Chaotic and ergodic properties of cylindric billiards

1999 ◽  
Vol 19 (5) ◽  
pp. 1127-1156 ◽  
Author(s):  
PÉTER BÁLINT
Keyword(s):  
The Other ◽  
Necessary Condition ◽  
Ergodic Properties ◽  
Other Hand ◽  
Transitivity Condition ◽  
The One ◽  
Special Case ◽  
Hard Ball

Chaotic and ergodic properties are discussed for various subclasses of cylindric billiards. A common feature of the studied systems is that they satisfy a natural necessary condition for ergodicity and hyperbolicity, the so-called transitivity condition. The relation of our discussion to former results on hard ball systems is twofold. On the one hand, by slight adaptation of the proofs we may discuss hyperbolic and ergodic properties of 3 or 4 particles with (possibly restricted) hard ball interactions in any dimensions. On the other hand, a key tool in our investigations is a kind of connected path formula for cylindric billiards, which together with the conservation of momenta gives back, when applied to the special case of hard ball systems, the classical connected path formula.

Leibniz on Apperception and Animal Souls

Dialogue ◽  
1994 ◽  
Vol 33 (4) ◽  
pp. 701-724 ◽  
Author(s):  
Murray Miles
Keyword(s):  
The Other ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Human Beings ◽  
Mental Processes ◽  
Other Hand ◽  
Forms Of Life ◽  
The One

InLeibniz: Perception, Apperception, and Thought, Robert McRae alleges a flat “contradiction” (McRae 1976, p. 30) at the heart of Leibniz's doctrine of three grades of monads: bare entelechies characterized by perception; animal souls capable both of perception and of sensation; and rational souls, minds or spirits endowed not only with capacities for perception and sensation but also with consciousness of self or what Leibniz calls (introducing a new term of art into the vocabulary of philosophy) “apperception.” Apperception is a necessary condition of those distinctively human mental processes associated with understanding and with reason. Insofar as it is also a sufficient condition of rationality, it is not ascribable to animals. But apperception is a necessary condition of sensation or feeling as well; and animals are capable of sensation, according to Leibniz, who decisively rejected the Cartesian doctrine that beasts are nothing but material automata. “On the one hand,” writes McRae, “what distinguishes animals from lower forms of life is sensation or feeling, but on the other hand apperception is a necessary condition of sensation, and apperception distinguishes human beings from animals” (McRae 1976, p. 30). “We are thus left with an unresolved inconsistency in Leibniz's account of sensation, so far as sensation is attributable both to men and animals” (ibid., p. 34).

scholarly journals Approximating Ideal Filters by Systems of Fractional Order

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Ming Li
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Point Of View ◽  
Present Approach ◽  
The Other ◽  
Necessary Condition ◽  
Ecg Signals ◽  
Other Hand ◽  
The One ◽  
Electrocardiogram Ecg

The contributions in this paper are in two folds. On the one hand, we propose a general approach for approximating ideal filters based on fractional calculus from the point of view of systems of fractional order. On the other hand, we suggest that the Paley and Wiener criterion might not be a necessary condition for designing physically realizable ideal filters. As an application of the present approach, we show a case in designing ideal filters for suppressing 50-Hz interference in electrocardiogram (ECG) signals.

scholarly journals Space, Place, Haven: Levinas’s Phenomenology of Home

Problemos ◽  
2020 ◽  
pp. 58-68
Author(s):  
Jolanta Saldukaitytė
Keyword(s):  
Emmanuel Levinas ◽  
The Other ◽  
Space And Place ◽  
Necessary Condition ◽  
Natural Place ◽  
Other Hand ◽  
The World ◽  
Positive Meaning ◽  
The One

By distinguishing between space and place, the article situates and analyses the meaning of the closest place – home – in the philosophy of Emmanuel Levinas. The effort to encounter transcendence, to escape, to leave, to not be attached a particular place, and not to be driven by a nostalgia to return, is dominant in Levinas’s philosophy. This article shows that dwelling in a place, as settling in a home, also has a positive meaning for Levinas. This positive meaning comes, however, not from an ontological but from an ethical relationship with a place. The home is shown as chosen place, warm and human, as opposed to a given or natural place. On the one hand, the home is a necessary condition for security, but also the very condition of interiority and activity, of having the place in the world in contrast to thrownness. On the other hand, it is not a place where I is embodied and rooted in like a vegetable, but a place where I welcome the other.

