Topological projection in mental space

I have considered how schema-based metaphorical mapping is crucial in the mental construction of scenes and episodes. Now I move from the metaphor of ‘mapping’ as a way of describing conceptual structure to exploring the metaphor of ‘projection’. Like ‘mapping’, schematic metaphorical ‘projection’ is a way of describing how image schemas are behind the multiple ways discourse contents may be construed in mental space. In cognitive linguistics, the ‘invariance principle’ is the claim that ‘image schema project a topological structure, and that this structure is always preserved by metaphor’ (Lakoff 1993: 229). Taking into account the topological nature of image schemas, abstract inferences are thought to be metaphorical versions of spatial inferences. In other words, ‘propositional inferences arise from the inherent topological structure of the image schemas projected by metaphor onto concepts like times, states, changes, actions, causes, purposes, means, quantity and categories’ (ibid.). This means that abstract reasoning is a special kind of imagistic reasoning, where schema topologies are metaphorically projected onto abstract domains. Topological properties are active in

discourse processing through metaphorical projection of image schemas in the SOURCE

DOMAIN onto the TARGET DOMAIN for the construction of scenes and the execution of

episodes. Metaphorical projections preserve the cognitive topology (i.e. image schema

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the TARGET DOMAIN. Adhering to the invariance principle, I understand the topology of

image schemas to be active in construing contents during discourse processing.

In cognitive discourse studies, image schemas are understood to ‘impose a topological and relational structure on the scene under conception’ (Hart 2013: 405). As previously stated, topological ‘projection’ goes unconsidered in the mapping diagrams of cognitive metaphor theory, but is currently being explored within alternative representational formats (cf. Chilton 2014; Hart 2014a). Moving forward, I begin to describe a representational format that poses a spatial background upon which metaphorical projections can occur. Any representational format of mental space must take into consideration the topological properties and relations arising from image schema projection. In the spatial modelling options discussed below, I first explore a strictly topological approach for modelling mental space. Afterwards, I look for ways to combine both topological and deictic features of mental models. I do so by adapting Chilton’s deictic space model (see Section 4.2), which assumes a three-dimensional conceptual background upon which discourse contents interact during conceptualisation. To first demonstrate a non-geometric way of modelling, consider this fictional example showing

a strictly topological method for representing image schema projection.23

Figure 5.2 Topological projection of image schemas in example sentence.

In discourse processing, the identity ‘I’ invoked in STM as AGENT is the first concept to

be located amongst all other contextually significant identities in LTM. In this example, once this identity is located and given subjective meaning, the identity category is

metaphorically placed in a state-of-being CONTAINER, in this case a state of ‘panic’. The

SOURCE from which the AGENT moves is a non-specified location and must either be

inferred or signaled elsewhere in the text. Notice that the AGENT and CONTAINER schemas

are co-present at this particular point in construing the scene within mental space.

Leaving the scene, the reader moves to an episode with the PATH schema prompted by the

verb ‘ran’, which stipulates motion towards the ‘apartment’. When moving to the GOAL

space, the word ‘luxury’ cues the superimposition of a SCALE schema, directing the

reader’s attention UP. Figure 5.2 illustrates how, within the span of a sentence, the reader

imagistically moves from AGENT and CONTAINER schemas interacting in constructing the

scene. Then, once the scene is set, the reader encounters a PATH schema where the agent

moves to a new location of interacting SCALE and GOAL schemas, which are all involved

in constructing the episode. This fictional example helps to demonstrate how image

23Garnham (1999: 47) states, ‘It is a reasonable that much of people’s reasoning about space can be explained by postulating non- Euclidean mental representations’. Many in the psycholinguistic community do not impose a geometric conception of space on abstract domains, reserving this for representations derived directly from our immediate perceptual experience (Freska and Barkowsky 1999). Luxury PATH Ran to GOAL Apartment Panic d d dfjkddfjdk AGENT I

I <AGENT> was in <CONTAINER> a panic, so I ran to <PATH> the luxury <SCALE> apartment <GOAL>.

