Harnad, S. (1982) Metaphor and mental duality. In: Language, mind and brain (T. Simon & R. Scholes, eds.) Hillsdale NJ: Erlbaum, 189 - 211.


Stevan Harnad
Department of Psychology
Princeton University
Princeton NJ 08544

I am going to attempt to argue, given certain premises, there are reasons, not only empirical, but also logical, for expecting a certain division of labor in the processing of information by the human brain. This division of labor consists specifically of a functional bifurcation into what may be called, to a first approximation, "verbal" and "nonverbal" modes of information- processing. That this dichotomy is not quite satisfactory, however, will be one of the principal conclusions of this chapter, for I shall attempt to show that metaphor, which in its most common guise is a literary, and hence a fortiori a "verbal" phenomenon, may in fact be more a function of the "nonverbal" than the "verbal" mode. (For alternative attempts to account for cognitive lateralization, see e.g. Bever, 1975; Wickelgren, 1975; Pendse, 1978.)

The bulk of this chapter will be discursive and general. I will proceed from a consideration of learning and perception to language and metaphor chiefly by what I hope will be conceded to be a logical route. (In the process, I shall have to introduce a number of special terms and concepts from what will at first appear wildly disparate domains of discourse; a glossary is provided to orient the reader.) I reserve facts about the real world and real brain for a brief coda at the end.


We must first agree upon the following premises:

(1) Action and thinking are in fact a function of the brain.

This paradoxically enough, is my least crucial premise, and could perhaps be replaced by some abstract epistemological principle. At worst, its rejection may render some of my concluding references to actual data concerning brain function less compelling in terms of their real-world locus: "Right" and "left" would have to be replaced by some less ontologically-committed terms. However, the underlying cognitive bifurcation to which they allude would still have some claim to validity.

(2) At least a significant portion of both action and thinking are governed by learning, i.e. they are somehow derived from experience by induction (Harnad, 1976).

This will be made more precise shortly. For now, it is sufficient to note that to deny this premise is to claim that there is no need to account for the "origins" of action and thinking through any general empiristic principles. They just "are" as they are, and ours is but to analyze the consequences of already "having" them, not to conjecture as to how they got that way (see footnote 1).

Perhaps I have depicted the denial of this premise in so peculiar a way as to assure that no one would actually endorse such a gambit. And yet this is the only coherent way I can formulate what I take to be the position of rationalists, extreme nativists, and any others who deny the existence of radical induction (see, for example, Chomsky, 1980).

(3) The brain (or, in the case of the denial of (1), some abstract epistemological principle) does not have an infinite rote memory; i.e. we cannot remember "everything."

(4) The experiential (phenomenal) world is of at least one order of complexity greater than that of memory (or its equivalent); i.e. there is always more "out there" than we can remember.


That premises (3) and (4) can be taken as empirical hypotheses rather than merely as premises is illustrated by the following: In a famous paper summarizing a good deal of research in psychophysics, George Miller (1956) showed that there are some rather narrow limits on our capacity to remember stimulus information (see Broadbent, 1975, for a recent updated version of these findings). Given a one-dimensional sensory continuum, say, the amplitude (loudness) spectrum of a sound of fixed timbre and pitch, human beings seem to be very restricted in the number of absolute levels of loudness they can remember. Up to seven distinct values along the amplitude spectrum can be reliably remembered, as demonstrated by the ability to assign an instance from each level a unique name whenever it is encountered. However, as the number of absolute judgments is pushed beyond this limit, as one attempts to segment the loudness spectrum more minutely, reliability falls off rapidly, and errors and confusion abound.

This phenomenon is by no means restricted to loudness. It is exhibited by other sensory continua as well, and is also demonstrable (with suitably generalized "limit" parameters) in higher-dimensional cases.

Miller interprets such psychophysical data as evidence for limits on our capacity to perform absolute discrimination. An absolute discrimination is any judgment requiring a unique memory. The best index of the possession of a unique memory in this sense is the capacity to assign a unique name: to identify the remembered input.

Miller contrasts these apparent orderly limitations of our absolute judgment with our relatively unpredictable capacities for relative discrimination or similarity judgement. To relatively discriminate is to distinguish two inputs (presented simultaneously or in rapid succession) as being identical or different, and to judge the degree and direction of the difference. Here no memory is required, but merely the capacity to make concurrent comparisons.

Miller remarks that not only do the limits on our capacity to perform relative discrimination not seem to obey the "magical number seven" rule, capriciously depending instead upon the particular input modality involved, but that invariably these limits dramatically exceed the absolute judgment limit. We are in all cases capable of far fewer absolute than relative judgments.

Now how are premises (3) and (4) borne out by this? There is support for (3) in an even stronger form than stated, for not only is it demonstrable that we remember less than we can perceive (which implies, a fortiori, that we remember less than there "is") but limits also on relative judgment show that we perceive less than there "is" (where "perceive" is taken to mean "being able to resolve by relative discrimination"). Therefore, not only is our memory (i.e., our capacity to remember experiences) finite, but even the instantaneous perceptual resolution of these experiences is limited. There is more information "out there" than we can perceive directly--which also strongly confirms (4).

Having established that at least (3) and (4) are not unreasonable, I shall now attempt to erect upon them some systematic generalizations. All I can vouch for besides, is clarity. (For a more elaborate development of this viewpoint, see Harnad, 1973.)


Given that the real world is informationally richer than our finite processing capacities, it follows that if there is to be any learning from experience, this must involve some reduction of experience. That is--and here I mobilize (1) as well: caveant idealists, mentalists, and disciples of Karl Lashley (1960)--the engram, or structural record of the experience, which is extracted and stored in the brain as a memory, will not be a faithful copy of the experience.

