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The modern history of paraconsistent logic is relatively short. Yet the subject has already been shown to be an important development in logic for many reasons. These involve the motivations for the subject, its philosophical implications and its applications. In the first half of this article, we will review some of these. In the second, we will give some idea of the basic technical constructions involved in paraconsistent logics. Further discussion can be found in the references given at the end of the article.
Inconsistent but Non-Trivial Theories
A most telling reason for paraconsistent logic is the fact that there are theories which are inconsistent but non-trivial. Clearly, once we admit the existence of such theories, their underlying logics must be paraconsistent. Examples of inconsistent but non-trivial theories are easy to produce. An example can be derived from the history of science. (In fact, many examples can be given from this area.) Consider Bohr’s theory of the atom. According to this, an electron orbits the nucleus of the atom without radiating energy. However, according to Maxwell’s equations, which formed an integral part of the theory, an electron which is accelerating in orbit must radiate energy. Hence Bohr’s account of the behaviour of the atom was inconsistent. Yet, patently, not everything concerning the behavior of electrons was inferred from it. Hence, whatever inference mechanism it was that underlay it, this must have been paraconsistent.
Dialetheias (True Contradictions)
The importance of paraconsistent logic also follows if, more contentiously, but as some people have argued, there are true contradictions (dialetheias), i.e., there are sentences, A, such that both A and ~A are true. If there are dialetheias then some inferences of the form {A , ~A} B must fail. For only true conclusions follow validly from the true premises. Hence logic has to be paraconsistent. A plausible example of dialetheia is the liar paradox. Consider the sentence: This sentence is not true. There are two options: either the sentence is true or it is not. Suppose it is true. Then what it says is the case. Hence the sentence is not true. Suppose, on the other hand, it is not true. This is what it says. Hence the sentence is true. In either case it is both true and not true.
Automated Reasoning
Paraconsistent logic is motivated not only by philosophical considerations, but also by its applications and implications. One of the applications is automated reasoning (information processing). Consider a computer which stores a large amount of information. While the computer stores the information, it is also used to operate on it, and, crucially, to infer from it. Now it is quite common for the computer to contain inconsistent information, because of mistakes by the data entry operators or because of multiple sourcing. This is certainly a problem for database operations with theorem-provers, and so has drawn much attention from computer scientists. Techniques for removing inconsistent information have been investigated. Yet all have limited applicability, and, in any case, are not guaranteed to produce consistency. (There is no algorithm for logical falsehood.) Hence, even if steps are taken to get rid of contradictions when they are found, an underlying paraconsistent logic is desirable if hidden contradictions are not to generate spurious answers to queries.
Belief Revision
As a part of artificial intelligence research, belief revision is one of the areas that have been studied widely. Belief revision is the study of rationally revising bodies of belief in the light of new evidence. Notoriously, people have inconsistent beliefs. They may even be rational in doing so. For example, there may be apparently overwhelming evidence for both something and its negation. There may even be cases where it is in principle impossible to eliminate such inconsistency. For example, consider the "paradox of the preface". A rational person, after thorough research, writes a book in which they claim A1, ... , An. But they are also aware that no book of any complexity contains only truths. So they rationally believe ~(A1 & ... & An) too. Hence, principles of rational belief revision must work on inconsistent sets of beliefs. Standard accounts of belief revision, e.g., that of Gärdenfors et al., all fail to do this since they are based on classical logic. A more adequate account is based on a paraconsistent logic.
Mathematical Significance
Other applications of paraconsistent logic concern theories of mathematical significance. Examples of such theories are formal semantics and set theory.
Semantics is the study that aims to spell out a theoretical understanding of meaning. Most accounts of semantics insist that to spell out the meaning of a sentence is, in some sense, to spell out its truth-conditions. Now, prima facie at least, truth is a predicate characterised by the Tarski T-scheme:
T(A) A,
where A is a sentence and A is its name. But given any standard means of self-reference, e.g., arithmetisation, one can construct a sentence, B, which means that ~T(B). The T-scheme gives that T(B) ~T(B). It then follows that T(B) & ~T(B). (This is, of course, just the liar paradox.)
The situation is similar in set theory. The naive, and intuitively correct, axioms of set theory are the Comprehension Schema and Extensionality Principle:
(y)(x)(x y A)
(x)(x y x z) y = z
where x does not occur free in A. As was discovered by Russell, any theory that contains the Comprehension Schema is inconsistent. For putting ‘y y’ for A in the Comprehension Schema and instantiating the existential quantifier to an arbitrary such object ‘r’ gives:
(y)(y r y y)
So, instantiating the universal quantifier to ‘r’ gives:
r r r r
It then follows that r r & r r.
The standard approaches to these problems of inconsistency are, by and large, ones of expedience. However, a paraconsistent approach makes it possible to have theories of truth and sethood in which the fundamental intuitions about these notions are respected. The contradictions may be allowed to arise, but these need not infect the rest of the theory.
The Philosophical Significance of Gödel’s Theorem
Paraconsistent logic also has important philosophical ramifications. One example of this concerns Gödel’s theorem. One version of Gödel’s first incompleteness theorem states that for any consistent axiomatic theory of arithmetic, which can be recognised to be sound, there will be an arithmetic truth - viz., its Gödel sentence - not provable in it, but which can be established as true by intuitively correct reasoning. The heart of Gödel’s theorem is, in fact, a paradox that concerns the sentence, G, ‘This sentence is not provable’. If G is provable, then it is true and so not provable. Thus G is proved. Hence G is true and so unprovable. If an underlying paraconsistent logic is used to formalise the arithmetic, and the theory therefore allowed to be inconsistent, the Gödel sentence may well be provable in the theory (essentially by the above reasoning). So a paraconsistent approach to arithmetic overcomes the limitations of arithmetic that are supposed (by many) to follow from Gödel’s theorem.
Systems of Paraconsistent Logic
The foregoing discussion indicates some of the motivations for paraconsistent logic, its applications and implications. We will now indicate some of the main approaches to paraconsistency. There are many different paraconsistent logics. Most of them can be defined in terms of a semantics which allows both A and ~A to hold in an interpretation. Validity is then defined in terms of the preservation of holding in an interpretation, and so ECQ fails. We will illustrate this with four kinds of propositional paraconsistent logics: non-adjunctive, non-truth-functional, many-valued, and relevant. (Paraconsistent quantified logics are straightforward extensions of these.) In all the following systems, not only ECQ fails, but so does the Disjunctive Syllogism (DS), defined as the following inference rule: {A, ~A B} B. In particular, then, if one defines the material conditional, A B, as ~A B (as usual) then modus ponens for this fails.
Non-Adjunctive Systems
Let us start with non-adjunctive systems, so called because the inference from A and B to A & B fails. The first of these to be produced was also the first formal paraconsistent logic. This was Jaskowski’s discussive (or discursive) logic. In a discourse, each participant puts forward some information, beliefs, or opinions. What is true in a discourse is the sum of opinions given by participants. Each participant’s opinions are taken to be self-consistent, but may be inconsistent with those of others. To formalise this idea, take an interpretation, I, to be one for a standard modal logic, say S5. Each participant’s belief set is the set of sentences true in a possible world in I. Thus, A holds in I iff A holds at some world in I. Clearly, one may have both A and ~A (but not A & ~A ) holding in an interpretation. Since modus ponens for fails, Jaskowski introduced a connective he called discussive implication, d, defined as (A B). It is easy to check that in S5 discussive implication satisfies modus ponens.
