This paper argues that phenomenal or internal metrical spaces are redundant posits. It is shown that we need not posit an internal space-time frame, as the physical space-time suffices to explain geometrical perception, memory and planning. More than the internal space-time frame, the idea of a phenomenal colour space has lent credibility to the idea of internal spaces. It is argued that there is no phenomenal colour space that underlies the various psychophysical colour spaces; it is parasitic upon physical and (...) psychophysical colour spaces. The argumentation is further extended to other sensory spaces and generalised quality spaces. (shrink)

There is a long and distinguished tradition in philosophy and psychology according to which the mind’s fundamental, foundational connection to the world is made by connecting perceptually to features of objects. On this picture, which we’ll call feature prioritarianism, minds like ours first make contact with the colors, shapes, and sizes of distal items, and then, only on the basis of the representations so obtained, build up representations of the objects that bear these features. The feature priority view maintains, then, (...) that our perception/knowledge of objects asymmetrically depends on our perception/knowledge of simple features. This paper has two aims. First, we will present evidence, drawn from a variety of perceptual effects, that feature prioritarianism cannot be true, since there are cases that speak against the priority of feature representations in perceptual processing. Instead, we claim that the evidence supports an alternative —-and more complex—- no-priority view. Second, we will offer a framework for a no-priority view that both captures the cases we cite and provides a more sensible architecture in which to understand a variety of productive projects in perceptual science, and show how the framework cross-cuts some recent discussions in philosophy of perception. (shrink)

For nearly thirty years, there has been a consensus (at least in English-speaking countries) that reductionism is a mistake and that there are autonomous special sciences. This consensus has been based on an argument from multiple realizability. But Jaegwon Kim has argued persuasively that the multiple realizability argument is flawed.1 I will sketch the recent history of the debate, arguing that much --but not all--of the anti-reductionist consensus survives Kim's critique. This paper was originally titled "Anti-Reductionism Strikes Back", but in (...) the course of writing the paper, I came to think that the concepts used in the debate would not serve either position very well. (shrink)

How veridical is perception? Rather than representing objects as they actually exist in the world, might perception instead represent objects only in terms of the utility they offer to an observer? Previous work employed evolutionary modeling to show that under certain assumptions, natural selection favors such “strict‐interface” perceptual systems. This view has fueled considerable debate, but we think that discussions so far have failed to consider the implications of two critical aspects of perception. First, while existing models have explored single (...) utility functions, perception will often serve multiple largely independent goals. (Sometimes when looking at a stick you want to know how appropriate it would be as kindling for a campfire, and other times you want to know how appropriate it would be as a weapon for self‐defense.) Second, perception often operates in an inflexible, automatic manner—proving “impenetrable” to shifting higher‐level goals. (When your goal shifts from “burning” to “fighting,” your visual experience does not dramatically transform.) These two points have important implications for the veridicality of perception. In particular, as the need for flexible goals increases, inflexible perceptual systems must become more veridical. We support this position by providing evidence from evolutionary simulations that as the number of independent utility functions increases, the distinction between “interface” and “veridical” perceptual systems dissolves. Although natural selection evaluates perceptual systems only on their fitness, the most fit perceptual systems may nevertheless represent the world as it is. (shrink)

Existing research in color naming and categorization primarily reflects two opposing views: A Cultural Relativist view that posits color perception is greatly shaped by culturally specific language associations and perceptual learning, and a Universalist view that emphasizes panhuman shared color processing as the basis for color naming similarities within and across cultures. Recent empirical evidence finds color processing differs both within and across cultures. This divergent color processing raises new questions about the sources of previously observed cultural coherence and cross-cultural (...) universality. The present article evaluates the relevance of individual variation on the mainstream model of color naming. It also presents an alternate view that specifies how color naming and categorization is shaped by both panhuman cognitive universals and socio-cultural evolutionary processes. This alternative view, expressed, in part, using an Interpoint Distance Model of color categorization, is compatible with new empirical results showing divergent color processing within and across cultures. It suggests that universalities in color naming and categorization may naturally arise across cultures because color language and color categories primarily reflect culturally modal linguistic mappings, and categories are shaped by universal cognitive constructs and culturally salient features of color. Thus, a shared cultural representation of color based on widely shared cognitive dimensions may be the proper foundation for universalities of color naming and categorization. Across cultures this form of representation may result from convergent responses to similar pressures on color lexicon evolution. (shrink)

