{} Metaphor and {theme}

In my Introduction to the Glossary of Literary Linkage Terms, I write, 'My approach is in part systematic and rigorous, sometimes at a high level of abstraction, but I see no contradiction between system and rigour and abstraction on the one hand and on the other, passion, compassion, activism, humour, an intense concern for the health of language and the vitality of culture, a whole range of other concerns. A systematic study can reveal gaps, new possibilities very clearly. The meticulous work of cartographers helped to show explorers exactly which regions were still unexplored, to suggest new areas for risk and adventure.'

In the first section after the Introduction, I write,

'The line

Our love calls tiny as a tuning fork

from Seamus Heaney's 'Summer Home' seems to me to be faulty, artistically poor, and the systematic and rigorous approach I use can help to explain exactly why.' The instinctive  feeling that something isn't quite right about the line, or the instinctive feeling that the line is hopeless, doesn't explain 'exactly why.'

My approach to metaphor makes use of my own {theme} theory. Not all the {themes} in the list below are used in the discussion but all of them can be used. The most important single {theme} is {linkage}, < >, which, like other {themes}, plays a fundamental role in the mind's making sense of experience - and concepts not originating in experience. Metaphor is concerned with similarity amidst dissimilarity, with {linkage} but also with {contrast}, ( ). For more detailed information about the {themes} and my approach, a study of {theme} theory: an introduction would be very useful (I have to say, essential) even though the page uses mainly philosophical and logical examples to illustrate the theory. From my introduction to {theme} theory:

'{theme} theory is completely general and philosophy is only one application-sphere. These illustrative examples are very diverse in subject matter and  in degree of abstraction: for example ethical argument, concrete problems in applied ethics, Nazi atrocities, Stalin, the death penalty, mathematical and philosophical relations, the completion of a  proof, scientific correlation.  There are also marked differences in tone: the tone appropriate to abstract and systematic subject matter but also forthright criticism, for example of Nietzsche, the juxtaposition sometimes of the abstract and  the impassioned.'

'{theme} theory is based upon the conscious, and justifiable, ignoring in many cases of sphere-boundaries, such as the boundaries separating the material sphere, the conceptual sphere, the spheres of the different senses. (Metaphor and simile too ignore sphere-boundaries, of course.  A mathematician may attack a problem in the mind just as a soldier may attack an all-too-concrete machine-gun post.) A scientific model may be material, the model constructed from materials of different kinds, such as wood and plastic, or the model may be purely conceptual, without material expression. Scientific modelling is an activity which can be practised in material or conceptual ways. Linkages may be material, such as a connecting rod in a mechanical system linking mechanical components or non-material, such as the ties of shared history linking, in some cases, nations.

Similarly, the {theme} {restriction} has material, social and conceptual application-spheres amongst others. The kind of {restriction} which can be called 'filtering' has strikingly different application-spheres. Examples: filtering a solid from a liquid, obviously an application in the material sphere, filtering to give the works accepted for publication or entry to an educational institution from the works or the people not accepted. In Max Black's conception of metaphor, the subsidiary subject acts as a filter on the principal subject. My approach gives to the filtering effect of metaphor a full context.

The {theme} {distance} has amongst its application-spheres  distance measured along a line in  a printed text,  distance measured  by surveying in a farmer's field,  but also aesthetic distances of various kinds, including harmonic modulation (remote keys in a musical work), modulation in poetry and the use of perspective in painting.  The editor Andrew Ortony's  introduction to the work of Srernberg, Tourangeau and Nigro (in Chapter 1 of 'Metaphor and thought') obviously lends itself to an interpretation in terms of {distance} as well as other {themes}:

'The basic construct that they employ is that of "semantic feature spaces." The idea is that a good metaphor utilizes regions it two remote conceptual spaces [conceptual spaces at great {distance} that occupy similar postions within each space. An important issue that they address is that of the "goodness" or "success" of a metaphor [success is low {restrition} on an evaluative application-sphere] which, they claim, depends on maximizing the distance between the different domains (feature spaces) involved, while minimizing the difference between the postions occupied by each term within each domain. This conception of the goodness or "aesthetic pleasingness" of a metaphor they contrast [an instance of the {theme} contrast] with a notion of the "comprehensibility" of a metaphor, which is enhanced by minimizing the distance between the domains themselves.' I indicate here only some of the {thematic} activity which takes place.

The terms 'tenor' and 'vehicle' which are used in many studies of metaphor are subject to far too much {restriction}. They aren't generally applicable, they are 'ad hoc.' Good theories attempt to generalize, but not to over-generalize. Separate explanations for events on the earth and events on the moon, for 'lunary' and 'sub-lunary' phenomena, were inadequate. Comprehensive theories and laws were needed which unified them. Newton's Law of Universal Gravitation accounted for the linkage by attraction of all the bodies in the universe, not just the bodies on the earth and moon.

List of {themes}:

{adjustment} Â
{contrast} ( )
{distance} D
{linkage} < >
{ordering} Ô
{resolution} ®
{restriction} ==
{reversal} «
{separation} //
{substitution} S

In the list, the name of each {theme} is followed by the symbol for the {theme}. Each {theme} is highlighted. Clicking on the {theme} gives access to a page which gives instances of the {theme}. These instances show something of the range of {theme} theory, which addresses the most diverse areas of human experience and knowledge.



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Seamus Heaney: Summer Home (Wintering Out)

John Donne: a Valediction forbidding mourning

Yeats: the Circus Animals' Desertion

Georg Trakl: Grodek

Paul Hurt: 'Sun firing ...'

Paul Hurt: 'Lincolnshire, asleep ...'
Mallarmé: 'Le vierge, le vivace et le bel aujourd' hui


I explain the terms I use and my distinctive approach to metaphor in the course of an examination of some uses of metaphor. For a full understanding, the entries should ideally be read in order.

Seamus Heaney: Summer Home (Wintering Out)

This is the closing line from 'Summer Home':

Our love calls tiny as a tuning fork.

