The enumeration of elements of c.e. sets in the theory of computability and computational complexity has already been investigated. However, the order of this enumeration has received less attention. The enumeration o...The enumeration of elements of c.e. sets in the theory of computability and computational complexity has already been investigated. However, the order of this enumeration has received less attention. The enumeration orders of elements of c.e. sets by means of Turing machines on natural numbers are investigated. In this paper, we consider the enumeration orders of elements of c.e. sets on rational numbers. We present enumeration order reducibility and enumeration order equivalence on rational numbers and propose some lemmas and theorems on these concepts. Also, we show that the theories here hold for Rc and we could repeat the same theories in this domain, in a same way.展开更多
The incredible extent of current environmental destruction justifies the modern concern to resist the alienated view of nature as a resource to exploit a totality of dead and meaningless objects, a totally disenchante...The incredible extent of current environmental destruction justifies the modern concern to resist the alienated view of nature as a resource to exploit a totality of dead and meaningless objects, a totally disenchanted world. In this spirit, modern philosophy tries to take nature seriously by recapturing a sense of nature＇s intrinsic value. Hegel respects nature to the extent that it bears the trace of the human mind, to the extent that it is forced ＂to speak the voice of reason.＂ Although there are grounds for being critical of the Hegelian project, especially because Hegel remains silent on the issue of our duties towards nature for the sake of nature and his argumentation serves the primordial desires of human reasoning and not the rights of nature itself, it is suggested that no matter how much inauthentic and incomplete is the recognition that the human mind acquires in its dialectical confrontations with nature. Hegelian phenomenology grants the human mind with a remarkable degree of self-certainty, necessary for all its subsequent educational enterprises.展开更多
文摘The enumeration of elements of c.e. sets in the theory of computability and computational complexity has already been investigated. However, the order of this enumeration has received less attention. The enumeration orders of elements of c.e. sets by means of Turing machines on natural numbers are investigated. In this paper, we consider the enumeration orders of elements of c.e. sets on rational numbers. We present enumeration order reducibility and enumeration order equivalence on rational numbers and propose some lemmas and theorems on these concepts. Also, we show that the theories here hold for Rc and we could repeat the same theories in this domain, in a same way.
文摘The incredible extent of current environmental destruction justifies the modern concern to resist the alienated view of nature as a resource to exploit a totality of dead and meaningless objects, a totally disenchanted world. In this spirit, modern philosophy tries to take nature seriously by recapturing a sense of nature＇s intrinsic value. Hegel respects nature to the extent that it bears the trace of the human mind, to the extent that it is forced ＂to speak the voice of reason.＂ Although there are grounds for being critical of the Hegelian project, especially because Hegel remains silent on the issue of our duties towards nature for the sake of nature and his argumentation serves the primordial desires of human reasoning and not the rights of nature itself, it is suggested that no matter how much inauthentic and incomplete is the recognition that the human mind acquires in its dialectical confrontations with nature. Hegelian phenomenology grants the human mind with a remarkable degree of self-certainty, necessary for all its subsequent educational enterprises.
