The icon is the type of sign connected to efficient representational features, and its manipulation reveals more information about its object. The LondonUndergroundDiagram (LUD) is an iconic artifact and a well-known example of representational efficiency, having been copied by urban transportation systems worldwide. This paper investigates the efficiency of the LUD in the light of different conceptions of iconicity. We stress that a specialized representation is an icon of the formal structure of the problem for (...) which it has been specialized. By embedding such rules of action and behavior, the icon acts as a semiotic artifact distributing cognitive effort and participating in niche construction. (shrink)
Patient-funded trials are gaining traction as a means of accelerating clinical translation. However, such trials sidestep mechanisms that promote rigor, relevance, efficiency, and fairness. We recommend that funding bodies or research institutions establish mechanisms for merit review of patient-funded trials, and we offer some basic criteria for evaluating PFT protocols.
Robert Brandom’s expressivism argues that not all semantic content may be made fully explicit. This view connects in interesting ways with recent movements in philosophy of mathematics and logic (e.g. Brown, Shin, Giaquinto) to take diagrams seriously - as more than a mere “heuristic aid” to proof, but either proofs themselves, or irreducible components of such. However what exactly is a diagram in logic? Does this constitute a semiotic natural kind? The paper will argue that such a natural kind (...) does exist in Charles Peirce’s conception of iconic signs, but that fully understood, logical diagrams involve a structured array of normative reasoning practices, as well as just a “picture on a page”. (shrink)
Arendt is a philosopher despite herself, and this paper uses the resources of her <<The Life of the Mind>> to develop her comparison of thinking as a 'departure' from the world with the fore-doomed attempt by Orpheus to bring from underground into the light of day. The paper investigates how thinking, though we 'lose' it in the speech and writing that makes it public, still can have the delicate power that Arendt attributes to it.
I’d like to begin, if I may, by repeating myself. When I spoke at the Institute’s official launch last June, I quoted W.V. Quine’s remark that logic is an old subject, and since 1879 it has been a great one; and I commented that whatever the truth of this, it is undeniably true that philosophy is an old subject and has been a great one since the 5th century BC. The foundation of an institute of philosophy in the University of (...)London has been, in my opinion, a great thing for philosophy and for the University. Our mission is to promote and support philosophy of the highest quality in all its forms, inside and outside the university. With our programmes of events, fellowships and research facilitation, I think we have been carrying out this mission pretty well since our foundation in 2005. But I have already said enough in public about the Institute. Given the occasion, it is appropriate for me to say something instead about philosophy itself. (shrink)
The aim of this article is to investigate the roles of commutative diagrams (CDs) in a speciﬁc mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...) of the reasons why CDs form a good notation is that they are highly mathematically tractable: experts can obtain valid results by ‘calculating’ with CDs. These calculations, take the form of ‘diagram chases’. In order to draw inferences, experts move algebraic elements around the diagrams. It will be argued that these diagrams are dynamic. It is thanks to their dynamicity that CDs can externalize the relevant reasoning and allow experts to draw conclusions directly by manipulating them. Lastly, it will be shown that CDs play essential roles in the context of proof as well as in other phases of the mathematical enterprise, such as discovery and conjecture formation. (shrink)
After describing some key features of life in an underground railroad and the nature of gray agency, Concepción illustrates how survivors of relationship slavery can stop levying misplaced blame on themselves without giving up the valuable practice of blaming. Concepción concludes that by choosing a relatively non-oppressive account of self-blame, some amount of internalized oppression can be overcome and the double bind of agency-denial and self-loathing associated with being an oppressively grafted agent can be reduced.
Albert Lautman. Mathematics, Ideas and the Physical Real. Simon B. Duffy, trans. London and New York: Continuum, 2011. 978-1-4411-2344-2 (pbk); 978-1-44114656-4 (hbk); 978-1-44114433-1 (pdf e-bk); 978-1-44114654-0 (epub e-bk). Pp. xlii + 310.
A detailed axiomatisation of diagrams (in affine geometry) is presented, which supports typing of geometric objects, calculation of geometric quantities and automated proof of theorems.