In the first part of the discussion, I refer to this diagram:

My approach to metaphor and simile is very different from the approach of Max Black in his influential study of metaphor, 'Models and Metaphor' (1962, Cornell University Press) but I think his study is a very useful one and I make use of two of his terms: principal subject and subsidiary subject. In 'More about Metaphor' (published in 'Metaphor and Thought,' edited by Andrew Ortony) he replaces these two terms with 'primary subject' and 'secondary subject' and explains that 'The duality of reference is marked by the contrast between the metaphorical statement's focus (the word or words used not-literally) and the surrounding literal frame. In 'Juliet is the sun,' 'Juliet' is the principal (or primary) subject and 'sun' is the subsidiary (or secondary) subject and Max Black refers to the interaction between them.

However, 'principal' and 'subsidiary' (as I use the terms) refer only to the {ordering} of the poem, in which the principal subject has {prior-ordering}, the subsidiary subject has {post-ordering}.

In the line 'Our love calls tiny as a tuning fork' there's interaction between 'love,' the principal subject, and 'tuning fork,' the subsidiary subject. I recognize the importance of interaction but I use to begin with a term at a much higher level of generality, linkage, which I notate symbolically as < >. In the diagram above, the principal and subsidiary subjects are shown as two coloured blocks. The linkage between them is shown as the broad blue line, the linkage line L1. For the time being, you can ignore the factors F1 - F4 in both Subjects and the thin blue line, another linkage line, L2, which links F2 in the Principal Subject and F2 in the subsidiary subject.

In the line 'Our love calls tiny as a tuning fork,' it's not love in general which is linked with the tuning fork in its entirety, but the magnitude of love and of the tuning fork: in both cases not substantial, tiny. This magnitude is a factor. Factorization is the process which identifies the relevant factors in both subjects, but I make use of the terms 'factor' and 'factorization' very widely, in accordance with the principle of greater generality.

A survey lists the factors, enclosing the factors in double brackets, (( ... )), but again, I use surveys for many other purposes. A survey of the factors relevant in general to 'love' and a survey of the factors relevant in general to 'tuning fork' are adequate if relevant factors aren't excluded. If a survey is claimed to be complete (containing all the relevant factors) then the completion indicator can be appended. The completion indicator is derived from the {theme} {completion}, which is notated symbolically . Most surveys are necessarily incomplete. A simple example of a survey which is complete is the survey of the states of a digital device, either 'on' or 'off:'
(( on, off )). If a survey is incomplete, then the negation of completion is shown as . The symbol for negation here is identical with one of the symbols used for negation in symbolic logic.

A survey of the factors for 'tuning fork' could include
F1, colour
F2, size or magnitude
F3, shape
F4, cost

which could be listed as the incomplete survey (( colour, magnitude, shape, cost )). F1 - F4 are given in the diagram above for this Subsidiary Subject but only F2 is identified in the diagram.

A survey of the factors for 'love' could include
F1, kind, such as erotic or non-erotic
F2, intensity or 'size'
F3, longevity, short-lasting or long-lasting.
F4, problematic or unproblematic status

which could be listed as the incomplete survey (( kind, intensity, longevity, status )). For each of these factors, amplification could be provided later. Very often, in the course of a discussion, matters are necessarily left unamplified at the time. Often, matters must be simply mentioned or described very briefly. I use '+ ... ' to indicate the possibility of amplification.

F1 - F4 are given in the diagram above for the Principal Subject but only F2 is identified. 'Magnitude' is admittedly a very inadequate way of expressing any factor of love, but it's an advantage to use the same term for love and tuning fork, both described in the line as 'tiny.' In this preliminary approach, which is necessarily concerned more with exposition than with nuances and complexity, or the wonders and frustrations of love, then the use of the inadequate term is allowable.

In the line from Seamus Heaney, there's obvious {restriction}. Of the Factors listed for the Principal and Subsidiary Subject, F2 is isolated. There's linkage, shown by the thin blue line, only between F2 in the two Subjects. In my notation, :- is used for 'is applied to' and the symbol == is used as the symbol for the {theme} {restriction}. So, == :- (F1, F2, F3, F4). Here, then, (F1, F2, F3, F4) is the application-sphere of {restriction} War  moderated by the Geneva conventions is a very different application-sphere of the same {theme}.

There's a linkage < > between the two subjects, which can be termed L1, and there's also a linkage between the two Factors in the two subjects, L2, but there's also a linkage between L2 and mathematical mapping, which can be termed L3.

The diagram above can be used to show mathematical mapping, with appropriate changes. The two coloured blocks now show two non-empty sets, P and S. F1 - F4 in P, or (P) F1 - (P) F4 and F1 - F4 in S, or (S) F1 - (S) F4 are now /elements/ of sets P and S. I use / ... / to show that here, I'm using the term 'elements' in an established sense, in this case the established mathematical study of mappings. (In the same way, if I use 'perturbation' in the established sense in which it's used in Physics, rather than 'perturbation' in the sense in which I use it in my study of metre, I write /perturbation/.) The mathematical mapping between F2 in the two subjects can be termed L4.

A mathematical mapping from P (the /domain/) to S (the /codomain/) is a rule which links each element of P with a single element of S. In a diagram which shows a mathematical mapping, arrows, not lines, link elements in the two sets. These arrows can be described, in my terminology, as lines which show {direction}. {direction}, like other {themes}, is at a high level of generality. It has application to such specific instances as directionality in mathematical mapping, the directionality of vectors as opposed to scalars, and directionality in the linkage between metaphorical Principal and Subsidiary Subject.

It's often convenient to show the linkages between Principal and Subsidiary Subject without the necessity of giving a diagram, which may not always be practicable. The linkage between principal subject and subsidiary subject can be shown by means of a linkage schema, which takes the form

[ ] < > [ ]

where [ ] are content brackets and < > are linkage brackets. So,

[Principal subject] < L1 > [Subsidiary subject]

At a lower level of generality, to show the linkage between the specific factor of magnitude in the two subjects:

[(P) F2] < L2 > [(S) F2].

If X isn't linked with Y, then I reverse the linkage brackets:

[ X ] > < [ Y ].

