Recent work suggests that people predict how objects interact in a manner consistent with Newtonian physics, but with additional uncertainty. However, the sources of uncertainty have not been examined. In this study, we measure perceptual noise in initial conditions and stochasticity in the physical model used to make predictions. Participants predicted the trajectory of a moving object through occluded motion and bounces, and we compared their behavior to an ideal observer model. We found that human judgments cannot be captured (...) by simple heuristics and must incorporate noisy dynamics. Moreover, these judgments are biased consistently with a prior expectation on object destinations, suggesting that people use simple expectations about outcomes to compensate for uncertainty about their physical models. (shrink)

The present research examines psychological momentum (PM), a perceived force that lay intuition suggests influences performance. PM theory is proposed to account for how momentum perceptions arise, and four studies demonstrate the influence of lay intuitions about PM on expectations regarding performance outcomes. Study 1 establishes that individuals share intuitions about the types of events that precipitate PM, and Study 2 finds that defeating a rival increases momentum perception. Study 3 provides evidence for the lay belief that as more PM (...) accumulates during a prior task, there should be more residual momentum left to carry over to a subsequent task, and Study 4 finds that an individual whose PM is interrupted is expected to have greater difficulty completing a task than is an individual whose steady progress is interrupted. Discussion focuses on linkages between PM and related constructs. (shrink)

This paper is an exploration of the role of intuition in physics. The ways in which intuition is appealed to in physics are not well understood. To the best of my knowledge, there is no analysis of the different contexts in which we might appeal to intuition in physics, nor is there any analysis of the different potential uses to which intuition might be put. In this paper I look to provide data that goes some way to (...) giving a sense of the different contexts in which intuition is appealed to in physics. As I note in the conclusion, there is still much work to be done but I hope that the work here provides us with a first step in the journey to properly understand the use to which intuitions are put in physics and science more generally. (shrink)

Ladyman and Ross do not think that contemporary metaphysics is in good standing. However, they do think that there is a version of metaphysics that can be made to work – provided we approach it using appropriate principles. My aim in this paper is to undermine some of their arguments against contemporary metaphysics as it is currently practiced.

This paper compares Cassirer´s and Bohr´s views on symbolic knowledge in quantum physics. Although both of them consider quantum physics as symbolic knowledge, for Cassirer this amounts to a complete renunciation to intuition in quantum physics, while according to Bohr only spatio-temporal images may provide the mathematical formalism of the theory with physical reference. We show the Kantian roots of Bohr´s position and we claim that his Kantian concept of symbol enables Bohr to account for the sensible (...) content of quantum theory as well as for its systematic relation to classical physics. (shrink)

Wolfgang Spohn’s paper I think clearly places him in the forefront of research on the theory of lawlikeness, and simultaneously on the methodology of inductive reasoning.

According to Kant, the axioms of intuition, i.e. space and time, must provide an organization of the sensory experience. However, this first orderliness of empirical sensations seems to depend on a kind of faculty pertaining to subjectivity, rather than to the encounter of these same intuitions with the real properties of phenomena. Starting from an analysis of some very significant developments in mathematical and theoretical physics in the last decades, in which intuition played an important role, we argue that (...) nevertheless intuition comes into play in a fundamentally different way to that which Kant had foreseen: in the form of a formal or “categorical” yet not sensible intuition. We show further that the statement that our space is mathematically three-dimensional and locally Euclidean by no means follows from a supposed a priori nature of the sensible or subjective space as Kant claimed. In fact, the three-dimensional space can bear many different geometrical and topological structures, as particularly the mathematical results of Milnor, Smale, Thurston and Donaldson demonstrated. On the other hand, it has been stressed that even the phenomenological or perceptual space, and especially the visual system, carries a very rich geometrical organization whose structure is essentially non-Euclidean. Finally, we argue that in order to grasp the meaning of abstract geometric objects, as n-dimensional spaces, connections on a manifold, fiber spaces, module spaces, knotted spaces and so forth, where sensible intuition is essentially lacking and where therefore another type of mathematical idealization intervenes, we need to develop a new form of intuition. (shrink)

This paper is addressed to the problem of how is applied mathematics possible?

