We present colorful illustrations of particular properties of functorial diamonds, in the sense of Scholze; namely profinite reflections as categorical colors.We discuss sight as site using representable functors in the condensed formalism. We illuminate diamonds using our novel constructions of categorical Ozma and Cinderella, the site of Oz, and condensed Through the Looking-Glass.

Saunders Mac Lane famously remarked that "Bourbaki just missed" formulating adjoints in a 1948 appendix (written no doubt by Pierre Samuel) to an early draft of Algebre--which then had to wait until Daniel Kan's 1958 paper on adjoint functors. But Mac Lane was using the orthodox treatment of adjoints that only contemplates the object-to-object morphisms within a category, i.e., homomorphisms. When Samuel's treatment is reconsidered in view of the treatment of adjoints using heteromorphisms or hets (object-to-object morphisms between objects (...) in different categories), then he, in effect, isolated the concept of a left representation solving a universal mapping problem. When dualized to obtain the concept of a right representation, the two halves only need to be united to obtain an adjunction. Thus Samuel was only a now-simple dualization away for formulating adjoints in 1948. Apparently, Bodo Pareigis' 1970 text was the first and perhaps only text to give the heterodox "new characterization" (i.e., heteromorphic treatment) of adjoints. Orthodox category theory uses various relatively artificial devices to avoid formally recognizing hets--even though hets are routinely used by the working mathematician. Finally we consider a "philosophical" question as to whether the most important concept in category theory is the notion of an adjunction or the notion of a representation giving a universal mapping property (where adjunctions arise as the special case of a bi-representation of dual universal mapping problems). (shrink)

Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, (...) a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (shrink)

The concept of quantum information is introduced as both normed superposition of two orthogonal sub-spaces of the separable complex Hilbert space and in-variance of Hamilton and Lagrange representation of any mechanical system. The base is the isomorphism of the standard introduction and the representation of a qubit to a 3D unit ball, in which two points are chosen. The separable complex Hilbert space is considered as the free variable of quantum information and any point in it (a wave function describing (...) a state of a quantum system) as its value as the bound variable. A qubit is equivalent to the generalization of ‘bit’ from the set of two equally probable alternatives to an infinite set of alternatives. Then, that Hilbert space is considered as a generalization of Peano arithmetic where any unit is substituted by a qubit and thus the set of natural number is mappable within any qubit as the complex internal structure of the unit or a different state of it. Thus, any mathematical structure being reducible to set theory is re-presentable as a set of wave functions and a subspace of the separable complex Hilbert space, and it can be identified as the category of all categories for any functor represents an operator transforming a set (or subspace) of the separable complex Hilbert space into another. Thus, category theory is isomorphic to the Hilbert-space representation of set theory & Peano arithmetic as above. Given any value of quantum information, i.e. a point in the separable complex Hilbert space, it always admits two equally acceptable interpretations: the one is physical, the other is mathematical. The former is a wave function as the exhausted description of a certain state of a certain quantum system. The latter chooses a certain mathematical structure among a certain category. Thus there is no way to be distinguished a mathematical structure from a physical state for both are described exhaustedly as a value of quantum information. This statement in turn can be utilized to be defined quantum information by the identity of any mathematical structure to a physical state, and also vice versa. Further, that definition is equivalent to both standard definition as the normed superposition and in-variance of Hamilton and Lagrange interpretation of mechanical motion introduced in the beginning of the paper. Then, the concept of information symmetry can be involved as the symmetry between three elements or two pairs of elements: Lagrange representation and each counterpart of the pair of Hamilton representation. The sense and meaning of information symmetry may be visualized by a single (quantum) bit and its interpretation as both (privileged) reference frame and the symmetries of the Standard model. (shrink)

That the state-of-affairs of cognitive science is not good is brought into figural salience in "What happened to cognitive science?" (Núñez et al., 2019). We extend their objective description of 'what's wrong' to a prescription of 'how to correct'. Cognitive science, in its quest to elucidate 'how we know', embraces a long list of subjects, while ignoring Mathematics (Fig. 1a, Núñez et al., 2019). Mathematics is known for making the unknown to be known (cf. solving for unknowns). This acknowledgement naturally (...) raises the question: does mathematical knowing inform knowing in general? Here we show that drawing parallels to mathematical knowing can facilitate the advancement of cognitive science (Lawvere, 1994). (shrink)

