This chapter covers number of Abstractionist views of modality. It considers three ways that Abstractionists might account for how possible worlds represent possibilities, rather than in terms of the categorial nature of worlds. First, there is Magical Abstractionism, according to which that question has no informative answer. Second, there is Linguistic Abstractionism, according to which possible worlds represent in the way that languages do. And finally, there is Pictorial Abstractionism, according to which possible worlds represent in (...) the way that pictures do. Pictorial Abstractionists might respond by trying to identify a feature that Concretist worlds have that their worlds don't, or vice versa. One way for something to be possible is for actual things to have the power to make it so. Since the notion of power is central to Aristotelian Modality, we get sub‐varieties of the view depending on one's metaphysical account of powers. (shrink)

Pictures are 2D surfaces designed to elicit 3D-scene-representing experiences from their viewers. In this essay, I argue that philosophers have tended to underestimate the relevance of research in vision science to understanding the nature of pictorial experience. Both the deeply entrenched methodology of virtual psychophysics as well as empirical studies of pictorial space perception provide compelling support for the view that pictorial experience and seeing face-to-face are experiences of the same psychological, explanatory kind. I also show that (...) an empirically informed account of pictorial experience provides resources to develop a novel, resemblance-based account of depiction. According to what I call the deep resemblance theory, pictures work by presenting virtual models of objects and scenes in phenomenally 3D, pictorial space. (shrink)

Abstractionism, which is a development of Frege's original Logicism, is a recent and much debated position in the philosophy of mathematics. This volume contains 16 original papers by leading scholars on the philosophical and mathematical aspects of Abstractionism. After an extensive editors' introduction to the topic of abstractionism, the volume is split into 4 sections. The contributions within these sections explore the semantics and meta-ontology of Abstractionism, abstractionist epistemology, the mathematics of Abstractionis, and finally, Frege's application (...) constraint within an abstractionist setting. (shrink)

ABSTRACT Is it possible to effect singular reference to mathematical objects in the abstractionist framework? I will argue that even if mathematical expressions pass the relevant syntactic and inferential tests to qualify as singular terms, that does not mean that their semantic function is to refer to a particular object. I will defend two arguments leading to this claim: the permutation argument for the referential indeterminacy of mathematical terms, and the argument from the semantic idleness of the terms introduced by (...) abstraction principles. (shrink)

Both traditional and naturalistic epistemologists have long assumed that the examination of human psychology has no relevance to the prescriptive goal of traditional epistemology, that of providing first-person guidance in determining the truth. Contrary to both, I apply insights about the psychology of human perception and concept-formation to a very traditional epistemological project: the foundationalist approach to the epistemic regress problem. I argue that direct realism about perception can help solve the regress problem and support a foundationalist account of justification, (...) but only if it is supplemented by an abstractionist theory of concept-formation, the view that it is possible to abstract concepts directly from the empirically given. Critics of direct realism like Laurence BonJour are correct that an account of direct perception by itself does not provide an adequate account of justification. However a direct realist account of perception can inform the needed theory of concept-formation, and leading critics of abstractionism like McDowell and Sellars, direct realists about perception themselves, fail to appreciate the ways in which their own views about perception help fill gaps in earlier accounts of abstractionism. Recognizing this undercuts both their objections to abstractionism and (therefore) their objections to foundationalism. (shrink)

The thesis of this paper is that Thomas Aquinas offers an alternative model of abstraction (the Active Principle Model) that overcomes the standard objections to abstractionism and expands our view of what an abstractionist theory might look like. I contend that this alternative model of abstraction has been invisible in plain sight, in Aquinas’s references to the mind’s abstractive mechanism as an “intellectual light.” Such language is not metaphorical but rather technical, signaling that intellectual abstraction is to be modeled (...) on the activity of physical light as he understood it from theories proposed by Avicenna and Averroes. The Active Principle Model requires us to rethink Aquinas’s account of how we come to know essences—a process that turns out to be much more tentative and incremental than previously thought. (shrink)

