Let K be a field and v a valuation on K. We discuss some properties of extensions w of v to the field K(X1, . . . , Xn) of rational functions in n variables over K, for which the residue field of w has transcendence degree n over the residue field of v. 2000 Mathematics Subject Classification: 12J20, 12F20. 1.Introduction LetK be a field and v a valuation onK. Residual transcendental extensions...

principality of existence, which is one of the most fundamental issues in primary philosophy, is one of the main branches of ṣadr al-muti’allihīn's philosophy and nearly all discourses of transcendental philosophy are considered to be based on it, to the extent that the transcendence of mullā ṣadrā’s philosophy is considered due to the transcendence of existence and the “existence” as his first...

To begin with, recall that a complex number α is said to be a root of a polynomial P (X) if P (α) = 0. A complex number α is said to be algebraic if there is a nonzero polynomial P (X), with integer coefficients, of which α is a root. The set of algebraic numbers is denoted by Q̄. A complex number α which is not algebraic is said to be transcendental. The following numbers are obviously algebrai...

Maharishi Mahesh Yogi approaches peace from collective consciousness, the holistic level of society where all its component parts are integrated. Collective consciousness arises from the consciousness of all individuals in society and reciprocally influences each individual’s consciousness and behavior. The basis of all levels of individual and collective consciousness is transcendental conscio...

two meanings regarding the principality of existence (isālat al-wujūd) can be inferred from the works and words of mulla sadra. one meaning is the objectivity of existence and essence on which many issues of transcendental philosophy are based. this meaning has deep philosophical consequences and implications. it seems that this meaning causes certain problems which make its acceptance tricky. ...

Hobson (2009) highlights the contribution of lucid dreaming research to the field of consciousness study. Hobson (2009) also sites a lack of paradigms and theoretical models of consciousness to advance lucid dreaming research. However in addition to Hobsons’ AIM model (Hobson, Pace-Schott & Stickgold, 2000), there exists discussions of developmental models of consciousness that include lucid dr...

In this essay, I argue that Wittgenstein attempted to clarify ethics through a procedure that, by analogy with “transcendental arguments”, call thought experiment”. Specifically, after offering brief perspectival account of both transcendental arguments and experiments, focus on experiment proposed in his 1929 Lecture Ethics, arguing it deserves the title “transcendental”.

Varga (2012) argues that the sense of reality disrupted in various psychopathologies, including derealization (DR) and depersonalization (DP), is pre-intentional (or in some sense, the product of a more basic, operative intentionality that is pre-predicative). This moves us away from the more dominant conceptions of delusion and the loss of sense of reality as problems best explained in terms o...