There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory. We give a heterodox treatment of adjoints using heteromorphisms that parses an adjunction into two separate parts. Then these separate parts can be recombined in a new way to define a cognate concept, the brain functor, to abstractly model the functions of perception and action of a brain. The treatment uses relatively simple category theory (...) and is focused on the interpretation and application of the mathematical concepts. (shrink)

Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics—with adjunctions being the primary lens. If adjunctions are so important in mathematics, then perhaps they will isolate concepts of some importance in the empirical sciences. But the applications of adjunctions have been hampered by an overly restrictive formulation that avoids heteromorphisms or hets. By reformulating an adjunction using hets, it is split into two parts, a left and a right semiadjunction. Semiadjunctions (...) (essentially a formulation of universal mapping properties using hets) can then be combined in a new way to define the notion of a brain functor that provides an abstract model of the intentionality of perception and action (as opposed to the passive reception of sense-data or the reflex generation of behavior). (shrink)

Many have urged that the biggest obstacles to a physicalistic understanding of consciousness are the problems raised in connection with the subjectivity of consciousness. These problems are most acutely expressed in consideration of the knowledge argument against physicalism. I develop a novel account of the subjectivity of consciousness by explicating the ways in which mental representations may be perspectival. Crucial features of my account involve analogies between the representations involved in sensory experience and the ways in which pictorial representations exhibit (...) perspectives or points of view. I argue that the resultant account of subjectivity provides a basis for the strongest response physicalists can give to the knowledge argument. (shrink)

Despite its centrality in the philosophy of cognitive science, there has been little prior philosophical work engaging with the notion of representation in contemporary NLP practice. This paper attempts to fill that lacuna: drawing on ideas from cognitive science, I introduce a framework for evaluating the representational claims made about components of neural NLP models, proposing three criteria with which to evaluate whether a component of a model represents a property and operationalising these criteria using probing classifiers, a popular analysis (...) technique in NLP (and deep learning more broadly). The project of operationalising a philosophically-informed notion of representation should be of interest to both philosophers of science and NLP practitioners. It affords philosophers a novel testing-ground for claims about the nature of representation, and helps NLPers organise the large literature on probing experiments, suggesting novel avenues for empirical research. (shrink)

How can we think about things in the outside world? There is still no widely accepted theory of how mental representations get their meaning. In light of pioneering research, Nicholas Shea develops a naturalistic account of the nature of mental representation with a firm focus on the subpersonal representations that pervade the cognitive sciences.

Many philosophers and psychologists have attempted to elucidate the nature of mental representation by appealing to notions like isomorphism or abstract structural resemblance. The ‘structural representations’ that these theorists champion are said to count as representations by virtue of functioning as internal models of distal systems. In his 2007 book, Representation Reconsidered, William Ramsey endorses the structural conception of mental representation, but uses it to develop a novel argument against representationalism, the widespread view that cognition essentially involves the manipulation of (...) mental representations. Ramsey argues that although theories within the ‘classical’ tradition of cognitive science once posited structural representations, these theories are being superseded by newer theories, within the tradition of connectionism and cognitive neuroscience, which rarely if ever appeal to structural representations. Instead, these theories seem to be explaining cognition by invoking so-called ‘receptor representations’, which, Ramsey claims, aren’t genuine representations at all—despite being called representations, these mechanisms function more as triggers or causal relays than as genuine stand-ins for distal systems. I argue that when the notions of structural and receptor representation are properly explicated, there turns out to be no distinction between them. There only appears to be a distinction between receptor and structural representations because the latter are tacitly conflated with the ‘mental models’ ostensibly involved in offline cognitive processes such as episodic memory and mental imagery. While structural representations might count as genuine representations, they aren’t distinctively mental representations, for they can be found in all sorts of non-intentional systems such as plants. Thus to explain the kinds of offline cognitive capacities that have motivated talk of mental models, we must develop richer conceptions of mental representation than those provided by the notions of structural and receptor representation. (shrink)