The central thesis (CT) that this paper upholds is that a picture depicts an object by generating in those who view the picture a visual experience of that object. I begin by presenting a brief sketch of intentionalism, the theory of perception in terms of which I propose to account for pictorial experience. I then discuss Richard Wollheim’s twofoldness thesis and explain why it should be rejected. Next, I show that the socalled unique phenomenology of pictorial experience is (...) simply an instance of perceptual indeterminacy. Lastly, I discuss a phenomenon associated with pictures that could be considered a problem for CT, and account for it by invoking the thesis that visual experience is cognitively penetrable. (shrink)

Abstractionism is a philosophical account of the ontology of mathematics according to which abstract objects are grounded in a process of abstraction. Abstraction involves arranging a domain of underlying objects into classes and then identifying … Continue reading Abstractionism →.

Are there objects that are “thin” in the sense that their existence does not make a substantial demand on the world? Frege famously thought so. He claimed that the equinumerosity of the knives and the forks suffices for there to be objects such as the number of knives and the number of forks, and for these objects to be identical. The idea of thin objects holds great philosophical promise but has proved hard to explicate. This book attempts to develop the (...) needed explanations by drawing on some Fregean ideas. First, to be an object is to be a possible referent of a singular term. Second, singular reference can be achieved by providing a criterion of identity for the would-be referent. The second idea enables a form of easy reference and thus, via the first idea, also a form of easy being. Paradox is avoided by imposing a predicativity restriction on the criteria of identity. But the abstraction based on a criterion of identity may result in an expanded domain. By iterating such expansions, a powerful account of dynamic abstraction is developed. (shrink)

Some (Podro, Lopes) think that sometimes our experience of pictures is ‘inflected’. What we see in these pictures involves, somehow, an awareness of features of their design. I clarify the idea of inflection, arguing that the thought must be that what is seen in the picture is something with properties which themselves need characterising by reference to that picture’s design, conceived as such. I argue that there is at least one case of inflection, so understood. Proponents of inflection have claimed (...) great significance for the phenomenon. But what might that significance be? Inter alia, I consider Lopes’s proposal that inflection solves a central problem in pictorial aesthetics, the ‘puzzle of mimesis’. I argue that the puzzle, and the proposed solution, both turn on aspects of Lopes’s conception of seeing-in. Other accounts of seeing-in can make no sense of either. I further argue that the phenomenon of inflection itself puts pressure on the sort of account Lopes offers. Thus it is hard to offer a view which both holds that inflection occurs and is able to make clear sense of why it matters. (shrink)

The idea that pictorial art can have cognitive value, that it can enhance our understanding of the world and of our own selves, has had many advocates in art theory and philosophical aesthetics alike. It has also been argued, however, that the power of pictorial representation to convey or enhance knowledge, in particular knowledge with moral content, is not generalized across the medium.

When I see a tree through my window, that particular worldly tree is said to be ‘in’, ‘on’, or ‘before’ my mind. My ordinary visual link to it is ‘intentional’. How similar to this link are the links between me and particular worldly trees when I see them in photographs, or in paintings? Are they, in some important sense, links of the same kind? Or are they links of importantly different kinds? Or, as a third possibility, are they at once (...) links of the same important kind and also links of importantly different sub-kinds within that kind? This paper takes up these taxonomical questions. After fleshing out (a bit) the characterisation of these different subject-object links, I explain and expand upon an approach to answering the taxonomical questions originally set out by Kendall Walton. I then follow this approach a certain distance, connecting it with the question of how to mark the boundary between perception and cognition. My investigations support the conclusion that the three types of links just described are not importantly different in kind. (shrink)

The philosophical problem of pictorial conversational implicatures can be summarized as follows: We have three propositions that are independently plausible and jointly inconsistent. -/- (Non-P) Anti-propositionalism: pictures do not have context-independent, conventionally encoded propositional content (propositional function). -/- (C) Only those representations can be used to convey conversational implicatures which have associated with them a context-independent, conventionally encoded propositional content (function). -/- (I) Pictures can be used to convey conversational implicatures. -/- There are three ways of responding to the (...) problem: affirm (Non-P) and (C) while denying (I); affirm (C) and (I) while denying (Non-P); or affirm (Non-P) and (I) while denying (C). (shrink)

ionism as a foundational programme in the philosophy of mathematics traditionally originates with Gottlob Frege. According to it, significant portions of mathematics (arithmetic, possibly r...

