Curry's paradox in contractionless constructive logic

We propose contractionless constructive logic which is obtained from Nelson's constructive logic by deleting contractions. We discuss the consistency of a naive set theory based on the proposed logic in relation to Curry's paradox. The philosophical significance of contractionless constructive logic is also argued in comparison with Fitch's and Prawitz's systems.     

A geo-logical solution to the lottery paradox, with applications to conditional logic

We defend a set of acceptance rules that avoids the lottery paradox, that is closed under classical entailment, and that accepts uncertain propositions without ad hoc restrictions. We show that the rules we recommend provide a semantics that validates exactly Adams?? conditional logic and are exactly the rules that preserve a natural, logical structure over probabilistic credal states that we call probalogic. To motivate probalogic, we first expand classical logic to geo-logic, which fills the entire unit cube, and then we project the upper surfaces of the geo-logical cube onto the plane of probabilistic credal states by means of standard, linear perspective, which may be interpreted as an extension of the classical principle of indifference. Finally, we apply the geometrical/logical methods developed in the paper to prove a series of trivialization theorems against question-invariance as a constraint on acceptance rules and against rational monotonicity as an axiom of conditional logic in situations of uncertainty.     

The corroboration paradox

Evidentiary propositions E ₁ and E ₂, each p-positively relevant to some hypothesis H, are mutually corroborating if p(H|E ₁ ∩ E ₂) > p(H|E _i ), i = 1, 2. Failures of such mutual corroboration are instances of what may be called the corroboration paradox. This paper assesses two rather different analyses of the corroboration paradox due, respectively, to John Pollock and Jonathan Cohen. Pollock invokes a particular embodiment of the principle of insufficient reason to argue that instances of the corroboration paradox are of negligible probability, and that it is therefore defeasibly reasonable to assume that items of evidence positively relevant to some hypothesis are mutually corroborating. Taking a different approach, Cohen seeks to identify supplementary conditions that are sufficient to ensure that such items of evidence will be mutually corroborating, and claims to have identified conditions which account for most cases of mutual corroboration. Combining a proposed common framework for the general study of paradoxes of positive relevance with a simulation experiment, we conclude that neither Pollock’s nor Cohen’s claims stand up to detailed scrutiny. I am quite prepared to be told…”oh, that is an extreme case: it could never really happen!” Now I have observed that this answer is always given instantly, with perfect confidence, and without any examination of the proposed case. It must therefore rest on some general principle: the mental process being something like this—“I have formed a theory. This case contradicts my theory. Therefore, this is an extreme case, and would never occur in practice.” Rev. Charles L. Dodgson      

The revenger's paradox

Conclusion Unlike the more commonly discussed paradoxes of deontic logic, the revenger's paradox is present not only in strong logics such as SDL, but also in much weaker logics that have been constructed to avoid the paradoxes of SDL. The paradox shows that any deontic logic with intersubstitutivity makes counter-intuitive truth assignments to some deontic expressions.However, the revenger's paradox does not pose as serious a problem as does Ross's paradox to the logics in which it occurs. A deontic logic in which Ross's paradox does not arise is preferable to one in which it does arise, even if the latter is subject to the revenger's paradox.     

The paradox of evolution

In the second (and expanded) version of Origin of the Species, Darwin introduces the term “advanced progressive development” in an attempt to describe the development of the more complex species from the simpler ones. More than 100 years have passed since Darwin tried to qualify and conceptualize the directional question of evolution, and very little progress has been made regarding the subject. The appearance of the species, from the simple to the more complex, is today an empirical fact, one which is no longer dependent upon any theory, including that of Darwin. This work examines the subject of advanced development in evolution by attempting to answer a few basic questions: What parameters may be used to evaluate complexity? Can any rules or order be identified as to the development of the species? Is the mechanism of “natural selection” sufficient to explain the direction or ‘purpose’ of evolution? Can the human race be included within the “rules” of Darwin's evolutionary theory?

The purpose of this essay is to develop and represent a new conceptual framework. Through this, it will be possible to offer a principle answer to all four questions.     

The paradox of creativity

Creativity seems to yield survival and reproductive benefits. Creative behaviors allow individuals to solve problems in new and appropriate ways, and thus to promote their survival. They also facilitate bonding and constitute a signal of one's fitness, favoring attraction of mates. However, to be creative, individuals often have to violate social norms in order to promote change. So far, this deviance induced by creative behaviors had not been seen as an adaptive disadvantage. This deviance entails negative consequences as social exclusion or ostracism, which are detrimental for both survival (e.g., reduced access to resources within the group) and reproduction (reduced reproductive fitness). Thus, the adaptive benefits yielded by creativity have to be nuanced by these potential disadvantages. The paradox of creativity proposes a finer-grained vision of the adaptive reasons why creativity has been maintained within the human species, has evolved, and is collectively regulated. Research perspectives are also proposed.