Paradoxes of the Always Already

This paper shows the relevance of findings from studying the logic of self-referential statements to Cultural studies, Black Cultural Studies in particular. Results following from the incompleteness of the systems in which these statements are quantified help to clear up a paradox stemming from current Afropessimist discourse.     

Paradoxes of Falsification

This paper deals with the concept of falsification in hypothesis testing research. A theoretical analysis of assumptions about falsifying behaviour and hypothesis-falsifying observations is presented, with two experimental studies. Both the theoretical analysis and the experimental results point to a number of paradoxes underlying the normative principle of falsification in cognitive psychology. First, subjects experience the falsificatory testing strategy as an impossible strategy to conduct. Obtaining falsifying results is a consequence of the quality of the hypothesis rather than of specific testing behaviour (Experiment 1 and Experiment 2). Second, under some conditions falsifying results impede rather than facilitate discovery (Experiment 2). Confirmatory testing and falsificatory testing, which have been the crucial concepts in the study of hypothesis-testing behaviour, may actually be questionable approaches to testing behaviour. The theoretical analysis is related to the standard analyses of Popper (1963) and Klayman and Ha (1987). The empirical results are discussed in relation to previous studies on falsificatory testing behaviour.     

Paradoxes of happiness

To get happiness forget about it; then, with any luck, happiness will come as a by-product in pursuing meaningful activities and relationships. This adage is known as the paradox of happiness, but actually it contains a number of different paradoxes concerning aims, success, freedom, and attitudes. These paradoxes enhance our understanding of the complexity of happiness and its interaction with other values in good lives, that is, lives which are happy as well as morally decent, meaningful, and fulfilling. Yet, each paradox conveys a one-sided truth that needs to be balanced with others. Happiness, understood as subjective well-being, involves positively evaluating our lives and living with a sense of well-being. As such, it should not be confused with either pleasure or normative conceptions of “true” happiness.     

Logical Consequence and the Paradoxes

We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are tightly related, and can be cleared up by adopting a particular substructural logic in place of classical logic. We then argue that our perspective can be justified via an informational semantics of contraction-free substructural logics.     

Minimalism and Paradoxes

This paper argues against minimalism about truth. It does so by way of acomparison of the theory of truth with the theory of sets, and considerationof where paradoxes may arise in each. The paper proceeds by asking twoseemingly unrelated questions. First, what is the theory of truth about?Answering this question shows that minimalism bears important similaritiesto naive set theory. Second, why is there no strengthened version ofRussell's paradox, as there is a strengthened Liar paradox? Answering thisquestion shows that like naive set theory, minimalism is unable to makeadequate progress in resolving the paradoxes, and must be replaced by adrastically different sort of theory. Such a theory, it is shown, must befundamentally non-minimalist.     

Paradoxes of qualitative research

In qualitative research paradoxes abound in research design, sampling, generalisation, ethics and the behaviour of the researcher. The ultimate paradox is that qualitative inquiry is impossible — both conceptually and practically — yet it still goes on. It must do so if the professions of counselling and psychotherapy are to advance.     

Antonyms and Paradoxes

Adjectives can be gradable or non-gradable and this aspect of their meaning is responsible for their different distribution and also for their classification into two different classes of antonyms. Non-gradable antonyms are called contradictories: they are neither true nor false together and exclude any middle term; gradable antonyms are called contraries: they are not simultaneously true, but may be simultaneously false. While with contraries a negative disjunction (neque...neque) can define an intermediate level, with contradictories it simply means that either term of the disjunction is excluded. There are however some Latin examples, such as neque vivus neque mortuus (`neither alive nor dead'), where the negation of a contradictory pair is used to convey a third, intermediate value. This third possibility is precisely what gives place to a paradox. Such an intermediate level can be defined also by terms like semivivus, semianimis (`half-dead'). Following Ducrot's theory on argumentation, such terms represent an argumentative attenuation, not with respect to life, rather with respect to death. With contradictories, in fact, the use of semi-, like the use of negation, gives the assertion of the opposite term as a result.     

Mental Causation and the Paradoxes of Explanation

In this paper I will discuss Kims powerful explanatory exclusion argument against the causal efficacy of mental properties. Baker and Burge misconstrue Kims challenge if they understand it as being based on a purely metaphysical understanding of causation that has no grounding in an epistemological analysis of our successful scientific practices. As I will show, the emphasis on explanatory practices can only be effective in answering Kim if it is understood as being part of the dual-explanandum strategy. Furthermore, a fundamental problem of the contemporary debate about mental causation consists in the fact that all sides take very different examples to be paradigmatic for the relation between psychological and neurobiological explanations. Even if we should expect some alignment in the explanatory scope of neurobiology and psychology/folk-psychology, there is no reason to expect that all mental explanations are exempted by physical explanations, since they do not in general explain the same phenomena.     

Definability and the Structure of Logical Paradoxes

Graham Priest 2002 argues that all logical paradoxes that include set-theoretic paradoxes and semantic paradoxes share a common structure, the Inclosure Schema, so they should be treated as one family. Through a discussion of Berry's Paradox and the semantic notion ‘definable’, I argue that (i) the Inclosure Schema is not fine-grained enough to capture the essential features of semantic paradoxes, and (ii) the traditional separation of the two groups of logical paradoxes should be retained.     

Liar-type Paradoxes and the Incompleteness Phenomena

We define a liar-type paradox as a consistent proposition in propositional modal logic which is obtained by attaching boxes to several subformulas of an inconsistent proposition in classical propositional logic, and show several famous paradoxes are liar-type. Then we show that we can generate a liar-type paradox from any inconsistent proposition in classical propositional logic and that undecidable sentences in arithmetic can be obtained from the existence of a liar-type paradox. We extend these results to predicate logic and discuss Yablo’s Paradox in this framework. Furthermore, we define explicit and implicit self-reference in paradoxes in the incompleteness phenomena.