What is the nature of number systems and arithmetic that we use in science for quantification, analysis, and modeling? I argue that number concepts and arithmetic are neither hardwired in the brain, nor do they exist out there in the universe. Innate subitizing and early cognitive preconditions for number— which we share with many other species—cannot provide the foundations for the precision, richness, and range of number concepts and simple arithmetic, let alone that of more complex mathematical concepts. Numbers and (...) arithmetic, and mathematics in general, have unique features—precision, objectivity, rigor, generalizability, stability, symbolizability, and applicability to the real world—that must be accounted for. They are sophisticated concepts that developed culturally only in recent human history. I suggest that numbers and arithmetic are realized through precise combinations of non-mathematical everyday cognitive mechanisms that make human imagination and abstraction possible. One such mechanism, conceptual metaphor, is a neurally instantiated inference-preserving cross-domain mapping that allows the conceptualization of abstract entities in terms of grounded bodily experience. I analyze how the inferential organization of the properties and “laws” of arithmetic emerge metaphorically from everyday meaningful actions. Numbers and arithmetic are thus—outside of natural selection—the product of the biologically constrained interaction of individuals with the appropriate cultural and historical phenotypic variation supported by language, writing systems, and education. (shrink)

Subfocal Color Categorization and Naming: The Role of Exposure to Language and Professional Experience The current state of the debate on the linguistic factors in color perception and categorization is reviewed. Developmental and learning studies were hitherto almost ignored in this debate. A simple experiment is reported in which 20 Academy of Fine Arts, Faculty of Painting students' performance in color discrimination and naming tasks was compared to the performance of 20 Technical University students. Subfocal colors were used. While there (...) was no difference in overall discrimination ability, AFA students had a much richer and specialized color vocabulary. Both groups also applied different strategies of discrimination and naming. However, naming system in neither group was coherent. This suggests that naming played primarily the role of markers for control processes rather than names for categories. It is concluded that up-to-date debate is too simplified and a complex model of interrelations between perceptual categorization and naming framed in the developmental context is needed rather than the search for a simple answer "language", "environment", or "perceptual universals". (shrink)

Language research is currently in a state of flux. The phenomenon of language is not merely the topic of investigation in linguistics, it is examined by a multitude of scholars with different scientific backgrounds. In order to examine how these various disciplines approach language, a think-tank was founded in 2002, called DITO, Dynamisch Inter(-en trans)disciplinair onderzoek, or Dynamic Inter- (and trans)disciplinary Research. The think-tank is located at the Belgian Vrije Universiteit Brussel (Free University of Brussels). This book provides short introductory (...) articles to the language research conducted by some of the think-tank’s most important members, from within the point of view of the following 5 disciplines: philosophy of evolutionary biology, cognitive science, neuroscience, sign language research and artificial intelligence. (shrink)

There is certainly a need for a framework to guide the study of the physiological mechanisms underlying the experience of music and the emotions that music evokes. However, this framework should be organised hierarchically, with musical anticipation as its fundamental mechanism.

Shepard has argued that a universal law should govern generalization across different domains of perception and cognition, as well as across organisms from different species or even different planets. Starting with some basic assumptions about natural kinds, he derived an exponential decay function as the form of the universal generalization gradient, which accords strikingly well with a wide range of empirical data. However, his original formulation applied only to the ideal case of generalization from a single encountered stimulus to a (...) single novel stimulus, and for stimuli that can be represented as points in a continuous metric psychological space. Here we recast Shepard's theory in a more general Bayesian framework and show how this naturally extends his approach to the more realistic situation of generalizing from multiple consequential stimuli with arbitrary representational structure. Our framework also subsumes a version of Tversky's set-theoretic model of similarity, which is conventionally thought of as the primary alternative to Shepard's continuous metric space model of similarity and generalization. This unification allows us not only to draw deep parallels between the set-theoretic and spatial approaches, but also to significantly advance the explanatory power of set-theoretic models. Key Words: additive clustering; Bayesian inference; categorization; concept learning; contrast model; features; generalization; psychological space; similarity. (shrink)