Specific linkages, such as the linkages involved in metaphor, mathematical mappings, the linkages of gravitational attraction, eg the gravitational attraction between earth and moon, the linkages of mathematical mapping, are obtained by thematic action, the action of {restriction}. {restriction} is applied to the linkage. Linkage is another application-sphere of {restriction}. Symbolically == :- < >.

Concepts, technical terms, techniques and notation should be useful not just for description but for evaluation, for example to assess relative poetic success and failure. The line

Our love calls tiny as a tuning fork

from Seamus Heaney's 'Summer Home' seems to me to be faulty, artistically poor, and the systematic and rigorous approach I use can help to explain exactly why. The line makes the claim that it's the tuning fork which is tiny, and which can be linked with the tiny 'magnitude' of love. But it's surely the ring of the tuning fork, its tiny sound, which is intended, not the small size of the tuning fork. In fact, Seamus Heaney is writing about a linkage between the Principal Subject and an unintended Subsidiary Subject.   What he's actually claiming, despite the wording of the line, is a linkage between the Principal Subject and a different Subsidiary Subject (which can be termed S2), the sound produced by the tuning fork. It's S1 which is shown in the diagram above. The factorization of S2 is very different, but includes size, in this case the small volume of sound produced by the tuning fork.

Unfortunately, when comprehensive factorization is carried out for S2, another factor is insistent, the fact that the tiny sound produced by a tuning fork dies away very quickly. The poet concentrates on one factor, expressed by 'tiny,' but the short-lived sound is insistent, at least for readers familiar with the sound of tuning forks. In the same way, a factor in an image, such as size, may be excluded or denied by the poet, who may make it clear that another factor, such as colour, is what counts in a metaphor or simile, but the associations of the excluded factor may be impossible to overlook.

Metaphor is sometimes described as finding similarity amongst dissimilarity. Linkage expresses similarity. Contrast expresses dissimilarity. I use contrast schemata as complements of linkage schemata, using italic rounded brackets to indicate contrast:

[ ] ( ) [ ].

If X isn't contrasted with Y, then I reverse the contrast brackets:

[ X ] )( [ Y ].

Metaphor is usually a source of marked contrast in the line, but often not the only source of marked contrast in the line.

In the line, 'Our love calls tiny as a tuning fork' everything here is part of the poem-sphere but 'tuning fork' is strongly contrasted. The line, and the rest of the poem, aren't concerned with tuning forks at all, except for this reference.

Contrast brackets, ( ... ) can be used not just as part of linkage schemata but to indicate contrasting material in the poem-sphere, as here:

Our love calls tiny as a (tuning fork.)

But [love] < 'tiny' > [tuning fork],

since both love and tuning fork are referred to as 'tiny.'

[tiny] < > [tuning fork] not just because the tuning fork is described as 'tiny' but also because of linkage by sound - both 'tiny' and 'tuning' begin with 't.'

To distinguish these, we can use two different sets of linkage brackets, inserting the information needed to distinguish between them into the brackets:

[tiny] < sound of initial 't' in 'tiny,' 'tuning fork' > [tuning fork].

[tiny] < description of magnitude > [tuning fork].

[Our love calls] ( ) [tiny] because 'calls' suggests something quite imposing or even powerful, whereas 'tiny' suggests something not at all imposing, weak.

It's obvious that the tuning fork, which inserts contrast into the poem-sphere, is only part of the complex linkages and contrasts of this line. The established notion that metaphor and simile are not paraphrasable receives support here. The actual wording of the line can't be disregarded.

I don't stress the transfer involved in metaphors and similes. Aristotle did stress transfer in his treatment in the 'Poetics.' He used the word , 'metaphora.' (Bekker Reference 57b.) Instead, I stress the {restriction} imposed by a metaphor or simile and the increase in semantic force which an effective metaphor or simile provides.

The words and concepts used in a poem have a range, which includes a range of factors. By using a metaphor or simile, the poet imposes {restriction} on the range, {restriction} on the factors. So, a poet could describe a thing as 'grey,' which has a wide range. By using a metaphor involving the feathers of a dove, the poet makes the grey particular, with a {restriction} on range. If the metaphor is used effectively, then the poet also achieves an increase in semantif force. The lesser degree of generality, the greater particularity of love described not just as 'tiny' but 'tiny as a tuning fork' isn't strongly marked, but there is an increase in semantic force.

I provide an entry for my concept of semantic force on the page Glossary: poetry:

Words (and concepts) with semantic force are used, heard, or read with an accompanying experience of intensity or forcefulness, for example, in a visceral or sensuous, an elevated or deeply anxious way. Although a person knows the meaning of many words, or can use many words meaningfully, words with semantic impact are particularly 'meaningful.' The primary linkage of 'semantic' here isn't with the very interesting academic study of semantics.

A person's active vocabulary and passive vocabulary are distinguished in linguistics. A person's active vocabulary (words which the person actually uses) is smaller than their passive vocabulary (words whose meaning is known but which the person does not use.) Words with semantic force are few in comparison with the active vocabulary and are subject to change in a more striking way. Words which once had semantic force for the person may no longer possess it. Words may acquire semantic force quite suddenly. Words may be used with semantic force on one occasion and not on another, owing, perhaps, to distraction or preoccupation. Words may be read or heard as well as used with semantic force.

These words are of the most varied kind. Examples are 'danger,' 'snow,' 'poignant,' 'classification' and 'mathematical set.' Where a word has rich connotations - 'danger,' for example - then using it with semantic force involves using the word with its more intense connotations. So attention is focussed on more immediate, real dangers, such as the experience of being in an active war zone, rather than more distant, if still real dangers, such as 'the dangers of smoking.' It may be direct and intense personal experience which gives a word semantic force, such as the experience of being shelled or shot at, but this is not a necessity.

Intellectual excitement may give to words, ideas and such entities as equations, real semantic force. The mathematician who devised the concept of the mathematical set wrote that when he thought of the word 'set' he experienced a chasm. The great botanist Linnaeus, who devised the binomial system of nomenclature, very likely used the word 'classification' in the same way.