Otherwise stated, I deny that we have analogue memories (at least insofar as absolute judgments are concerned). In fact, I claim that even if we did have potentially infinite rote memories, our brains would still be obliged to perform some reduction, i.e., some discarding or suppression of information. This follows from the induction postulate (2), since the rote registering of each unique experience in its full uniqueness would make it impossible for one to be anything but a reflex automaton with a very rich spiritual life. To be able to learn by induction is to be able to extract regularities from the flux of experience: to select the invariant and recurrent, and discard the irrelevant and "unique."

To illustrate with the Miller paradigm: If, in learning to identify a sound of a specific loudness, one had attempted to incorporate into the engram all the unique information potentially available upon first hearing--including, of course, the polysensory context in which it had occurred, the concurrent state of one's gut or of one's soul, not to mention one's (presumably) unique sense of each temporal instant--then nothing could ever be subsequently identified, for nothing could ever exactly recur. Hence the induction would be a logical impossibility. (No induction without reduction!)

I did promise a more precise definition of induction. The paradigm for induction (otherwise known as the absolute discrimination paradigm, for obvious reasons) is the following:

An inductor is said to have performed induction, if having been confronted with experiential inputs, some of which (positive instances) are invariant with respect to the presence of some property (or properties) and some of which (negative instances) are invariant with respect to the absence of this property (or properties), the inductor can, after a sufficiently large sample of inputs, reliably produce exclusively in the presence of the positive instances, a unique, arbitrary output. This output must be unique, in the sense that it is associated with the positive instances and the positive instances alone; and it must be arbitrary, in the sense that (a) it was demonstrably not already associated with the positive instances prior to the induction ("non-apriority") and (b) it is not structurally isomorphic with the positive instances ("non-iconicity").

Precision has its drawbacks. Expressed in the vernacular, induction, or absolute discrimination learning, consists of learning to uniquely identify something from experience. The rule is that you must not have been able to identify it previously, and that your means of identification must not be iconic (i.e. not an analogue copy of what you are identifying).

That the first of these conditions (non-apriority) actually implies the second (non-iconicity) is easily shown. If the identification were allowed to be a structural copy of some sort, we would be in danger of falling into an analogue of the analogue-memory problem discussed earlier. Suppose one were allowed to "identify" a certain loudness by simultaneously vocalizing with commensurate loudness, or perhaps matching it by turning the potentiometer of an oscillator that emits a sound of continuously variable amplitude. This task one could presumably accomplish without the need of prior experience (ignoring now the improvement that may result from "mere exposure" to such a task), which would violate the constraint that one must have been demonstrably unable to perform the identification a priori. (Mark well, for future reference, the similarity of this iconic pseudo-induction to relative judgment).


It should also be apparent why "absolute discrimination" is a more accurate term for induction than "identification." To illustrate: If I place an object on a table (let it be, for the sake of argument, a bowl of potato soup) and demand that you "identify" it, you may be justifiably perplexed as to what it is that I want you to say. In fact, you would be entitled to reply with anything from "a concrete visual object" to "potato-soup- Charlie at time t." On the other hand, if it were flanked on either side by a plant and a hat, you may be more comfortable in identifying it as "the food"; or, if surrounded instead by various soups, as "the Vichyssoise," etc.

These more determinate cases reveal that in any identification, a discrimination or distinction from among a definite set or context of alternatives is either implicitly or explicitly involved. Technically, the receipt of "information" means the reduction of uncertainty, and uncertainty is defined against a set of alternative outcomes, much as in the casting of dice. A foray into information theory would not be appropriate here, but let it be understood that what I mean by the context associated with every identification could be formulated quite rigorously (Garner, 1974; Olson, 1970).

The role of context is as critical in the actual learning of an absolute discrimination as it was in the above cases, which involved the mere exercise of an already-learned absolute discrimination. In the simplest sort of induction, consisting of only the dichotomy of positive and negative instances, it is the negative instances that provide the balance of the context against which the invariant properties underlying the absolute discrimination are extracted. Without such a clearly-defined complement to the positive instances, the number of invariants underlying identification would quickly escalate into that indeterminate, irreducible state-of-affairs, already twice avoided in this discussion, in which an instance would have to be encoded in its infinite (and inutile) uniqueness (cf. Luria, 1968; Borges, 1969; Haber, 1979).

What I am claiming is that we do not tell apart "potato soup" from "the rest of the world," but only from various definite subclasses of the rest of the world. Notice that in this particular case I say that we "do not" rather than "cannot," for there do of course exist what philosophers have called "natural kinds" to simplify a good deal of our inductive life (Marler, 1976; Rosch & Lloyd, 1978). However, I have throughout this discussion always been keeping one eye on the most difficult sort of case, namely that in which the experiential inputs vary continuously along several sensory dimensions, rather than falling neatly into certain prefabricated physical or perceptual categories.

The example of sound amplitude was just such a difficult case. And of course there are innumerable others, of multidimensional and polysensory varieties, such as complex geometric forms, acoustic timbres and sound sequences, complex daily events and sequences of experiences--in fact, any experience that varies along an actual continuum (or a "virtual" continuum, in virtue of unresolvable information complexity). And this is not yet to have mentioned purely abstract cases, such as the "space" from which I discriminated the foregoing list of examples.

In fact, space itself is the best example. Loci in space do not constitute "natural kinds," and when we name loci according to an imposed set of coordinates, these constitute a reduction, with a certain definite grain, adapted to some specific discriminative context.