If emotion is not an arbitrary compilation of fixed types of (descriptive, conceptual, conative, prescriptive) content, nor a state that can be reduced to other types of pre-existing (perceptual, cognitive, behavioral) states, then what sort of thing is it really? Tom Cochrane has proposed that emotions are valent representations of situated concerns. Valent representation is a type of mental content whose function is to detect the presence or absence of certain conditions; what makes that type of content valent is that (...) without needing the mediation of any other state, a response is triggered that is disposed to increase or decrease the presence of the condition represented. I raise doubts about the plausibility of that account in light of recent work in philosophy of biology and philosophy of mind. (shrink)

Structural representations are increasingly popular in philosophy of cognitive science. A key virtue they seemingly boast is that of meeting Ramsey's job description challenge. For this reason, structural representations appear tailored to play a clear representational role within cognitive architectures. Here, however, I claim that structural representations do not meet the job description challenge. This is because even our most demanding account of their functional profile is satisfied by at least some receptors, which paradigmatically fail the job description challenge. Hence, (...) the functional profile typically associated with structural representations does not identify representational posits. After a brief introduction, I present, in the second section of the paper, the job description challenge. I clarify why receptors fail to meet it and highlight why, as a result, they should not be considered representations. In the third section I introduce what I take to be the most demanding account of structural representations at our disposal, namely Gładziejewski's account. Provided the necessary background, I turn from exposition to criticism. In the first half of the fourth section, I equate the functional profile of structural representations and receptors. To do so, I show that some receptors boast, as a matter of fact, all the functional features associated with structural representations. Since receptors function merely as causal mediators, I conclude structural representations are mere causal mediators too. In the second half of the fourth section I make this conclusion intuitive with a toy example. I then conclude the paper, anticipating some objections my argument invites. (shrink)

Cognitive representations are typically analysed in terms of content, vehicle and format. While current work on formats appeals to intuitions about external representations, such as words and maps, in this paper we develop a computational view of formats that does not rely on intuitions. In our view, formats are individuated by the computational profiles of vehicles, i.e., the set of constraints that fix the computational transformations vehicles can undergo. The resulting picture is strongly pluralistic, it makes space for a variety (...) of different formats, and is intimately tied to the computational approach to cognition in cognitive science and artificial intelligence. (shrink)

This dissertation argues that mental representation is identical to phenomenal consciousness, and everything else that appears to be both mental and a matter of representation is not genuine mental representation, but either in some way derived from mental representation, or a case of non-mental representation.

In this article, network science is discussed from a methodological perspective, and two central theses are defended. The first is that network science exploits the very properties that make a system complex. Rather than using idealization techniques to strip those properties away, as is standard practice in other areas of science, network science brings them to the fore, and uses them to furnish new forms of explanation. The second thesis is that network representations are particularly helpful in explaining the properties (...) of non-decomposable systems. Where part-whole decomposition is not possible, network science provides a much-needed alternative method of compressing information about the behavior of complex systems, and does so without succumbing to problems associated with combinatorial explosion. The article concludes with a comparison between the uses of network representation analyzed in the main discussion, and an entirely distinct use of network representation that has recently been discussed in connection with mechanistic modeling. (shrink)

This paper engages critically with anti-representationalist arguments pressed by prominent enactivists and their allies. The arguments in question are meant to show that the “as-such” and “job-description” problems constitute insurmountable challenges to causal-informational theories of mental content. In response to these challenges, a positive account of what makes a physical or computational structure a mental representation is proposed; the positive account is inspired partly by Dretske’s views about content and partly by the role of mental representations in contemporary cognitive scientific (...) modeling. (shrink)

According to a standard representationalist view cognitive capacities depend on internal content-carrying states. Recent alternatives to this view have been met with the reaction that they have, at best, limited scope, because a large range of cognitive phenomena—those involving absent and abstract features—require representational explanations. Here we challenge the idea that the consideration of cognition regarding the absent and the abstract can move the debate about representationalism along. Whether or not cognition involving the absent and the abstract requires the positing (...) of representations depends upon whether more basic forms of cognition require the positing of representations. (shrink)