An artistic discussion on the critical potential of African American expressive culture In a major reassessment of African American culture, Phillip Brian Harper intervenes in the ongoing debate about the “proper” depiction of black people. He advocates for African American aesthetic abstractionism—a representational mode whereby an artwork, rather than striving for realist verisimilitude, vigorously asserts its essentially artificial character. Maintaining that realist representation reaffirms the very social facts that it might have been understood to challenge, Harper contends that (...) class='Hi'>abstractionism shows up the actual constructedness of those facts, thereby subjecting them to critical scrutiny and making them amenable to transformation. Arguing against the need for “positive” representations, Abstractionist Aesthetics displaces realism as the primary mode of African American representational aesthetics, re-centers literature as a principal site of African American cultural politics, and elevates experimental prose within the domain of African American literature. Drawing on examples across a variety of artistic production, including the visual work of Fred Wilson and Kara Walker, the music of Billie Holiday and Cecil Taylor, and the prose and verse writings of Ntozake Shange, Alice Walker, and John Keene, this book poses urgent questions about how racial blackness is made to assume certain social meanings. In the process, African American aesthetics are upended, rendering abstractionism as the most powerful modality for Black representation. (shrink)

It is generally recognised that an adequate resemblance-based account of depiction must specify some standard of correctness which explains how a picture’s content differs from the content we would attribute to it purely on the basis of resemblance. For example, an adequate standard should explain why stick figure drawings do not depict emaciated beings with gargantuan heads. Most attempts to specify a standard of correctness appeal to the intentions of the picture’s maker. However, I argue that the most detailed such (...) attempt to date is incomplete. I argue that an adequate standard can be given only if one construes a picture’s content as being pictorially implicated, in a way analogous to that in which Grice explains an utterance’s meaning as being conversationally implicated. I propose a theory of pictorial implicature and use it as the basis for an intention-based standard of correctness. I show how this standard is able to explain both the ways in which the content of pictures differs from the content we would attribute to them solely on the basis of resemblance, and how we are able to apply an intention-based standard of correctness even though we lack any independent knowledge of the intentions of pictures’ makers. (shrink)

PREFACE The semiotic approach to pictorial or audiovisual communication has been the special concern of a number of ...

I propose a number of criteria for the adequacy of an account of pictorial realism. Such an account must: explain the epistemic significance of realistic pictures; explain why accuracy and detail are salient to realism; be consistent with an accurate account of depiction; and explain the features of pictorial realism. I identify six features of pictorial realism. I then propose an account of realism as a measure of the information pictures provide about how their objects would look, (...) were one to see them. This account meets the criteria I have identified and is superior to alternative accounts of realism. (shrink)

Richard Wollheim famously argued that figurative pictures depict their scenes, in part, in virtue of their ability to elicit a unique type of visual experience in their viewers, which he called seeing-in. According to Wollheim, experiences of seeing-in are necessarily twofold, that is, they involve two aspects of visual awareness: when a viewer sees a scene in a picture, she is simultaneously aware of certain visible features of the picture surface, the picture’s design, and the scene depicted by the picture. (...) Even though Wollheim’s notion of twofoldness has been very influential, a number of philosophers have put forward powerful arguments against it. In this paper, I defend the claim that some pictorial experiences are twofold in Wollheim’s sense. My argument has two parts. In the first part, I provide a phenomenal contrast argument in favor of twofoldness. In the second part, I respond to what I take to be the most important objections against twofoldness. I believe that both parts together provide strong support for the claim that some pictorial experiences are twofold in Wollheim’s sense. (shrink)