In a good poem, words are used with greater semantic force. In a poor poem, they are used with no semantic force, in a routine or inert way. Deviance or deviation (established terms in stylistics, associated with the Prague school of linguistics) is particularly associated with poetic language. However, deviance can characterize mediocre poetry. Semantic force is a better 'indicator' of good poetry than deviance. This is not to imply that the more vivid the language, the greater the poem. There is a vividness in Seamus Heaney's poetic descriptions of growing up on a farm in Ulster, and a vividness in some of Robert Frost's descriptions of rural New England, which cannot be matched in the work of, for example, Rilke.

I don't argue here for the greater stature of Rilke, but I simply state my conviction that a great poet conveys wider semantic force than a lesser poet, or conveys aspects of semantic force which, it can be argued, are more fundamental. It is for this last reason that I myself regard Kafka as so important amongst twentieth century imaginative writers of prose, despite his restricted range. He has given massive semantic force to such an unexpected word as 'unzugaenglichkeit,' 'inaccessibility,' 'unapproachability,' which appears in the section 'Before the Law' in 'The Trial' and which underlies the whole of his novel 'The Castle.' Another, more familiar example in Kafka is 'verhaftet,' 'arrested.' The writer, however, who used words with greater semantic force than any other is, of course, Shakespeare.

The examples I've given vary very much in intensity. There's no necessary positive linkage between intensity and importance or artistic success. In fact, the idea of semantic force has to be extended, to include 'semantic significance.' A linkage with taste: many people crave more and more intense flavours, more and more highly spiced food, and neglect subtleties of flavour. I'm impressed by a passage from John Ruskin, who in Lecture 3 of 'The Queen of the Air' compares a Persian manuscript and a Turner drawing, the Persian manuscript intense in colour, the Turner drawing drab by comparison: 'One of the ruby spots of the eastern manuscript would give colour enough for all the red that is in Turner's entire drawing.' But it's the Turner drawing which he claims has more 'semantic significance.'

The principal subject and the subsidiary subject are subject to {ordering}. The principal subject has {prior-ordering} and the subsidiary subject has {post-ordering}. Although both love and the tuning fork are part of the poem-sphere, it's love which is a principal subject of the poem. The tuning fork isn't. The tuning fork belongs not only to the poem-sphere but to another sphere, the reference-sphere. The tuning fork is a single subsidiary subject and shown as such in the diagram above. As a poem proceeds, there's more likely to be continuity in the main subject of a poem, such as love, than in the reference-sphere, although this is not to say that it will necessarily be the only subject. Although there may well be replacement of primary subject, the replacement of subsidiary subject by another in the reference-sphere will be more frequent, or there may be one or two subsidiary subjects, to which reference is made only for a short time in the flux of the poem-sphere. The subsidiary subjects are referents in the reference-sphere.

John Donne: A Valediction forbidding mourning

This is one of the more widely quoted poems in studies of metaphor. The poem-sphere is very varied, but love and the two souls of the lovers constitute, for the most part, the principal subject. The reference sphere contains subsidiary subjects as varied as 'Moving of th' earth,' a reference to earthquakes or perhaps the Copernican heliocentric theory, 'trepidation of the spheres,' perturbations in the motions of the celestial spheres (compare my use of perturbation in the study of metre) and the celebrated subsidiary subject of the compasses.

The compasses are not simply mentioned. Unlike the tuning fork in 'Summer Home,' their use in the poem-sphere is extensive, amounting to :- Ô, a {re-ordering}. This subsidiary subject almost becomes, for a time, the primary subject, or at least one part of a conjugate primary subject: « :- Ô.

This {re-ordering} can be viewed as artistically unsuccessful. Dr Johnson said of the image of the compasses that 'it may be doubted whether absurdity or ingenuity has the better claim.' There does seem the faintest touch of absurdity in the use to which the image is put, and the faintest touch of absurdity seems inherent in the image. The ingenuity is all too evident.

I account for these impressions in terms of factorization. There's no need for an exhaustive ((survey)) of the factors. The overall shape and metallic properties of the compasses are enough.

The overall shape of the compasses is obtrusive to some extent but is also required, since the two arms of the compass represent the two souls of the lovers. This is a factor (it can be termed F1) which should obviously not be 'filtered out' by the poet. But the metallic nature of the compasses (it can be termed F2) is a factor which is unwanted, not contributing anything important to the poem and not adding usefully to the complexity of the poem. It isn't filtered out completely in the poem.

Successful filtering: == :- (F1, F2) F1.

Here, is read as 'gives,' or more accurately as 'directs to.' The {theme} symbolized by has obvious importance in the study of metaphor. For example, it can give an interpretation of interaction, as in Max Black's view of the interaction between primary and secondary subject. This interaction can be regarded as having a {linkage} with the interaction of the Central Processing Unit (CPU) of a computer and other components. The CPU 'requests' information from other components and 'receives' it. The {direction} of flow of information can be interpreted as {direction} to and {direction} from. (Compare the {direction} of forces involved in a book resting on a table, according to Newton's Third Law of Motion: the force of the book on the table has a {direction} from book to table, the 'action,' and there's an equal force with {direction} from table to book, the 'reaction.') Action in metaphor is unidirectional, reaction in metaphor is unidirectional and both of them view metaphorical processes in isolation, but 'interaction' is bi-directional.

Although it's interesting to view metaphor in terms of information transfer and the {direction} of information transfer, I don't think this is one of the most fruitful approaches. Far better to view the {linkage} between the poem sphere and the reference sphere in terms of poyphony. From my discussion of Seamus Heaney's The Grauballe Man: 'Seamus Heaney in 'The Grauballe Man' and some of his other poems is writing 'chordally,' to produce poetry of great richness and resonance. Lines of poetry, like the music for unaccompanied violin in Bach's Partitas and Sonatas, aren't inherently chordal or polyphonic. Bach gave chords to the violin and the strong impression of polyphony, so that often the one line has the richness of other implied lines.' Here, I allude to the fact that the violin, unlike the piano, is restricted to one line of music, except for temporary double-stopping and chords.

See also my discussion on the page Concrete poetry:

Poetry's {restriction} to monophony is potentially a very great disadvantage. The disadvantage is overcome by such devices as ambiguity, which in effect gives two or even more lines - lines of meaning, that is - and the resonance of poetic language, which gives 'poetic harmony' ('poetic harmony' understood not in a hackneyed, sentimental way.)

