scholarly journals What the Tortoise Said to Achilles: Lewis Carroll’s paradox in terms of Hilbert arithmetic

2021 ◽  
Author(s):  
Vasil Penchev
Keyword(s):  
The Other ◽  
Formal Structure ◽  
Lewis Carroll ◽  
Other Hand ◽  
Logical Paradox ◽  
The One ◽  
The Liar ◽  
As If

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure

scholarly journals What the Tortoise Said to Achilles: Lewis Carroll’s Paradox in Terms of Hilbert Arithmetic

2021 ◽  
Author(s):  
Vasil Penchev
Keyword(s):  
Hidden Variables ◽  
Formal Structure ◽  
Lewis Carroll ◽  
First Order ◽  
Logical Paradox ◽  
Completeness Of Quantum Mechanics ◽  
The One ◽  
In Virtue Of ◽  
The Liar ◽  
Completeness Theorems

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems).

scholarly journals What the Tortoise Said to Achilles: Lewis Carroll’s paradox in terms of Hilbert arithmetic

2021 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Hidden Variables ◽  
Formal Structure ◽  
Lewis Carroll ◽  
First Order ◽  
Logical Paradox ◽  
Completeness Of Quantum Mechanics ◽  
The One ◽  
In Virtue Of ◽  
The Liar ◽  
Completeness Theorems

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achillesand the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox thereforenaturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems).

Configuration of Quadrivalent Atoms

1929 ◽  
Vol 25 (2) ◽  
pp. 219-221
Author(s):  
T. M. Lowry
Keyword(s):  
The Other ◽  
Tetrahedral Configuration ◽  
X Ray ◽  
Metallic Atom ◽  
Other Hand ◽  
Function Change ◽  
The One ◽  
Image Position ◽  
Octahedral Configuration ◽  
As If

Two alternative views have been expressed in regard to the configuration of quadrivalent atoms. On the one hand le Bel and van't Hoff assigned to quadrivalent carbon a tetrahedral configuration, which has since been confirmed by the X-ray analysis of the diamond. On the other hand, Werner in 1893 adopted an octahedral configuration for radicals of the type MA6, e.g. inand then suggested that “the molecules [MA4]X2 are incomplete molecules [MA6]X2. The radicals [MA4] result from the octahedrally-conceived radicals [MA6] by loss of two groups A, but with no function-change of the acid residue…. They behave as if the bivalent metallic atom in the centre of the octahedron could no longer bind all six of the groups A and lost two of them leaving behind the fragment [MA4]” (p. 303).

The Genesis of Mind

1862 ◽  
Vol 7 (40) ◽  
pp. 461-494 ◽  
Author(s):  
Henry Maudsley
Keyword(s):  
The Other ◽  
Human Being ◽  
Close Resemblance ◽  
Other Hand ◽  
Being There ◽  
The One ◽  
As If

As it has ever been the custom of man to act as if he were eternal, and lavishly to scatter the limited force which he embodies as though the supply were inexhaustible, it produces no unaccustomed surprise to witness the useless expenditure of force which is so frequently made at the present time. It may even, perhaps, be deemed a token of some modesty, that the being, who since his first formation has been continually occupied in metaphysical regions with the investigation of the origin of all things, should be content for a while to amuse himself with physical theories concerning his own origin. That which is to be regretted in the new and comparatively praiseworthy occupation is the old evil of hasty theorizing on the one hand, and on the other hand, the evil, scarcely less ancient, of an impetuous eagerness to demolish any theory, however plausible, which comes athwart a favourite prejudice. What though the anatomist does discover a very close resemblance and very slight differences between the structure of a gorilla and the structure of a human being; there is no need, on that account, that mankind in a feeling of injured dignity should angrily rouse up and disclaim the undesired relationship. Whatever may be said or written, it is quite plain after all that a man is not a gorilla, and that a gorilla is not a man; it is furthermore manifest that gorillas do not breed men now-a-days, and that we have not the shadow of any evidence to guide us in forming; an opinion as to what they may have clone in times past. The negative testimony of Du Chaillu, who says that he searched in vain in the gorilla region for any intermediate race or link between it and man, scarcely adds anything to the conviction of the non-existence of any such link, which has long been universally entertained.*