The thesis advanced in this paper is that human experience encompasses not only elements registered by the exteroceptive and interoceptive senses, but also elements received intuitively, in a direct and spontaneous mode. Findings at the cutting edge of quantum physics and brain research support the hypothesis that the brain can receive information not only through nerve-signals conducted from the senses but also through quantum resonance at the level of cytoskeletal structures. Confirmation of this hypothesis would provide a physical foundation (...) for the spontaneous intuitions that surface occasionally in consciousness. Recognizing that some varieties of intuitions are bona fide perceptions of the world beyond the brain and body would enlarge our view of the scope of human experience and support assumptions about the existence of subtle informational ties between humans, as well as between humans and nature. Keywords: apprehension—intuition—information—nonlocality—quantum physics—quantum brain theory. (shrink)

The process of theory development in physics is a very complex one. The best scientists sometimes proceed on the basis of their physical intuition, ignoring serious conceptual or mathematical objections well known to them at the time.The results soon justify their actions: but the removal of these objections is often not possible for a very long time. Four examples are presented: Newton, Schrödinger, Dirac, Dyson. Some thoughts on this “unreasonableness≓ are offered.

Numerous philosophers have recently tried to defend physicalism regarding phenomenal consciousness against dualist intuitions, by explaining the existence of dualist intuitions within a purely physicalist framework. David Papineau, for example, suggested that certain peculiar features of some of our concepts of phenomenal experiences (the so-called “phenomenal concepts”) led us to commit what he called the “Antipathetic Fallacy”: they gave us the erroneous impression that phenomenal experiences must be distinct from purely physical states (the “intuition of distinctness”), even though they are (...) not. Papineau’s hypothesis has been accepted, though under other names and in different forms, by many physicalist philosophers. Pär Sundström has tried to argue against Papineau’s account of the intuition of distinctness by showing that it was subjected to counterexamples. However, Papineau managed to show that Sundström’s counterexamples were not compelling, and that they could be answered within his framework. In this paper, I want to draw inspiration from Sundström, and to put forth some refined counterexamples to Papineau’s account, which cannot be answered in the same way as Sundström’s. My conclusion is that we cannot explain the intuition of distinctness as the result of a kind of “Antipathetic Fallacy”. (shrink)

Does the physicalist have to fold his hand in admitting that Mary gains new knowledge, or can he accommodate this intuition and still maintain that all facts are physical facts?

The idea that there could be spatially extended mereological simples has recently been defended by a number of metaphysicians (Markosian 1998, 2004; Simons 2004; Parsons (2000) also takes the idea seriously). Peter Simons (2004) goes further, arguing not only that spatially extended mereological simples (henceforth just extended simples) are possible, but that it is more plausible that our world is composed of such simples, than that it is composed of either point-sized simples, or of atomless gunk. The difficulty for these (...) views lies in explaining why it is that the various sub-volumes of space occupied by such simples, are not occupied by proper parts of those simples. Intuitively at least, many of us find compelling the idea that spatially extended objects have proper parts at every sub-volume of the region they occupy. It seems that the defender of extended simples must reject a seemingly plausible claim, what Simons calls the geometric correspondence principle (GCP): that any (spatially) extended object has parts that correspond to the parts of the region that it occupies (Simons 2004: 371). We disagree. We think that GCP is a plausible principle. We also think it is plausible that our world is composed of extended simples. We reconcile these two notions by two means. On the one hand we pay closer attention to the physics of our world. On the other hand, we consider what happens when our concept of something—in this case space—contains elements not all of which are realized in anything, but instead key components are realized in different features of the world. (shrink)

One of the world’s leading philosophers offers aspiring thinkers his personal trove of mind-stretching thought experiments. Over a storied career, Daniel C. Dennett has engaged questions about science and the workings of the mind. His answers have combined rigorous argument with strong empirical grounding. And a lot of fun. Intuition Pumps and Other Tools for Thinking offers seventy-seven of Dennett’s most successful "imagination-extenders and focus-holders" meant to guide you through some of life’s most treacherous subject matter: evolution, meaning, mind, and (...) free will. With patience and wit, Dennett deftly deploys his thinking tools to gain traction on these thorny issues while offering readers insight into how and why each tool was built. Alongside well-known favorites like Occam’s Razor and reductio ad absurdum lie thrilling descriptions of Dennett’s own creations: Trapped in the Robot Control Room, Beware of the Prime Mammal, and The Wandering Two-Bitser. Ranging across disciplines as diverse as psychology, biology, computer science, and physics, Dennett’s tools embrace in equal measure light-heartedness and accessibility as they welcome uninitiated and seasoned readers alike. As always, his goal remains to teach you how to "think reliably and even gracefully about really hard questions." A sweeping work of intellectual seriousness that’s also studded with impish delights, Intuition Pumps offers intrepid thinkers—in all walks of life—delicious opportunities to explore their pet ideas with new powers. (shrink)