Conclusion

2021 ◽  
pp. 297-304
Author(s):  
Guy Elgat
Keyword(s):  
Alternative Conception ◽  
The Other ◽  
Necessary Condition ◽  
Other Hand ◽  
The One

The concluding chapter addresses an apparent aporia: on the one hand, we have the Nietzschean argument that one must be causa sui for guilt to be justified, but on the other hand, we have the Heideggerian argument that not being causa sui is a necessary condition for guilt to be possible. The conclusion explains why this is only an apparent aporia. An alternative conception of guilt is sketched, one that rejects Nietzsche’s view of guilt as a form of self-punishment but retains Heidegger’s view that guilt expresses our normative commitments. This conception shows how guilt might nevertheless be justified.

Skepticism, Belief, and the Criterion of Truth

Apeiron ◽  
2013 ◽  
Vol 46 (3) ◽  
pp. 327-344
Author(s):  
Whitney Schwab
Keyword(s):  
The Other ◽  
Necessary Condition ◽  
Epistemic Attitude ◽  
Other Hand ◽  
Pyrrhonian Skepticism ◽  
Central Argument ◽  
The One ◽  
Suspension Of Judgment

Abstract This paper deals with Pyrrhonian skepticism. It argues that the central argument presented by Jonathan Barnes in favor of the view that skepticism precludes the possession of any belief fails. In brief, Barnes maintains that, because skepticism requires suspending judgment whether criteria of truth exist, no skeptic can, consistently with her skepticism, possess a criterion of truth; this entails, he argues, that no skeptic can make any judgments about anything and, hence, cannot come to possess any beliefs. I evaluate this argument in two ways: first, if we understand criteria of truth along the lines proposed by Sextus’ Hellenistic opponents, the argument fails because such criteria were introduced to guarantee that at least some of our beliefs could count as knowledge, and not to guarantee the very possibility of making judgments in the first place. Second, if we broaden our conception of a criterion of truth, such that a criterion is any standard against which an impression can be evaluated, the argument fails because it equivocates on the notion of ‘possession’. On the one hand, in the sense in which someone must possess such a criterion in order to make judgments, the skeptic’s suspension of judgment concerning their existence does not entail that she does not possess a criterion of truth. On the other hand, in the sense in which the skeptic does not possess such a criterion, possession of a criterion of truth is not a necessary condition for making judgments. Thus, I conclude that the skeptics’ epistemic attitude towards the existence of criteria of truth (i.e. suspension of judgment) does not entail that skeptics cannot possess any beliefs.

The structure of knowledge

2021 ◽  
Vol 153 (3) ◽  
pp. 269-290
Author(s):  
Nadja Germann
Keyword(s):  
Formative Period ◽  
The Other ◽  
Islamic World ◽  
Other Hand ◽  
Intellectual Traditions ◽  
The One ◽  
Structure Of Knowledge ◽  
New Religion ◽  
Special Case

Medieval architectures of knowledge designed in the Islamic world constitute a special case: They neatly reflect the competition between different intellectual traditions and approaches. On the one hand, there are those classifications that are centered on what was perceived as the indigenous sciences during the formative period, i.e. those sciences that arose in connection with the new religion, Islam, and the language of its revelation, Arabic. On the other hand, scholars eagerly took over and adapted disciplines deriving from non-Arab and non-Muslim cultures, primarily Greek science and philosophy. These traditions, however, transmitted their own conceptions of knowledge that partly stood in conflict with Arabic-Islamic ideas. In this article, I first give an overview of the various approaches and then concentrate on Fārābī and Avicenna, in order to trace a remarkable development: the gradual dissolution of boundaries both within and between the different scientific spheres and paradigms on epistemological grounds.

scholarly journals Panpsychism, Conceivability, and Dualism Redux

2019 ◽  
Vol 34 (1) ◽  
pp. 157-172
Author(s):  
Hane Htut Maung
Keyword(s):  
Philosophy Of Mind ◽  
Natural World ◽  
The Other ◽  
Contemporary Philosophy ◽  
Conceivability Argument ◽  
Other Hand ◽  
The One ◽  
Strong Reading ◽  
Special Case

In contemporary philosophy of mind, the conceivability argument against physicalism is often used to support a form of dualism, which takes consciousness to be ontologically fundamental and distinct from physical matter. Recently, some proponents of the conceivability argument have also shown interest in panpsychism, which is the view that mentality is ubiquitous in the natural world. This paper examines the extent to which panpsychism can be sustained if the conceivability argument is taken seriously. I argue that panpsychism’s ubiquity claim permits a strong reading or a weak reading. This presents a dilemma. On the one hand, the strong reading, which is typically characterised as a form of monism, is undermined by the conceivability argument. On the other hand, the weak reading, while compatible with the conceivability argument, turns out just to be a special case of dualism. I also show that the related position of panprotopsychism cannot provide a tenable monist position because it too cannot withstand the challenge of the conceivability argument. Therefore, if the conceivability argument is taken seriously, then we are committed to a dualist metaphysics, regardless of whether or not we accept the ubiquity claim.