In this paper, we defend a novel, multidimensional account of representational unification, which we distinguish from integration. The dimensions of unity are simplicity, generality and scope, non-monstrosity, and systematization. In our account, unification is a graded property. The account is used to investigate the issue of how research traditions contribute to representational unification, focusing on embodied cognition in cognitive science. Embodied cognition contributes to unification even if it fails to offer a grand unification of cognitive science. The study of this (...) failure shows that unification, contrary to what defenders of mechanistic explanation claim, is an important mechanistic virtue of research traditions. (shrink)

The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility. However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being always probabilistically coherent with infinitely precise degrees (...) of belief and full knowledge of all a priori truths. Ordinary subjects do not look very rational when compared to the kinds of agents usually talked about in decision theory. In this paper, I will develop an expected utility representation theorem aimed at the representation of those who are neither probabilistically coherent, logically omniscient, nor expected utility maximisers across the board—that is, agents who are frequently irrational. The agents in question may be deductively fallible, have incoherent credences, limited representational capacities, and fail to maximise expected utility for all but a limited class of gambles. (shrink)

Many debates in philosophy focus on whether folk or scientific psychological notions pick out cognitive natural kinds. Examples include memory, emotions and concepts. A potentially interesting type of kind is: kinds of mental representations (as opposed, for example, to kinds of psychological faculties). In this chapter we outline a proposal for a theory of representational kinds in cognitive science. We argue that the explanatory role of representational kinds in scientific theories, in conjunction with a mainstream approach to explanation in cognitive (...) science, suggest that representational kinds are multi-level. This is to say that representational kinds’ properties cluster at different levels of explanation and allow for intra- and inter-level projections. (shrink)

Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a result, we (...) should reject these claims, and lay the foundations of decision theory on firmer ground. (shrink)

Arguably the most foundational principle in perception research is that our experience of the world goes beyond the retinal image; we perceive the distal environment itself, not the proximal stimulation it causes. Shape may be the paradigm case of such “unconscious inference”: When a coin is rotated in depth, we infer the circular object it truly is, discarding the perspectival ellipse projected on our eyes. But is this really the fate of such perspectival shapes? Or does a tilted coin retain (...) an elliptical appearance even when we know it’s circular? This question has generated heated debate from Locke and Hume to the present; but whereas extant arguments rely primarily on introspection, this problem is also open to empirical test. If tilted coins bear a representational similarity to elliptical objects, then a circular coin should, when rotated, impair search for a distal ellipse. Here, nine experiments demonstrate that this is so, suggesting that perspectival shapes persist in the mind far longer than traditionally assumed. Subjects saw search arrays of three-dimensional “coins,” and simply had to locate a distally elliptical coin. Surprisingly, rotated circular coins slowed search for elliptical targets, even when subjects clearly knew the rotated coins were circular. This pattern arose with static and dynamic cues, couldn’t be explained by strategic responding or unfamiliarity, generalized across shape classes, and occurred even with sustained viewing. Finally, these effects extended beyond artificial displays to real-world objects viewed in naturalistic, full-cue conditions. We conclude that objects have a remarkably persistent dual character: their objective shape “out there,” and their perspectival shape “from here.”. (shrink)

Many philosophers have understood the representational dimension of affective states along the model of sense-perceptual experiences, even claiming the relevant affective experiences are perceptual experiences. This paper argues affective experiences involve a kind of personal level affective representation disanalogous from the representational character of perceptual experiences. The positive thesis is that affective representation is a non-transparent, non-sensory form of evaluative representation, whereby a felt valenced attitude represents the object of the experience as minimally good or bad, and one experiences that (...) evaluative standing as having the power to causally motivate the relevant attitude. I show this view can make sense of distinctive features of affective experiences, such as their valence and connection to value in a way which moves beyond current evaluativist views of affect. (shrink)

Nick Shea’s Representation in Cognitive Science commits him to representations in perceptual processing that are about probabilities. This commentary concerns how to adjudicate between this view and an alternative that locates the probabilities rather in the representational states’ associated “attitudes”. As background and motivation, evidence for probabilistic representations in perceptual processing is adduced, and it is shown how, on either conception, one can address a specific challenge Ned Block has raised to this evidence.