Non-Truth-Functional Logics
The study of non-truth-functional systems was initiated by da Costa (who has also produced several other kinds of system). The main idea here was to maintain the apparatus of some positive logic, say classical or intuitionistic, but to allow negation in an interpretation to behave non-truth-functionally. Thus, take an interpretation to be a function which maps formulas to 1 or 0; & , , and behave in the usual (classical) way, but the value of ~A is independent of that of A. In particular, both may take the value 1. Negation has no significant properties under these semantics. Various properties of negation may be obtained by adding further constraints on interpretations. If we add the requirements that, for any A, either A or ~A must take the value 1 (giving the Law of Excluded Middle) and that whenever ~~A takes the value 1, so does A, we obtain the core of da Costa’s systems Ci , for finite i. If we start with an appropriate semantics for positive intuitionist logic, and proceed in the same way, we obtain da Costa’s logic C. If we write A for ~(A & ~A) then it is natural to take it as expressing the consistency of A. Further postulates constraining how A behaves differentiate between the Ci systems for finite i.
Many-Valued Systems
Perhaps the simplest way of generating a paraconsistent logic, first proposed by Asenjo, is to use a many-valued logic, that is, a logic with more than two truth values. The formulas which hold in a many-valued interpretations are those which have a value said to be designated. A many-valued logic will therefore be paraconsistent if it allows both a formula and its negation to be designated. The simplest strategy is to use three truth values: true (only) and false (only), which function as in classical logic, and both truth and false (which, naturally, is a fixed point for negation). Both varieties of truth are designated. This is the approach of the paraconsistent logic LP. If one adds a fourth value, neither true nor false, which behaves in an appropriate way, one obtains Dunn’s semantics for First Degree Entailment. If one takes the truth values to be the real numbers between 0 and 1, with a suitable set of designated values, the logic will be a natural paraconsistent fuzzy logic.
Relevant Logics
Relevant logics were pioneered by Anderson and Belnap. World-semantics for them were developed by R. and V.Routley and Meyer. In an interpretation for such logics, conjunction and disjunction behave in the usual way. But each world, w, has an associate world, w*; and ~A is true at w iff A is false, not at w, but w*. Thus, if A is true at w, but false at w*, A & ~A is true at w. To obtain the standard relevant logics, one needs to add the constraint that w** = w. As is clear, negation in these semantics is an intensional operator. (There are also versions of world-semantics for relevant logics based on Dunn’s four-valued semantics. In these, negation is extensional.)
The concern with relevant logics is not so much with negation as with a conditional connective, (satisfying modus ponens). Semantics for this are obtained by furnishing each interpretation with a ternary relation, R. In the simplified semantics of Priest, Sylvan and Restall, worlds are divided into normal and non-normal. If w is a normal world, A B is true at w iff at all worlds where A is true, B is true. If w is non-normal, A B is true at w iff for all x, y, such that Rwxy, if A is true at x, B is true at y. (Validity is defined as truth preservation over normal worlds.) This gives the basic relevant logic, B. Stronger logics, such as the logic R, are obtained by adding constraints on the ternary relation. Further details concerning relevant logics can be found in the article on that topic in this encyclopedia.
Bibliography
For Paraconsistent Logic and Paraconsistency in general, see:
Priest, G., Routley, R., and Norman, J. (eds.) Paraconsistent Logic: Essays on the Inconsistent, Philosophia Verlag, München, 1989.
Priest, G. "Paraconsistent Logic", Handbook of Philosophical Logic (second edition), forthcoming.
On Dialetheism, see:
Priest, G. "Logic of Paradox", Journal of Philosophical Logic, Vol. VIII, pp. 219-241, 1979.
Priest, G. In Contradiction: A Study of the Transconsistent, Martinus Nijhoff, Dordrecht, 1987.
For Automated Reasoning, see:
Belnap, N.D., Jr. "A Useful Four-valued Logic: How a computer should think", Entailment: The Logic of Relevance and Necessity, Vol II, A.R. Anderson, N.D. Belnap, Jr, and J.M. Dunn, Princeton University Press, 1992, first appeared as "A Usuful Four-valued Logic", Modern Use of Multiple-valued Logic, J.M. Dunn and G. Epstein (eds.), D.Reidel Publishing Company, Dordrecht, 1977, and "How a Computer Should Think", Comtemporary Aspects of Philosophy, G. Ryle (ed.), Oriel Press, 1977.
For Belief Revision, see:
Restall, G. and Slaney, J. "Realistic Belief Revision", Technical Report: TR-ARP-2-95, Automated Reasoning Project, Australian National University, 1995.
Tanaka, K. "Paraconsistent Belief Revision", to appear.
For Non-Adjunctive Systems, see:
Jaskowski, S. "Propositional Calculus for Contradictory Deductive Systems", Studia Logica, Vol. XXIV, pp. 143-157, 1969, first published as "Rachunek zdah dla systemow dedukcyjnych sprzecznych", Studia Societatis Scientiarun Torunesis, Sectio A, Vol. I, No. 5, pp. 55-77, 1948.
da Costa, N.C.A. and Dubikajtis, L. "On Jaskowski’s Discussive Logic", Non-Classical Logics, Modal Theory and Computability, A.I. Arruda, N.C.A. da Costa and R. Chuaqui (eds.), North-Holland Publishing Company, Amsterdam, pp.37-56, 1977.
Schotch, P.K. and Jennings, R.E. "Inference and Necessity", Journal of Philosophical Logic, Vol. IX, pp. 327-340, 1980.
For Non-Truth-Functional Systems, see:
da Costa, N.C.A. "On the Theory of Inconsistent Formal Systems", Notre Dame Journal of Formal Logic, Vol. XV, No. 4, pp. 497-510, 1974.
da Costa, N.C.A. and Alves, E.H. "Semantical Analysis of the Calculi Cn", Notre Dame Journal of Formal Logic, Vol. XVIII, No. 4, pp. 621-630, 1977.
Loparic, A. "Une etude semantique de quelques calculs propositionnels", Comptes Rendus Hebdomadaires des Seances de l’Academic des Sciences, Paris 284, pp. 835-838, 1977.
For Many-Valued Systems, see:
Asenjo, F.G. "A Calculus of Antinomies", Notre Dame Journal of Formal Logic, Vol. XVI, pp. 103-5, 1966.
Dunn, J.M. "Intuitive Semantics for First Degree Entailment and Coupled Trees", Philosophicl Studies, Vol. XXIX, pp. 149-68, 1976.
Kotas, J. and da Costa, N. "On the Problem of Jaskowski and the Logics of Lukasiewicz", Non-Classical Logic, Model Theory and Computability, A.I. Arruda, N.C.A da Costa, and R. Chuaqui (eds.), North Holland Publishing Company, Amsterdam, pp. 127-39, 1977.