Two Methodological Worlds Apart? Praises and Critiques from a European Comparativist

2006 ◽  
Vol 14 (3) ◽  
pp. 332-335 ◽  
Author(s):  
Benoît Rihoux
Keyword(s):  
The Other ◽  
Social Scientists ◽  
Social Inquiry ◽  
Other Hand ◽  
The One ◽  
As If

Social scientists who strive to reflect on their research “while they're doing it” (Becker 1998) live in very fortunate times. On the one hand, it seems as if an increasing number of scholars want to do a little more than simply apply ready-made recipes. On the other hand, a few key volumes have recently been published that move beyond ready-made recipes. In my personal top three, I would most probably place Mahoney and Rueschemeyer (2003), George and Bennett (2005), and—last but not least—the volume discussed in this symposium. What distinguishes Rethinking Social Inquiry (RSI) from the two other volumes, in my view, is that it has a broader agenda and hence a broader ambition.

scholarly journals Formal power and real authority: the involvement of governance norms or principles

2018 ◽  
pp. 107-127
Author(s):  
Emmanuel Picavet
Keyword(s):  
Political Science ◽  
The Other ◽  
Formal Structure ◽  
Formal Treatment ◽  
The Real ◽  
Contemporary Research ◽  
Other Hand ◽  
Or Economics ◽  
The One ◽  
Formal Power

In several avenues of contemporary research, much attention is devoted to the contrast between the real authority of institution and their formal power, in the analysis of institutional funtionings; also in the study of the relationships between institutions on the one hand, rules, principles or norms on the other hand. Such a contrast appears to be based on familiar observations: the capacity of institutions to get their preferred outcomes (their so-called „real authority”) is sometimes loosely connected with the hierarchical prerogatives of the considered institutions (their „formal power”). More particularly, current studies of the „migration authority” bring out possible shitts in real authority while there is no changein the formal structure of power. This article will partly consist  in the explanation of recent results of common reaserch in project „Delicom”, in which a formal treatment of the distinction has been put foward. This approach will be set against the background of recent contributions in political science or economics (in the works of Ph. Aghion and J. Tirole, J. Backhaus, L. Thorlakson). The revelance of the problematic for the study of competence delegation among institutions will be stressed all along.

Drei Phantasiestücke (3)

2017 ◽  
Author(s):  
Seth Brodsky
Keyword(s):  
East Germany ◽  
The Other ◽  
Quarter Century ◽  
Other Hand ◽  
Society Of The Spectacle ◽  
The Media ◽  
The One ◽  
Empty Signifier ◽  
As If ◽  
The Revolution

In the quarter century since the collapse of East Germany, the uncountable reflections that flower the media landscape inevitably turn to music. And when they do, they waffle. There is something untimely, and uncanny, about this waffling. It is as if the tensions structuring music's role in the heady days of the late 1960s were being therapeutically replayed twenty years later: 1968 yet again as the fetish object. On the one hand, music here is the fantasmatic sound of revolution itself, of truth speaking to power, and power falling to pieces under the weight of truth's irrefutable audibility, equal parts libido and righteousness. On the other hand, it is the traumatic reminder of failure, and the disenchanting premise that this “society of the spectacle” was not so powerful after all—that the revolution, in merely appearing, failed to show up. Judging from the examples of Hasselhoff, Rostropovich, and Bernstein, this chapter argues that music seems woven perfectly into a master's discourse: a process of shoring up a sovereign, of suturing itself to an empty signifier, producing a split subject, and precipitating an excessive enjoyment in the form of an object of desire.