In philosophical thought experiments, as in ordinary discourse, our understanding of verbal case descriptions is enriched by automatic comprehension inferences. Such inferences have us routinely infer what else is also true of the cases described. We consider how such routine inferences from polysemous words can generate zombie intuitions: intuitions that are ‘killed’ (defeated) by contextual information but kept cognitively alive by the psycholinguistic phenomenon of linguistic salience bias. Extending ‘evidentiary’ experimental philosophy, this paper examines whether the ‘zombie argument’ against materialism (...) is built on zombie intuitions. We examine the hypothesis that contextually defeated stereotypical inferences from the noun ‘zombie’ influence intuitions about ‘philosophical zombies’. We document framing effects (‘zombie’ vs ‘duplicate’) predicted by the hypothesis. Findings undermine intuitions about the conceivability of ‘philosophical zombies’ and address the philosophical ‘hard problem of consciousness’. Findings support a deflationary response: The impression that principled obstacles prevent scientific explanation of how physical processes give rise to conscious experience is generated by philosophical arguments that rely on epistemically deficient intuitions. (shrink)

Geometrical and physical intuition, both untutored andcultivated, is ubiquitous in the research, teaching,and development of mathematics. A number ofmathematical ``monsters'', or pathological objects, havebeen produced which – according to somemathematicians – seriously challenge the reliability ofintuition. We examine several famous geometrical,topological and set-theoretical examples of suchmonsters in order to see to what extent, if at all,intuition is undermined in its everyday roles.

The paper examines new innovative ideas coming from contemporary empirical researches of perception, language and mind in cognitive and evolutionary psycho_logy. From these researches it follows, that our minds are equipped with certain innate physical, language and psychological principles. The respective disciplines are sometimes referred to as intuitive physics and intuitive psychology. These new empirical data have important consequences in the methodology od social sciences. They are a challenge for the traditional model, in which language and mind (...) are seen first of all as cultural and social products. (shrink)

In this paper, I intend to show that it’s a serious mistake to construe the role of sensible representation in Kant’s work as a nonconceptual content (in the contemporary and technical sense of “content”), which, like a mental indexical would refer to what appears in space and time in the so-called de re form. The interpretation I advance and further support is this: without possessing a representational content, sensible representation must be understood as the basic epistemic relation between the subject (...) and the physical entities in space and time she is acquainted with. Immediate reference of sensible intuition to their respective objects is to be understood as a form of knowledge by acquaintance. I call my own interpretation relationalism. (shrink)

Art interprets the visible world, physics charts its unseen workings--making the two realms seem completely opposed. But in Art & Physics, Leonard Shlain tracks their breakthroughs side by side throughout history to reveal an astonishing correlation of visions. From teh classical Greek sculptors to Andy Warhol and Jasper Johns, and from Aristotle to Einstein, aritsts have foreshadowed the discoveries of scientists, such as when Money and Cezanne intuited the coming upheaval in physics that Einstein would initiate. In (...) this lively and colorful narrative, Leonard Shlain explores how artistic breakthroughs could have prefigured the visionary insights of physicists on so many occasions throughtout history. Provacative and original, Art & Physics is a seamless integration of the romance of art and the drama of science...and exhilarating history of ideas. (shrink)

The authors aim to reinstate a spirit of philosophical enquiry in physics. They abandon the intuitive continuum concepts and build up constructively a combinatorial mathematics of process. This radical change alone makes it possible to calculate the coupling constants of the fundamental fields which? via high energy scattering? are the bridge from the combinatorial world into dynamics. The untenable distinction between what is?observed?, or measured, and what is not, upon which current quantum theory is based, is not needed. (...) If we are to speak of mind, this has to be present? albeit in primitive form? at the most basic level, and not to be dragged in at one arbitrary point to avoid the difficulties about quantum observation. There is a growing literature on information-theoretic models for physics, but hitherto the two disciplines have gone in parallel. In this book they interact vitally. (shrink)