For Relevant Systems, see:
Dunn, J.M. "Relevant Logic and Entailment", Handbook of Philosophical Logic, Vol. III: Alternatives to Classical Logic, D. Gabbay and F. Guenthner (eds.), D.Reidel Publishing Company, Dordrecht, pp. 117-224, 1986.
Routley, R., Plumwood, V., Meyer, R.K., and Brady, R.T. Relevant Logics and Their Rivals, Atascadero, Ridgeview, CA, 1982.
Restall, G. "Simplified Semantics for Relevant Logics (and some of their rivals)", Journal of Philosophical Logic, Vol. XXII, pp. 481-511, 1993.
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Related Entries
dialetheism [dialethism] | logic: relevance | mathematics: inconsistent
Copyright © 1996, 2000 by
Graham Priest
University of Melbourne
g.priest@unimelb.edu.au
and
Koji Tanaka
Macquarie University
Koji.Tanaka@mq.edu.au
Twice true metaphors
Harris Kollias
Submitted to Dr. Peter Alward and Dr. John Woods
Metaphors have been variously characterized and in this paper there are three approaches which I will consider (though these are not the only approaches that exist; most notably lacking is Max Black’s interaction theory of metaphor which has been overlooked solely because of considerations of time). The first approach I will examine is the elliptical or covert simile theory of metaphor in which metaphors are covert similes without the attendant ‘like’ or ‘as’. Next, I examine Davidson’s view that metaphors are instances of literally interpreted category mistakes, grammatical deviance or conversational maxim flouting that are not amenable to paraphrase without relevant loss. The third approach which I consider involves examination of two theories, one of Bergmann and the other of Stern, whose thrust is that metaphors may assert propositions without reliance on conversion to, or analysis of, a covert simile. Settling on Stern’s demonstrative theory of metaphor and noting some objections to it, I examine what Cohen calls ‘twice true’ examples, in which a metaphorical expression is both literally true and metaphorically true. I then argue that we are able to say two things at once with the same utterance.
I: Speech Acts
The words
(1) snow is white
can be used to do a number of things. For instance, I might ask if snow is white or, I might, in an inebriated moment, be commanding yellow snow to alter its jaundiced visage:
(2) Snow is white?
(3) Snow is white.
With (2) I’m asking a question, (3) I’m commanding. With some rewriting I could express a hypothetical, (4) or a prayer, (5):
(4) If you take off those rose tinted glasses you’ll see that snow is white.
(5) I pray that the snow is white.
Questioning, commanding, hypothesizing and praying are all illocutionary acts (though this list is not exhaustive). Above I introduced the types of illocutionary acts I intended to perform however, no one, not even philosophers, introduces each and every illocutionary act and this isn’t just because it necessitates an infinite regress; illocutionary acts don’t always have to be introduced. An utterance often cues us to the type illocutionary act. So, while the type of illocutionary act can be given explicitly like I did when I introduced (2) through (5), it can also be got from punctuation as in the question (2), the heightened tone indicated by the italics in the command (3), from the structure of the sentence as in the conditional (4), or outright as in the performative “pray” in (5). This little analysis of (2) through (5) is not an exhaustive list of what cues us as to what illocutionary act is performed but more on this later.
Another illocutionary act, the one that I’m concerned with in this paper, is assertion. I will take it that the goal of asserting is “to get the listener to adopt some attitude towards the propositional content, e.g. belief in it” And, with Bergmann, propositional content is language independent, “something that can be represented as a function from possible worlds into truth-values, or, equivalently, a set of possible worlds (those worlds to which the function assigns the value true).” Now I’ll assert (1)
(6) Snow is white.
Here, with (6), I hoped to get you to believe what the words literally mean, that snow is white. This isn’t always the case. Often enough what I say, interpreted literally, is not what I mean and this isn’t just because I’m a chronic dissembler or that I glory in the perplexity of others. There can also be a gap between what I as a speaker say and what I hope to get you to believe. Examples of these, malapropism and irony respectively, both appear in the next section. That what is said, what is meant and what it is that a speaker hopes to get the listener to adopt can all be different; and how, or indeed if, they are related can be a tricky business and talking about it is helped by setting out some terminology. An utterance is the act of saying, the block in between silences; compare this with what is said. The individual doing the uttering I’ll call the speaker. I will call the individual or group interpreting an utterance the hearer.
II: Malapropisms and Irony
Before getting to metaphor, I’ll take up two examples of how sentence meaning and speaker meaning can be different: a malapropism ridden sample of Mrs. Malaprop’s dialog and irony, both with the hope of illustrating how an utterance’s literal meaning doesn’t necessarily coincide with utterer’s meaning. For comparison’s sake, keep the following metaphor in mind
(7) Juliet is the sun.
First let us consider a part of one of Mrs. Malaprop’s utterances in The Rivals:
(8) … a nice derangement of epitaphs!
interpreted literally, it doesn’t make much sense. But, we know that when she utters (8) she intends to say
(9) … a nice arrangement of epithets!
The cause(s) of Mrs. Malaprop’s malapropisms is (are?) difficult to decide; presumably she has an exceptionally tin ear and can’t distinguish “derangement” from “arrangement”, “epitaphs” from “epithets”. An alternate explanation might be that she repeats words in a way that she thinks she heard them in situations that seem appropriate and the words of both her malapropism and the original utterance aren’t examined at all, she’s merely parroting. For present purposes her pathology doesn’t matter, it matters only that Mrs. Malaprop utters (8), presumably speaker means (9) and successfully imparts it. But how does this happen, (8) and (9) under literal interpretation don’t mean the same thing. What Mrs. Malaprop utters, in under what I take to be the simplest (though not the only) analysis, is a ludicrous mispronunciation. It’s like this: Malaprop utters (8), presumably speaker means (9) and by accident of homophony imparts the speaker meaning, i.e. the literal interpretation of (9). Her utterances are instances of loose homophony (they sort-of sound like something that when literally interpreted make sense) and the only barrier between (8) and what she speaker meant (9) is identifying the appropriate words that are loosely homophonous. So, while (8) and (9) don’t literally mean the same thing and there aren’t any semantic hoops to jump through that would tell you how to get from (8) to (9), the speaker’s meaning is still imparted. What is said and what is imparted don’t have to be the same, they don’t have to have the same meaning or even be semantically related. At this point I’d like to mention it seems that (7) and metaphor in general are not instances where homophony would factor into what’s imparted.
Irony is a weirder thing (for me) than malapropism: the literal meaning of an utterance must be decipherable yet what’s imparted is not what the utterance, literally interpreted, asserts. An ironic utterance relies on sentence meaning to impart speaker meaning but unlike malapropisms the sentence meaning and speaker meaning are semantically related. In irony speaker meaning and sentence meaning are opposite each other. For instance, I might say of the recently passed -and unusually cold-month of March 2002:
(10) This past March was balmy.
While this utterance’s literal meaning is that March 2002 was very warm as far as Marches in Southern Alberta go, my intent is not to impart that. The speaker’s (in this case my) meaning and what is imparted would be
(11) March 2002 was very cold.