Concrete poetry opens up remarkable new possibilities - poetic complexity given by the interaction of word and image. If the words, whether part of a line of poetry or not, are regarded as having a linkage with a musical melody, the images can be regarded as having a linkage with an accompaniment. Or the two elements can be regarded as having a linkage with polyphony. In essence, they contribute to layering of the poem, which gives opportunities for satisfying complexity.

The poem sphere isn't inherently polyphonic, but the reference sphere gives the strong impression of polyphony, so that the one line has the richness and resonance of other implied lines.

But it would be a mistake to view the primary subject as always more prominent, the secondary subject as always less prominent. The primary subject has {prior-ordering} in that the poem is obviously 'about' it rather than the secondary subject. 'A Valediction forbidding mourning' is about 'two soules' rather than compasses. This {ordering} is confirmed by the fact that the primary subject of the 'two soules' continues in the poem-sphere but the secondary subject of the compasses has {restriction} in time. Often, in a poem, one primary subject is illustrated by a number of different secondary subjects.

All the same, whilst the secondary subject lasts in the poem sphere, it may have {prior-ordering} in semantic force and significance, so that it's the focus of attention and the primary subject seems temporarily subdued or even 'implied.' I refer to whichever subject has {prior-ordering} in semantic force or significance as dominant and the other subject as recessive. There's a further possibility, that the two subjects are co-dominant. [these terms] < > [terms in genetics] of course.

In this verse paragraph from 'A Valediction forbidding mourning,' the 'two soules,' the primary subject, and the compasses, the secondary subject seem to me more or less co-dominant: Referring to the 'two soules:'

If they be two, they are two so
As stiffe twin compasses are two,
Thy soule the fixt foot, makes no show
To move, but doth, if the' other doe.

In the next verse paragraph, the compasses seem dominant and the 'two soules' recessive. 'leanes' refers more obviously to compasses than souls, as does 'it.'

And though it in the centre sit,
Yet when the other far doth rome,
It leanes, and hearkens after it,
And growes erect, as that comes home.

In the verse paragraph after this, even though 'circle' refers more obviously to compasses, the possessives 'thou,' 'mee,' 'thy,' 'my,' and 'I' give dominance to the two souls:

Such wilt thou be to mee, who must
Like th' other foot, obliquely runne,
Thy firmnes makes my circle just,
And makes me end, where I begunne.

Yeats: The Circus Animals' Desertion

This is the complete section (Section III) which contains this line,

In the foul rag and bone shop of the heart.

Those masterful images because complete
Grew in pure mind but out of what began?
A mound of refuse or the sweepings of a street,
Old kettles, old bottles, and a broken can,
Old iron, old bones, old rags, that raving slut
Who keeps the till. Now that my ladder's gone
I must lie down where all the ladders start
In the foul rag and bone shop of the heart.

The subjects, factors and linkages in the last line of the poem can be represented by this diagram:

Here, it isn't denied that the heart has more than one factor but the factor 'foulness' completely dominates: has {prior-ordering}. It isn't denied that the rag and bone shop has more than one factor but again the factor 'foulness' completely dominates: has {prior-ordering}. The shop is explicitly described as 'foul.'

The factors of the heart other than foulness, F2 here, are suppressed completely, but not so the factors of the rag and bone shop other than foulness. The other factors are imperfectly filtered: ® :- (F1 ... Fn of subsidiary subject) (F2).

There are factors such as clutter which are obtrusive, and the general or typical appearance of a rag and bone shop. Clutter doesn't amount to 'foulness' and the general appearance of a rag and bone shop may seem interesting, worth exploring rather than foul. So this line presents the common difficulty of making {restriction} :- (factors) precise enough.

In isolation, the last line has {direction} from 'heart,' the principal subject, to 'foul rag and bone shop,' the secondary subject, in the reference sphere. But it's obvious that there has been {reversal} and that the refuse and detritus, from 'a mound of refuse' to 'foul rag and bone shop' are dominant.

A fruitful way of looking at the linkages of metaphor is by considering {distance}. This {theme} has application-spheres as varied as {distance} on the Cartesian plane, {distance} in four-dimensional geometry, {distance} between keys -{distance} between C major and G major is smaller than  {distance} between C major and E major) and the {distance} which is the subject of my extended discussion, Modulation in the poetry of Jared Carter. Metaphorical {distance} is a further application.

I use datum plane for the 'starting point' for {distance). In surveying, the datum plane is the horizontal plane from which vertical distances - heights and depths - are calculated. A piece of music in C major has C major as its datum plane of tonality. Modulations to G major and remote keys are related to this datum plane. A poem which obviously concerns pleasant, everyday experience has this experience as its datum plane of experience. Any mention or exploration of extreme experience is at remote {distance} from this datum plane. A poem which obviously concerns extreme experience has extreme experience as its datum plane of experience. Any mention or exploration of pleasant, everyday experience is at remote {distance} from this datum plane. In uses of metaphor, the principal subject is the datum plane and the subsidiary subject is at {distance} from it.

The primary subject of the poem-sphere may be concerned with love or another human emotion, but at all times in a matter of fact or even stunted way, and may make use of various metaphors, various subsidiary subjects in the reference sphere, strikingly different from the principal subject and each other, but linked by the fact that all of them are matter of fact or even stunted. In {direction} to each of the subsidiary subjects, {distance} is small.

It's common for poems to extend only a short {distance} into the reference sphere, much less common for poems to extend to remote areas.

Georg Trakl: Grodek

Here, my translation is literal and preserves the {ordering}:- words of the original.

Grodek is the Polish town where Trakl attempted suicide in 1914. He had been serving as a medical lieutenant on the Eastern front but could do nothing for the casualties of battle. He died later from an overdose of drugs. The poem describes the sinister and ominous setting of battle.