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schemas are involved in topological projection of situational structure. To further demonstrate the topological projection of image schemas occurring during online processing (Figure 5.3), I provide a breakdown of sentence (13) of Weatherman manifesto visited twice before (see Sections 4.1.6 and 5.1.2).

We are within <CONTAINER> the heartland <CENTRE-PERIPHERY> of a worldwide <SURFACE>

monster. A country <AGENT> so <SCALE> rich <GOAL> from its worldwide plunder <PATH/FULL- EMPTY> that even the crumbs doled out to <PATH> the enslaved <ENABLEMENT> masses within its borders <CONTAINER> provide for material existence very much above <SCALE> the conditions

<GOAL> of the masses of people of the world <PART-WHOLE>.

Figure 5.3 Schema-based metaphorical projection of topological relations in Weatherman manifesto.

In this exert, the protagonists are located inside of a ‘worldwide monster’ CONTAINER,

specifically in the part of the monster that is of central importance (‘the heartland’). Here, America is described as a large, frightening creature that is able to extend its reach

throughout the globe. In the passage, the monster is transformed into ‘a country’ as

AGENT. The PATH of this monster-country is to take advantage of international disorder by

plundering raw materials from underprivileged countries abroad. In doing so, the monster

reaches its GOAL of possessing an abundance of material wealth, which is construed as an

excess with the help of the SCALE-UP schema. Moving to the next proposition, the AGENT

space is still in play but moves now from the international to domestic theatre, where the

monster’s PATH is rationing crumbs to ‘enslaved masses’. This conjures up an image of

the giant monster sparsely distributing bread crumbs to its unfortunate captives contained within US borders. The noun ‘borders’ construes the situation where the reader’s

attention is guided to a specific portion of the CONTAINER topology. With the lexical cue

‘borders’, the boundary line of the CONTAINER is foregrounded instead of the space either

in or outside. Moving to the GOAL portion, one encounters the superimposition of both

SCALE and PART-WHOLE schemas, which enables the reader to conceptualise a material

state of being that is ‘very much above’ that of the world masses.

Now that I have briefly considered a strictly topological description of schema-based metaphorical projection, I revisit the previous example sentence, ‘I was in a panic, so I

d d

dfjkddfjdk Very Much Above

AGENT Monster/ Country d d dfjkddfjdk So PATH/ SURFACE Plunder US GOAL Rich PATH

Crumbs Doled Out to Enslaved Masses d d dfjkddfjdk World American Border We Masses of People GOAL Mass Conditions

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ran to the luxury apartment’, while also paying attention to deictic space. I re-examine it with the intention of exploring topological relations within geometric conceptual space. Remember, this is a conceptual space which in discourse is co-constructed by writer and reader such that it forms a momentary intersubjective mental space for purposes of communication and coordination of action (see Section 4.2.1). Using the basic deictic space configuration, in Figure 5.4 I model the protagonist (‘I’) as an entity existing

within a negatively evaluated CONTAINER (‘in a panic’). Within deictic space the reader

places the protagonist in the past upon the -t-axis, moving along a PATH from the past into

the present by taking account of the tense of the verb phrase (‘ran to’). The destination

reached (‘apartment’) is construed as the GOAL of the AGENT, which is modified by a

superimposed SCALE schema (‘luxury’) at the end of the A-P-G schema. The reader can

infer that instead of remaining in a state of ‘panic’, the protagonist has reached a new

evaluative state of safety within the confines of a ‘luxury’ (SCALE-HI) ‘apartment’

(CONTAINER).

Figure 5.4 Topological and deictic projections of image schemas in example sentence.

The apartment is located at the deictic centre as, in this example, I am presuming that the speaker is recounting the event from the apartment. In deictic space modelling, one must take account of the speaker’s current ‘ground’, which requires some knowledge of the context in which the text was produced. If this same story were recounted from another location later on, that would have to be taken into consideration in the model. With this example, I am attempting to model meaning construction within topological and geometric configurations as they occur in the minds of text-consumers. With this representational format, discourse analysts can take account of where imagistic constraints appear within a space, time and evaluation coordinate system (see Section 4.2.2).