stuart (Eds).
Computing, Philosophy, and Cognitive
Science: The Nexus and the Liminal,
Cambridge: Cambridge Scholars Press, 53-74.
Pietarinen, A.-V. (2008) On the Diagrammatic
Logic of Existential Graphs: A Case Study of
Commands. Proc. Diagrams 2008, Lecture
Notes in Computer Science, Springer.
Pietarinen, A.-V. (to appear) Peirce and the Logic
of Image. Semiotica.
Peirce, C.S. (1998) The Essential Peirce 2. The
Peirce Edition Project. Bloomington: Indiana
University Press.
Peirce, C.S. (1931-58) (CP) Collected Papers of
C.S. Peirce. Harvard: Harvard University Press.
Searle, J. (1979) Expression and Meaning.
Cambridge: Cambridge University Press.
Turner, M. & Fauconnier, G. (1995) Conceptual
Integration and Formal Expression. Metaphor
and Symbolic Activity 10, 183-203.
No Psychologism The mechanism of metaphoric
comparison in terms of the composition of
iconically conceived ideas does not imply a lapse
into cognitive psychology. Metaphor is a matter of
truth and falsity, and hence non-literal meaning,
and that meaning admits of a comprehensive
logico-semantic theory.
Counterexamples? Searle (1979) argued that
metaphors exist that have nothing to do with
similarity (and thus with Peirce’s notion of
parallelism), such as “Julia is icy.” There is no
reasonable comparison, according to Searle,
between being icy and being insensitive.
The answer is that similarity comparisons need
not be based on the interpretation of simple
qualities of predicates, but in the consequences of
the application of those predicates across different
situations. There is a clear-cut parallelism between
the effects of something being cold and something
being insensitive, such as making you shiver or
going goosey. Thus Searle presents no trouble for
the theory. Indeed, how Peirce originally
suggested expressions to be interpreted was
precisely in terms of the sum total of their effects
and consequences.
Conclusions
I outlined a novel logical and semantic theory of
metaphoric meaning. The theory appeals to
similarity comparisons through the composition of
concepts. Composition is seen as an operation
involving
contemplation
of
iconic
and
diagrammatic representations. Metaphors are true
or false, and cognitive theories can be dispensed
with.
Acknowledgments
Supported by the University of Helsinki
Excellence in Research Grant (Project 4701321)
and Chancellor’s 2008 Travel Grant.
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