The sounding' and 'autumn' of this line have been anticipated in the 'resounding' and 'autumnal' of the opening of the poem:

As Trakl uses 'tönen' in both places, in connection with the loud sound of the deadly weapons and the soft sound of the dark flutes ('tönen' can be used for soft and loud sounds) it seems best to translate by 'resound' and 'sound.' Michael Hamburger and Christopher Middleton (in 'Modern German Poetry') translate the line 'Und leise tönen ...' as 'And softly the dark flutes of autumn sound in the reeds' and 'Und leise tönen ...' as 'At nightfall the autumn woods cry out / With deadly weapons ...' Here, 'cry out' obscures the linkage with the soft sound of the flutes. My reason for preferring 'evening' as a translation of 'Abend' rather than their 'nightfall' is that 'evening' can be regarded as the time of day which corresponds with the {ordering} of autumn in the seasons of the year. See also my comments on my poem 'Spring dawn ...' In the opening of the poem, 'die goldnen Ebenen / Und blauen Seen' the golden plains and the blue lakes,' the gold and blue are still visible. By night, they will have vanished. But this is the end of evening. Night soon falls, 'unfängt die Nacht / Sterbende Krieger,' 'night embraces dying warriors.'

In the line

the principal subject is a composite, that is, it has linked elements. There is a place, the reeds, a time of day, evening, not expressed in this line but carried over from the opening line, and a time of the year, autumn. (German uses 'die Jahreszeiten,' literally 'the year-times,' for 'the seasons.)

The secondary subject is 'the dark flutes.' Flutes belong to the reference sphere. The flute is an instrument not generally regarded as 'dark.' In section 186 of 'Beyond Good and Evil,' Nietzsche writes that pessimism and the flute are incompatible: ' ... Schopenhauer, though a pessimist, really - played the flute. Every day, after dinner: one should read his biography on that. And incidentally: a pessimist, one who denies God and the world but comes to a stop before morality - who affirms morality and plays the flute ... what? is that really - a pessimist?' (Translated by Walter Kaufmann.) Here, Nietzsche gives as evidence that Schopenhauer was no pessimist his affirmation of morality and his playing the flute. The lower register of the flute is darker than its upper register, with a linkage with the 'chalumeau' register of the clarinet, but the bright and brilliant upper register is the more characteristic.

{resolution} ® is carried out to 'split up' 'the one' 'to give' separate (but often linked) components. 'Factorization' is a non-systematic term. The components it produces are the factors. {resolution} is the thematic process. 'It's necessary to carry out a thematic process' is symbolized as '.' So,

® :- (the flute) (lower, darker register higher, more brilliant register).

'Autumn' can also be resolved. Alistair Cooke, 'Letters from America, 1946 - 1951,' 'The Fall of New England,' 'The best of English poets have celebrated the rich, sombre English autumn, but an American fall bears little resemblance to that 'season of mists and mellow fruitfulness'. Many famous Britons have put on on record their astonishment at the youthful, trumpeting quality of the fall, at the hot days and the Mediterranean blue skies encircling a landscape of blinding scarlet and gold.' The autumn of Grodek is far closer to the English autumn than the New England fall, in its darkness and sombreness (the sun is described as 'düster,' 'gloomy, dark, dismal,' referring to thoughts and the sense of foreboding as well as light,) but closer to the New England fall in being not muted, as in the second and third line, 'die goldnen Ebenen / Und blauen Seen,' 'the golden plains and the blue lakes.' So,

® :- (autumn) (English autumn, New England fall, the autumn of Grodek.)

The darkness of the dark flutes has to be understood as a successor to the context which includes the visual 'golden plains' and the 'blue lakes' and the stridency and clamour of the deadly weapons. These are now gone, and the dark flutes belong to the aftermath (compare my poem concerned with another aftermath), counterpoint the earlier slaughter and counterpoint the last lines of the poem, which include 'Die heisse Flamme des Geistes,' 'the hot flame of the spirit.'

In practical, everyday contexts, one thing can have many functions, one-many functionality. In mathematical mapping, one-many mapping is distinguished from one-one mapping. In poetics, one word or phrase can have more than function.

Paul Hurt: 'Sun firing ...

This poem of mine shows [ambiguity] < > [metaphor]. There are clear metaphors and many more ambiguities. The terms already introduced can be applied to ambiguities as well as metaphors: the poem sphere, the reference sphere, principal subject and subsidiary subject, mapping, linkage. Below, the mapping-linkages are shown by blue lines, as before, and each of the mapping-linkages shown is a one-many mapping. ('Many' here is not a large number, of course, but more than one.)

Before the insert in the centre of the poem, the main metaphor is lunar, the battlefield transformed (by, for example, the crashing of tree-trunks) into a world without vegetation. Photographs of such battlefields as Passchendaele show a world like this.

This poem is an example of interline poetry. Contrasting material, shown in a smaller print size in the image which first gives the poem, is inserted into the main body of the text. In the insert, the metaphor is to do with gardening. This is the parable of the gardener,' developed by the atheist philosopher Antony Flew in 'Reason and Responsibility.'

Let us begin with a parable. It is a parable developed from a tale told by John Wisdom in his haunting and revolutionary article "Gods." Once upon a time two explorers came upon a clearing in the jungle. In the clearing were growing many flowers and many weeds. One explorer says, "Some gardener must tend this plot." The other disagrees, "There is no gardener." So they pitch their tents and set a watch. No gardener is ever seen. "But perhaps he is an invisible gardener." So they set up a barbed-wire fence. They electrify it. They patrol with bloodhounds. (For they remember how H. G. Well's The Invisible Man could be both smelt and touched though he could not be seen.) But no shrieks ever suggest that some intruder has received a shock. No movements of the wire ever betray an invisible climber. The bloodhounds never give cry. Yet still the Believer is not convinced. "But there is a gardener, invisible, intangible, insensible, to electric shocks, a gardener who has no scent and makes no sound, a gardener who comes secretly to look after the garden which he loves." At last the Sceptic despairs, "But what remains of your original assertion? Just how does what you call an invisible, intangible, eternally elusive gardener differ from an imaginary gardener or even from no gardener at all?"

In this parable we can see how what starts as an assertion, that something exist or that there is some analogy between certain complexes of phenomena, may be reduced step by step to an altogether different status, to an expression perhaps of a "picture preference." The Sceptic says there is no gardener. The Believer says there is a gardener (but invisible, etc.) ... Someone may dissipate his assertion completely without noticing that he has done so. A fine brash hypothesis may thus be killed by inches, the death by a thousand qualifications.