(10) is literally false. What is pragmatically imparted is (11) but it is because of (10) (though not (10) alone). I successfully impart (11) because, by accident of personal experience and or the explicitly included context, the hearer knows that March 2002 has been an unusually cold March. But why does it work, how is it that I successfully impart (11)? Answering “because the use of (5) was ironic” isn’t an explanation. It’s true that (10) was uttered and I speaker meant (11) and I imparted (11) successfully because it was recognized that I was engaging in the use of the trope irony but that doesn’t explain how we know to go from (10) to (11). The imparted assertion (11), which is the illocutionary force of (10), requires a literal interpretation of (10), I can’t get to (11) without understanding (10). I utter (10) but impart its contradiction, (11) but why?
What I did when I uttered (10) was exploit the Gricean conversational maxim of quality: “Try to make your contribution one that is true.” (10) has literal meaning but the literal meaning was false and this falsity implicated (11). I could have uttered (10) in an ironic tone, I could have prefixed (10) with an expletive, I could have uttered it while nursing my frost bitten appendages, cueing the hearer to perform the implication and not instead think me deluded. The mechanisms of conversational implicature, according to Grice, turn on the utterer’s not following the ‘Cooperative Principle’ of conversation. When we converse we have certain expectations of our interlocutors and when these expectations are not realized we know that perhaps something other than the literal meaning of what’s uttered is the illocutionary force of that utterance. We expect, and our interlocutors in return, that the literal meaning of what each of us utter contains sufficient information (no more, no less), that it is true, that it is relevant to the conversation, and that it is intelligible and obvious. Implication occurs because we’re so completely in the sway of the Cooperative Principle that we attempt to go from a sentence meaning that doesn’t conform to the Cooperative Principle to a meaning that does. When conversational implicature occurs we are attempting to realign an utterance’s literal meaning in a way that makes it informative, as the Cooperative Principle suggests. A sort of ‘benefit of the doubt’ applies to speaker intentions and people can be generally expected to provide true or relevant information. Taking advantage of this is what Grice refers to as exploiting a conversational maxim.
Grice’s Cooperative Principle has been invoked by some metaphor theorists to explain what cues us to existence of metaphor and prompts us to perform a metaphorical interpretation of an utterance. Metaphors, these theorists argue, flout conversational maxims (most often the maxim of quality). Consider, however, Lynn Tirrell’s twice true example. A CEO is in her office idly passing a few minutes before a meeting in the next room. Storm clouds are forming outside and the meeting next door promises to be unpleasant for everyone involved. While looking out through a window she says
(12) There’s a storm brewing.
The sentence meaning here isn’t false yet felicitous metaphorical interpretation is possible that does not flout Gricean maxims. It is appropriately informative and perspicuous. While it is probably true that a metaphorical interpretation must be cued and it is true that it’s an interesting question, I will not address the topic in this paper.
III: Simile Theory
Of course, when literally interpreted, (7) is false; however, it doesn’t seem that it’s false in the same way as say, if were to assert:
(13) Snow is blue.
(13) is a false assertion. The difference between (13) and (7), say the classical theorists which include Aristotle and Cicero and the intellectual inheritors of elliptical simile theory, is that (7) is short hand for
(14) Juliet is like the sun.
The answer according to elliptical simile theorists, then, to the question of why (13) is false and (7) is, well, not, is that the sentence meaning of (7) is the sentence meaning of (14) and hence not false. For the purposes of finding a semantic relation between (7) and (14) this is superficially a good thing since ‘like’ness is easy. Juliet is like the sun in her warmth or splendor or some such thing or class of things all of which are true.
That’s quick and convenient but if ‘like’ acts as it seems to, that is, by plugging ‘like’ into the appropriate place in a metaphor we get a phrase whose sentence meaning is what the speaker wants to impart then we have a problem. If we can ‘uncover’ the covert simile within a metaphor with ‘like’ and the simile has a sentence meaning that is the speaker meaning of the metaphor then metaphors are inane. Davidson argues that the similes produced by inserting ‘like’ into metaphors makes them trivial; everything is like everything in some way or another. Juliet is like the sun but so is a Christmas ornament, after all, it’s spherical and so is the sun. If (7) and (14) are semantically equivalent they suffer from the reasonable insistence that not only is Juliet like the sun, but so is Cygnus 1 and an entire universe of stars and worse, they’re quantifiably more like the sun than is Juliet. No? Well, how about for every proposition that you identify for a likeness relation between Juliet and the sun I can produce at least one more proposition for a likeness relation between Lady Montague and the sun or for that matter Stalin and the sun.
So far, I can be justly accused of using ‘like’ infelicitously by considering it in a non contextual way and by extension, infelicitously casting the elliptical simile theory. Tony Veale points out that if the ‘like’ness relation is comparative, to hold it has to hold under common features, that is, it should hold under
(15) The sun is like Juliet.
since ‘X is like Y’ allows that ‘Y is like X’. Moreover, if similes and metaphors are semantically equivalent and hence interchangeable I should then be allowed
(16) The sun is Juliet.
Intuitively, we no longer have the same metaphor. Whatever it is that ‘like’ is doing in simile, it can’t be doing it in a literally comparative way. If that’s the case, what is the utility of turning metaphors into similes? Elliptical simile theory doesn’t deliver on the promise of providing a literally interpretable rephrasing of a metaphorical expression.
IV: Davidson
Davidson’s positive claims about what metaphors mean are limited and he is concerned mostly with rehearsing a number of criticisms against the existence of figurative interpretation. For Davidson metaphorical meaning falls entirely within the domain of use and just what ‘use’ is isn’t clearly defined by Davidson. Instead we are left with the rather bold (and bald) insistence that metaphors have their literal meaning and no other special meaning besides; they say what they literally say and that’s all. Therefore, a paraphrase of metaphorical expression would be nothing other than a paraphrase of literal meaning. Metaphorical interpretation doesn’t rely on a non-standard interpretation instead, its effects are on the hearer in an ‘in-the-head’ way. It seems then, that metaphor has no metaphorical illocutionary force but has perlocutionary force on belief or outlook or perspective. So, while there may in some sense be metaphorically asserted propositions, those propositions don’t exhaust what a metaphor means. There is a semantic gap between what’s said literally -speaker meaning or no- and what’s imparted. In terms of the earlier vocabulary sentence meaning and speaker meaning are one and the same but what’s imparted is not paraphraseable without relevant loss, it is unique to the words in a metaphor.
Quickly, here is what I agree with Davidson about: 1) the original (literal) meanings of the words in metaphors are required to interpret metaphors; 2) further and further study of a metaphorical expression results in further and further things we want to mention; and 3) propositions generated by metaphors don’t necessarily exhaust metaphorical meaning. For example knowing the meaning of (7) requires us to be able to literally interpret Romeo’s words, thinking it over we can come up with more and more ways that Juliet might metaphorically be the sun, and a list of ways in which Juliet is metaphorically the sun doesn’t paraphrase it without relevant loss.
