Causality is Undefinable Toward a Theory of Hierarchical Definability
نویسنده
چکیده
Attempts to formulate mathematically precise definitions of basic concepts such as causality, randomness, and probability, have a long history. The concept of generalized definability that is outlined in this project suggests that such definitions may not exist. Furthermore, it suggests that existing definitions of many basic concepts, among them those of stability, statistical independence, and Pareto-optimality, may need to be redefined.
منابع مشابه
Fuzzy Logic as a Basis for a Theory of Hierarchical Definability (THD)
Attempts to formulatemathematically precise definitions of basic concepts such as causality, randomness and probability have a long history. The concept of hierarchical definability that is outlined in the following suggests that such definitions may not exist. Furthermore, it suggests that existing definitions of many basic concepts, among them those of linearity stability, statistical indepen...
متن کاملDefinable fixed points in modal and temporal logics : A survey
The paper presents a survey of author’s results on definable fixed points in modal, temporal, and intuitionistic propositional logics. The well-known Fixed Point Theorem considers the modalized case, but here we investigate the positive case. We give a classification of fixed point theorems, describe some classes of models with definable least fixed points of positive operators, special positiv...
متن کاملModal Definability in Enriched Languages
The paper deals with polymodal languages combined with standard semantics defined by means of some conditions on the frames. So a notion of "polymodal base" arises which provides various enrichments of the classical modal language. One of these enrichments, viz. the base £(R,-R), with modalities over a relation and over its complement, is the paper's main paradigm. The modal definability (in th...
متن کاملs . ge n - ph ] 2 6 Ju n 20 06 DEFINABILITY IN PHYSICS
The concept of definability of physical fields in a set-theoretical foundation is introduced. We propose an axiomatic set theory and show that the Schrödinger equation and, more generally, a nonlinear sigma model can be derived from a null postulate and that quantization of fields is equivalent to definability. We find that space-time is relational in this theory. Some examples of the relevance...
متن کامل00 4 Definability and a Nonlinear Sigma Model
The concept of definability of physical fields in a set-theoretical foundation is introduced. A set theory is selected in which we get mathematics enough to produce a nonlinear sigma model. Quantization of the model requires only a null postulate and is then shown to be necessary and sufficient for definability in the theory. We obtain scale invariance and compactifica-tion of the spatial dimen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001