The development of capability: the content of potential and the potential of content

2004 ◽  
Vol 46 (1) ◽  
pp. 7-10 ◽  
Author(s):  
Reva Brown ◽  
Sean McCartney
Keyword(s):  
Real World ◽  
The Other ◽  
The Real ◽  
Other Hand ◽  
The One ◽  
Definition Of ◽  
The Individual ◽  
As If

All too often discussion of Capability proceeds as if it is clear what ‘Capability’ is: and that all that is required is the ascertaining of means for developing it. This paper seeks to explore the meanings of Capability. It provides two broad meanings, and discusses the paradoxes inherent in the application of these to the real world of management and business. On the one hand, Capability is defined as Potential, what the individual could achieve. Potential is an endowment, which is realised by the acquisition of skills and knowledge, i.e. the acquisition of Content. On the other hand, Capability is defined as Content: what the individual can (or has learned to) do. This Content has been acquired by, or input into, the individual, who then has the Potential to develop further. So there are different routes to Capability, depending on the definition of Capability one chooses. All of this impinges on the development of Capability. This leads us on to a consideration of whether the ‘Development of Capability’ is a meaningful concept.

scholarly journals Perception and Passivity Can the Passive Pre-Givenness Be Phenomenalized?

Phainomenon ◽  
2017 ◽  
Vol 26 (1) ◽  
pp. 13-35
Author(s):  
Pedro M. S. Alves
Keyword(s):  
Phenomenological Approach ◽  
Phenomenological Analysis ◽  
The Other ◽  
Phenomenological Method ◽  
Other Hand ◽  
Passive Synthesis ◽  
Starting Point ◽  
Primitive Forms ◽  
The One ◽  
As If

Abstract In what follows, I intend to address an issue which is at the boundaries of the phenomenological method of reflective explication, and that, in this sense, points to some limitations of the phenomenological approach to consciousness and mind. I am referring to an aporetic situation that is at the heart of the phenomenological analysis of passivity. On the one hand, phenomenology shows, at least indirectly, a passive life that is beyond the first steps of the activity of the ego in the receptive, affective life. This is something that is beyond the rising of an ego, and from which a phenomenology of the ego-form of subjective life could be addressed. On the other hand, the analytic and conceptual tools of the phenomenological method have no grips on this basic realm of subjective life. As a result, Husserl’s analysis of passivity starts with the evidence of a pre-affective, pre-egoic realm, from which a phenomenology of the ego could be developed. However, Husserl’s analyses end up with the denegation of this dimension, as if it was invisible for the phenomenological method. As a consequence, the starting point of the analysis is not passivity proper, but rather the primitive forms of receptivity, which is already a first layer of the activity of the ego. Instead of an analysis of the ego-polarization (the “birth” of the ego), the egoic layer of conscious life is simply presupposed. A phenomenology of the ego-form is, thus, at the same time promised and denied. This aporetic situation is visible in the alteration of the concept of a passive pre-givenness in Husserl’s Analysis Concerning Passive Synthesis.

What Is Wrong With a Thumping Liar

2018 ◽  
Vol 43 ◽  
pp. 83-96
Author(s):  
Yotam Benziman ◽  
Keyword(s):  
Henry James ◽  
Joint Venture ◽  
The Other ◽  
Other Hand ◽  
The One ◽  
The Liar

I address the puzzle of the supposed wrongness of “a thumping liar” (a term I borrow from a story by Henry James.) On the one hand, it seems that the more you lie, the more wrong you commit. On the other hand, the more you lie, the more people are aware that you are not telling the truth, the less can you deceive them, the less can you wrong them. The liar who is known as such seems to cause no harm. I show how according to some analyses such a person would not even be considered to be lying, which is surely mistaken. I claim that he is both lying and bullshitting, thus challenging Frankfurt’s distinction between the two terms. The thumping liar excludes himself from being a meaningful part in the joint venture of conversation. It is himself that he mainly harms.

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