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- Achille C. Varzi, The Plan of a Square.I found the following manuscript while rummaging through the papers of a Square. I believe it is the same Square the Reverend Edwin A. Abbott wrote about in Flatland, a text that was written exactly one hundred and twenty-five years ago (in 1884) but that still retains all of its charm and freshness. It tells of the adventures of a Square, a per- fectly two-dimensional being, with no depth, citizen of a world that is similarly two di- mensional and depthless, who one day had the good fortune of receiving a visit from a Sphere: the three-dimensional being par excellence. What’s more, he had the even greater fortune of being given the opportunity to briefly visit the great three-dimensional world that his guest came from—our three-dimensional world. He visited and experienced this place—for him, this was a mystic experience—before falling back for all eternity into the total flatness of Flatland: the flat world, lacking depth; the world with nothing over or under it, the world in which cars and airplanes alike, so to speak, belong to the same category, and everything, literally everything, is reduced to fragile shadows on an enor- mous and eternally illuminated floor. (Which does not mean that Flatland was a per- fectly democratic world. Power was in the hands of the caste of Circles, most certainly not in the hands of the infamous Irregular Polygons.) I said that the Square’s experience was in a certain sense a mystical experience, and it is not difficult to imagine why. It is almost as if we were given the opportunity to visit a four-dimensional world, a world which we have no knowledge of, and whose shapes, beauties and dangers we could never have imagined. For us the three dimensions are eve- rything: they constitute a habitat so natural that to us it seems impossible to imagine different spaces, new and unknown dimensions, and uncommon shapes. And I am not thinking of the temporal dimension: that dimension we know far too well..Reading list | Discuss | Edit | Categorize |My bibliography
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The main purpose of this paper is to demonstrate that the analysis of the kinematical effects of special relativity holds the key to answering the question of the dimensionality of the world. It is shown that these effects and the experiments which confirmed them would be impossible if the world were three-dimensional. Section 2 shows that relativity of simultaneity, conventionality of simultaneity, and the existence of accelerated observers in special relativity would be impossible if the world were three-dimensional. Section 3 deals with the dimensionality of physical objects and demonstrates that the relativistic length contraction and the twin paradox would be impossible if the physical bodies involved in these relativistic effects were three-dimensional objects.
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| | Scholar | More options ... In their papers for this issue, Sterelny and Sutton provide a dimensional analysis of some of the ways in which mental and cognitive activities take place in the world. I add two further dimensions, a dimension of manipulation and of transformation. I also discuss the explanatory dimensions that we might use to explain these cases.
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| | Other links: dx.doi.org springerlink.com | Scholar | At my library | More options ... In this paper, I shall defend externalism for the contents of perceptual experience. A perceptual experience has representational properties; it presents the world as being a certain way. A visual experience, for example, might present the world to a subject as containing a surface with a certain shape, lying at a certain distance, in a certain direction; perhaps a square with sides about 30 cm, lying about one metre in front of the subject, in a direction about 20 degrees to the left of straight ahead.
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| | Scholar | At my library | More options ... . Each predicate of the Aristotelian square of opposition includes the word “is”. Through a twofold interpretation of this word the square includes both classical logic and non-classical logic. All theses embodied by the square of opposition are preserved by the new interpretation, except for contradictories, which are substituted by incommensurabilities. Indeed, the new interpretation of the square of opposition concerns the relationships among entire theories, each represented by means of a characteristic predicate. A generalization of the square of opposition is achieved by not adjoining, according to two Leibniz’ suggestions about human mind, one more choice about the kind of infinity; i.e., a choice which was unknown by Greek’s culture, but which played a decisive role for the birth and then the development of modern science. This essential innovation of modern scientific culture explains why in modern times the Aristotelian square of opposition was disregarded.