Suppose I see a man standing somewhere in a large circular field, and someone asks me where he is ("Identify his locus"). I may say that he is "between center and five o'clock," or "in the fourth quadrant," or "in the circle," or "out there"--depending on what I conceive to be the alternatives. In fact, if there were a dozen people out there, that would simplify things for me considerably (provided they were not standing too close together). But I can no more state his "absolute" locus than any object's "absolute" identity (cf. Rosch & Lloyd, 1978).


These examples are meant to illustrate that absolute discriminations are not performed "in vacuo" (and so they are, in this sense, not really "absolute"). They are performed within a context of alternatives that focus that reduction of experience necessary for the practice of induction. In fact, I claim that experience is reduced to what is in each case very close to the minimal set of invariants required to perform a particular identification. These, and only these, are "committed to memory," in the sense of being encoded in an engram constituting a "record" of that experience.

Such a record provides a finite and tractable package that can be stored and reliably recalled by name. In fact, the role of the identifying response, the arbitrary, unique name, is to provide a reliable, exclusive means of access to the engram. I call such encoding "categorical" because it has well-defined category boundaries. In particular, any input continua involved have been "quantized," in the sense that certain entire regions of continuous variation have been reduced to an effectively equivalent discrete unit. Instances have been reduced to their invariants.

Here are some examples: A "zebra" belongs to a prefabricated physical category, which, when it is learned, involves ignoring the within-category variation from a "zebra-Charlie" to a "zebra- Fred." "Red" is (probably) a prefabricated perceptual category, a segment of a physical continuum that is innately quantized by the visual system (Bornstein, 1975). Within its boundaries, the differences between a "scarlet" and a "vermillion" are ignored. The musical acoustic categories "A" or "C#" (Siegel & Siegel, 1977) and the phonemic categories "/ba/" or "/ga/" (Eimas, 1975; Liberman, 1976; Pastore, 1976) may (perhaps) be quantized by the process of induction alone (this is not yet known for sure{Every time a category turns out to be innate, it entails passing the epistemological burden to evolution. The inductivist holds himself accountable for the acquisition of our categories, the nativist only for their structure and deployment. Radical inductivism, which is the position adopted here, assumes that there is significant acquisition during ontogeny. See Harnad, 1976 and Dennett, 1980.}); within the boundaries of these categories too, variation is ignored. Finally, if we focus upon "zebra-Charlie," "vermillion," "C#," and "/ga/," we may find that we have been reduced to the limits of categorical grain altogether, so that we could not make further absolute discriminations even if we cared to.


At this point an interesting paradox ought to be suggesting itself. What have I been doing here, contemplating these various absolute discriminations that I can and do make? I have claimed that, due to limits on my memory (and constraints on induction) I am forced to encode experiences in a highly reduced form. As a consequence, I extract certain information from instances and store that information alone, under some name or other, discarding all else. If this is indeed the case, then at some particular time t when I am either perceiving or contemplating in my mind an instance out of one of my categories, I ought to be aware only of some sort of abstract skeleton. And yet I seem to be aware of a good deal more! In particular, when I see or imagine a man on a large field, he seems to be occupying a very specific, unique position, even though, in the case of actually perceiving him, I may be unable to recall after a few moments what the unique position was, precisely; and in the case of imagining him, I may be unable to describe my image beyond a definite (verbal) grain of resolution. What sort of processing is involved in my immediate perception and in my iconic imagery?

In fact, forget about induction and absolute discrimination for the moment: How is it that I am able to perform relative discrimination or similarity judgment at all? If my engrams consist of reduced extractions and abstractions, how is this (albeit ephemeral from the anamnestic viewpoint) holistic experience, similarity judgment, possible at all? It would seem that if ab ovo I am reducing and quantizing and ignoring as I learn, the world should be getting steadily more and more fragmented--not to mention that I can hardly conceive how it ought to have looked to me prior to my ever having extracted any categories at all! And yet my experience seems to be, and always to have been, uniformly and continuously whole for as long as I can recall!{Indeed, this could be taken as a fifth postulate, mediating the strong confirmation of (3) and (4): viz (5) Immediate experiences seems phenomenally continuous and holistic.} Is that sense of "recall" a contradiction in terms?

This is the stage at which a cognitive bifurcation appears to be forced upon us. Perhaps we do not establish engrams (let us call them bounded engrams) only of the kind I have already described. Perhaps we have another representational system as well, one that also registers a trace or "engram" worthy of being called a "memory" (cf. Pylyshyn, 1973). However, I am not prepared to retract any of my premises, and consequently this second representational system, if it exists, must occupy a rather peculiar status. Its engrams, if they are not of the same highly reduced sort as the bounded ones, cannot be expected to subserve absolute discrimination. Moreover, they cannot have names. They cannot be addressed reliably; and being thus overdetermined in their uniqueness, there must be considerable overlap and confusability among them (from the absolute discrimination point- of-view).

In fact, if this second species of engram consists of analogues of my naive, continuous, instant-to-instant experience, then it seem impossible to think of them as "bounded" at all, as I am not aware of any "quantization" of my experience. Certainly the "natural kinds" and other wholesale categories I erit gratis provide a kind of intrinsic segmentation, but they are probably already named and encoded in bounded engrams, and probably also best handled via that system. What about everything else? What about timbres and melodies, forms and spatial configurations I've never named? How do I remember a face? Is all that detail that distinguishes faces I now (and name) encoded in bounded engrams somewhere? Could I go ahead and quantize the spectrum of Chinese faces that way too? What about instance-to-instance variation of a face--all its subtle nuances of expression? I see those too, but from the standpoint of naming and quantizing, they seem to present literally boundless alternatives for one lifetime!

