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Parrondo's paradox (PP) is a fundamental principle in nonlinear science where the alternation of individually losing strategies leads to a winning outcome. In this topical review, we provide the first systematic panorama of the synergy…
Information (I) is defined as the amount of the data after data compression. The first law of information theory: the total amount of data L (the sum of entropy S and information I) of an isolated system remains unchanged. The second law of…
Modern physics is founded on two mainstays: mathematical modelling and empirical verification. These two assumptions are prerequisite for the objectivity of scientific discourse. Here we show, however, that they are contradictory, leading…
Philosophers writing about the ravens paradox often note that Nicod's Condition (NC) holds given some set of background information, and fails to hold against others, but rarely go any further. That is, it is usually not explored which…
Gray (2015) argued that the Fermi paradox (FP) is a misnomer, and it is not a valid paradox. Gray also speculated that the argument was misattributed to Fermi, whose lunchtime remarks did not pertain to the existence of extraterrestrial…
We study the effects of individual perceptions of payoffs in two-player games. In particular we consider the setting in which individuals' perceptions of the game are influenced by their previous experiences and outcomes. Accordingly, we…
The so-called paradoxes of material implication have motivated the development of many non-classical logics over the years \cite{aA75,nB77,aA89,gP89,sH96}. In this note, we investigate some of these paradoxes and classify them, over minimal…
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
The combination of evidence in Dempster-Shafer theory is compared with the combination of evidence in probabilistic logic. Sufficient conditions are stated for these two methods to agree. It is then shown that these conditions are minimal…
In this work, Gibbs paradox was discussed from the view of observer. The limitations of real observer are analyzed quantitatively. The entropy of mixing was found to be determined by both the identification ability and the information…
Social discrimination seems to be a persistent phenomenon in many cultures. It is important to understand the mechanisms that lead people to judge others by the group to which they belong, rather than individual qualities. It was recently…
The method of maximum entropy has been very successful but there are cases where it has either failed or led to paradoxes that have cast doubt on its general legitimacy. My more optimistic assessment is that such failures and paradoxes…
The friendship paradox -- the observation that, on average, one's friends have more friends than oneself -- admits two common formulations depending on whether averaging is performed over edges or over nodes. These two definitions, the…
We colour every point x of a probability space X according to the colours of a finite list x_1, ...., x_k of points such that each of the x_i, as a function of x, is a measure preserving transformation. We ask two questions about a…
It is shown that the "twin paradox" arises from comparing unlike entities, namely perceived intervals with eigenintervals. When this lacuna is closed, it is seen that there is no twin paradox and that eigentime can serve as the independent…
There has been a surge of recent interest in the Wigner's Friend paradox, sparking several novel thought experiments and no-go theorems. The main narrative has been that Wigner's Friend highlights a counterintuitive feature that is unique…
Simpson's paradox and collapsibility are two closely related concepts in the context of data analysis. While the knowledge about the occurrence of Simpson's paradox helps a statistician to draw correct and meaningful conclusions, the…
This paper introduces the basic concepts of information theory. Based on these concepts, we regard the states in the state space and the types of ideal gases as the symbols in a symbol set to calculate the mixing entropy of ideal gas…
Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on the rule-following…
The analysis of the arguments within the limits of the classical thermodynamics that lead to the Gibbs paradox was made. Features of preconditions used in the derivation of the entropy of mixing of ideal gases that caused the appearance of…