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| | Scholar | At my library | More options ... In a modal system of arithmetic, a theory S has the modal disjunction property if whenever $S \vdash \square\varphi \vee \square\psi$ , either $S \vdash \square\varphi$ or $S \vdash \square\psi. S$ has the modal numerical existence property if whenever $S \vdash \exists x\square\varphi(x)$ , there is some natural number n such that $S \vdash \square\varphi(\mathbf{n})$ . Under certain broadly applicable assumptions, these two properties are equivalent.
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| | Other links: jstor.org | Scholar | At my library | More options ... This paper pursues two aims. First, to show that the block universe view, regarding the universe as a timelessly existing four-dimensional world, is the only one that is consistent with special relativity. Second, to argue that special relativity alone can resolve the debate on whether the world is three-dimensional or four-dimensional. The argument advanced in the paper is that if the world were three-dimensional the kinematic consequences of special relativity and more importantly the experiments confirming them would be impossible.
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| | Scholar | More options ... Murray MacBeath, in his essay ``Time's Square'', describes a fictitious scenariowhere various physical observations made by the participants would, he claims, invitethe interpretation that time for them is two-dimensional. In the present paper, however, Iargue that such observations come close to underdetermining the hypothesis of time's twodimensionality;for a rival hypothesis - that, under certain circumstances, the observationscan be explained in terms of the familiar time dilation effects predicted by special relativity- almost fits the evidence as well. That is, under certain (albeit artificial) circumstances theworld can already behave almost as though it were temporally two-dimensional.
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| | Other links: jstor.org | Scholar | At my library | More options ... The world is complex, dynamic, multidimensional; the paper is static, flat. How are we to represent the rich visual world of experience and measurement on mere flatland?
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| | Scholar | More options ... When I open my eyes and look at a Rubik’s cube, there is something it is like for me visually in looking at it. Various color qualities are presented to me, and they are arranged in a specific pattern. By having an experience with this particular phenomenal character I am also thereby visually representing the world outside my experience as being a certain way. If I experience a blue square to the left of a red square, the world outside my experience is represented as being one way. As I turn the cube, and come to view a green square to the left of another green square, I have an experience with a different phenomenal character. But I also come to represent the world differently. In virtue of the difference in phenomenology there is a corresponding difference in how the world is represented as being. Moreover, it seems that any two experiences with the same phenomenal character will share a certain sort of intentional content.1 If two subjects have phenomenally identical experiences, there is an important sense in which the way the world appears to them is precisely the same. I will call this intentional content that supervenes on phenomenal character “phenomenal content”. But how are we to understand this notion of “ways of appearing”? Most philosophers who have acknowledged the existence of phenomenal content have held that the way something appears to a subject is simply a matter of the properties..
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| | Scholar | More options ... The everyday experience of someone, or something, getting in one’s face reveals a depth that is the difference between a world that is intrusive and a world that is respectful. This depth, I argue, should be conceived, not in feet and inches, but in terms of violation and honor. I explore three factors that contribute to this depth’s emergence. First, I examine our body’s capacity, at the level of sense experience, for giving the world a figure/ground structure; this structure insures that most of the world we are in constant contact with, nonetheless, keeps its distance as background. I demonstrate the importance of this figure/ground structure to the depth of our world by considering the experience of people with autism; for those with autism, this structure seems to be, if not entirely missing, at least substantially less robust than our own. Next, I examine our body’s ability, at the level of more personal experience, to handle the world; our handling of the world, which rests on the acquisition of specific skills, transforms things that could easily assault us into the usually motionless objects we tend to take for granted. I demonstrate the importance of these skills to the depth of our world by considering the experience of Gregg Mozgalla; until recently, Mozgalla, who has cerebral palsy, could only lurch, rather than walk, through the world. Finally, I draw on the work of the artist Mierle Ukeles to examine the maintenance work that other people, at a broader social level, perform; other’s maintenance work keeps in good condition a world that, by falling into bad condition, could easily intrude on us.
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| | Other links: dx.doi.org | Scholar | At my library | More options ... Discussion of Achille C. Varzi, The plan of a square
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