So the engrams of this second representational system cannot be "bounded" in the same sense as those subserving absolute discrimination. They must to a great extent blend continuously and namelessly into one another, preserving their irreducible uniqueness, but doing so anonymously, without benefit of an absolute identity. They may be available in an immediate sense for short-term iconic memory, and they may be more-or-less available later on, in mental imagery. But they are bound to be less tractable than bounded engrams.

Note that naming is something you do. It is a motor act, and the motor system is a voluntary one. Likewise, verbal imagery seems to have retained a degree of this conative control. Hence the apparent possibility of "thinking" in words.

Iconic imagery, on the other hand, never enjoyed a voluntary status in overt behavior--or did it? Certainly not in overt verbal behavior. However, recall the forbidden class of iconic responses: responses such as drawing, singing, playing a musical instrument, mimicry, etc. Could these not provide a substrate for rendering some unbounded engrams more tractable? Being continuous, iconic responses cannot, of course, provide boundaries such as the category boundaries provided by names. But they can subserve a modicum of conation, so that we are, to a degree, able to "think" iconically. However, to the extent that these images have not been under such prior motor control, they are destined to be a good deal more"self-willed" (in the sense of their will, not ours) than mental verbalization.{The mental analogues of scanning eye-movements (which are, to an approximation, iconic responses) may facilitate visual imagery, but not reliably. Images persist in maintaining a perverse degree of independence, so we must often be resigned to being passive spectators of a relatively autonomous, dreamlike display.}


One avenue of possible control over unbounded engrams has not yet been explored. Are they not, after all, associated somehow (even if only indirectly and unreliably) with their bounded counterparts? Obviously this association is not unique or one- to-one, but many-(many-many)-to-few, in virtue of the uniqueness and multiplicity of the unbounded engrams relative to the reduced bounded ones. Moreover, it is not clear, given the unbounded nature of unbounded engrams, how effective any association of this sort can be conceived to be. However, it seems reasonable to suppose that, among the various gradients of association from engram to engram provided by variables such as structural similarity, temporal or spatial contiguity in experience, "natural kinds" and iconic responses, a special relationship with corresponding bounded engrams should not be excluded. Hence, if I think "zebra," it seems reasonable to suppose that I might be more likely to stir one of the unbounded engrams of "zebra-Fred" than of "potato-soup-Charlie."

So language, as one manifestation of this interaction between bounded representations and their homologous unbounded counterparts,{That there is interaction (of this and other sorts, discussed later) between the bounded and unbounded representational systems is an extremely important feature of the model proposed here. (For one thing, it implies that a portion, at least, of my title is a misnomer: we are dealing, not with "mental" duality, but with cognitive duality, within one "mind.") The two representational systems, neither viable alone, work in concert in information-processing, each making its unique contribution. Some tasks may have a stronger "loading" on one than the other, but the presence of the other is still felt. For example, after absolute-discrimination learning, relative discrimination is demonstrably modified, such that intracategory similarities are anced and intercategory differences are accentuated. This is the "perceptual boundary" effect in the categorical perception whereby /ba/'s sound more like /ba/'s and /ga/'s like /ga/'s, although the underlying acoustic variable, the formant transition, is continuous.} does seem to have some sway over images, even if not a strong or absolute one. And, apropos of language, it also seems appropriate to inquire whether there might not be unbounded engrams of a purely "linguistic" sort. I did make some enigmatic allusion earlier to "abstract" spaces from which I had "pulled" certain verbal illustrations. What might that mean?

I confess that I have some difficulty in being specific about this (principally because the "images" underlying my conceptions at this point wax elusively abstract), but perhaps it is not unreasonable to suppose that abstract properties and relations have structural characteristics that are, as such, amenable in principle to an iconic representational.

For example, suppose that we are learning an absolute discrimination: that of name "quadrupeds" (within the context of creatures possessing various quantities of limbs). Why shouldn't the property of "four-limbedness" (or even just "fourness"), which is extracted during such a piece of induction, have parallel to its "bounded" duties, an unbounded representation as well? I do not mean the "fourness" that is intrinsically embedded in each unbounded engram of a particular quadruped, but a bonus unbounded encoding on the basis of fourness's disembodied existence in the bounded representation: an (unbounded) engram of a (bounded) engram. If it has not been too far-fetched to suppose an interaction between bounded and unbounded representations in my earlier suggestion that the name of a bounded engram may (sometimes) evoke an unbounded image, then perhaps it does not go too much farther now to suppose that the abstract properties of bounded engrams have their unbounded images too. If that is the case, then these derivative unbounded engrams are in a sense "linguistic" (if the naming process in absolute discrimination is conceded to be linguistic), or at any rate an abstract offshoot of a linguistic process.

A third sense in which language might impinge upon unbounded representations would be the converse of the above, namely, the formation of a bounded engram on the basis of input from unbounded engrams. This is a very important case, and in fact much less tenuous than the preceding one. I will return to this case later, and will now add only that there is nothing in the nature of induction which would rule out the possibility of learning on the basis of internal inputs: Since unbounded representations, too, are derived from experience, the establishment of a bounded category, later demonstrable externally, but essentially based upon the internal hypothesis- testing with unbounded "memories" as raw material, would certainly be a bona fide case of induction.

Yet another sort of interaction between language and unbounded representations would of course be via the icons of words themselves: words in their pure sound value, or in song, or verse.