This paper discusses the intellectual relationship between Meinong and Twardowski, focusing on their ideas about representations and judgements, which are in part extraneous to Franz Brentano’s philosophy. The two philosophers addressed similar topics and their respective positions can be seen to overlap in some regards. This is shown by looking at their views on judgements about relations, intuitive and non‑intuitive representations, and Twardowski’s represented judgements, which display some strong analogies with Meinong’s assumptions.

Kant's most sustained discussion of obscure representations can be found in the first book of his Anthropology from a Pragmatic Point of View. What is puzzling is that in the middle of the section devoted to the topic, Kant asserts that “because this field can only be perceived in his passive side as a play of sensations, the theory of obscure representations belongs only to physiological anthropology, and so it is properly disregarded here.” So, do obscure representations belong to pragmatic (...) anthropology or not? Kant's official position is that they do not, yet the textual evidence—we find discussions of obscure representations in 20 years of his work on pragmatic anthropology—suggests that they do, in fact, belong here. Most of the literature on obscure representations focuses on their contribution to cognition and none has clarified what it would mean to assume a “pragmatic point of view” on obscure representations, and to study them in the context of pragmatic anthropology. My aim in this paper is to provide such clarification, focusing on Kant's discussion of our propensity to “play with” obscure representations and what he calls our “art of obscuring.”. (shrink)

Memory is not a unitary phenomenon. Even among the group of long-term individual memory representations (known in the literature as declarative memory) there seems to be a distinction between two kinds of memory: memory of personally experienced events (episodic memory) and memory of facts or knowledge about the world (semantic memory). Although this distinction seems very intuitive, it is not so clear in which characteristic or set of interrelated characteristics lies the difference. In this article, I present the different criteria (...) proposed in the philosophical and scientific literature in order to account for this distinction: (1) the vehicle of representation; (2) the grammar of the verb “to remember”; (3) the cause of the memory; (4) the memory content; and (5) the phenomenology of memory representations. Whereas some criteria seem more plausible than others, I show that all of them are problematic and none of them really fulfill their aim. I then briefly outline a different criterion, the affective criterion, which seems a promising line of research to try to understand the grounds of this distinction. (shrink)

Classic change blindness is the phenomenon where seemingly obvious changes which coincide with visual disruptions (such as blinks or brief blanks) go unnoticed by an attentive observer. Some early work into the causes of classic change blindness suggested that any pre-change stimulus representation is overwritten by a representation of the altered post-change stimulus, preventing change detection. However, recent work revealed that even when observers do maintain memory representations of both the pre- and post-change stimulus states, they can still miss the (...) change, suggesting that change blindness can also arise from a failure to compare the stored representations. Here we study slow change blindness, a different but related phenomenon that occurs even in the absence of visual disruptions when the change occurs sufficiently slowly, to determine whether it could be explained by conclusions from classic change blindness. Across three different slow change blindness experiments we found that observers, who consistently failed to notice the change, had access to at least two memory representations of the changing display. One representation was precise but short-lived: a relatively detailed representation of the more recent states of slow-change display, but fragile. The other representation lasted longer but was fairly general: stable but too coarse to differentiate the various stages of the changing display. These findings suggest that although multiple representations are formed, the failure to compare hypothesis might not explain slow change blindness; even if a comparison were made, the representations formed would be either too sparse (longer term stores) or too fragile (short-lived stores) for such a comparison to be informative about a change. (shrink)

A straightforward way of thinking about perception is in terms of perceptual representation. Perception is the construction of perceptual representations that represent the world correctly or incorrectly. This way of thinking about perception has been questioned recently by those who deny that there are perceptual representations. This article examines some reasons for and against the concept of perceptual representation and explores some potential ways of resolving this debate. Then it analyzes what perceptual representations may be: if they attribute properties to (...) entities, what are these attributed properties, and what are the entities they are attributed to. (shrink)