An issue of disagreement, which I explore more fully in section VII and was mentioned in passing earlier, involves the characterization of metaphor as categorically false, grammatically deviant or maxim flouting. Davidson is prepared to admit that while most metaphors are categorically false or more generally grammatically deviant, they all at flout at least one conversational maxim. (7) is categorically false and “business is business” is patently true. Where his example “business is business” is tautologically true, it’s true to a vapid degree and hence violates the maxim of quality (maybe quantity as well) the contribution of a patent truth isn’t informative. This prima facie doesn’t account for twice true examples in which the literal interpretation is informative.
If metaphorical expressions are potentially inexhaustible since continued attention brings more and more to the fore --and this due to their literal meaning-- then what about their literal meaning is potentially inexhaustible? Davidson explains this question simply under the rubric of use. This would suggest context dependency, but literal meanings for Davidson are not context dependent:
Literal meaning and literal truth-conditions can be assigned to words and sentences apart from particular contexts of use. This is why adverting to them has genuine explanatory power. (436, Davidson)
By hewing so closely to what he calls the literal but eschewing context, he has in mind literal meaning in an eccentric sense for someone who insists that ‘use’ is a lynchpin of metaphorical meaning. Indexicals are legitimate linguistic expressions in which context shifts reference. The existence of indexicals and demonstratives within that class (more on demonstratives later) makes the above quote untenable since
(17) I am here.
Uttered by Harris Kollias (17) refers to someone and some place other than Davidson yet Davidson is free to utter (17) confident that no one could rightly (with respect to (17) ) call him an utterer of false sentences.
Allow for context dependency in Davidson’s account. There’s a difference between being able to generate, with appropriate creativity and resources, infinitely many propositions from a given metaphorical expression and those propositions that might be generated by a real cognitive agent, a human cognitive agent (who is also a contextual constraint), in a given context. We could have too many or none. If I were to utter “the small round floor which makes us passionate” and you had never read Dante or Davidson, and we were not outside, and moreover our conversation until that point had nothing whatever to do with the earth (I had decided to change the subject abruptly), you would not have even the slightest idea of where to start in interpreting my utterance much less what I had intended by it. “The small round floor which makes us passionate” has no content without context. Davidson can deny that contexts are never so constrained as to exhaust or make content finite but if this is so then words have to have ‘special’ meanings for where else might these contents come from if not from context? Use happens somewhere; in a book, in chapter, in a paragraph, in a sentence, in the course of conversation -it happens in a context. The fewer the contextual constraints or cues, the less there is to fix content; unfixed content is ambiguous content and my uttering of “that small round floor that makes us passionate” without appropriate context is so ambiguous as to be devoid of content altogether. The literal meaning is about as intelligible as a phonetic reproduction of Saturnian, and I, I’m embarrassed to admit, have no grasp of Saturnian at all. Even if the utterance was more complete than Davidson’s, for example I said “the small round floor that makes us passionate” instead of just a nod towards earth and uttering “floor” a competent language user wouldn’t have a clue that there was some utterance that should be interpreted metaphorically. That Saturnian has benefit of seeing where the nod was directed that nod was a demonstration, in this case an ostensive definition, all that was happening was another episode of teaching. You could have thought whatever you liked, thinking of Dante or the how that floor made us passionate but your use was not a metaphorical one, as tempting as it is to hitch the “Metaphor as Demonstrative” project to it.
If Davidson is right then metaphor is a black box, utterly inscrutable, its magic worked by ‘use’ for which there can be no thorough accounting. I can’t quite pin my discomfiture with this, perhaps because it exudes mysticism putting metaphor alongside koans in as much as the literal leads to the unfathomable or at least unspeakable. I don’t know how to explain “the sound of one hand clapping” for instance. Putting aside whether koans have explanations, Davidson may well have a point and the opening to this paragraph was an overstatement. A better way to put it: the most interesting thing about a metaphorical expression isn’t necessarily, in the case of insightful metaphors, the propositional content. Davidson labors under the stated incompatibility between insight and propositional content, however, irrespective of whether the propositional content of metaphorical expressions exhausts the worth of that expression, we shouldn’t confuse part of an explanatory theory with the whole (should it exist) theory. Metaphors might mean more than what a theory about how metaphors may be used to assert but that doesn’t entail that such a theory is wrong. What’s more, propositions on their own don’t account for understanding.
In sum, what I take from Davidson’s account is this: literal interpretation is required to interpret a metaphor, continued contemplation of a metaphor can produce more meanings that can be attributed to that metaphor and propositions don’t necessarily sum up a metaphor’s meaning. My agreement in all of these points however, is qualified and is fleshed out in later sections.
V: Bergmann
Merrie Bergmann’s account of metaphor is concerned with showing that metaphors may be successfully used to assert. A metaphorical assertion for Bergmann “is a direct function of salient characteristics associated with (at least) part of the expression.” Not everything that could be interpreted of a metaphor is interpreted of a metaphor. Contextual constraints limit the range of interpretation. Additionally, that some metaphors may not assert does not entail that no metaphor can assert.
For a metaphor to be used to assert it must be identified as a metaphor and it must also be identified that the metaphor is being used to assert. Just what it can assert derives from the context in which it occurs and whether the author’s intent, in conjunction with context, is identified.
First let’s consider salience. What is salient for Bergmann is what is distinctive about a thing or thought, those characteristics that top our lists of characteristics. For Bergmann the very possibility of a metaphorical use of language turns on salient characteristics.
What is distinctive of all metaphorical uses of language (whether the purpose is to assert or to do something else) is that the content of what is communicated is a direct function of salient characteristics associated with (at least) part of the expression -rather than the literal meaning of that part.
A good way to think of salience is the television game show “Family Feud”. For those lucky enough to have passed unblemished through western civilization here is a quick synopsis: two teams of four (usually composed of members of the same family but sometimes these teams are comprised of individuals who are co-workers; regardless, the teams are comprised of language users who have substantially shared time with each other) attempt to guess the members of the ordered set of replies to a public survey. These surveys are requests for information of the form “Name an activity which you would be engaged in if you were a tailor,” “Name an occupation that requires a computer” “Name an item likely to be found on the table during thanksgiving dinner,” and so on. The point of the exercise is to name the most commonly named occupations, vegetables, items of clothing or things depending on the content of the information request. What’s important to note is that those 100 people surveyed, and whose answers are used as the basis for this game show, do not provide 100 different answers; there is a clustering around roughly five or ten responses. That is to say, there are salient characteristics belonging to the notion of, say, tailoring held in common by language users.
The problem is of course, that put on the spot, the two teams of four people in “Family Feud” have trouble thinking of all of the most popular responses to the surveys. This makes for a marginally more interesting television program but why the discrepancy between the results of the surveys and the results of the eight language users? We can note that these requests for information are insular, they are asked without much in the way of context (they are bare requests for information, and conversations leading up to those requests are perfunctory or at minimum, utterly unknown to the teams). Moreover the situational context in which the information requests are made to the survey respondents (we can imagine that they are polled at a shopping mall or at home, randomly via telephone) differ from a television studio. The situation is unique, language users are unique; the set of salient characteristics isn’t rigid, salience is not universal, nor need it be lasting.