We are in a state of impending crisis. And the fault lies in part with academia. For two centuries or so, academia has been devoted to the pursuit of knowledge and technological know-how. This has enormously increased our power to act which has, in turn, brought us both all the great benefits of the modern world and the crises we now face. Modern science and technology have made possible modern industry and agriculture, the explosive growth of the world’s population, global (...) warming, modern armaments and the lethal character of modern warfare, destruction of natural habitats and rapid extinction of species, immense inequalities of wealth and power across the globe, pollution of earth, sea and air, even the aids epidemic (aids being spread by modern travel). All these global problems have arisen because some of us have acquired unprecedented powers to act, via science and technology, without also acquiring the capacity to act wisely. We urgently need to bring about a revolution in universities so that the basic intellectual aim becomes, not knowledge merely, but rather wisdom – wisdom being the capacity to realize what is of value in life, for oneself and others, thus including knowledge and technological know-how, but much else besides. (shrink)
Michael Dummett says in the preface to his book on Frege that he is always disappointed when a book lacks a preface. ‘it is like arriving at someone’s house for dinner’ Dummett says ‘and being conducted straight into the dining room’. I feel the same way about inaugural lectures. To give an inaugural lecture is in part an acknowledgement of a professional honour, and in part an opportunity to pay a personal tribute to the institution which has honoured you in (...) this way. It is not difficult, and a pleasant task, to do this. My professorship has no predecessor, of course, but I hope that this does not disqualify me from saying something about what I owe to UCL and to its philosophy department. The intellectual character of the department as it is now was largely shaped by the influence of the late Richard Wollheim. I am sorry to say that I did not know Richard Wollheim well, and it is a cause of great sadness for the whole department that Richard was never able to return to the department as he had planned to do before he died last autumn. But I nonetheless feel the influence he left in the department, and I would like to pay a small tribute to it here. (shrink)
Carnal Appetites does not fully work out a single coherent thesis. Rather, it is a preliminary exploration of a set of issues about food, culture and identity. Here is how Probyn describes her project: “The aim of this book is simple but immodest. Through the optic of food and eating, I want to investigate how as individuals we inhabit the present: how we eat into cultures, eat into identities, indeed eat into ourselves. At the same time I am interested in (...) the question of what’s bothering us, what’s eating us now?” (2-3). Chapters explore shame, disgust, caring, sensuality, colonialism, racism, and global capitalism. (shrink)
The aim of this book is to promote understanding and enjoyment of the arts. With this aim in mind, Lyas introduces the key issues of philosophical aesthetics through examples drawn from high and popular culture, and from a variety of art forms, from music and painting to literature and poetry. The book is pitched as a springboard into undergraduate courses in aesthetics and as an introduction to philosophical aesthetics for the general reader. It is refreshing to read a book on (...) aesthetics written by someone for whom problems in aesthetics are more than just grist for the academic mill. That this is the case shows not only in his choice of examples but also in the perspective he brings to them. Lyas argues, for example, that one must feel the merit of the work for oneself; rather then simply, as he puts it, assuming 'that certain things are worth studying ("in the canon" as they put it)' and then performing 'various classificatory dances round them' (p.75). The question for appreciation, he reminds us, is why those things in the canon deserve to be there. According to Lyas, teaching aesthetics is not simply a matter of imparting a body of knowledge to the student. Instead, the teacher's role is to develop capacities in the student for an appreciative experiencing (p.131). (shrink)
Review of a recent monograph arguing that an analysis of the works of Isocrates is necessary to get a clear view of mid-fourth-century B.C. philosophy, including Plato and Aristotle.