This essay presents a fully inferentialist-expressivist account of scientific representation. In general, inferentialist approaches to scientific representation argue that the capacity of a model to represent a target system depends on inferences from models to target systems. Inferentialism is attractive because it makes the epistemic function of models central to their representational capacity. Prior inferentialist approaches to scientific representation, however, have depended on some representational element, such as denotation or representational force. Brandom’s Making It Explicit provides a model of how (...) to fully discharge such representational vocabulary, but it cannot be applied directly to scientific representations. Pursuing a strategy parallel to Brandom’s, this essay begins with an account of how surrogative inference is justified. Scientific representation and the denotation of model elements are then explained in terms of surrogative inference by treating scientific representation and denotation as expressive, analogous to Brandom’s account of truth. The result is a thoroughgoing inferentialism: M is a scientific representation of T if and only if M has scientifically justified surrogative consequences that are answers to questions about T. (shrink)

Much recent cognitive neuroscientific work on body knowledge is representationalist: “body schema” and “body images”, for example, are cerebral representations of the body (de Vignemont 2009). A framework assumption is that representation of the body plays an important role in cognition. The question is whether this representationalist assumption is compatible with the variety of broadly situated or embodied approaches recently popular in the cognitive neurosciences: approaches in which cognition is taken to have a ‘direct’ relation to the body and to (...) the environment. A “direct” relation is one where the boundaries between the body and the head, or between the environment and the animal are not theoretically important in the understanding of cognition. These boundaries do not play a theoretically privileged role in cognitive explanations of behavior. But representationalism appears to put a representational veil between the locus of cognition and that which is represented, making cognitive relations to the body and to the environment be indirect, with a high associated computational load. For this reason, direct approaches have tried to minimize the use of internal representations (Suchman 1987; Barwise 1987; Agre and Chapman 1987; Brooks 1992; Thelen and Smith 1994; van Gelder 1995; Port and van Gelder 1995; Clark 1997, 1999; Rupert 2009, p. 180). Does a cognitive neuroscience committed to direct relations rule out a representationalist approach to body knowledge? Or is direct representationalism possible? (shrink)

This is a chapter from my introductory book *Perception* covering the representational view of experience. I use the Ramsey-Lewis method to define the theoretical term "experiential representation". I clarify and discuss various questions for representationalists, for instance, "how rich is the content of experience?" and "is the content of visual experience singular or general?" Finally, I address some objections to representationalism - in particular, that it cannot explain perceptual presence (John Campbell), and that it cannot explain the "laws of appearance" (...) (constraints on how things can appear). (shrink)

This paper develops a theory of analog representation. We first argue that the mark of the analog is to be found in the nature of a representational system’s interpretation function, rather than in its vehicles or contents alone. We then develop the rulebound structure theory of analog representation, according to which analog systems are those that use interpretive rules to map syntactic structural features onto semantic structural features. The theory involves three degree-theoretic measures that capture three independent ways in which (...) a system can be more or less analog. We explain how our theory improves upon prior accounts of analog representation, provides plausible diagnoses for novel challenge cases, extends to hybrid systems that are partially analog and partially symbolic, and accounts for some of the advantages and disadvantages of representing analogically versus symbolically. (shrink)

The main task of this paper is to understand if and how static images like photographs can represent and/or depict temporal extension (duration). In order to do this, a detour will be necessary to understand some features of the nature of photographic representation and depiction in general. This important detour will enable us to see that photographs (can) have a narrative content, and that the skilled photographer can 'tell a story' in a very clear sense, as well as control and (...) guide the attention of the spectator of the photograph. The understanding and defence of this claim is a secondary aim of this paper, and it will then allow us to provide a good treatment of the particular case of photographic representation and depiction of temporal extension. (shrink)