Since Bergmann’s account of salience as given doesn’t distinguish between the extensions of the parts of expressions which serve towards communication of whatever it is that a metaphorical expression might communicate (hereafter called the focus) and intensions thereof, I will with the help of Stern, try to point out that it must. The problem with accounts that attempt to explain metaphor via the extensions of the focus is that extensions are not necessarily substitutable; members of the set of extensions of “the sun” substituted into (7) do not necessarily preserve metaphorical expression. For instance Stern point out that substituting the focus of (7) for a member of the set of the extensions of ‘the sun’
(18) Juliet is a blob of gas 9 light minutes away from the earth.
produces a metaphorical expression, which, when taken outside of the context of Romeo and Juliet that can’t helped but be considered an insult. Pasted back into the play, it’s hard to tell what it might assert.
To take another example, here’s the dialogue between the Sphinx and Oedipus.
(19) Sphinx: “What is that which walks with 4 legs at in the morning, 2 legs at noon and 3 legs at dusk?”
(20) Oedipus: “Man is that which walks with 4 legs in the morning, 2 legs at noon and 3 legs at dusk.”
(21) Over the course of a human’s life one crawls on all fours as a child, at the peak of life walks upright on two legs and as the end of life nears needs their two legs steadied by a third ‘leg’, a cane.
Notice how the Sphinx’s metaphorical question gains its illocutionary ‘puzzling force’ by exploiting our tendency to examine extensions? We consider the sets of extensions of “in the morning” = {12:00AM…11:59AM}, “noon” = {12:00PM} and “dusk” {4:00PM … 11:00PM}. You then examine the set of walking things {aardvarks, androids, …, zoraptera} and cross reference it with the previously mentioned sets trying vainly subtraction or addition of legs morning through evening but you’re on the wrong track. If approached from intensions, “in the morning” would (picking relevant qualities for brevity) be beginning, growth/nascence; “noon” middle, fullness/fruition; “dusk” end, waning; all of these in virtue of their order in a day and in the metaphor, over the course of a life. Similarly for “walk” being a journey through a life as well as “legs” being means of support, carrying us through life. Even examining intensions I must admit that I still would have suffered the wrath of the Sphinx. Without better contextual clues it would still be too difficult but, I think it’s fair to say that examining extensions would get you nowhere and the Sphinx a belly full of Thebans.
The difficulty of the riddle, however, does not reside in some semantic ambiguity of the constituents. “Morning”, “noon” and “dusk” are not polysemous like say, “can” is, nor is there some syntactic ambiguity like in “I saw John’s dog driving to work today”. Rather, we need the recognition that it requires a metaphorical interpretation. The riddle (if not the Sphinx) means for us to interpret its query metaphorically but denies us any cue, grammatical or conversational maxim flouting beyond the omission of a cue. However, the question is meant to be difficult and I’m not sure that complying with one maxim doesn’t necessitate flouting another. To give away too much information about the riddle ruins the point (quantity) but lack of ambiguity again ruins the point (perspicuity). Even with a metaphorical interpretation in hand nothing but the answer to the riddle makes us fully understand the metaphorical expression.
The above criticism aside, I don’t reject Bergmann’s account so much as I think it needs a more fully realized mechanism for picking out salient characteristics and a description of how those characteristics function with metaphor.
VI: Stern
Like Bergmann, Stern too believes that metaphors may be used to assert and also like Bergmann thinks that context dependency is important to that end. As mentioned in the Davidson section, demonstratives have context dependent features. Stern’s account seeks to subsume metaphorical expressions into the class of demonstratives utilizing Kaplan’s theory of demonstratives. The process by which this is undertaken is an examination of three Kaplanian concepts: character, content and context.
Each of character, content and context has specific meaning in Kaplan’s theory involving the identification of elements within literal meaning. Context is the world where a demonstrative is uttered. Character is the linguistic meaning of an expression that remains constant through all contexts. And content is the propositional content that varies with context but is identified by a function or rule that is identified with the character of the expression. A refinement to this suggested by Alward is that we consider context to be a world centered on the speaker and content as a function from possible worlds to the extensions of those worlds.
Before getting into demonstratives it might be best to start a bit more simply by looking first at indexicals which don’t require accompanying demonstrations. Whoever says ‘I’ refers to themselves, without any requirement of finger pointing. Similarly ‘today’ and ‘now’ require no further information to refer to a time. The character of (17) remains constant: ‘I’ picks the speaker; ‘here’ picks the place of utterance; ‘I’ has the content “Harris” when I say it, while ‘I’ has the content “Donald Davidson” when Davidson says it. Fully, according to Braun, the content, say “Harris is on a chair” or “Donald Davidson is behind a lectern” varies with who utters it and when it is uttered and the content is true or false at the world centered on the speaker of the context. ‘I’ is directly referential; ‘I’ drops out and is replaced not with some property but with the speaker in the world centered on the speaker.
Demonstratives require more elaboration than indexicals. That elaboration for Kaplan consists in pointing gestures or the directing intention (Demonstratives 1989a and Afterthoughts 1989b respectively). Like indexicals demonstratives are directly referential, what’s more is they can refer to properties. The paradigmatic demonstrative is ‘that’ used in conjunction with a pointing gesture. From here, Stern notes that Kaplan is prepared to accept describing as a form of demonstrating, and it seems intuitively true. Doesn’t it seem that I can demonstrate something by describing it? The paradigm case of the demonstration ‘that’ is one of pointing to “that guy with the martini.” Isn’t ‘that guy’ being painted in your mind with description by the finger pointed at him in the sense that in the minds eye he’s being described with contextual information of all sorts? Your finger like the long arm of a scaling device, your mind’s eye the short, translating coordinate geometry into your mind along with color and, relative to my manner of pointing, your particular disdain or admiration? For descriptive demonstration “Kaplan introduces a special demonstrative symbol ‘Dthat’ which, completed by a (non-rigid) definite description ö, yields a directly referential term ‘Dthat[ö]’ whose referent at all circumstances is the (same) individual actually denoted by ö in its context of utterance.”
This broader conception of demonstratives allows Stern to begin his program of subsuming metaphorical interpretation into demonstration since explicit ‘thats’ are not required. With this as the entry point Stern notes the features of metaphor which Davidson has insisted make metaphorical interpretation impervious to semantic analysis and on which Bergmann expounds: the sensitivity of metaphorical interpretation to context of utterance. Bergmann rightly notes that metaphorical interpretation can be ephemeral and constructs an example illustrative of just that. Here is a reproduction of Bergmann’s example that I had promised earlier:
John: Look at how blue the sky is today!
Joe: Sure is. What a great color … and not a cloud in sight. When the sky is that blue, the air seems fresher … crisper … it really makes you feel good.
John: Yeah, it sure is a good feeling. Like everything’s gonna be great, when the sky is that blue.
Joe: Mmm … Hey -even the news report was blue today for a change-lotsa good stuff.