This long essay was published in Vital Beauty, a collection including Wendy Steiner and Tim Ingold, which investigates the possibility of new ways toward beauty. This is my first encounter with Hartshorne’s Diagram of Aesthetic Values, a mandala-like structure explaining the relations between aesthetic experiences. The essay looks into the awkward history of the diagram in Hartshorne’s philosophy, its connection to Max Dessoir’s work, to Whitehead’s chapter on beauty in Adventures of Ideas and the notion of creativity in (...) Schelling. (shrink)
The Australian philosopher Philip Gerrans ambitiously tries to provide a general theory about the formation of delusions that should enclose neuronal, cognitive and phenomenological levels of description. His theory is defined as narrative and it is grounded on the so called “default thoughts”, that consist in simulations, autobiographical narrative fragments produced by the Default Mode Network (DMN). The DMN is a powerful simulation system that evolved to allow humans to simulate and imagine experiences in the absence of an eliciting stimulus. (...) Such imaginative/simulative process is precariously disciplined by the Self’s demands of narrative coherence. The Author’s aim is to waive the notion of belief and the causal role played by the impairments of fixation-beliefs system in the onset of delusions, as predicted by the principle doxastic theories. (shrink)
We challenge the prevalent opinion that consumption does not seem to matter as much as production and defy the fetishism of industrial work. We explore the implications of the premise that under conditions of cognitive capitalism consumption dictates what production does, when and how. We explain that in a post-industrial global society and economy fashion, branding, instant gratification of desires, and ephemeral consumer tastes govern production and consumption. The London riots of August 2011 send us a warning that consumption (...) and cognitive capitalism are asphyxiating in the structures and norms of industrial capitalism that are still in place. (shrink)
For an Aristotelian observer, the halo is a puzzling phenomenon since it is apparently sublunary, and yet perfectly circular. This paper studies Aristotle's explanation of the halo in Meteorology III 2-3 as an optical illusion, as opposed to a substantial thing (like a cloud), as was thought by his predecessors and even many successors. Aristotle's explanation follows the method of explanation of the Posterior Analytics for "subordinate" or "mixed" mathematical-physical sciences. The accompanying diagram described by Aristotle is one of (...) the earliest lettered geometrical diagrams, in particular of a terrestrial phenomenon, and versions of it can still be found in modern textbooks on meteorological optics. (shrink)
CATEGORY: Philosophy play; historical fiction; comedy; social criticism. -/- STORYLINE: Katherine, a neurotic American lawyer, meets Christianus for a philosophy session at The Late Victorian coffee shop in London, where they also meet Wendy the waitress and Baldy the player. Will Katherine be able to overcome her deep depression by adopting some of Christianus’s satisfactionist ideas? Or will she stay unsatisfied and unhappy by stubbornly sticking to her own neti-neti nothingness philosophy? And what roles do Baldy, Wendy, and the (...) Okefenokee Man-Monster have in this connexion? -/- TOPICS: In the course of this philosophy play, Katherine and Christianus discuss many things: friendship, a Renoir painting, global warming, elephant conservation, freemasons, Prince of Wales and his tiger-hunting experience in Nepal, Victorian Chartism and a Kennington Common daguerreotype, a Mortality Proof, and, last but not least, Baldy, Wendy, and the gory plot of the Okefenokee Man-Monster. -/- NOTES: This work features elaborate footnotes and comments (including full bibliographical references) by the author, to enhance the reader's experience of the play and its philosophizing characters. (shrink)
This document diagrams the forms OIA, OIE, OII, and OIO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
This document diagrams the forms EEA, EEE, EEI, anD EEO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
This document diagrams the forms EOA, EOE, EOI, and EOO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
This document diagrams the forms EIA, EIE, EII, and EIO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
This document diagrams the forms IOA, IOE, IOI, and IOO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
This document diagrams the forms OOA, OOE, OOI, and OOO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
This document diagrams the forms AIA, AIE, AII, and AiO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
This document diagrams the forms EAA, EAE, EAI, and EAO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
This document diagrams the forms AAA, AAE, AAI, and AAO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
This document diagrams the forms IEA, IEE, IEI, and IEO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
This document diagrams the forms IIA, IIE, III, and IIO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
This document diagrams the forms OEA, OEE, OEI, and OEO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
This document diagrams the forms AOA, AOE, AOI, and AOO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
This document diagrams the forms IAA, IAE, IAI, and IAO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
This document diagrams the forms OAA, OAE, OAI, and OAO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