This paper deals with the Stoic concept of misprinted representation (φαντασία παρατυπωτική), which has received little attention compared to other concepts of Stoic epistemology and philosophy of mind. I aim at showing that a better understanding of this concept is important for grasping some elements of the Stoic account of mental representations that have been ignored or misunderstood in modern Stoic scholarship. First, by clarifying the status of the misprinted representation as a genuine representation, we can understand what it means (...) (and does not mean) to say, from the Stoic point of view, that the intentional object of a representation is the external object that caused it. Second, by understanding this issue, we obtain some resources to deal with the ambiguity of the preposition ἀπό in the definition of cognitive representation. Thus, the concept of misprinted representation proves to be important for appropriately understanding the Stoic concepts of representation and cognitive representation. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

The current orthodoxy in cognitive science, what I describe as a commitment to deep representationalism, faces intractable problems. If we take these objections seriously, and I will argue that we should, there are two possible responses: 1. We are mistaken that representation is the locus of our cognitive capacities — we manage to be the successful cognitive agents in some other, non-representational, way; or, 2. Our representational capacities do give us critical cognitive advantages, but they are not fundamental to us (...) qua human beings. As Andy Clark has convincingly argued, antirepresentationalism, option one, is explanatorily weak. Consequently, I will argue, we need to take the second option seriously. In the first half of the paper I rehearse the problems with the current representational view and in the second half of the paper I defend and give a positive sketch of a two-systems view of cognition – a non-representational perceptual system coupled with a representational language-dependent one – and look at some consequences of the view. (shrink)

Since its formal definition over sixty years ago, category theory has been increasingly recognized as having a foundational role in mathematics. It provides the conceptual lens to isolate and characterize the structures with importance and universality in mathematics. The notion of an adjunction (a pair of adjoint functors) has moved to center-stage as the principal lens. The central feature of an adjunction is what might be called “determination through universals” based on universal mapping properties. A recently developed “heteromorphic” theory (...) about adjoints suggests a conceptual structure, albeit abstract and atemporal, for how new relatively autonomous behavior can emerge within a system obeying certain laws. The focus here is on applications in the life sciences (e.g., selectionist mechanisms) and human sciences (e.g., the generative grammar view of language). (shrink)

According to orthodox representationalism, perceptual states have constitutive veridicality or accuracy conditions. In defense of this view, several philosophers—most notably Tyler Burge—employ a realist strategy that turns on the purported explanatory ineliminability of representational posits in perceptual science. I argue that Burge’s version of the realist strategy fails as a defense of orthodox representationalism. However, it may vindicate a different kind of representationalism.

Epistemic justifications for democracy have been offered in terms of two different aspects of decision-making: voting and deliberation, or ‘votes’ and ‘talk.’ The Condorcet Jury Theorem is appealed to as a justification in terms votes, and the Hong-Page “Diversity Trumps Ability” result is appealed to as a justification in terms of deliberation. Both of these, however, are most plausibly construed as models of direct democracy, with full and direct participation across the population. In this paper, we explore how these results (...) hold up if we vary the model so as to reflect the more familiar democratic structure of a representative hierarchy. We first recount extant analytic work that shows that representation inevitably weakens the voting results of the Condorcet Jury Theorem, but we question the ability of that result to shine light on real representative systems. We then show that, when we move from votes to talk, as modeled in Hong-Page, representation holds its own and even has a slight edge. (shrink)

The Enhanced Indispensability Argument appeals to the existence of Mathematical Explanations of Physical Phenomena to justify mathematical Platonism, following the principle of Inference to the Best Explanation. In this paper, I examine one example of a MEPP—the explanation of the 13-year and 17-year life cycle of magicicadas—and argue that this case cannot be used defend the EIA. I then generalize my analysis of the cicada case to other MEPPs, and show that these explanations rely on what I will call ‘optimal (...) representations’, which are representations that capture all that is relevant to explain a physical phenomenon at a specified level of description. In the end, because the role of mathematics in MEPPs is ultimately representational, they cannot be used to support mathematical Platonism. I finish the paper by addressing the claim, advanced by many EIA defendants, that quantification over mathematical objects results in explanations that have more theoretical virtues, especially that they are more general and modally stronger than alternative explanations. I will show that the EIA cannot be successfully defended by appealing to these notions. (shrink)