There may well have been some readers who were not prepared to grant that in this discussion of discrimination, naming and memory I have hitherto broached upon "linguistic" matters at all. For their benefit I shall immediately introduce: the proposition.{I do not wish to enter into the philosophical dispute as to whether there "exist" special abstract entities underlying sentences. My propositions merely constitute the information conveyed by declarative sentences.} It seems clear that in a universe in which inductors are busily displaying their capacity to perform induction, they are likely to be confronted with many of the same or similar instances in different contexts. "Potato-soup-Charlie" may put in a number of appearances as "food" or as "Vichyssoise" or as a "concrete visual object." It does not seem reasonable to treat him as a total stranger on every occasion. In particular, if I already know "potato-soup- Charlie," I really only have to hear his name in learning to discriminate "Vichyssoise." I need only be told that "Vichyssoise" is, in point of fact, good old "potato-soup- Charlie," in order to be able to perform (at least in part) that new discrimination.

Now, one might be inclined to argue that such a state-of-affairs does not satisfy my criteria for induction: that under such conditions one could identify correctly from the first actually- encountered instance onward (following the proposition), implying that the learning was a priori.

In one sense this would certainly be true, for if you have not previously known "potato-soup-Charlie" you would not have known "Vichyssoise" from being told that it was he. But were you incapable of understanding a proposition, then even possessing prior acquaintance of Charlie you could not benefit from the additional propositional information in learning to name "Vichyssoise." Furthermore, ignorance is certainly demonstrable prior to the actual receipt of the propositional information. So the capacity to comprehend and encode propositional information must be regarded as a means of learning: a very rapid and powerful means.

I will not attempt to enter into the problem of the nature of propositional understanding (see e.g. Katz, 1976, Steklis & Harnad, 1976a), but it seems clear that propositions provide information about category relations, in particular, those of membership and category-inclusion. Negation is presumably mastered from positive and negative instantiation, and the logical connectives, quantifiers, and rules of inference can be picked up by induction (to the extent that they are not already erent in induction). With such an arsenal, an inductor can spare himself a lot of learning from experience (as long as there is someone else around to provide him with the pre-emptive propositional information).

It is also clear that the propositional communication of information--for communication it is, as contrasted with the perceptual extraction of information by discrimination learning from instances--must be intimately linked with bounded representations, upon which it must draw for its atomic terms, and upon which it acts via the information it provides. In particular, I will claim that category relations are revised and updated on the basis of propositional information, as demonstrable, for example, by an altered use of name subsequent to the receipt of such information.


The orderly state of affairs in the bounded system (names, categories, revision, updating) in contrast to the unreliability and intractibility of the unbounded system, owes its existence in large part, I claim, to a certain critical property of the boundaries of bounded engrams. These boundaries have the property of being bivalent, that is, governed by (two-valued) logic. More precisely, within a particular discriminative context, category boundaries have the remarkable property of enforcing exclusive membership.{I do not, of course, deny the existence of probabilistic, "fuzzy" sets (Zadeh & Fu, 1975) in perception and cognition. However, in naming, absolute discrimination and categorical perception it is clear that bivalent boundaries prevail. For reasons too complicated to discuss here, I also regard the so-called "nonbivalent" logics (see, for example, Rescher, 1969) as irrelevant to the considerations at hand.}

I shall illustrate with the simplest kind of context: the dichotomy. An (intracontextural) instance must be either in the positive category, or not in it; not both, and not neither. In such a consistent (and hence, in principle, learnable) paradigm, the mutual-exclusiveness of positive and negative instances is rigidly reflected in the nature of the bounded engram, and in particular in the nature of its boundary, which is "impermeable" to membership. There is nothing mysterious here, just a faithful reflection of a real-world consistency, as evidenced by the rational use of names. Given that he is a contextual candidate for the category "food," "potato-soup-Charlie" either is or is not a member; not both, not neither.

The same can definitely not be said of the various unbounded engrams of "vermillion," for example. Bereft of names and not absolutely discriminable, it is not possible to take boundaries between them, and hence it makes no sense to attempt to make bivalent distinctions.

At the propositional level (which is clearly the territory of the bounded system) bivalence is also eloquently operative. If you tell me that "Socrates" is a "man," then I duly assign him membership in that category. This, in turn, determines that his is "mortal," for my category "man" is contained in my category "mortal." It follows that my category structure is such that if you told me "Socrates" was "immortal" I would either not believe you, or begin to ponder as to where my categories might require revision. (Needles to recall, underlying any such reshuffling of categories are the very bounded engrams--names, invariants, bivalent boundaries--of which I have been speaking.)


But what about the unbounded system? Suppose I have learned that "Socrates" was indeed a "man," and then you insisted that he was "immortal." I have already said that it is likely that--in accordance, perhaps, with a Quinean principle of "minimal mutilation" of the categorical structure (Quine, 1969), my bounded system would reject this. Does my unbounded system do likewise? First it would be well to check if it has understood the question!

I have already suggested that names may somehow weakly resonate in their unbounded counterparts. Suppose in this case they in fact do so. I have accessed some of the unbounded "Socrates" and the unbounded "immortals." What then? In the propositional case, the critical link is the copula "is" (or "is not"). That link embodies the propositional claim (or denial) to the tune of which the bounded engrams perform so admirably. In the present case, they have given their answer: "That does not compute."

What do the unbounded engrams say? First, it must be ascertained just what it is that they have heard. Have they heard the "is"? Or, more precisely, have they understood the "is," which is to say, have they understood what it is that is being proposed here? I claim that they have not.

Abandoning the anthropomorphic rhetoric: Whatever it is that the bounded system "has" in being able to process propositional information, the unbounded system hasn't got it. I would venture the guess that the critical property has a lot to do with bivalence and category boundaries. Whereas in the bounded case the propositional information is decoded as something proposed or claimed concerning category relations, in the unbounded case the information is merely construed as the apposition of (the unbounded engrams of) the subject and the predicate.

