Logique et Analyse
http://poj.peeters-leuven.be/content.php?url=journal&journal_code=LEA
Recent articles(De)motivating Glutspoj@peeters-leuven.behttp://dx.doi.org/10.2143/LEA.246.0.3286440
http://poj.peeters-leuven.be/content.php?url=article&id=3286440
Wed, 10 Jul 2019 07:33:50 +0000Should Mathematics Play Dice?poj@peeters-leuven.behttp://dx.doi.org/10.2143/LEA.246.0.3286441
http://poj.peeters-leuven.be/content.php?url=article&id=3286441
Wed, 10 Jul 2019 07:35:12 +0000Paradeduction in Axiomatic Formal Systemspoj@peeters-leuven.behttp://dx.doi.org/10.2143/LEA.246.0.3286442
http://poj.peeters-leuven.be/content.php?url=article&id=3286442
Wed, 10 Jul 2019 07:36:20 +0000
This paper presents the concept of <i>paradeduction</i> in order to justify that we can overlook contradictory information taking into account only what is consistent. Besides that, it uses paradeduction to show that there is a way to transform any logic, introduced as an axiomatic formal system, into a paraconsistent one.
On the Nature of Discrete Space-Timepoj@peeters-leuven.behttp://dx.doi.org/10.2143/LEA.246.0.3286443
http://poj.peeters-leuven.be/content.php?url=article&id=3286443
Wed, 10 Jul 2019 07:52:47 +0000
In this work, the relativistic phenomena of Lorentz-Fitzgerald contraction and time dilation are derived using a modified distance formula that is appropriate for discrete space. This new distance formula is different than the Pythagorean theorem but converges to it for distances large relative to the Planck length. First, four candidate formulas developed by different people over the last 70 years are discussed. Three of the formulas are shown to be identical for conditions that best describe discrete space. It is shown that this new distance formula is valid for all size-scales, from the Planck length upwards, and solves two major problems historically associated with the discrete space-time (DST) model. One problem it solves is the widely believed anisotropic nature of most discrete space models. Just as commonly believed is the second problem: the incompatibility of DST's concept of an <i>immutable</i> atom of space and the length contraction of this atom required by special relativity. The new formula for the calculations of distance in DST solves this problem. It is shown that length contraction of the atom of space <i>does not occur</i> for any relative velocity of reference frames. It is also shown that time dilation of the atom of time does not occur. Also discussed is the possibility of any object being able to travel at the speed of light for specific temporal durations given by an equation derived in this work. Also discussed is a method to empirically verify the discreteness of space by studying any observed anomalies in the motion of astronomical bodies, such as differences in the bodies' inertial masses and gravitational masses. The importance of the new distance formula for causal set theory and other theories of quantum gravity is also discussed.