In this paper, we will examine the role that intuitions and responses to thought experiments play in confirming or disconfirming theories of reference, using insights from both debates as our starting point. Our view is that experimental evidence of the type elicited by MMNS does play a central role in the construction of theories of reference. This, however, is not because such theory construction is accurately characterized by "the method of cases." First, experimental philosophy does not directly collect data about (...) intuitions, but rather about peoples responses to thought experiments, which may reflect their intuitions but may well not. Second, unusually in the case of the theory of reference, experimental prompts involve elicitation of the phenomenon under investigation—that is, referring—and it is the reference facts rather than the intuitions that a theory of reference should capture. Finally, "best fit" models like the method of cases are inconsistent with the actual practice of semantic theorists, who appeal to general principles of theory construction as well as considerations native to the theory of reference, often in the service of rejecting intuitions. Indeed, Kripke himself viewed several claims of his theory as unintuitive, but felt no pressure to alter them on that account. These facts, we'll argue, suggest that the relevance of experimental methods in the theory of reference cannot be straightforwardly extended to other fields: an experimental prompt containing Newtons two rocks tied together in empty space may elicit referring, and may also elicit intuitions, but it doesn't also elicit the phenomenon under investigation. Furthermore, the considerations native to the theory of reference are not part of physics, which has its own distinct set of principles and considerations. This suggests that an evaluation of the centrality of intuitions/ responses to thought experiments in philosophical methodology must proceed in a piecemeal fashion. We conclude that the potential contributions of experimental philosophy will take different forms in different sub-fields of philosophical inquiry. (shrink)

When people are trying to determine whether an entity is capable of having certain kinds of mental states, they can proceed either by thinking about the entity from a *functional* standpoint or by thinking about the entity from a *physical* standpoint. We conducted a series of studies to determine how each of these standpoints impact people’s mental state ascriptions. The results point to a striking asymmetry. It appears that ascriptions of states involving phenomenal consciousness are sensitive to physical factors in (...) a way that ascriptions of other states are not. (shrink)

This paper considers the impact which developments in neuroscience seem likely to have on our inherited, intuitive psychology ? the system of beliefs called ?folk psychology? by enthusiasts for its elimination. The paper argues that while closer relations between a developing genuinely scientific cognitive psychology and a burgeoning neurological understanding are to be welcomed, physiology will not reduce psychology, and the concepts belonging to intuitive psychology will be transformed and enriched, but not discredited or discarded, when psychology, in (...) its cognitive form, emerges as a science with genuine explanatory power. The analogy between belief and desire, on one hand, and witches and phlogiston, on the other, is rejected. So is the parallel between folk psychology and folk physics. We face the choice, on Churchland's principles, between the rejection of historical, literary, and moral culture, and accepting a dualism in human thought which despairs of a comprehensively naturalistic vision of ourselves. (shrink)

The evidential value of moral intuitions has been challenged by psychological work showing that the intuitions of ordinary people are affected by distorting factors. One reply to this challenge, the expertise defence, claims that training in philosophical thinking confers enhanced reliability on the intuitions of professional philosophers. This defence is often expressed through analogy: since we do not allow doubts about folk judgments in domains like mathematics or physics to undermine the plausibility of judgments by experts in these domains, (...) we also should not do so in philosophy. In this paper I clarify the logic of the analogy strategy, and defend it against recent challenges by Jesper Ryberg. The discussion exposes an interesting divide: while Ryberg’s challenges may weaken analogies between morality and domains like mathematics, they do not affect analogies to other domains, such as physics. I conclude that the expertise defence can be supported by analogical means, though care is required in selecting an appropriate analog. I discuss implications of this conclusion for the expertise defence debate and for study of the moral domain itself. (shrink)

