Set Theory and Logic

1904 Submissions

[3] viXra:1904.0145 [pdf] submitted on 2019-04-07 17:06:59

“Fuzzy Time”, a Solution of Unexpected Hanging Paradox (a Fuzzy Interpretation of Quantum Mechanics)

Authors: Farzad Didehvar
Comments: 6 Pages.

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzifying Turing Machines but seemingly there is no need to fuzzify time. Throughout this article, we try to change this picture and show why it is helpful to consider the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Paraconsistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time.
Category: Set Theory and Logic

[2] viXra:1904.0129 [pdf] submitted on 2019-04-06 14:00:21

The Surprise Exam Paradox: Students Should be Surprised on Wednesday or Tuesday.

Authors: Tomonori Hirasa
Comments: 2 Pages.

The students in the surprise exam story reasoned that no surprise exam could take place on any day of the week. Actually, however, the students were surprised on Wednesday by the teacher's surprise exam. In this paper, we show where the students' reasoning went wrong and that students should be surprised on Wednesday or Tuesday.
Category: Set Theory and Logic

[1] viXra:1904.0095 [pdf] submitted on 2019-04-04 08:40:19

Propositional Logic Without The Deduction Theorem

Authors: Henry Wong
Comments: 3 Pages.

In propositional logic, given a set of axioms, we can derive formulas. Here we present the derivations of some formulas without the use of the Deduction Theorem. The derivations are presented compactly with only few referrals to other theorems. Most textbooks in this subject avoid this kind of approach.
Category: Set Theory and Logic