Examples from Archimedes, Galileo, Newton, Einstein, and others suggest that fundamental laws of physics were—or, at least, could have been—discovered by experiments performed not in the physical world but only in the mind. Although problematic for a strict empiricist, the evolutionary emergence in humans of deeply internalized implicit knowledge of abstract principles of transformation and symmetry may have been crucial for humankind's step to rationality—including the discovery of universal principles of mathematics, physics, ethics, and an account of free will that (...) is compatible with determinism. (shrink)

A productive way to think about imagistic mental models of physical systems is as though they were sources of quasi‐empirical evidence. People depict or imagine events at those points in time when they would experiment with the world if possible. Moreover, just as they would do when observing the world, people induce patterns of behavior from the results depicted in their imaginations. These resulting patterns of behavior can then be cast into symbolic rules to simplify thinking about future problems and (...) to reveal higher order relationships. Using simple gear problems, three experiments explored the occasions of use for, and the inductive transitions between, depictive models and number‐based rules. The first two experiments used the convergent evidence of problem‐solving latencies, hand motions, referential language and error data to document the initial use of a model, the induction of rules from the modeling results, and the fallback to a model when a rule fails. The third experiment explored the intermediate representations that facilitate the induction of rules from depictive models. The strengths and weaknesses of depictive modeling and more analytic systems of reasoning are delineated to motivate the reasons for these transitions. (shrink)

We disagree with Juslin & Vll's (J&V's) thesis that music-evoked emotions are indistinguishable from other emotions in both their nature and underlying mechanisms and that music just induces some emotions more frequently than others. Empirical evidence suggests that frequency differences reflect the specific nature of music-evoked emotions: aesthetic and reactive rather than utilitarian and proactive. Additional mechanisms and determinants are suggested as predictors of emotions triggered by music.

Does natural selection favor veridical percepts—those that accurately depict objective reality? Perceptual and cognitive scientists standardly claim that it does. Here we formalize this claim using the tools of evolutionary game theory and Bayesian decision theory. We state and prove the “Fitness-Beats-Truth Theorem” which shows that the claim is false: If one starts with the assumption that perception involves inference to states of the objective world, then the FBT Theorem shows that a strategy that simply seeks to maximize expected-fitness payoff, (...) with no attempt to estimate the “true” world state, does consistently better. More precisely, the FBT Theorem provides a quantitative measure of the extent to which the fitness-only strategy dominates the truth strategy, and of how this dominance increases with the size of the perceptual space. The FBT Theorem supports the Interface Theory of Perception, which proposes that our perceptual systems have evolved to provide a species-specific interface to guide adaptive behavior, and not to provide a veridical representation of objective reality. (shrink)

Classical (Bayesian) probability (CP) theory has led to an influential research tradition for modeling cognitive processes. Cognitive scientists have been trained to work with CP principles for so long that it is hard even to imagine alternative ways to formalize probabilities. However, in physics, quantum probability (QP) theory has been the dominant probabilistic approach for nearly 100 years. Could QP theory provide us with any advantages in cognitive modeling as well? Note first that both CP and QP theory share the (...) fundamental assumption that it is possible to model cognition on the basis of formal, probabilistic principles. But why consider a QP approach? The answers are that (1) there are many well-established empirical findings (e.g., from the influential Tversky, Kahneman research tradition) that are hard to reconcile with CP principles; and (2) these same findings have natural and straightforward explanations with quantum principles. In QP theory, probabilistic assessment is often strongly context- and order-dependent, individual states can be superposition states (that are impossible to associate with specific values), and composite systems can be entangled (they cannot be decomposed into their subsystems). All these characteristics appear perplexing from a classical perspective. However, our thesis is that they provide a more accurate and powerful account of certain cognitive processes. We first introduce QP theory and illustrate its application with psychological examples. We then review empirical findings that motivate the use of quantum theory in cognitive theory, but also discuss ways in which QP and CP theories converge. Finally, we consider the implications of a QP theory approach to cognition for human rationality. (shrink)