Anarchism in Deleuze

2019 ◽  
Vol 13 (2) ◽  
pp. 267-292
Author(s):  
Jernej Kaluža
Keyword(s):  
Political Action ◽  
Practice Theory ◽  
Theory And Practice ◽  
The Other ◽  
Necessary Condition ◽  
Other Hand ◽  
Basic Ideas ◽  
The One

In this article, we argue that Deleuze's philosophy could be understood as anarchistic in a specifically defined meaning. The imperative of immanence of thought, which we explicate mainly through the reading of Deleuze's Spinoza, on the one hand establishes indivisibility between theory and practice and on the other hand paradoxically orders disobedience. We argue for a thought that is immanent, adequate with its inner practice, for thought that cannot be forced. That is the basis on which we combine the reading of Deleuze, Spinoza, Nietzsche and some basic ideas from the contemporary anarchistic movement (Graeber) and the anarchistic tradition (Stirner). We do not try to argue for a certain form of political action. Our goal is to establish a field of thought, that is by its innermost ontological principles anarchistic: practice must be accompanied by its own theory. Adequate thought cannot be forced. This is a necessary condition for each consistent practice-theory.

Elements and Knowledge in the Theaetetus

Elenchos ◽  
2013 ◽  
Vol 34 (2) ◽  
pp. 299-326
Author(s):  
Jie Tian
Keyword(s):  
Present Article ◽  
Necessary Conditions ◽  
The Other ◽  
Necessary Condition ◽  
The Third ◽  
Other Hand ◽  
Adequate Definition ◽  
Dream Theory ◽  
The One ◽  
Definition Of

Abstract Plato's Theaetetus develops an inquiry concerning the definition of knowledge. Famously, after Socrates and Theaetetus have discussed the three candidates for the definition of knowledge, the end of the dialogue seems to leave us in a situation of aporia. The present article focuses on the last hypothesis raised in the dialogue and tries to determine whether this hypothesis can be seen, under appropriate qualification, as acceptable within a Platonic framework. This hypothesis is connected with a dream theory that unfolds two crucial factors for understanding the definition of knowledge, i.e. elements and logos. So the aim of this paper is twofold: on the one hand, to make clear what elements properly are; on the other hand, to find an account of logos suitable to make it a necessary condition for the definition of knowledge. As will emerge from this paper, the first two candidates for the definition of knowledge are indeed not sufficient for gaining an adequate definition, but they nonetheless foreshadow the third hypothesis and are necessary conditions for understanding the third one.

scholarly journals Procedural Errors in the Evidentiary Process and Their Impact on Criminal Proceedings in the Slovak Republic

2021 ◽  
Vol 13 (2) ◽  
pp. 96-110
Author(s):  
Ivana Mokra
Keyword(s):  
Law Enforcement ◽  
Slovak Republic ◽  
The Other ◽  
Necessary Condition ◽  
Criminal Proceedings ◽  
Other Hand ◽  
Procedural Error ◽  
The One ◽  
Insight Into

The lawful procedure in evidentiary process is a conditio sine qua non of the admissibility of evidence. In other words, it is a necessary condition for the admission of evidence in criminal proceedings. The violation of this condition leads to procedural errors leading to the unlawfulness of the evidence, as a result of which the accused may be acquitted. For this reason, it's the aim of this article, not only to define the procedural errors, whose incidence is particularly noticeable in providing evidence by law enforcement authorities involved in criminal proceedings, but also to analyse their impact on the outcome of the criminal proceedings, i.e. the decision about the guilt and punishment of the accused and on the basis of a specific example, to point out shortcomings which would be appropriate to prevent de lege ferenda. The presented article provides, on the one hand, a brief insight into the basic terminology related to the mentioned topic, explains the content and purpose of the legislation and on, the other hand, acquires more practical view, based on an analysis of selected example of procedural error in evidentiary process.

Sign in / Sign up

Export Citation Format

Share Document