Finetuning and Naturalness are extra-empirical theory assessments that reflect our expectation how scientific theories should provide an intuitive understanding about the foundations underlying the observed phenomena. Recently, the absence of new physics at the LHC and the theoretical evidence for a multiverse of alternative physical realities, predicted by our best fundamental theories, have casted doubts about the validity of these concepts. In this essay we argue that the discussion about Finetuning should not predominantly concentrate on the desired features (...) a fundamental theory is expected to have, but rather on the question what a theory needs to qualify as fundamental in the first place. By arguing that a fundamental description of the Universe should possess zero entropy, we develop a ‘holistic’ concept for the most fundamental layer of reality: The fundamental description of the Universe is the Universe itself, understood as an entangled quantum state. Adopting a universal applicability of quantum mechanics, in this framework the behavior of subsystems can be understood as the perspectival experience of an entangled quantum Universe perceived through the “lens of decoherence”. In this picture the fundamental reality is non-local, and finetuned coincidences in effective theories may be understood in a way similar to EPR-correlations. This notion provides a fresh view on the topic of Naturalness and Finetuning since it suggests that Finetuning problems and hints for anthropic explanations are an artifact of theories building up on subsystems rather than on the fundamental description. Recent work in quantum gravity aiming at an understanding of spacetime geometry from entanglement entropy could be interpreted as a first sign of such a paradigm shift. (shrink)

This book explores whether physics points to a reductive or an emergent structure of the world and proposes a physics-motivated conception of emergence that leaves behind many of the problematic intuitions shaping the philosophical conceptions. Examining several detailed case studies reveals results that point to stability conditions playing a crucial though underappreciated role in the physics of emergence. This contextual emergence has thought-provoking consequences for physics and beyond.

The Concept of Physical Law is an original and creative defense of the Regularity theory of physical law, the concept that physical laws are nothing more than descriptions of whatever universal truths happen to be instanced in nature. Professor Swartz clearly identifies and analyzes the arguments and intuitions of the opposing Necessitarian theory, and argues that the standard objection to the Regularity theory turns on a mistaken view of what Regularists mean by 'physical impossibility'; that it is impossible to construct (...) an empirical test that can distinguish between events Necessitarians call 'mere accidents' and those they call 'nornologically necessary', and that the Necessitarian theory cannot account fot human beings' free wills. Other topics in this important work include: the distinction between instrumental scientific laws and true physical laws; the distinction between failure and doom; potentialities; miracles and marvels; predictability and uniformity; statistical and numerical laws; and necessity-in-praxis. (shrink)

La conception des mathématiques chez Poincaré est une pièce maîtresse de sa théorie de la connaissance. Les mathématiques y jouent un rôle constitutif et médiateur, très proche de celui que Kant leur avait assigné dans sa Critique. Afin d’éclaircir les rapports complexes entre les notions d’intuition, de construction et de convention chez Poincaré, nous nous appuyons sur les analogies et les contrastes avec la source kantienne. La continuité et la cohérence de la théorie de la connaissance de Poincaré en sortent (...) renforcées.Poincaré’s philosophy of mathematics plays a key role in his general philosophy of knowledge. Mathematics is considered, by Poincaré, as a constitutive element of experience and it plays a “schematic” role between the conventional frameworks of geometry and theoretical physics on one hand and, on the other hand, sensations. We stress the Kantian roots of such a conception of mathematics, trying to explain the respective importance of the notions of intuition, construction and convention in Poincaré’s theory of knowledge. (shrink)

The motivating question of this paper is: ‘How are our beliefs in the theorems of mathematics justified?’ This is distinguished from the question ‘How are our mathematical beliefs reliably true?’ We examine an influential answer, outlined by Russell, championed by Gödel, and developed by those searching for new axioms to settle undecidables, that our mathematical beliefs are justified by ‘intuitions’, as our scientific beliefs are justified by observations. On this view, axioms are analogous to laws of nature. They are postulated (...) to best systematize the data to be explained. We argue that there is a decisive difference between the cases. There is agreement on the data to be systematized in the scientific case that has no analog in the mathematical one. There is virtual consensus over observations, but conspicuous dispute over intuitions. In this respect, mathematics more closely resembles stereotypical philosophy. We conclude by distinguishing two ideas that have long been associated -- realism (the idea that there is an independent reality) and objectivity (the idea that in a disagreement, only one of us can be right). We argue that, while realism is true of mathematics and philosophy, these domains fail to be objective. One upshot of the discussion is that even questions of fundamental physics may fail to be objective in roughly the sense that the question, ‘Is the Parallel Postulate is true?’, understood as one of pure mathematics, fails to be. Another is a kind of pragmatism. Factual questions in mathematics, modality, logic, and evaluative areas go proxy for non-factual practical ones. -/- . (shrink)

