Ambiguous figures and representationalism

Macpherson (Nous 40(1):82–117, 2006) argues that the square/regular diamond figure threatens representationalism, construed as the theory which holds that the phenomenal character is explained by the nonconceptual content of experience. Her argument is the claim that representationalism is committed to the thesis that differences in the experience of ambiguous figures, the gestalt switch, should be explained by differences in the NCC of perception of these figures. However, with respect to the square/regular diamond and some other ambiguous figure representationalism fails to offer a unified account of how representational content makes them ambiguous. In this paper, I aim, first, to offer a representationalist account of ambiguous figures and, second, to examine and rebut Macpherson’s arguments. My main point is that in each ambiguous figure Macpherson discusses there are differences in representational content that can explain differences in phenomenal character or content. The representational differences are due to the ways the Cartesian frame of reference in which perceptual content is always cast cuts the figure, underlying different properties of the figure with respect to the axes of the Cartesian frame of reference.     

Ambiguous figures and representationalism

Ambiguous figures pose a problem for representationalists, particularly for representationalists who believe that the content of perceptual experience is non-conceptual (MacPherson in Nous 40(1):82–117, 2006). This is because, in viewing ambiguous figures, subjects have perceptual experiences that differ in phenomenal properties without differing in non-conceptual content. In this paper, I argue that ambiguous figures pose no problem for non-conceptual representationalists. I argue that aspect shifts do not presuppose or require the possession of sophisticated conceptual resources and that, although viewing ambiguous figures often causes a change in phenomenal properties, this change is accompanied by a change in non-conceptual content. I illustrate the case by considering specific examples.     

Good Samaritans, Good Humanitarians

abstract   Duties of beneficence are not well understood. Peter Singer has argued that the scope of beneficence should not be restricted to those who are, in some sense, near us. According to Singer, refusing to contribute to humanitarian relief efforts is just as wrong as refusing to rescue a child drowning before you. Most people do not seem convinced by Singer's arguments, yet no one has offered a plausible justification for restricting the scope of beneficence that doesn't produce counterintuitive results elsewhere. I offer a defence of this restricted scope by introducing the notion of unique dependence, a notion that is both intuitively attractive and theoretically grounded. It explains why your reason to rescue the drowning child is more stringent than your reason to contribute to humanitarian relief, while blocking the conclusion that we have no reason at all to aid distant sufferers.     

Hidden figures are ever present

Preference judgments about alternative interpretations of unambiguous patterns can be explained in terms of a rivalry between a preferred and a second-best interpretation (cf. Leeuwenberg & Buffart, 1983). We tested whether this second-best interpretation corresponds to a suppressed but concurrently present interpretation or whether it merely reflects an alternative view that happens to be preferred less often. Two patterns were present immediately following each other with a very short onset asynchrony: a complete pattern and one out of three possible subpatterns of it, corresponding to the best, the second best, or an odd interpretation of the complete pattern. Subjects indicated which subpattern was presented by choosing among the three subpatterns shown after each trial. The scores, corrected for response-bias effects, indicated a relative facilitation of the second-best interpretation, in agreement with its predicted "hidden" presence. This result is more in line with theories that capitalize on the quality of the finally selected representation than with processing models aimed at reaching one single solution as fast and as economically as possible.     

Priming effects with ambiguous figures

We varied the format and semantic content of primes to determine the degree to which they would influence the interpretation of ambiguous figures. The primes were objects or object names that were related in some way to one of the two organizations of the ambiguous figures. In Experiment 1, we provided some normative data regarding the stimulus materials, whereas in Experiment 2, an orienting question was used to focus attention on the semantic relationship between the prime and the figure. In Experiment 3, we used the orienting question to divert attention away from the relationship by asking about physical features of the figures. Recognition responses to biased versions of the figures and to new figures were measured. Primes that were loosely and indirectly associated with one of the two interpretations of an ambiguous figure were found to be effective at biasing the interpretation of an ambiguous figure in the direction of the primed alternative but only if attention was focused on the semantic relationship between the two stimuli. Attention to the physical characteristics of the stimuli during encoding eliminated the prime's influence on complex object perception. These findings are consistent with the conceptual priming literature and extend those of some recent studies (Balcetis & Dale, 2007; Feist & Gentner, 2007), which show that the interpretation of complex figures can be biased by the advanced presentation of related verbal information.     

Some thoughts on impossible figures

Based on an artistic analysis of the construction of "impossible figures," their structure and the origin of the perceptual effects they induce are discussed, including the use of a basic indeterminate space of intersection, penetration of indeterminate solids, and symmetry. These and other points are illustrated by 17 progressively more complex figures constructed by the author.     

Disambiguating ambiguous figures by selective attention

The present study was designed to investigate the hypothesis that the formation of a given percept of an ambiguous figure results from focusing attention on a focal area that contains features significant for this percept but not for the alternative one. Two such focal areas were designated for the two competing interpretations of the bird/plane and duck/rabbit ambiguous figures. Detecting a letter following the figure was faster when the letter appeared in the focal area of the perceived interpretation than in the focal area of the alternative one. Furthermore, directing attention to a given focal area shortly before the presentation of the figure increased the likelihood of forming the corresponding interpretation rather than the alternative one. Results suggest that maintaining different interpretations of the same ambiguous figure is mediated by focusing attention on different parts of the figure.     

Organizing the properties of impossible figures

The empirical study of impossible figures requires that independent variables be well-specified. This paper provides an aid for such a task by developing a classification system which partitions cornered torus figures into meaningful subsets. These can be used to identify both formal and psychological properties of known as well as unknown possible and impossible figures in much the same manner as with the periodic table of chemical elements. The classification is polytopic (for demensional) and is formally, not empirically, derived. Coherent three-dimensional and two-dimensional forms of the system are possible without loss of information.     

Area perception in simple geometrical figures

The results of experiments on visual perception of area of circles and squares are reported. Pairs of geometrical figures were presented simultaneously on an oscilloscope screen. While one of them was fixed, the other one was controlled by an experimental subject. The task of the subject was to match the area of the variable figure to the area of the fixed one. The obtained data show underestimation of the area of circle when compared with square. A mathematical model designed to explain this phenomenon is proposed here. The image function defined as a low-pass filtered (blurred) version of the figure is employed for this purpose. Then, instead of the position of the image function maxima, the position of a threshold value is used for area computation.