What is special about photographs? Traditional photography is, I argue, a system that sustains factive pictorial experience. Photographs sustain pictorial experience: we see things in them. Further, that experience is factive: if suchandsuch is seen in a photograph, then suchandsuch obtained when the photo was taken. More precisely, photographs are designed to sustain factive pictorial experience, and that experience is what we have when, in the photographic system as a whole, everything works as it is supposed to. (...) In this respect photographs differ from handmade pictures, and from other information-preserving tools, such as the readings on a geiger counter. This distinctive feature can be used to explain what is epistemically special about photographs, and also to give an account of the distinctive phenomenology of looking at a photograph rather than a handmade picture. All this provides the background against which to assess claims that digital photography differs from traditional in certain key ways. (shrink)

A discussion of the philosophical prospects for basing a neo-Fregean theory of classes on a principle that attempts to articulate the limitation-of-size conception.

In Thin Objects: An Abstractionist Account, Linnebo offers what he describes as a “simple and definitive” solution to the bad company problem facing abstractionist accounts of mathematics. “Bad” abstraction principles can be rendered “good” by taking abstraction to have a predicative character. But the resulting predicative axioms are too weak to recover substantial portions of mathematics. Linnebo pursues two quite different strategies to overcome this weakness in the case of set theory and arithmetic. I argue that neither infinitely iterated abstraction (...) nor abstraction on possible specifications fully resolves the bad company problem. (shrink)

Richard Wollheim famously argued that figurative pictures depict their scenes, in part, in virtue of their ability to elicit a unique type of visual experience in their viewers, which he called seeing-in. According to Wollheim, experiences of seeing-in are necessarily twofold, that is, they involve two aspects of visual awareness: when a viewer sees a scene in a picture, she is simultaneously aware of certain visible features of the picture surface, the picture’s design, and the scene depicted by the picture. (...) Even though Wollheim’s notion of twofoldness has been very influential, a number of philosophers have put forward powerful arguments against it. In this paper, I defend the claim that some pictorial experiences are twofold in Wollheim’s sense. My argument has two parts. In the first part, I provide a phenomenal contrast argument in favor of twofoldness. In the second part, I respond to what I take to be the most important objections against twofoldness. I believe that both parts together provide strong support for the claim that some pictorial experiences are twofold in Wollheim’s sense. (shrink)

In our everyday discourse we make frequent reference to pictorial narratives. We exclaim on the hunt scene in the cave painting, the frenzy unfolding in the graffiti, the adventure of the baby in the book illustration, and the disintegration of a marriage in the oil painting. Yet a more precise question concerning narrators and their relation to these so-called pictorial narratives remains overlooked. Theoretical debates in narratology are still primarily focused on literary narratives and so pictures remain relatively (...) neglected as a class. Kendall Walton is an exception. He argues that the literary narrator is necessary to provide access to the story as ‘he mediates the reader’s access to the rest of the fictional world’. He says that pictorial narratives cannot sustain narrators akin to literary counterparts. But this seems to be at odds with how we understand paintings such as Marriage A-la-Mode, where events are arguably recounted to the viewer with wicked humour. This paper has two main aims. The first is to set out what is meant by ‘pictorial narrators’ by providing a succinct and up-to-date guide to the discussions that have touched on this issue. The second is to explore the possibility that pictorial narratives imply pictorial narrators. (shrink)

The question whether art is of any epistemic value is an old question in the philosophy of art. Whereas many contemporary artists, art-critics, and art-historians answer this question affirmatively, many contemporary philosophers remain skeptical. If art is of epistemic significance, they maintain, then it has to contribute to our quest of achieving our most basic epistemic aim, namely knowledge.Unfortunately, recent and widely accepted analyses of knowledge make it very hard to see how art might significantly contribute to the quest of (...) achieving this aim. Hence, by the lights of recent epistemology, it is questionable whether art is of any epistemic value. In order to hold on to the epistemic value of art, one has three options: (a) reject the recent analyses of knowledge that make the epistemic value of art questionable, (b) accept the recent analyses of knowledge but argue that they are compatible with the epistemic value of art, or (c) find another epistemic aim (besides knowledge) and show that art is of significant help in achieving this aim. In this paper I will argue that, at least with respect to pictorial art, option (c) seems promising. By reconsidering some basic insights and ideas from Nelson Goodman we can identify (objective) understanding as an epistemic aim to which pictorial art makes a significant contribution. (shrink)