And in this, it seems to me, lies the peculiar danger, the endemic evil, of theological utterance. Take such utterances as "God has a plan," "God created the world," "God loves us as a father loves his children." They look at first sight very much like assertions, vast cosmological assertions. Of course, this is no sure sign that they either are, or are intended to be, assertions ...' He goes on to question these assertions.

'Is He still alive' is a reference to 'the death of God,' most often associated with Nietzsche. 'He' is capitalized in the insert to make the reference to God more obvious.

After the insert, the main metaphor is to do with fertilizing the soil, which continues the reference to gardening. Soil is often fertilized with the organic fertilizers blood and bone-meal. On the battlefield, the devastated land, which grows next to nothing, is fertilized with the blood and bones of the combatants. There's a further metaphor, of healing and medical treatment, as in the words 'dressing' and 'treated.'

Paul Hurt: 'Lincolnshire, asleep ...'

This poem of mine was suggested by a passage in Jack Currie's 'Lancaster Target:' 'At Modane, the railway ran from Grenoble to Turin, deep under the Graian Alps...Our task...was to block the tunnel...We arrived early in the target area, and circled high among the Alpine peaks, gazing at magnificent Mont Blanc, towering massive in the moonlight, with our target to the south and Lake Geneva to the north.' However, there was no collision in Jack Currie's account and the poem is fictional. See also my fictional poem about the collision of two other bombers, the 'exploding concrete poem' Collision.

The poem is about the disaster which overtook a bomber flying over the Alps. The bomber might have cleared the mountain, if only just. As it was, a wing tip made contact with the mountain but then the bomber's flight was deflected. It turned towards the mountain, crashed into it and exploded. This is a grim parody of a romantic encounter, with the mountain as a reticent lover or bride.

The poem reflects, of course, the social background, including the sports they played, of a proportion of the English who lost their lives in the Second World War, as in many  other wars. King's College is the Cambridge College and Wadham is the Oxford College. The pilot was educated at King's College Cambridge. The cricketer from Wadham was another member of the crew.

The metaphors belong to these reference-spheres:
(1) romantic meeting
(2) sport - rowing
(3) sport - cricket

The diagram given for the poem presents the different ambiguous meanings clearly but diagrams aren't always practicable. In the design of computer programs, a common interface has advantages, rather than slightly different or very different interfaces for presenting essentially the same information. In the discussion of ambiguity and metaphor, the use of a common presentation is preferable to differences in wording when essentially the same procedure is being followed. The procedure amounts to distinguishing the different meanings of a word or phrase. {resolution}, ® :- (the word or phrase) (different meanings, eg meaning (1) meaning (2) ). is the symbol for {diversification}. Here, it's read as OR. By using this symbol in discussions of ambiguity, the different meanings are distinguished concisely and clearly. + is 'amplification,' the giving of additional information. The presentation gives the main information, clearly and concisely. The amplification gives additional discussion which will usually be necessary.

Using this common presentation for ambiguities in the poem 'Lincolnshire asleep ...'

® :- ('subdued' in 'a mountain subdued') ('subdued' (1) the fact that at the time, the mountain had been brought under enemy control) ('subdued' (2) reserved,' 'demure.')
® :- ('in white') ('in white' (1) mountain covered by snow 'in white' (2) 'dressed in white.')

® :- ('felt a bump') ( (1), feeling a bump as the pilot's wing tip made contact with the mountain lightly (2) reference to the 'bump' of a 'bumping race:' + (Collins English Dictionary: 'esp.at Oxford and Cambridge, a race in which rowing eights start an equal distance one behind the other and each tries to bump the boat in front.') ) There's also forward reference to the 'Wadham cricketer: ( 'bump ball. ' Collins English Dictionary: 'Cricket. a ball that bounces into the air after being hit directly into the ground by the batsman.')

The fact that {resolution}, ® is applied here is obvious from the context and can be omitted. I do this from this point onwards.

('an uncertain oarsman') ( (1) negation of the common use of 'certain,' as in 'a certain young man from ...' (2) 'uncertain' of where he was, an uncertainty in navigation (3) 'uncertain of what he should do as pilot of the aircraft.')

('saw the catch') ( (1) an unexpected drawback - meiosis here (2) a catch in cricket, a fielder catching the ball hit by the batsman before it touches the ground.)

('struck up a match') ( (1) igniting a match, the bomber viewed as combustible (2) entering into a romantic relationship.)

Mallarmé: 'Le vierge, le vivace et le bel aujourd' hui'

The opening verse-paragraph of 'Le Vierge, le vivace et le bel aujourd' hui,' followed by my translation.

Le vierge, le vivace et le bel aujoud'hui
Va-t-il nous déchirer avec un coup d'aile ivre
Ce lac dur oublié que hante sous le givre
Le transparent glacier des vols qui n'ont pas fui!

The pristine, the vibrant, the beautiful today -
will it with a blow of its drunken wing tear
this forgotten lake - hard, haunted beneath the frost
by the transparent glacier of flights unflown!

Glaciers (and lakes) appear in the opening and closing lines of another poem by Mallarmé, Le Pitre châtié, 'The Clown Punished:

Yeux, lacs avec ma simple ivresse de renaître


Ce fard noyé dans l' eau perfide des glaciers.

Eyes, lakes with my simple drunkenness to be reborn


this make-up drowned in the deceitful water of glaciers.

In poetry, 'le vivace,' the vivacious, generally has the decisive advantage over ideas, such as the symbolist ideas which would justify the use of glaciers in these poems by Mallarmé, or any ideas which would justify the use of glaciers in the poetry of Seamus Heaney. The music critic Donald Francis Tovey wrote that when the human voice enters instrumental music, the voice tends to dominate, the instruments become background. The concreteness of a glacier which, with all its associations, is unsuitable for a given poem, remains a dominating and jarring presence in the foreground, any justification from theory or a manifesto in the background, with lesser semantic force.

