Foundations of Science

, Volume 19, Issue 3, pp 289–306 | Cite as

Reality, Systems and Impure Systems

  • J. Nescolarde-SelvaEmail author
  • J. L. Usó-Doménech


Impure systems contain Objects and Subjects: Subjects are human beings. We can distinguish a person as an observer (subjectively outside the system) and that by definition is the Subject himself, and part of the system. In this case he acquires the category of object. Objects (relative beings) are significances, which are the consequence of perceptual beliefs on the part of the Subject about material or energetic objects (absolute beings) with certain characteristics.The IS (Impure System) approach is as follows: Objects are perceptual significances (relative beings) of material or energetic objects (absolute beings). The set of these objects will form an impure set of the first order. The existing relations between these relative objects will be of two classes: transactions of matter and/or energy and inferential relations. Transactions can have alethic modality: necessity, possibility, impossibility and contingency. Ontic existence of possibility entails that inferential relations have Deontic modality: obligation, permission, prohibition, faculty and analogy. We distinguished between theorems (natural laws) and norms (ethical, legislative and customary rules of conduct).


Connotation Denotation Impure sets Impure systems Reality  Sign Significance Significant Subject System 


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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of AlicanteAlicanteSpain
  2. 2.Department of MathematicsUniversity of Jaume ICastelló de la PlanaSpain

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