The Concept of Evenness/Unevenness: Less Evenness or More Unevenness?

While evenness is understood to be maximal if all types (species, genotypes, alleles, etc.) are represented equally (via abundance, biomass, area, etc.), its opposite, maximal unevenness, either remains conceptually in the dark or is conceived as the type distribution that minimizes the applied evenness index. The latter approach, however, frequently leads to conceptual inconsistency due to the fact that the minimizing distribution is not specifiable or is monomorphic. The state of monomorphism, however, is indeterminate in terms of its evenness/unevenness characteristics. Indeed, the semantic indeterminacy also shows up in the observation that monomorphism represents a state of pronounced discontinuity for the established evenness indices. This serious conceptual inconsistency is latent in the widely held idea that evenness is an independent component of diversity. As a consequence, the established evenness indices largely appear as indicators of relative polymorphism rather than as indicators of evenness. In order to arrive at consistent measures of evenness/unevenness, it seems indispensable to determine which states are of maximal unevenness and then to assess the position of a given type distribution between states of maximal evenness and maximal unevenness. Since semantically, unevenness implies inequality among type representations, its maximum is reached if all type representations are equally different. For given number of types, this situation is realized if type representations, when ranked in descending order, show equal differences between adjacent types. We term such distributions “stepladders” as opposed to “plateaus” for uniform distributions. Two approaches to new evenness measures are proposed that reflect different perspectives on the positioning of type distributions between the closest stepladders and the closest plateaus. Their two extremes indicate states of complete evenness and complete unevenness, and the midpoint is postulated to represent the turning point between prevailing evenness and prevailing unevenness. The measures are graphically illustrated by evenness surfaces plotted above frequency simplices for three types, and by transects through evenness surfaces for more types. The approach can be generalized to include variable differences between types (as required in analyses of functional evenness) by simply replacing types with pairs of different types. Pairs, as the new types, can be represented by their abundances, for example, and these can be modified in various ways by the differences between the two types that form the pair. Pair representations thus consist of both the difference between the paired types and their frequency. Omission of pair frequencies leads to conceptual ambiguity. Given this specification of pair representations, their evenness/unevenness can be evaluated using the same indices developed for simple types. Pair evenness then turns out to quantify dispersion evenness.

Vagueness

This chapter centres on what it terms the Vagueness Trilemma: that what may impress as the only three possible types of view about what vagueness is—namely, that it is a matter of semantic indeterminacy, that it originates in rebus, and the epistemicist idea that it is a matter of our ineluctable ignorance about fully determinate matters— are each open to serious, indeed arguably fatal, objections. The chapter is organized about the possible attitudes to three interrelated, nodal theses. Bivalence—are borderline statements bivalent? Third possibility—do they possess some third alethic status—lack of truth value or some third truth value? And Verdict Exclusion: is knowledge of truth value precluded in borderline cases? It is argued that there are five consistent combinations of acceptance and non-acceptance of the three nodal issues, and that an attitude of agnosticism to all three, and a consequent broadly intuitionistic attitude to vagueness, is the way out of the Trilemma.

Sources of legal indeterminacy

Traditional analyses characterise or identify vagueness and ambiguity as the sole or primary sources of legal indeterminacy. In this article, I identify and characterise various other sources of legal indeterminacy. In addition to the semantic indeterminacy of vagueness and ambiguity, philosophers of language have identified conversational, pragmatic, and contextual indeterminacy, each of which is capable of generating a ‘hard case’ as applied to the legal sphere. Nor is all legal indeterminacy linguistic in nature. Following Henry Prakken, I identify non-monotonicity, or the fact that legal inferences are defeasible, as a final source of legal indeterminacy. Each source of legal indeterminacy thus identified includes case-law examples to aid in the discussion.

Locke on Fixing Ideas

I argue that Locke’s distinction between ‘determined’ and ‘undetermined’ ideas incorporates an account of semantic indeterminacy: if the complex idea to which a general term is annexed is ‘undetermined’, the term lacks a determinate extension. I propose that a closer look at this account of semantic indeterminacy illuminates various charges of confusion, misuse and abuse of language Locke levels against his philosophical contemporaries.

Making Sense of Dignity: A Starting Point

Although appeals to human dignity became quite popular after the end of War World II in various moral and legal settings, the term retained an air of semantic indeterminacy, and scholars are of opposing minds concerning its usefulness and significance. In this essay I intend to offer a sketch of a “deflationary” account of human dignity – viewed as one moral value among many others – according to which it is conceived as the minimal respect we prima facie owe to our own personality, as well as to the personality of everyone else without any restriction or exception. This account is accompanied by a justification, which does not presuppose the endorsement of a particular moral theory, and envisages dignity as a bulwark to counter the morally abhorrent consequences of many categorical and normatively tainted dichotomies western societies have created.

Forms of Indeterminacy

In the first chapter, linguistic indeterminacy is defined in terms of unclarity in linguistic content. Based on this general definition, three main forms of linguistic indeterminacy are differentiated:there is semantic indeterminacy, pragmatic indeterminacy, and conversational vagueness. Lexical ambiguity, syntactic ambiguity and polysemy as well as semantic vagueness are forms of semantic indeterminacy. Speech act ambiguity, presupposition indeterminacy, and implicature indeterminacy obscure what the utterance's illocutionary force is, what it presupposes, and what it implicates, respectively. They are forms of pragmatic indeterminacy. Another form is impliciture indeterminacy, which is most relevant when a contextually valued standard is implicited, i.e., in the form of standard-relativity. Conversational vagueness, finally, appears most commonly when an utterance is unclear due to the over-generality of its expressions.

REALISMO E INDETERMINATEZZA NEI FONDAMENTI DELLA MATEMATICA

Two of the most influential foundational approaches in the philosophy of mathematics of the past thirty years, i.e. neologicism and ante rem mathematical structuralism, suffer from metaphysical and semantic indeterminacy. My present aim is to offer an explanation of this phenomenon and provide a solution in terms of arbitrary reference.