Pictorial free perception reports are sequences in comics or film of one unit that depicts an agent who is looking, and a following unit that depicts what they see. This paper proposes an analysis in possible worlds semantics and event semantics of such sequences. Free perception sequences are implicitly anaphoric, since the interpretation of the second unit refers to the agent depicted in the first. They are argued to be possibly non-extensional, because they can depict hallucination or mis-perception. The (...) semantics proposed here employs an account of anaphora using discourse referents, a formalized possible worlds semantics for pictorial narratives, and, to model the epistemic consequences of perceptual events, the event alternative construction from dynamic epistemic logic. In intensional examples, the second unit depicting what is seen is analyzed as embedded. It is argued that a semantics for embedding where the attitudinal state of the depicted agent is required to entail the semantic content of the picture attributes too much information to the agent. This is addressed with a model of normal looking, and a semantics for the embedding construction that uses existential quantification over alternatives, rather than universal quantification. (shrink)

The focus of this paper is on E. H. Gombrich's claim that pictorial perception is a case of illusion. My aim is to point out that, on the one hand, the interpretation of this claim that is widely accepted in pictorial theory is not supported by Gombrich's analysis of pictorial perception; and, on the other hand, that the interpretation of the claim that I see as more compatible with Gombrich's analysis is not consistent with relevant facts about (...) our relation to pictures. However, I will argue, Gombrich's elaboration of the claim of illusion is significant to the extent that it highlights important aspects of the system of pictorial representation. (shrink)

In this paper, I present two crucial problems for Wolff’s metaphysics of quantities: 1) The structural identification problem and 2) the Pythagorean problem. The former is the problem of uniquely defining a general algebraic structure for all quantities; the latter is the problem of distinguishing physical quantitative structure from mathematical quantities. While Wolff seems to have a consistent and elegant solution to the first problem, the second problem may put in jeopardy his metaphysical view on quantities as spaces. After drawing (...) a parallelism between Wolff’s treatment of quantitative structures and Frege’s conception of quantitative domain, I propose a solution to the Pythagorean problem based on the idea that mathematical structures are the result of applying an abstraction principle on physical quantitative structures. In particular, I propose the view that abstraction may be seen as the operation of structure determination which transforms concrete physical quantities (i.e. undetermined structures) into abstract mathematical quantities (fully determined structures of thin and shallow objects). Keywords: Metaphysics of Quantities, Abstraction Principles, Locationism. (shrink)

I discuss certain representative accounts of metaphysical emergence falling into three broad categories, assessing their prospects for satisfying certain criteria; the ensuing dialectic has a bit of the Goldilocks fable about it. At one end of the spectrum are what I call ‘scientistic’ accounts, which characterize metaphysical emergence by appeal to one or another specific feature commonly registered in scientific descriptions of seeming cases of emergence; such accounts, I argue, typically fail to provide a clear basis for ensuring incompatibility with (...) ontological reduction, and thus fail to guarantee satisfaction of the criterion of appropriate contrast (§2). At the other end of the spectrum are what I call ‘abstractionist’ accounts, which characterize emergence in terms floating free of scientific notions; such accounts, I’ll argue, typically fail to guarantee satisfaction of the criterion of illuminating contrast (§3). I’ll then look at several accounts of metaphysical emergence that are what I call ‘substantive’, in appealing to familiar relations or posits which are properly metaphysical, while being intelligibly connected to scientific relations and posits. As we’ll see, the resources of such accounts are up to the tasks of blocking ontological reduction and of enabling investigations into metaphysical emergence to proceed in an illuminating way (§4). I close with some methodological morals (§5). (shrink)