David Hume is generally agreed to be the most important English-speaking philosopher either present or past, and the empiricist philosophy he presents in Book I, Part I of 'A Treatise of Human Nature' is relevant here. Section I begins, 'All the perceptions of the human mind resolve themselves into two distinct kinds, which I shall call IMPRESSIONS and IDEAS. The difference betwixt these consists in the degrees of force and liveliness, with which they strike upon the mind, and make their way into our thought or consciousness. Those perceptions which enter with most force and violence, we may name impressions; and under this name I comprehend all our sensations, passions and emotions, as they make their first appearance in the soul. By ideas I mean the faint images of these in thinking and reasoning.'

Later, 'I must must make use of the distinction of perceptions into simple and complex ... I observe, that many of our complex ideas never had impressions, that corresponded to them, and that many of our complex impressions never are exactly copied in ideas. I can imagine to myself such a city as the New Jerusalem, whose pavement is gold and walls are rubies, tho' I never saw any such.'

The ideas necessary to accommodate the glaciers in the poetry of Seamus Heaney and the far more complex poetry of Mallarmé are complex ideas, which involve {restriction}:- factors of the glaciers and {ordering}. These ideas may well be ineffective in cancelling the vivacity of the glaciers, viewed as wholes. The filtering of factors may be ineffective, for many readers if not all. See also my discussion of cancellation and non-cancellation in connection with Seamus Heaney's poem 'Wordsworth's Skates,' ('District and Circle').

Even so, the vivacity of the glaciers is subject to {modification}, in the light of experience, thought, study. Hume's account has the disadvantage of being overly passive and inadequate in its isolation of 'force and liveliness.' His account has to be supplemented with a consideration of genetic considerations.

Spinoza gives a corrective to this mistaken emphasis. In 'Imagination and Consciousness' ('The Principles of Art') R G Collingwood points out that the philosophy of Spinoza is a corrective to domination by feelings. Our life, 'from being a continuous passio, an undergoing of things, can become a continuous actio, or doing of things.' (Although the quotation he gives from Spinoza's 'Ethics' immediately afterwards has no direct bearing on this.) Including R G Collingwood's comment after the quotation, ''Affectus qui passio est, desinit esse passio, simulatque eius claram et distinctam formamus ideam.' (Ethics, part v, prop. 3). As soon as we form a clear and distinct idea of a passion, it ceases to be a passion.'

My translation of this proposition, 'An emotion which is passive ceases to be passive as soon as we form a clear and distinct idea of it.' R G Collingwood is surely confusing passivity ('passio' in the original) with passion ('affectus' in the original.) 'Affectus' is difficult to translate. Emotion is stressed, but 'affectus' also refers to bodily state and idea.

Stuart Hampshire, in his book 'Spinoza' refers to 'the helpless irrationality of normal human loves and hates, desires and aversions, and their entire independence of conscious thought and purpose,' and to 'the transition from the normal life of passive emotion and confused ideas' to the free 'life of active emotion and adequate ideas,' which can be achieved by 'making the patient more self-conscious.'

Spinoza uses the verbs 'agere' and 'pati,' their meanings explained in the definitions of Part III of the 'Ethics.' 'agere' is to be active, 'pati' to be passive, as when our emotions are beyond our control. Nobody is entirely active or entirely passive but to become more active and less passive is a good. Christopher Norris (in 'Spinoza and the Origins of Modern Critical Theory') stresses 'Spinoza's understanding of the constant interaction between 'passive' and 'active' ideas, [although 'ideas' is too restrictive] or the extent to which errors brought about by force of circumstance ... may yet become the starting-point for a process of critical reflection that points a way beyond those errors.'

Hume's psychology (and ethical theory) reflects a passivity which is inadequate - but this isn't in the least to give it the amplification needed to do it justice. Reading not just immensely self-conscious writers such as Mallarmé but writers such as Seamus Heaney with preliminary notions of passivity, not activity (notions which are applicable to reading as well as to such matters as human folly and weakness) is inadequate. By these preliminary notions, glaciers have an unexamined vivacity which makes them poetically ineffective, but the more active reading may well not give {modification} of ineffectiveness. I think that the conscious isolation of factors, the conscious consideration of the {ordering} of factors and of {restriction}:- (factors) in this case gives results which are close to those obtained by a more passive reading. This is an example of what I call alignment, the alignment in this case of active and passive reading.

The primary functions of a word are different from the metaphorical functions of the word. The word may or may not be well adapted to these additional functions. This is the case even when the primary use has a clear origin in past metaphorical use. As examples, cars may well be resistant to metaphorical use, as in Seamus Heaney's poem Squarings xxxvi. So also are glaciers, used ineffectively by Seamus Heaney.

'My 'dual-purpose' text is an  example of one-many design.  One object, text, can have more than one function. It can be used to give information, or to convey things that are more than information. It can also be used for navigation, as on the page Poems. By clicking on the text, the user is taken to the top of the page. Similarly for images, which have a primary function, such as providing information or enjoyment, and other possible functions, such as navigation in a Web page. By clicking on a poem in image form, the user is taken to the top of the page.

'What about letters and other objects of written communication? Their primary function is semantic, to convey information and things that are more than information in the distinctive setting of written communication. Using letters and other objects of written communication for visual design is problematic. Are they really multi-functional, capable of being one-many design elements?

'The lines which are used in drawing are capable of almost infinite variety in their length, shape, emphasis and placing. The lines which are letters and other objects of written communication are subject to severe {restriction}. The particular shapes of so many letters aren't particularly suited to general design. Many of them have projections, are bulbous. The shapes can be subjected to {modification} so that they are more suitable for the purposes of a particular design, but obviously the {modification} is subject to {restriction}. After a certain point, the letter becomes unrecognizable as the letter.

[one-many functions here] < > [mathematical functions or mappings]

More on mathematical one-many functions or mappings (the terms are synonymous here):

If S and T are two non-empty sets, a mapping from S into T assigns a unique element of T to each element of S. Concisely, the mapping f : S / / T where S is the domain of f and T is the codomain of f. A one-many function or mapping can associate a single member of the domain with more than one member of the range of a function. The range is the set of values taken by a function as its argument varies through its domain.