By apposition{The term "appositional" is due to one of the most imaginative and articulate of the exponents of hemisphere differences, the neurosurgeon Joseph E. Bogen, who has generously left its meaning open for later users:

The difficulty in characterizing the ability of the right hemisphere arises largely from our ignorance--we have barely scratched the surface of a vast unknown. We would do well therefore to choose arbitrarily a word, homologous in structure with the word "propositional" but sufficiently ambiguous to permit provisional use. For example, we can say that the right hemisphere has a highly developed `appositional' capacity. This term implies a capacity for apposing or comparing of perceptions, schemas, engrams, etc., but has in addition the virtue that it implies very little else. If it is correct that the right hemisphere excels in capacities as yet unknown to us, the full meaning of `appositional' will emerge as these capacities are further studied and understood. (Bogen, 1969, pp. 149-156)}

I simply mean the juxtaposing or pairing of the engrams, in much the way they are paired in a relative discrimination or similarity judgment. In fact, a similarity judgment is precisely what the essence of such an apposition is.


The apposition of unbounded engrams yields a holistic comparison in which the irrelevant, continuous properties vanquished from bounded engrams by reduction are free to reveal structural congruities to which the bounded system was "blind." This is not to say that the bounded system can never be privy to such revelations. On the contrary, the interaction between the two systems of which I spoke earlier allows the bounded system to extract invariants with unbounded engrams as input. All that the "blindness" of the bounded system is meant to imply is that it cannot "discover" these structural congruities by its own devices: It can only exegesize them once they are presented.

This concept of the exegesis of appositions by the bounded system is a rather critical one, and so I will attempt to explicate it in some detail. Consider the apposition of "Socrates" and "immortal": "Socrates is immortal." This proposition is literally false. But I have said that, as far as the unbounded system is concerned, this is not a proposition, but an apposition. Now if a proposition is literally false, it makes sense to deny it. But does it make sense to deny an apposition?

Consider first that an apposition can be regarded as trivially "true" if it is formulated as: "I have apposed the unbounded engrams "Socrates" and `immortal'," or "It is possible to appose...." However, this would be to construe it as a propositional claim, which it is not.

Second, one might be inclined to infer that what is really meant by the apposition is that "Socrates" is like an "immortal": that they are in some sense similar. I reply that this too is true, but not quite to the point. Certainly, since there is structural congruity, there is similarity. But one may still be inclined to deny that there is "relevant" similarity.

Given the unbounded nature of unbounded engrams, anything is potentially "similar" to anything else, in the sense of being potentially apposable and sharing some structural attributes. This is yet another manifestation of the "analogue memory" phenomenon discussed at the outset; for experiences, in their unbounded uniqueness, grade continuously into one another, with no basis for any categorical distinctions. Things may be more similar or less similar, but not "non-similar."

So one can deny "relevant" similarity of an apposition, but not similarity simpliciter. And even this is to construe the apposition propositionally, which is to beg the question. However, the matter of "relevant" similarity does cast some light on the phenomenon of exegesis I mentioned earlier. One is inclined to ask: "Relevant with respect to what?", and the only reply I can conceive of is: "The categories."

What I mean by the "exegesis" of an apposition is the testing of whether the structural congruities it reveals are in any sense "relevant" to the bounded representation, and if so, to update the latter accordingly. In that sense, appositions may be very important in the generation of models and hypotheses in science (Hesse, 1966).

To exegesize an apposition is to find or impose a categorical context that makes a corresponding (nontrivial) proposition literally true. The holistic comparison is replaced by a categorical approximation, with a categorial invariant substituted for the structural congruity: a reduction of the type always attendant upon category extraction. The similarity is quantized: "Socrates is like an immortal in that his ideas are still actively discussed today, etc." (See Verbrugge & McCarrell, 1977).


I have discussed the role of apposition in intellectual creativity elsewhere (Harnad, 1973). At this time I would like to consider another sort of "relevance." For this purpose I must make a brief foray into the domain of affect.

It is certainly the case that emotions have "natural kinds" (anger, fear, desire, etc.), for which we no doubt have bounded categories. But in a much more important sense, emotions are continuous, and it is their subtle nuances and blends that are so salient to us. These ineffable and indeed often unique variations are not amenable to categorical encoding. Moreover, in the reductive process involved in the establishment of bounded engrams, surely "emotion" would be the first thing to be dropped as irrelevant! Attention has often been drawn to the relative "freedom from affect" that so strikingly characterizes language as distinct from other symbolic and communicational systems (Steklis & Harnad, 1976).

So emotion is much more likely to be handled via the unbounded system, both in the sense that emotional experience is more amenable to iconic representation, and in the sense that the affective context of cognitive experience is more likely to be incorporated into the unbounded engram.


Now, for those who have been straining for some time to hear an explicit formulation of the role of the unbounded system in metaphor, let me count the ways:

a. I have argued that a name may have some better-than- chance probability of evoking corresponding unbounded images.

b. Names themselves have iconic properties as pure sound.

c. There may be unbounded engrams of bounded engrams; i.e., abstract and indeed verbal properties have iconic structure.

d. Unbounded engrams have the potential to reveal, through apposition, structural properties and congruities to which the bounded system is blind (Socrates is immortal).

e. Bounded engrams can be extracted from unbounded engrams, by the exegesis of an apposition, a form of internal hypothesis- testing.

f. Unbounded engrams have a "de re" emotional quality, of which the bounded one have been purged.