In this article, I argue that popular explanatory frameworks in perceptual psychology suggest the truth of color realism. I focus on perceptual judgments and their evidential basis: namely perceptual representation. I first draw a distinction between two sorts of normativities with respect to which we can evaluate representational capacities and systems: biological and psychological normativities. The former is defined in terms of evolutionary fitness, and the latter in terms of representational accuracy. Generally, representational systems achieve psychological and biological success hand (...) in hand, but in special circumstances, a representational system can be such that it serves the organism best while not generally furnishing the organism with accurate representations. I argue in this essay that an explanation how and why our ancestors developed color vision that cleaves its biological success conditions from its psychological success conditions cannot be given unless we are prepared to say the same about the visual perception of distance and other geometrical features of the world. Moreover, it is difficult to see how the anti-realist could begin to specify psychological success conditions for color representations. Hence, we ought to accept the biological utility of color vision as evidence that it is typically representationally successful, and regard our perceptual judgments about color as generally true. (shrink)

Measuring perceived similarity is an important issue in visual perception of faces, since a measure of the perceived similarity between faces may be used to investigate fundamental tasks like face categorization and recognition. Despite its fundamental role, measuring perceived similarity between faces is not trivial from both a theoretical and methodological point of view. In this paper we present theoretical arguments that undermine the method currently most used to measure perceived similarity between faces in visual perception, and we propose an (...) alternative method. We finally compare the two methods and find some empirical evidence that the proposed method can provide a more reliable evaluation of the perceived similarity between faces. (shrink)

Shepard has supposed that the mind is stocked with innate knowledge of the world and that this knowledge figures prominently in the way we see the world. According to him, this internal knowledge is the legacy of a process of internalization; a process of natural selection over the evolutionary history of the species. Shepard has developed his proposal most fully in his analysis of the relation between kinematic geometry and the shape of the motion path in apparent motion displays. We (...) argue that Shepard has made a case for applying the principles of kinematic geometry to the perception of motion, but that he has not made the case for injecting these principles into the mind of the percipient. We offer a more modest interpretation of his important findings: that kinematic geometry may be a model of apparent motion. Inasmuch as our recommended interpretation does not lodge geometry in the mind of the percipient, the motivation of positing internalization, a process that moves kinematic geometry into the mind, is obviated. In our conclusion, we suggest that cognitive psychologists, in their embrace of internal mental universals and internalization may have been seduced by the siren call of metaphor. Key Words: apparent motion; imagery; internalization; inverse projection problem; kinematic geometry; measurement; metaphors of mind. (shrink)

We consider the question of the manner of the internalization of the geometry and topology of physical space in the mind, both the mechanism of internalization and precisely what structures are internalized. Though we will not argue for the point here, we agree with the long tradition which holds that an understanding of this issue is crucial for addressing many metaphysical and epistemological questions concerning space.

A possible solution is offered to help resolve the “two times problem” regarding the veridical and illusory nature of time. First it is recognized that the flow of time is part of a wider array of temporal experiences referred to as manifest time, all of which need to be reconciled. Then, an information gathering and utilizing system model is used as a basis for a view of manifest time. The model IGUS robot of Hartle that solves the “unique present” debate (...) is enhanced with veridical and illusory components of not only the flow of time but also the larger entity of manifest time, providing a dualistic IGUS robot that represents all of the important temporal experiences. Based upon a variety of prior experiments, that view suggests that the veridical system is a reflection of accepted spacetime cosmologies and through natural selection begets the illusory system for functional purposes. Thus, there are not two opposing times, one outside and one inside the cranium. There is just one fundamental physical time which the brain developed, now possesses and is itself sufficient for adaption but then enhances. The illusory system is intended to provide a more satisfying experience of physical time, and better adaptive behavior. Future experiments to verify that view are provided. With a complete veridical system of temporal experiences there may be less need to reify certain temporal experiences so that the two times problem is less of a problem and more of a phenomenon. (shrink)