This document diagrams the forms AEA, AEE, AEI, and AEO, including all four figures. Each form and figure has the following information: (1) Premises as stated: Venn diagram showing what the premises say; (2) Purported conclusion: diagram showing what the premises claim to say; (3) Relation of premises to conclusion: intended to describe how the premises and conclusion relate to each other, such as validity or contradiction. Used in only a few examples; (4) Distribution: intended to create a (...) system in which each syllogism has a unique code. In each premise and conclusion, the terms are each assigned a one or a zero, based on whether the term is distributed; (5) Rules: lists the rules of the syllogism and shows whether that particular syllogism follows, violates, or is unaffected by, each rule. (shrink)
Without doubt, there is a widespread usage of visualisations in science. However, what exactly the _epistemic status_ of these visual representations in science may be remains an open question. In the following, I will argue that at least some scientific visualisations are indispensible for our cognitive processes. My thesis will be that, with regard to the activity of _learning_, visual representations are of relevance in the sense of contributing to the aim of _scientific_ _understanding_. Taking into account that understanding can (...) be regarded as an epistemic desideratum in its own right, I will argue that, at least in some instances, no understanding can be achieved without the aid of visualisations. Consequently, they are of crucial importance in this process. Moreover, to support this thesis we will make use of some findings in educational psychology. (shrink)
Neuron diagrams are heavily employed in academic discussions of causation. Stephen Mumford and Rani Lill Anjum, however, offer an alternative approach employing vector diagrams, which this paper attempts to develop further. I identify three ways in which dispositionalists have taken the activities of powers to be related: stimulation, mutual manifestation, and contribution combination. While Mumford and Anjum do provide resources for representing contribution combination, which might be sufficient for their particular brand of dispositionalism, I argue that those resources are not (...) flexible enough to further accommodate either stimulation or mutual manifestation. Representational tools are provided to address these limitations, improving the general value of the vector model for dispositionalist approaches to causation. (shrink)
Transformed RAVAL NOTATION solves Syllogism problems very quickly and accurately. This method solves any categorical syllogism problem with same ease and is as simple as ABC… In Transformed RAVAL NOTATION, each premise and conclusion is written in abbreviated form, and then conclusion is reached simply by connecting abbreviated premises.NOTATION: Statements (both premises and conclusions) are represented as follows: Statement Notation a) All S are P, SS-P b) Some S are P, S-P c) Some S are not P, S / PP (...) d) No S is P, SS / PP (- implies are and / implies are not) All is represented by double letters; Some is represented by single letter. No S is P implies No P is S so its notation contains double letters on both sides. -/- RULES: (1) Conclusions are reached by connecting Notations. Two notations can be linked only through common linking terms. When the common linking term multiplies (becomes double from single), divides (becomes single from double) or remains double then conclusion is arrived between terminal terms. (Aristotle’s rule: the middle term must be distributed at least once) -/- (2)If both statements linked are having – signs, resulting conclusion carries – sign (Aristotle’s rule: two affirmatives imply an affirmative) -/- (3) Whenever statements having – and / signs are linked, resulting conclusion carries / sign. (Aristotle’s rule: if one premise is negative, then the conclusion must be negative) -/- (4)Statement having / sign cannot be linked with another statement having / sign to derive any conclusion. (Aristotle’s rule: Two negative premises imply no valid conclusion) Syllogism conclusion by Tranformed Raval’s Notation is in accordance with Aristotle’s rules for the same. It is visually very transparent and conclusions can be deduced at a glance, moreover it solves syllogism problems with any number of statements and it is quickest of all available methods. By new Raval method for solving categorical syllogism, solving categorical syllogism is as simple as pronouncing ABC and it is just continuance of Aristotle work on categorical syllogism. It’s believed that Boole's system could handle multi-term propositions and arguments, whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, it’s claimed that Aristotle's system could not deduce: "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is a rectangle is a square that is a quadrangle". Above conclusion is reached at a glance with Raval's Notations (Symbolic Aristotle’s syllogism rules). Premise: "No (square that is a quadrangle) is a (rhombus that is a rectangle)" Raval's Representations: S – Q, S – Q / Rh – Re, Rh – Re Premise: "No (rhombus that is a rectangle) is a (square that is a quadrangle)". Raval's Representations: Rh – Re, Rh – Re / S – Q, S - Q Conclusion: "No (quadrangle that is a square) is a (rectangle that is a rhombus)" Raval’s Representations: Q – S, Q – S / Re – Rh, Re – Rh As “ Q – S” follows from “S – Q” and “Re – Rh” from “Rh – Re”. Given conclusion follows from the given premises. Author disregards existential fallacy, as subset of a null set has to be a null set. -/- . (shrink)
It is customary to draw a circle to represent a collection of objects. This makes it easy to represent logical relations between classes thanks to topological relations between spaces. The aim of this paper is to discuss the process by which spaces represent visually classes.
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