I claim a metaphor constitutes an apposition in the sense I have defined it earlier. It is not a proposition. (Does it make sense to "deny" that "Night is a blanket"?){Originally, I relied heavily on the "mismatch" or incongruity view of metaphor, according to which the literal construal of a metaphor should be false or anomalous. Although I still feel that this holds for most metaphors, counterexamples such as "No man is an island"-- arising from a seminar on metaphor at Princeton University in 1980-81, attended by Andrew Ortony, George Miller and others (see Ortony, 1976b)--have persuaded me that the literal construal may also merely be trivial or irrelevant. In any event, there must be some cue, erent or contextual, that the literal construal is not the appropriate one to consider.

The Princeton metaphor seminar also had the unintentional effect (certainly not endorsed by the other participants) of radicalizing my view of metaphor to the extent of making me provisionally conjecture than any literal utterance can be construed as a metaphor--that any proposition can be treated as an apposition--although not necessarily a good one. By way of taking up my challenge to propose the most doggedly literal of utterances for me to try to turn into a trope, the seminar (or rather, A. Ortony) proposed 3 27=3.

Although grumbling that I could have discounted the example as part of a formal proprietary vocabulary--in English but not of it--I accepted the challenge, even eschewing pun-like tricks-- appositionally quite cricket--such as in the (literal) construal: "The cube (-shaped) root of (tree number) twenty-seven is three (years old)." Here are my two candidates, the first admittedly involving a few extra appositions, but the second (drawing on numerology), entirely self-contained:


I love thee
As sev'n and twenty's cube root's three.
If I loved thee more,
Twelve squared would overtake one-forty-four.

That same ubiquitous Platonic force.
That sets prime numbers' unrelenting course
When its more consequential work is done
Again of two of us will form a one.


One short of perfection
Mortal and mean
Yet within twenty-seven
Nobler roots coil unseen

Another issue that loomed large in the Princeton seminar was that of the difference between literal and "metaphoric" similarity, especially the asymmetry of the latter (Ortony, 1979a). In brief, the difference between the two kinds of similarity in the appositional/propositional model is that literal similarity is based on shared invariant properties and category co-membership, which is in turn governed by the categorical distinctions we have made: Co-categorized things appear more alike, and things separated by category boundaries seem more different. Appositional or "predistinctive" similarity, on the other hand, is governed by any of the structural features of the objects (or engrams) being apposed, irrespective of category boundaries: congruities of form, shared associations, or any other commonality that is perceived upon apposing them. Such similarities are predistinctive, in the sense that they have the potential to subserve categorical distinctions (given an appropriate context of alternatives--see main text concerning "exegesis"), but they are not yet based on having made those distinctions.

Finally, in my view the "asymmetry" of metaphoric similarity derives form the asymmetry of the (explicit or implied) underlying subset/set relations expressed by propositions. "A is B"--which is, not coincidentally, the canonical form for a metaphor, and only secondarily yields "A is a kind of B" and "A is like B"--is equivalent to "A is a member of B" or "A is a subset of B," which is an asymmetrical relation. It may be that some stage of the appositional process is symmetric, but the process of exegesis is constrained by the categorical, hierarchical structure of our bounded representational system, so eventually the membership/containment relation must prevail. (And even in literal comparisons of objects at the same hierarchical level there is the useful--and asymmetric-- convention of expressing the unfamiliar in terms of the familiar: "a tangello is like an orange" rather than "an orange is like a tangello" was the example must debated in the Princeton seminar.)} The apposition is based upon structural congruities between the unbounded engrams evoked by the words. These unbounded engrams may be chiefly sensory (as in a above) or they may be more abstract (as in c). The apposition may be at several levels at once, e.g. in that the names used may themselves have iconic properties (b). The apposition may have "relevant" cognitive consequences (d) that may even result in new bounded categories (e), but their "relevance" may also be a purely emotional one (f). Moreover, the structural congruities that emerge from appositions may have an intrinsic emotional value of their own, a criterion of "relevance" more likely to be appreciated by the unbounded system than the bounded one.


It remains only to add that, in the real world, the two sides of our real brain appear to function in certain specialized ways that bifurcate along lines suggestive of those I have been discussing here (Harnad, 1973).

If certain parts of the left cerebral hemisphere are injured, various aphasias, or language disorders result. Among these may be: the loss of the capacity to name objects (Benson, 1979), inability to generate or understand sentences (H caen, 1967), and deficits in analytic reasoning and the formation of abstract concepts (Goldstein, 1948; Jackson, 1958). The role of the left hemisphere in language-related behavior is also confirmed in people without brain injury by monitoring the electrical activity over various regions of the scalp during the performance of verbal tasks (Galin & Ornstein, 1972).

The functions of the right hemisphere are not that well defined. Its injury disrupts "nonverbal IQ," which, if examined minutely, consists of sensory-perceptual performance, the perception of spatial relations, the perception and production of musical sounds, and the recognition of faces (H caen, 1962; Wertheim, 1969; see review by Bradshaw & Nettleton, 1981). There is also evidence that the right hemisphere, after an operation that splits the brian, has been shown to be initially unable to speak, and capable only of rudimentary understanding of isolated nouns (Sperry & Gazzaniga, 1967) (although there is evidence for considerable recovery years later, Zaidel, 1978). Many of these results have also been confirmed in the normal, uninjured brain (Harnad, Doty, Goldstein, Jaynes & Krauthamer, 1977).