There is a long standing debate as to whether or not time is ‘real’ or illusory, and whether or not human time is a direct reflection of physical time. Differing spacetime cosmologies have opposing views. Exactly what human time entails has, in our opinion, led to the failure to resolve this ‘two times’ problem. To help resolve this issue we propose a dualistic model of human time in which each component has both an illusory and non-illusory aspect. With the dualistic (...) model we are able to provide experimental tests for all of the human time assertions of 10 chosen spacetime cosmologies. The illusory aspect of the ‘present,’ i.e. a ‘unique present’ was confirmed. An information gathering and utilizing system was constructed using a virtual reality apparatus allowing the observer to experientially roam back and forth along the worldline ad lib. The phenomenon of ‘change’ was experimentally found to be illusory at high frequency observation and non-illusory at low frequency observation, the latter phenomenon coinciding with ‘change’ referred to in the ‘Order of Time’ and ‘Relativity Refounded’ views. Additional experiments are presented indicating that both motion and temporality are dualistic. In sum, the dualistic model of human time allows for the existence of both illusory and non-illusory aspects of human time that are not in conflict with one another. It also provides experimental evidence for various spacetime cosmological assertions regarding human time. (shrink)

Perceptual completion fills the gap for discrete perception to become continuous. Similarly, dynamic perceptual completion provides an experience of dynamic continuity. Our recent discovery of the ‘happening’ element of DPC completes the total experience for dynamism in the flow of time. However, a phenomenological explanation for these experiences is essential. The Snapshot Hypotheses especially the Dynamic Snapshot View provides the most comprehensive explanation. From that understanding the ‘two times’ problem can be addressed. The static time of spacetime cosmologies has been (...) irreconcilable with the dynamic FOT. Dismissing the FOT as an illusion is unsatisfactory. Therefore, we provide four hypotheses for the TTP.1) Since cosmological static time demands that all events are discrete, DPC elements for dynamism should likewise be expected to be discrete and accounted for by a snapshot phenomenology such as the DSV. 2) If temporality can be demonstrated to be similar to apparent motion by being a snapshot phenomenon and not demanding temporal extension it would confirm the DSV and permit reconciliation with static time. 3) If the ‘present moment’ is subjective as static time theories suggest, it should be possible experimentally for an observer to choose his own ‘present’ by moving to various points in the past with the aid of virtual reality. 4) If dynamism e.g. motion can be precluded without significant information loss or violating physics principles it is a cognitive add-on, thereby contradicting non-static time theories which suggest that time is ‘real.’ We confirm those hypotheses. (shrink)

The idea that perceptual and cognitive systems must incorporate knowledge about the structure of the environment has become a central dogma of cognitive theory. In a Bayesian context, this idea is often realized in terms of “tuning the prior”—widely assumed to mean adjusting prior probabilities so that they match the frequencies of events in the world. This kind of “ecological” tuning has often been held up as an ideal of inference, in fact defining an “ideal observer.” But widespread as this (...) viewpoint is, it directly contradicts Bayesian philosophy of probability, which views probabilities as degrees of belief rather than relative frequencies, and explicitly denies that they are objective characteristics of the world. Moreover, tuning the prior to observed environmental frequencies is subject to overfitting, meaning in this context overtuning to the environment, which leads (ironically) to poor performance in future encounters with the same environment. Whenever there is uncertainty about the environment—which there almost always is—an agent's prior should be biased away from ecological relative frequencies and toward simpler and more entropic priors. (shrink)

We criticise Shepard's notions of “invariance” and “universality,” and the incorporation of Shepard's work on inference into the general framework of his paper. We then criticise Tenenbaum and Griffiths' account of Shepard (1987b), including the attributed likelihood function, and the assumption of “weak sampling.” Finally, we endorse Barlow's suggestion that minimum message length (MML) theory has useful things to say about the Bayesian inference problems discussed by Shepard and Tenenbaum and Griffiths. [Barlow; Shepard; Tenenbaum & Griffiths].

The standard approach to the so-called paradoxes of identity has been to argue that these paradoxes do not essentially concern the notion of identity but rather betray misconceptions on our part regarding other metaphysical notions, like that of an object or a property. This paper proposes a different approach by pointing to an ambiguity in the identity predicate and arguing that the concept of identity that figures in many ordinary identity claims, including those that appear in the paradoxes, is not (...) the traditional philosophical concept but one that can be defined in terms of relevant similarity. This approach to the paradoxes will be argued to be superior to the standard one. (shrink)

Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that (...) are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. (shrink)

