Freedom, Discipline and Bondage

Philosophy ◽  
1949 ◽  
Vol 24 (89) ◽  
pp. 133-143
Author(s):  
Maurice Cranston

I believe we could learn more about freedom if we talked less about freedom. Because “freedom” is a word with singular prestige, various moral philosophers have embodied it in their teaching and claimed to set forth its true characteristics. Many words employed in philosophical controversy are ambiguous. “Freedom,” I think, is one of the most troublesome. I propose to attempt some disentanglement.To begin with, there is a sense in which the meaning of “freedom” seems to present no difficulties. This sense occurs in such a remark as: “That animal was in captivity and now it is free.” I shall call this “simple freedom” and what it means is the absence of constraint. Thus applied there would probably be general agreement about the word. The difficulties arise when we come to consider freedom as pertaining to human persons. Here the distinction between simple freedom and the more philosophical definitions of the word will emerge.On the simple definition a man is free if constraint is absent, and that is all there is to it. But this will not do for most philosophers.It is pointed out that man is a special case in that he experiences conflicting desires. He wills a thing and he does not will it; or he wills something and at the same time he wills something else which is incompatible with it. Man, we are reminded, is a rational creature, but besides his rational will he is subject to the solicitations of impulses and desires which are not rational. Therefore, it is argued, the mere absence of constraint is not a sufficient condition of human freedom and hence not a sufficient definition of the word “freedom” as applied to human persons.

1981 ◽  
Vol 4 (3) ◽  
pp. 531-549 ◽  
Author(s):  
Miklós Szijártó

The correspondence between sequential program schemes and formal languages is well known (Blikle and Mazurkiewicz (1972), Engelfriet (1974)). The situation is more complicated in the case of parallel program schemes, and trace languages (Mazurkiewicz (1977)) have been introduced to describe them. We introduce the concept of the closure of a language on a so called independence relation on the alphabet of the language, and formulate several theorems about them and the trace languages. We investigate the closedness properties of Chomsky classes under closure on independence relations, and as a special case we derive a new necessary and sufficient condition for the regularity of the commutative closure of a language.


1987 ◽  
Vol 10 (4) ◽  
pp. 671-692 ◽  
Author(s):  
Ahmed I. Zayed

In this paper we extend the definition of the continuous Jacobi transform to a class of generalized functions and obtain a generalized inversion formula for it. As a by-product of our technique we obtain a necessary and sufficient condition for an analytic functionF(λ)inReλ>0to be the continuous Jacobi transform of a generalized function.


2009 ◽  
Vol 18 (5) ◽  
pp. 691-705 ◽  
Author(s):  
GYÖRGY ELEKES ◽  
MIKLÓS SIMONOVITS ◽  
ENDRE SZABÓ

We give a very general sufficient condition for a one-parameter family of curves not to have n members with ‘too many’ (i.e., a near-quadratic number of) triple points of intersections. As a special case, a combinatorial distinction between straight lines and unit circles will be shown. (Actually, this is more than just a simple application; originally this motivated our results.)


Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1018
Author(s):  
Xhevdet Thaqi ◽  
Ekrem Aljimi

: In this paper, we consider the relation of more than four harmonic points in a line. For this purpose, starting from the dependence of the harmonic points, Desargues’ theorems, and perspectivity, we note that it is necessary to conduct a generalization of the Desargues’ theorems for projective complete n-points, which are used to implement the definition of the generalization of harmonic points. We present new findings regarding the uniquely determined and constructed sets of H-points and their structure. The well-known fourth harmonic points represent the special case (n = 4) of the sets of H-points of rank 2, which is indicated by P42.


Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.


2012 ◽  
Vol 22 (06) ◽  
pp. 1250130
Author(s):  
CHANGMING DING

This paper deals with intertwined basins of attraction for dynamical systems in a metric space. After giving a general definition of intertwining property, which is preserved by a topological equivalence between dynamical systems, we present a sufficient condition to guarantee the existence of intertwined basins for dynamical systems in ℝn.


1972 ◽  
Vol 2 (1) ◽  
pp. 127-133
Author(s):  
Harold Morick

In the last two decades, there has been a great deal of interest in providing an intentional criterion of the psychological. Of the various ones proferred, it seems to me that the best was the earliest, which was Chisholm’s initial criterion in his 1955 essay “Sentences about Believing.” In this present paper I first single out a basic misconception pervading the recent literature on intentionality and suggest that a consequence of this misconception has been the futile attempt to use the notion of intentionality to provide a kind of definition of “mind”; that is, to use intentionality to provide a necessary and sufficient condition for the psychological. Secondly, I point out how intentionality as captured by my own criterion is indispensable in that it is an essential property of certain particulars (persons) which are basic to our conceptual scheme and apparently basic to any conceptual scheme whatsoever.


2021 ◽  
Vol 45 (02) ◽  
pp. 237-258
Author(s):  
ABSOS ALI SHAIKH ◽  
TRAN QUOC BINH ◽  
HARADHAN KUNDU

The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metrics. It is shown that a generalized pp-wave spacetime is Ricci generalized pseudosymmetric, 2-quasi-Einstein and generalized quasi-Einstein in the sense of Chaki. As a special case it is shown that pp-wave spacetime is semisymmetric, semisymmetric due to conformal and projective curvature tensors, R-space by Venzi and satisfies the pseudosymmetric type condition P ⋅ P = −13Q(S,P). Again we investigate the sufficient condition for which a generalized pp-wave spacetime turns into pp-wave spacetime, pure radiation spacetime, locally symmetric and recurrent. Finally, it is shown that the energy-momentum tensor of pp-wave spacetime is parallel if and only if it is cyclic parallel. Again the energy momentum tensor is Codazzi type if it is cyclic parallel but the converse is not true as shown by an example. Finally, we make a comparison between the curvature properties of the Robinson-Trautman metric and generalized pp-wave metric.


Author(s):  
Christian Haesemeyer ◽  
Charles A. Weibel

This chapter provides the main steps in the proof of Theorems A and B regarding the norm residue homomorphism. It also proves several equivalent (but more technical) assertions in order to prove the theorems in question. This chapter also supplements its approach by defining the Beilinson–Lichtenbaum condition. It thus begins with the first reductions, the first of which is a special case of the transfer argument. From there, the chapter presents the proof that the norm residue is an isomorphism. The definition of norm varieties and Rost varieties are also given some attention. The chapter also constructs a simplicial scheme and introduces some features of its cohomology. To conclude, the chapter discusses another fundamental tool—motivic cohomology operations—as well as some historical notes.


2019 ◽  
pp. 9-20
Author(s):  
Paul Humphreys

The need to solve analytically intractable models has led to the rise of a new kind of science, computational science, of which computer simulations are a special case. It is noted that the development of novel mathematical techniques often drives scientific progress and that even relatively simple models require numerical treatments. A working definition of a computer simulation is given and the relation of simulations to numerical methods is explored. Examples where computational methods are unavoidable are provided. Some epistemological consequences for philosophy of science are suggested and the need to take into account what is possible in practice is emphasized.


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