Jeff McMahan's impressive recent defence of the embodied mind theory of personal identity in his highly acclaimed work The Ethics of Killing has undoubtedly reawakened belief that physical continuity is a necessary component of the relation that matters in our self-interested concern for the future. My aim in this paper is to resist this belief in a somewhat roundabout way. I want to address this belief in a somewhat roundabout way by revisiting a classic defence of the belief that enormous (...) changes in the contents of a person's psychology does not preclude justified fear of future pain. I have in mind Bernard Williams' The Self and the Future (1970) in which he argues, against the psychological view, that physical continuity is necessary for survival. I examine Williams' second thought experiment which ostensibly supports that intuition and afterwards defend two related claims. First, I argue that a close examination of the second thought experiment reveals that one's prior commitments to a particular criterion of personal identity can influence one's response to that thought experiment. Second, I argue that Williams' second thought experiment is set out in questionbegging terms. I do not claim, however, that the intuition under consideration lacks justification; I only claim that Williams' second thought experiment does not provide the needed support. (shrink)

The view that mathematics deals with ideal objects to which we have epistemic access by a kind of perception has troubled many thinkers. Using ideas from Husserl’s phenomenology, I will take a different look at these matters. The upshot of this approach is that there are non-material objects and that they can be recognized in a process very closely related to sense perception. In fact, the perception of physical objects may be regarded as a special case of this more universal (...) way of recognizing objects of any kind. (shrink)

In this paper, I examine what is for Plato and all those who follow in his footsteps the ne plus ultra of cognition, namely, intuition (nous or noēsis). This is the paradigm of cognition, meaning that all forms of human (and even animal) cognition are inferior manifestations of this. Intuition is mental seeing, analogous to physical seeing. Among embodied souls, it is seeing a unity of some sort manifested in some diversity or plurality. Thus, someone who sees that the Morning (...) Star is the Evening Star, or that S at t1 is identical with S at t2, or that f = ma, etc., sees the unity ‘behind’ the diversity. The disembodied intellect that is the Demiurge (or, for Aristotle, the Unmoved Mover) sees paradigmatically the diversity of all intelligible being as a unity. Because mental seeing or intuition is paradigmatic for all cognition, cognition is essentially a unificatory process. Plato's method of collection and division displays both this process and its reverse. In the light of this core doctrine, I examine some of the insights that Platonists, especially Plotinus and Proclus, arrived at regarding a host of issues, including the nature of the first principle of all and the nature of normativity. (shrink)

A thoroughly physical view on reality and our common sense view on agency and free will seem to be in a direct conflict with each other: if everything that happens is determined by prior physical events, so too are all our actions and conscious decisions; you have no choice but to do what you are destined to do. Although this way of thinking has intuitive appeal, and a long history, it has recently began to gain critical attention. A number (...) of arguments have been raised in defense of the idea that our will could be genuinely free even if the universe is governed by deterministic laws of physics. Determinism and free will have been argued to be compatible before, of course, but these recent arguments seem to take a new step in that they are relying on a more profound and concrete view on the central elements of the issue, the fundamental laws of physics and the nature of causal explanation in particular. The basic idea of this approach is reviewed in here, and it is shown how a careful analysis of physics and causal explanation can indeed enhance our understanding of the issue. Although it cannot be concluded that the problem of free will would now be completely solved (or dissolved), it is clear that these recent developments can bring significant advancement to the debate. (shrink)

Why we get the world wrong -- Intuitive theories of the physical world -- Matter : what is the world made of? How do those components interact? -- Energy : what makes something hot? What makes something loud? -- Gravity : what makes something heavy? What makes something fall? -- Motion : what makes objects move? What paths do moving objects take? -- Cosmos : what is the shape of our world? What is its place in the cosmos? -- (...) Earth : why do continents drift? Why do climates change? -- Intuitive theories of the biological world -- Life : what makes us alive? What causes us to die? -- Growth : why do we grow bigger? Why do we grow older? -- Inheritance : why do we resemble our parents? Where did we get our traits? -- Illness : what makes us ill? How does illness spread? -- Adaptation : why are there so many lifeforms? How do they change over time? -- Ancestry : where do species come from? How are they related? -- How to get the world right. (shrink)

The Archimedean Axiom is often held to be an intuitively obvious truth about the geometry of physical space. After a general discussion of the varieties of geometrical intuition that have been proposed, I single out one variety which we can plausibly be held to have and then argue that it does not underwrite the intuitive obviousness of the Archimedean Axiom. Generalizing that result, I conclude that the Axiom is not intuitively obvious.