The neurologist Head (1963) has noted that "When an aphasic [left-hemisphere injured] cannot employ more abstract terms, he often uses descriptive phrases, similies and metaphorical expressions in an appropriate manner." And, in an uncannily apt extended metaphor of his own, an appositional allegory,{Was the present chapter itself anything more than an "appositional allegory," with no literal connection to the real brain and real cognitive processing? In my introductory chapter for this volume I conceded that the present chapter was not yet "neoconstructive." And I have certainly given evidence of having little sympathy for hemisphere "mythology" (Steklis & Harnad, 1976b), even going to the length of repudiating an instance of my own earlier intemperate zeal (Harnad, 1972). I fondly regard this chapter as an exegesis of that earlier work, but whether the categories and invariants it has extracted (bounded and unbounded engrams, proposition and apposition, context, exegesis) are apt or relevant enough to warrant revising and updating his category structure, the reader must be the one to judge.} Bruner (1962, p. 2-5) has written:

The right is order and lawfulness, le droit...eaching for knowledge with the right hand is science. Yet to say only that much of science is to overlook one of its excitements, for the great hypotheses of science are gifts carried in the left hand...it has been proposed that art students can seduce their proper hand to more expressiveness by drawing first with the left...And should we say that reaching for knowledge with the left hand is art? Again it is not enough, for as surely as the recital of a daydream differs from the well- wrought tale, there is a barrier between undisciplined fantasy and art. To climb the barrier requires a right hand adept at technique and artifice....One thing has become increasingly clear in pursuing the nature of knowing. It is that the conventional apparatus of the psychologist--both his instruments of investigation and the conceptual tools he uses in the interpretation of his data--leaves one approach unexplored. It is an approach whose medium of exchange seems to be the metaphor paid out by the left hand. It is a way that grows happy hunches and `lucky' guesses, that is stirred into connective activity by the poet and the necromancer looking sidewise rather than directly. Their hunches and intuitions generate a grammar of their own--searching out connections, suggesting similarities, weaving ideas loosely in a trial web...f he is lucky or if he has subtle psychological intuition he will from time to time come up with hunches, combinatorial products of his metaphoric activity. If he is not fearful of these products of his own subjectivity, he will go so far as to tame the metaphors that have produced the hunches, tame them in the same sense of shifting them from the left hand to the right hand by rendering them into notions that can be tested.



1. Action and thinking are a function of the brain.

2. A significant portion of action and thinking are governed by learning; i.e., they are derived from experience by induction.

3. The brain does not have an infinite rote memory.

4. The experiential world is of at lest one order of complexity greater than memory; i.e. there is always more "out there" than it is possible to remember.

[*5. Immediate experience seems to be continuous and holistic.]


ABSOLUTE DISCRIMINATION: identification of a class of inputs by the reliable assignment of a unique arbitrary motor response, i.e. a name.

ANALOGUE MEMORY: an engram that is isomorphic with the experience of which it is a record: a one-to-one correspondence that transforms but does not reduce input information.

APPOSITION: the collation or juxtaposition of two unbounded engrams (as contrasted with the prediction of properties of subjects in the case of the proposition); propositions are bivalent, appositions are not.

BIVALENCE: two-valued logic, consisting of the truth values "true" and "false," which stand in a mutually exclusive and exhaustive relation to one another (either-or, not both, and not neither).

BOUNDED ENGRAMS: engrams underlying the categories formed during absolute discrimination or induction; the information encoded in bounded engrams consists of that minimal set of invariants which must be retained so as to perform reliable absolute discrimination.

CATEGORY: an absolutely discriminated class of inputs for which a bounded engram has been formed.

CATEGORY-BOUNDARY: the limits of the extension of a category; these may be concrete, as in the case of a quantized sensory continuum (the boundary between red and orange or /ba/ and /da/) or abstract, as in the case of conceptual.

CONTEXT: a set of alternatives that is associated with every absolute discrimination; the simplest context is a dichotomy, consisting of the class of positive and negative instances.

ENGRAM: the structural trace of an experience as retained in the brain; the physical substrate of memory.

To EXEGESIZE an apposition is to find or impose a categorical context that makes a corresponding (nontrivial) proposition literally true. The holistic comparison is replaced by a categorical approximation, with a categorical invariant substituted for the structural congruity.

ICONIC RESPONSES: responses that are isomorphic to--analogues of--stimulus input (as contrasted with arbitrary responses, having no systematic relation to the structure of the input).

INDUCTION: learning to perform absolute discrimination from experience with instances.

An INDUCTOR is said to have performed induction if, having been confronted with experiential inputs, some of which (positive instance) are invariant with respect to the presence of some property (or properties) and some of which (negative instances) are invariant with respect to the absence of this property (or properties), this inductor can, after a sufficiently large sample of inputs, reliably produce, exclusively in the presence of the positive instances, a unique, arbitrary output. This output must be unique in the sense that it is associated with the positive instances, and the positive instances alone; and it must be arbitrary inn the sense that (a) it was demonstrably not already associated with the positive instances prior to the induction ("non-apriority") and (b) it is not structurally isomorphic with the positive instances ("non-iconicity").

INVARIANT PROPERTY: any property that is shared by a class of inputs, as distinguished from another class that lacks it.

PROPOSITION: a claim that something is the case; always formulable as a statement about category relations; e.g. "Socrates is a man" claims that the member of the singular category "Socrates" is contained in the category "man."

REDUCTION: the discarding or suppression of irrelevant information in the formation of the engram underlying absolute discrimination; what is discarded or suppressed is always determined by the context of alternatives; only invariants are retained.

RELATIVE DISCRIMINATION: (or similarity judgment): the comparison of two inputs (presented simultaneously or successively) yielding a response that indicates whether the inputs are identical or different, and if different, the magnitude and direction of the difference (relative to other pairs of inputs).

STRUCTURAL CONGRUITY: the unbounded counterpart of invariant property; the structural properties shared by two unbounded engrams; a kind of similarity.

UNBOUNDED ENGRAMS: engrams that are analogues of experience; because they are not reduced, they cannot be assigned names, and cannot subserve absolute discrimination.


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