This paper examines a form of pictorial realism that has epistemic import. Gombrich and Schier claim that some pictures are realistic because they convey accurate information. The difficulty is that judgments of realism vary across cultural and historical contexts. Goodman counters that pictures belong to different systems and realistic pictures belong to familiar systems. However, this does not explain the revelatory realism' of pictures in novel systems. I propose that two views can be combined: a realistic picture is one (...) which belongs to a system that conveys the kind of information that suits the needs of users in a context. (shrink)

Pictorial representation is a subject of interest to both cognitive science and aesthetics. Standard theories of depiction often draw on vision science, and vision science must give an account of picture perception. I offer a critical overview of standard theories of depiction and argue that none of them is adequate. I then describe ways in which new theories of perception blend elements of representationalism with an emphasis on attention and motor control. Such theories, in effect, limit the reliance on (...) mental representation in perceptual tasks. This work provides the basis for a theory of depiction in which pictorial representation is explained in terms of both mental representations and perceptual strategies. I argue that, in the case, the mental representations are most plausibly individuated by the functional and conceptual roles, rather than by causal links to the external world. (shrink)

We discuss abstraction principles in the context of modal and temporal logic. It is argued that abstractionism conflicts with both serious presentism and serious actualism.

This mixed method study (Explanatory Design - the Participant Selection Model) investigated the use of joint drawing (the Family Squiggle) as a family climate assessment tool for hearing families who have a deaf / hard of hearing (D/HH) child. The goal was to evaluate the possibilities of applying a quantitative approach to characterize the pictorial phenomena produced by hearing families who have a D/HH child, and then apply qualitative research approaches to better understand the meaning of these phenomena. Twenty-eight (...) hearing families (parents and child) whose child was diagnosed as D/HH and used hearing devices (hearing aids, implant) were recruited along with 16 families with a hearing child of a similar age enrolled in a mainstream school. The sessions involved a joint drawing followed by a family interview. In the quantitative stage, pictorial phenomena for which there was a significant association between the phenomena and the group of families were defined. These were: (1) The number of dominant images, (2) Images occupying less than a quarter of the page. (3) Images with accentuated outlines. (4) Moderate colorfulness with four to five colors in each drawing. (5) Minimal representation of the face. (6) Concrete rather than creative titles. (7) Muting of conflictual themes. (8) Images reminiscent of hearing devices (hearing aids, implant). In the qualitative phase, interviews were conducted with the hearing families with a D/HH child to better understand the meaning of these pictorial phenomena. The findings suggest that each of these phenomena represent the preoccupation of the family with deafness / being hard of hearing, capture a certain aspect of family dynamics, and together provide a broader and deeper picture of the family climate and the interactions between the child's family and hearing. This assessment tool may thus be utilized when verbal tools cannot be easily applied. (shrink)

Pictorial representations such as diagrams and figures are widely used in scientific literature for explanatory and descriptive purposes. The intuitive nature of pictorial representations coupled with texts foster a better understanding of the objects of study. Biological mechanisms and processes can be clearly illustrated and grasped in pictures. I argue that pictorial representations describe biological phenomena by telling stories. I elaborate on the role of narrative structures of pictures in the frontier research using a case study in (...) immunology. I articulate that pictures with an inherent narrative structure are crucial in biological sciences. (shrink)

A language is a system of signs used for communication, and linguists are tasked with, among other things, uncovering the syntax and semantics of such systems. In this paper I explore to what extent pictures fit this characterization of a language and hence would fall within the domain of linguistics. I conclude that at the very least there are well-defined systems of depiction for which we can give a precise semantics, in a familiar possible worlds framework, although pictorial propositions (...) are not derived via the linguistically familiar lexicon and recursive composition rules, but via geometric projection. I then show how sequences of pictures, like sequences of utterances, can be used to form coherent discourses. I explore in some detail extensions of the formal discourse semantics of Segmented Discourse Representation Theory to deal with comics, i.e. storytelling through picture sequences. I focus specifically on the representation of events in comics, and the integration of both symbolic and iconic elements. (shrink)