The democratic criteria for representation in the European Union are complex since its representation involves several delegation mechanisms and institutions. This paper develops institutional design principles for the representation of peoples and individuals and suggests reform options of the European Union on the basis of the theory of multilateral democracy. In particular, it addresses how the equality of individuals can be realised in EU representation while guaranteeing the mutual recognition of peoples. Unlike strict intergovernmental institutions, the EU requires an additional (...) and independent legislative chamber in which individuals are directly represented. However, strict equality of individuals cannot be the guiding principle for this chamber. In order to avoid the overruling of peoples through supranational majorities, it is necessary to bind the chamber's composition by a principle of degressive proportionality. The representation of peoples, on the other hand, needs to be connected to their domestic democratic institutions. (shrink)

We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infi nite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfi es a condition that we call Polarization.

Linguistic representations are taken by some to be representations of something, specifically of Standard Linguistic Entities, such as phonemes, clauses, noun phrases etc. This perspective takes them to be intentional. Rey (2021) further argues that the SLEs themselves are inexistent. Here I argue that linguistic representations are simply structures, abstractions of brain states, and hence not intentional, and show how they nevertheless connect to the systems that use them.

Cognition is commonly taken to be computational manipulation of representations. These representations are assumed to be digital, but it is not usually specified what that means and what relevance it has for the theory. I propose a specification for being a digital state in a digital system, especially a digital computational system. The specification shows that identification of digital states requires functional directedness, either for someone or for the system of which it is a part. In the case or digital (...) representations, to be a token of a representational type, where the function of the type is to represent. [An earlier version of this paper was discussed in the web-conference "Interdisciplines" https://web.archive.org/web/20100221125700/http://www.interdisciplines.org/adaptation/papers/7 ]. (shrink)

The idea that there are representations with a double direction of fit has acquired a pride of place in contemporary debates on the ontology of institutions. This paper will argue against the very idea of anything at all having both directions of fit. There is a simple problem which has thus far gone unnoticed. The suggestion that there are representations with both directions of fit amounts to a suggestion that, in cases of discrepancy between a representation and the world, both (...) should change—the representation and the world. But that would merely amount to another discrepancy, and so both should change again, ad infinitum. The paper will first elucidate the notion of a “direction of fit” and clarify how the criticism to be presented here differs from earlier criticisms (Section 1).The next section sheds some light on why and how acts and attitudes with both directions of fit have seemed to play a part in explaining the existence of institutional reality (Section 2). The next sections present the argument against any representations with both directions of fit, relying on a normative understanding of the distinction. The argument will have three steps (Sections 3, 4, and 5). The section that follows shows that the criticism also applies to the dispositional understanding of the notion of a direction of fit (Section 6), and then the paper asks whether a third kind of reading would be available (Section 7) and whether the infallibility of the relevant representations would be of help (Section 8). Finally, the paper assesses briefly the consequences of dropping the notion of two directions of fit (Section 9). (shrink)

One of the most significant characteristics of intentional states is the fact that they represent their intentional objects under selec￾tive aspects (or modes of presentation); that is, that they manifest an aspectual shape (Searle, 1992). Surprisingly however, although this remarkable feature is widely recognized little has been done to explain what makes representation aspect-relative in the first￾place. In this article I attempt to outline an answer to this question. I begin with a critique of Searle’s explanation of aspectual shape as (...) nchored in conscious experience. I argue next that, since to represent an object under an aspect is to represent it relative to a selective set of properties, the task – from the perspective of a theory of mental representation – is to explain what makes intentional states property-relative. It is then argued that while this task cannot be handled properly by standard (in particular computational-representational) theories of mental representa￾tion, a shift towards an action-based framework for theories of perception and representation promises to provide the key with which to unlock the puzzle. (shrink)

This chapter is devoted to criticisms of the views of propositions defended by my co-authors, Jeff King and Scott Soames. The focus is on criticism of their attempts to explain the representational properties of propositions. The criticisms are varied, but one theme is a tension between their view that our actions can explain the representational properties of propositions and their commitment to the idea that propositions have their representational properties essentially.