‘Blue’ doesn’t seem to have what we usually -saliently-think of when talking about blue. Instead of an utterance like “I’m blue today” having a speaker meaning like “I’m feeling depressed” it has one like “I’m feeling cheerful today”. This, like all cheer, will pass but the spontaneous and ephemeral association of blue with something other than depression is context dependency that metaphorical expressions have in common with demonstratives.
There is a sense in which we might say that Stern is picking up where Bergmann left off in trying to show metaphors act like demonstratives in that they direct us to noticing metaphorically relevant salience. Stern believes, and I along with him, that context includes contextual presuppositions. We have beliefs, prejudices, stereotypes in mind individually, in common that aren’t necessarily known that affect the environment in which utterances occur. We as speakers and hearers both aren’t pristine, we’re preloaded. This is a refinement of Bergmann’s salience in that where Bergmann has salience covering all contextual presuppositions Stern splits them into two sets: the ‘Family Feud’ presuppositions the productive (p-) presupposition set and the (f-) filter set.
The filter set is culled from the p-presupposition set. The filter set is comprised of propositions that can be consistently asserted and aren’t redundant, the rest don’t factor into metaphorical interpretation.
All of this needn’t be explicit or even an accurate reflection of what the speaker (or hearer) believes; what is required is for the description to be associated with the descriptive demonstration. Gorillas aren’t brutish creatures but call someone a gorilla and you’ve labeled them a threat because stereotypically gorillas are brutish though most know the stereotype to be false. The possibility of truth or falsity of a metaphorically asserted proposition requires that both the speaker and the hearer have in common common filter sets. These sets don’t necessarily have to be temporally prior to the utterance however, since something like conversational implicature functions in these sets. Intuitively, this seems fair. Often enough in the course of conversation you’ll hear something to the effect of “Oh, now I see where you’re coming from” and I think that this is a sign of presupposition set rejigging.
Stern coins the term ‘Mthat’ and has it function similarly to ‘Dthat’ except that Mthat yields properties where ‘Dthat’ yields individuals and ‘Mthat’ functions to make character context sensitive: “‘Mthat’denotes a function from the (stable) character of ö to the (non-stable) character of ‘Mthat[ö]’”. Mthat ranges across as little or as much of the character of an expression as you might want and more than once on the same expression. So in the case of (7) it might be applied like “Juliet is ‘Mthat’[the sun]” or as much or as few of the words generating grammatically admissible metaphorical characters. In a more complex metaphorical expression ‘Mthat’ would also range over noun phrases. Until this point context’s role isn’t semantic, it serves to pick out non-stable metaphorical characters, these characters are potential candidates for metaphorical interpretation.
At the second stage of Stern’s account the content(s) of characters are determined by examining the context sets p and f at which point (stage three) the truth or falsity of content in the context is evaluated. The difference between these two middle stages is that in the stage in which evaluation occurs, what is actually the case during the circumstance of the context. I have to admit that at this point I’m unsure what Stern is getting at since it seems to me that the circumstance of the context is itself a feature of the context. The best explanation I can give is that the actual time of evaluation has features that aren’t included in the p and f sets because these features occur at the instant of evaluation.
At the last stage context serves to determine whether the metaphor conforms to what Stern refers to as “Grice-like” maxims. That is, is it appropriate -does it communicate what the author intended to impart, was it more abstruse than warranted, did it fail by being too difficult to interpret or spurious?
So far, so good provided that demonstratives behave as Kaplan says. With regard to a Kaplanian theory of demonstratives Stern’s theory suffers from two problems.
If the ‘Mthat’ operator can be justified, it inherits the difficulty with complex that phrases that ‘Dthat’ does. Specifically, since it ranges over noun phrases, it is more appropriately a complex demonstrative. Complex that phrases are of the form That(ö) where ö is a noun phrase like say, ö=book under the table. A problem with ‘that’ acting on a noun phrase is that it doesn’t necessarily refer. “For on the direct reference view, the predicative material that combines with ‘that’ to form a ‘that’ phrase partly determines the character, and hence the referent in the context of utterance, of the ‘that’ phrase.” That is to say, in the case of ‘Mthat’, the ‘that’ phrase doesn’t necessarily refer to a property since character is being affected by ‘Mthat’.
(22) She (pointing to a bedraggled Juliet in a fun house mirror) is the moon.
And then, anaphorically referring to (22)
(23) That moon is not the sun. (addressing Juliet).
It matters that the character of the expression is itself subject to change. At the time of utterance of (22) I was mistakenly identifying Juliet and (23)’s character changed into a metaphorical contradiction.
My second concern is related to the first and regards what I take to be the stripping of illocutionary force that an expression might have besides any it might have under metaphorical interpretation. The examination of this concern will comprise section VII.
VII: The Twice True
For a demonstrative account of metaphor sentence meaning drops out, loses its illocutionary force and is replaced by metaphorically derived meaning and whatever illocutionary force it might metaphorically have.
Stern’s (1985) theory of metaphor places metaphor (with the suggestion that this can apply to other tropes) in the class of demonstratives. The purpose of this move is to explicitly recognize the context dependency of metaphorical expressions without committing the interpretation to an extreme polysemy of metaphorical expression and hence charges of ambiguity as well as to maintain the role that metaphorical character plays in the interpretation of metaphorical expression. In thumbnail, we go about this is as follows: Interpretation of metaphorical expression requires a literal reading of its constituents and whole, but the literal interpretation does not necessarily have a place in the metaphorical interpretation. That is, the literal character of an expression (stable or not) does not necessarily have a role in determining the content of a metaphorical expression. This is similar to what occurs in demonstrative expressions not interpreted metaphorically in that what is said, the description of that counts as a demonstration disappears during the determination of content since the demonstration is considered to be directly referential. So, while I’m currently not very concerned about the context sensitive character that the Mthat operator creates might disappear (taking Mthat to work like dthat), it seems that the lack of consideration exhibited for metaphorical character would likely be repeated for a literal character that is even further removed in the interpretive process outlined by Stern.
In this section I intend to examine a few more twice true examples in which the literal interpretation cannot conveniently disappear. I intend to show that a theory which requires that an interpretation be literal or metaphorical cannot cope effectively with expressions that can successfully assert propositions conveyed both literally and metaphorically.
Consider first the expression
(21) The [professor is a] rock [that] is becoming brittle with age.
where, without the contextual information that it was uttered by geology students of their aging professor, “The rock” has no discernable [dare I say referent] metaphorical interpretation. The entire utterance, murmured, conspiratorial and perhaps a sad realization, is a retarded demonstration using the students’ recent encounter with the professor anaphorically. There’s a set of shared contextual presuppositions that’s immediate to the experience. The p set includes actual rocks but what’s important to note here is that they’re not in the filter set actual rocks aren’t relevant. While it’s true that “rock” appears in (21) what’s being asserted hasn’t got anything to do with any ordinary sense of environmental erosion. It is true that some actual rocks are becoming brittle with age but it’s not relevant to the conversation. (21) while twice true is not twice true in a way that matters to what speaker intends to impart.