The rejection of behaviorism in the 1950s and 1960s led to the view, due mainly to Noam Chomsky, that language must be studied by looking at the mind and not just at behavior. It is an understatement to say that Chomskyan linguistics dominates the field. Despite being the overwhelming majority view, it has not gone unchallenged, and the challenges have focused on different aspects of the theory. What is almost universally accepted, however, is Chomsky’s view that understanding language demands a (...) theory that posits mental states that represent rules of language. Call this claim, following Cowie (1999), Representationalism or (R). According to (R), ‘‘[e]xplaining language mastery and acquisition requires the postulation of contentful mental states and processes involving their manipulation’’ (Cowie, 1999, p. 154). Although (R) is nothing more than the general assumption on which cognitive psychology is founded applied to the case of language, even it has had its detractors. Critics have argued that linguistic competence should not in fact be thought of as based on the possession of a body of linguistic knowledge but should be thought of, rather, as a kind of skill. This is an important challenge because one might be inclined to think that no recognizable form of Chomskyan linguistics could withstand the falsification of (R). In this paper we attempt to show that in fact (R) could be false without doing much damage to Chomskyan linguistics at all. Indeed, it is possible that the Chomskyan position could be made more coherent by adopting the view we will sketch. Our claim, therefore, is that critics of (R) might be right, but that this does not obviously make them serious critics of the Chomskyan program. (shrink)

Visual space can be distinguished from physical space. The first is found in visual experience, while the second is defined independently of perception. Theorists have wondered about the relation between the two. Some investigators have concluded that visual space is non-Euclidean, and that it does not have a single metric structure. Here it is argued that visual space exhibits contraction in all three dimensions with increasing distance from the observer, that experienced features of this contraction are not the same as (...) would be the experience of a perspective projection onto a fronto-parallel plane, and that such contraction is consistent with size constancy. These properties of visual space are different from those that would be predicted if spatial perception resulted from the successful solution of the inverse problem. They are consistent with the notion that optical constraints have been internalized. More generally, they are also consistent with the notion that visual spatial structures bear a resemblance relation to physical spatial structures. This notion supports a type of representational relation that is distinct from mere causal correspondence. The reticence of some philosophers and psychologists to discuss the structure of phenomenal space is diagnosed in terms of the simple materialism and the functionalism of the 1970s and 1980s. (shrink)

Experiments with remote perception and Random Event Generators (REG) performed over the last decades show small but significant anomalous effects. Since these effects seem to be independent of spatial and temporal distance, they appear to be in disagreement with the standard scientific worldview. A very simple explanation of quantum mechanics is pre- sented, rejecting all unjustified claims about the world. A view of mind in agreement with cognitive neuroscience is introduced. It is argued that mind and consciousness are emer- gent (...) properties of the brain and are understandable without any nonphysical assumptions. A plausible explanation of the results of anomalous experiments, based on the concept of synchronicity, introduced by C.G. Jung and advocated by W. Pauli, is offered. A proof is given that strong correlations should exist between any systems that once interacted. Synchronicity events between parts of the brain and physical objects may be sufficient to explain the results of anomalous experiments. Standard physics is sufficient to understand these phenomena. Motto. (shrink)

Kurt Gödel wrote (1964, p. 272), after he had read Husserl, that the notion of objectivity raises a question: “the question of the objective existence of the objects of mathematical intuition (which, incidentally, is an exact replica of the question of the objective existence of the outer world)”. This “exact replica” brings to mind the close analogy Husserl saw between our intuition of essences in Wesensschau and of physical objects in perception. What is it like to experience a mathematical proving (...) process? What is the ontological status of a mathematical proof? Can computer assisted provers output a proof? Taking a naturalized world account, I will assess the relationship between mathematics, the physical world and consciousness by introducing a significant conceptual distinction between proving and proof. I will propose that proving is a phenomenological conscious experience. This experience involves a combination of what Kurt Gödel called intuition, and what Husserl called intentionality. In contrast, proof is a function of that process — the mathematical phenomenon — that objectively self-presents a property in the world, and that results from a spatiotemporal unity being subject to the exact laws of nature. In this essay, I apply phenomenology to mathematical proving as a performance of consciousness, that is, a lived experience expressed and formalized in language, in which there is the possibility of formulating intersubjectively shareable meanings. (shrink)