Next, let’s look again at Tirrell’s twice true example (12). Recall that in this example a business executive gazes out of a window, dark clouds coalescing while saying “There’s a storm brewing,” before entering a particularly prickly labor dispute. Can’t she be asserting both propositions, namely that there is a rainstorm in the making outside and that what waits for her in the next room has the makings of a row? She can, I think you’ll grant (and Stern does grant), realize once she’s asserted (12), that it also has a metaphorical meaning. Alternately, her mind may have been wandering and though she was eyes open, facing the window, she was uttering (12) intending to impart the metaphorical interpretation of (12) and noticed after snapping back from her reverie the state of the weather. In both of these scenarios the propositions are conveyed one after another. She thinks one thing, and then another; asserts one proposition, and then another, in serial fashion. Could she not have intended to assert both at once, that is, in parallel? I think that she can.
So as it happens, I do have another problem with Stern and Bergmann’s accounts: that the propositional contents conveyed by an assertion in a twice true example, metaphorical and literal, are presented one at a time. Bergmann says this and in “Demonstratives” Kaplan seems committed to a one demonstration, one demonstratum and hence, so is Stern.
Suppose that my friend an avid climber and compulsive thief and I are career criminals and in our debauched history I had uttered to her
(22) You’re about to fall.
while she repelled down a cliff, the ropes of her climbing gear frayed. The gear was, of course, stolen and my intent, in addition to asserting my belief that she should remain on the ledge where she was resting because of the dangerous state of her ropes, was to assert using metaphor that the child whose climbing gear she had stolen earlier in the day was at that moment glancing up the rock face and that the climber/skater/thief should hide her face so as to avoid detection by her young victim. Here the propositions were serial; climber/ thief apprehended the propositional content of the metaphor only after being identified by her victim.
Like many say, prison is like college for criminals: my friend the climber/thief came out a cannier thief, I knew it and she knew it. (22) was unlikely to have made clear to the climber/thief that the child victim was near (there witnessing what he hoped were the opening acts of a cliff side calamity) - at least not with the immediacy that I’d like i.e. that the utterance be apprehended simultaneously literally and metaphorically. Alright, now that I’ve added some background and loaded the filter presupposition sets, consider this later case when I uttered
(23) You’re skating on thin ice.
directed at my friend the climber/thief’s impetuous revelry on the local pond during spring thaw. It is again used to assert two proposition at once: one interpreted literally is the reminder that the ice is likely to break and the climber/thief/skater may soon be swimmer and, interpreted metaphorically, that the climber/thief/skater’s behaviour (say the earlier theft of those skates and their present use in front of the person victimized by the theft) is likely to result in her arrest. In this example, like Tirrell’s of the executive gazing out a window and (22), there is no apparent requirement that the propositions be presented serially. Two propositions, both true, from the same utterance. Moreover, my intent in making the utterance was that it be interpreted in both a literal and a metaphorical way. No conversational maxims were violated or flouted, indeed, by stating the proposition that the skater’s behaviour was going to get her arrested via metaphor, I traded on knowledge that was exclusive to myself and the climber/thief/skater: my utterance was peculiarly meaningful to the skater/thief and not the victim of the theft. The victim could interpret my utterance in the literal way, agree or not as to its truthfulness; the victim might also interpret the utterance metaphorically and think me a scold. Leaving aside that I really might be a scold and hence (23) might be a thrice true utterance, the victim is unaware of my warning or complicity. Sure from the victim’s perspective I’m flouting the maxim of quality but my conversation was not with her but the thief, and irrespective of whether my assertions are heeded, I’m in compliance with Gricean maxims. when I uttered (23) at the pond it was entirely clear; no exploitation nor flouting of conversational maxims required, I utilized the filter set that was common to me and my friend. My utterance was interpreted both literally and metaphorically in parallel.
I suppose that it could be that the expression “You’re on thin ice.” has two contexts of utterance, contexts that by their disparateness make them ersatz temporally separate. One context, the globally accessible context, is the one where the ice is likely to crack. The other context is the one where I am asserting, via metaphorical expression, that the fun may soon be over since the victim is present and may recognize the climber/skater/thief, and is private between us. This, I think, would entail that climber/skater/thief and I were severally in two states of mind because if such internal mental state separateness is required it seems so severe that we can never speak of speaker centered world coherently. I like that less than the possibility of asserting two propositions at once using the same utterance and finally successfully imparting those two propositions at once.
VIII: Some Concluding Remarks
Why so much fuss over serial versus parallel propositional content? My first intuition is that it’s prophylactic; parallel propositions suggest ambiguity and that’s just what Bergmann and Stern are careful to remove from their papers, ambiguity is what Hobbes damns metaphors them out of the language of philosophy and science over; so, better to avoid parallel propositional content altogether.
At some point in every account I’ve read thus far ambiguity is accounted for and removed; in the later papers this job is lumped in with pragmatics. That it is possible to produce an example where there are two propositions imparted and these delivered in parallel means, at least for utterances that can be interpreted metaphorically, that pragmatics isn’t the catchall some would like for it to be. I’m not trading on ambiguity in my imparting of information to climber/skater/thief though it may appear so to the victim.
If ambiguity means no decidability, then the foregoing examples don’t suffer this problem, no decision as to which proposition is asserted need be made since both are intended. Perhaps a problem with the ambiguity of twice true metaphorical expressions is that we don’t have a way of deciding which of the generated propositions to go with. At minimum we can have a literal propositional content and a metaphorical propositional content from a single utterance at once, and the 2 imparted meanings don’t interfere with each other insofar as one meaning doesn’t impede the other meaning’s understanding. There’s a ‘kosherness’ thereby suggested that at least makes it allowable to impart 2 meanings at once that it is reasonable to extend to a metaphor generating more than one metaphorical proposition. “Juliet is {P1, P2, P3, …Pn}” isn’t subject to more worry than “Juliet is warm” and “Juliet is my reason for living” since how large subscript ‘n’ is limited and the filter set, while perhaps changing with each generated interpretation, is informed by each interpretation as well.
I want to make clear that I don’t think that the possibility of a single expression being used to assert one proposition under literal interpretation and another proposition under metaphorical interpretation and perhaps yet another proposition under a different interpretation opens the door to every possible interpretation having propositional content that’s always asserted all at once. We have to realize along with Woods and Gabbay that cognitive agents have limits. People don’t think every possible thought and an account of metaphor (or any account of interpretation) that does not refer back to actual human ability lacks credibility. Metaphors are uttered by real cognitive agents with real cognitive abilities with expectations of imparting what real cognitive agents are capable of imparting.
While propositional content doesn’t necessarily paraphrase a metaphorical expression, I don’t think anyone has said it did. This was noticed at least as far back as Descartes and there with intuiting. Propositions asserted by mathematics don’t singly amount to the understanding of a theorem instead, they amount to a bunch of propositions. Thinking about one of them without thinking about the others won’t get you an understanding of a theorem. It might be that metaphors which can’t be paraphrased without relevant loss are metaphorically and parallely asserting more than one proposition. So, while some insist that the meaning of unparaphraseable metaphors is due to the inappropriateness of propositions to the task of capturing metaphorical meaning, I tend to disagree on the grounds that propositions apprehended together do amount to something that, if it isn’t understanding, is something like it.
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