note on Sorites series

Vagueness does not necessarily come in with vague predicates, nor need it be expressed by them , but undoubtedly 'vague predicates' are traditionally in the focus of main stream discussions of vagueness. In her current modal logic presentation and discussion of the Sorites paradox Susanne Bobzien[1] lists among the properties of a Sorites series a rather weak modal tolerance principle governing the 'grey zone' containing the borderline cases of the Sorites series, which later proves crucial for her solution of the Sorites paradox by use of epistemic interpreted modal operators in 1st order modal logic. We suggest (for different research interest) instead a non-modal description of the switch in the grey zone (respecting tolerance), by resort to similarity sequences, thus getting tangent to two other areas of research in the field. Let's say -any way- the Sorites paradox vanishes, the Sorites series does not

Beyond Kuhn: Methodological Contextualism and Partial Paradigms

Kuhn’s view of science is as follows. Science involves two key phases: normal and extraordinary. In normal science, disciplinary matrices (DMs) are large and pervasive. DMs involve “beliefs, values, techniques, and so on shared by the members of a given community” (Kuhn 1996, 175). “And so on” is regrettably vague, but Kuhn (1977, 1996) mentions three other key elements: symbolic generalizations (such as F=dp/dt), models (such as Bohr’s atomic model), and exemplars. These components of DMs overlap somewhat. For instance, symbolic generalizations may feature in techniques and beliefs, and models may exhibit values. To be a (genuine) scientist, in the normal science phase, is to puzzle solve within the boundaries of the DM. It is to buy into the ruling dogma (Kuhn 1963) and to accept that “failure to achieve a solution discredits only the scientist ... ‘It is a poor carpenter who blames his tools’” (Kuhn 1996, 80). Puzzle solving involves a wide variety of activities, includin

Two-wise and Three-wise Similarity, and Non-deductive Analogical Arguments

This paper will add to the discourse on analogical arguments by showing that they need not be deductively reconstructed in common contexts of persuasion. Analogical arguments have varying degrees of similarity, which helps us to understand their varying degrees of strength. Pace Shecaira (2013) it will be argued that this is a common and useful way of examining analogical arguments. It will be shown that deductive reconstruction does not adequately capture the needed degrees of strength. Let us start with two-wise similarity claims. Subject S1 says that the disputed case C1 is (relevantly) similar to C2 and should be treated as x, just as C2 is. S2 says that C1 is (relevantly) similar to C3 and should be treated as y, just as C3 is. S1 may counter with a three-wise similarity claim: C1 is more similar to C2 than it is to C3, because…, so C1 should be treated as x. Think of lawyers in court. It will be shown that the evaluation of analogical arguments in these contexts turns in a central way on similarity, and that deductive reconstructions get in the way of a proper understanding of the preceding

The Age of Trickery

This is partly fictional. It is chiefly a reconstruction (not always faithful) of Hume’s fundamental uses of notions of similarity, mostly based on Enquiry. It is the first part (out of four) of a monograph on the evolution of similarity toolmaking. Histories of doctrines are common in our discipline, not so for histories of tools; this is what it’s about. What’s disturbing: I write as if I were talking about the customs and beliefs of ancient tribes instead of real philosophers. Advantages: helps focus on what similarity tools are apt to, I don’t have to worry about my Hume being merely MY Hume; more fun. Here is the thematic layout: 1.1: (very fictional) methodological introduction; page 2. 1.2: on the origin of ideas + missing shade of blue; p. 4. 1.3: the Xenophobia model; p. 12. 1.4: case studies of cognitive trickery; p. 16 : 1.4.1: arguments from experience; p. 17. 1.4.2: the idea of necessary connection; p. 21. 1.4.3: abstract and very general ideas; p. 23. 1.5: conceptual distinctions between used similarity tools and a few comments; p. 29

The Metaphysical Significance of the Ugly-Duckling Theorem

According to Satosi Watanabe's "theorem of the ugly duckling", the number of predicates satisfied by any two different particulars is a constant, which does not depend on the choice of the two particulars. If the number of predicates satisfied by two particulars is their number of properties in common, and the degree of resemblance between two particulars is a function of their number of properties in common, then it follows that the degree of resemblance between any two different particulars is a constant, which does not depend on the choice of the two particulars either. Avoiding this absurd conclusion requires questioning assumptions involving infinity in the proof or interpretation of the theorem, adopting a sparse conception of properties according to which not every predicate corresponds to a property, or denying that degree of resemblance is a function of number of properties in common. After arguing against the first two options, this paper argues for a version of the third which analyses degrees of resemblance in terms of degrees of naturalness of common properties. In the course of doing so, it presents a novel account of natural propertie

Mathematical Aspects of Similarity and Quasi-analysis - Order, Topology, and Sheaves

The concept of similarity has had a rather mixed reputation in philosophy and the sciences. On the one hand, philosophers such as Goodman and Quine emphasized the „logically repugnant“ and „insidious“ character of the concept of similarity that allegedly renders it inaccessible for a proper logical analysis. On the other hand, a philosopher such as Carnap assigned a central role to similarity in his constitutional theory. Moreover, the importance and perhaps even indispensibility of the concept of similarity for many empirical sciences can hardly be denied. The aim of this paper is to show that Quine’s and Goodman’s harsh verdicts about this notion are mistaken. The concept of similarity is susceptible to a precise logico-mathematical analysis through which its place in the conceptual landscape of modern mathematical theories such as order theory, topology, and graph theory becomes visible. Thereby it can be shown that a quasi-analysis of a similarity structure S can be conceived of as a sheaf (etale space) over S

on the epistemological significance of arguments from non transitive similarity

This paper aims to argue for, else illustrate the epistemological significance of the use of non transitive similarity relations, mapping only to "types", as methodologically being on a par with the use of transitive similarity relations (equivalence relations), mapping as well to "predicates". In this paper the sketch of an exact but simple geometrical model of the above construct is followed by mentioning respective use cases for non transitive similarity relations from science and humanities. A well known metaphysics example is elaborated along these lines to some extent

The Metaphysics of Resemblance

The topic of this study is the resemblance of individuals. The underlying contention of this dissertation is that the resemblance of individuals is a taxing and challenging philosophical topic. Two main claims are defended in this study to support this contention. The first of these claims is that resemblance is not a binary relation but a monadic multigrade property. The second of these claims is that the metaphysics of resemblance and the metaphysics of properties are distinct, although not independent, philosophical issues. That resemblance is not binary but a monadic multigrade property makes resemblance taxing in at least two ways. First, resemblance is traditionally conceived of as a binary relation and on my account this traditional view is wrong. Second, a metaphysical account of multigrade properties is in itself a challenging issue. That the metaphysics of resemblance and the metaphysics of properties are distinct is motivated by the fact that an answer to the central question of the metaphysics of resemblance, which I identify as the question of whether the resemblance facts are context-relative, is not determined by any positioning on the central debate in the metaphysics of properties: the debate between the realist and the nominalist. Authors engaged in the realist/nominalist debate often address the central question of the metaphysics of resemblance in few words as their interest in resemblance is usually no more than an epiphenomenom of their interest in properties. It is one goal of this study to convince the reader that the central question of the metaphysics of resemblance needs to be addressed with more depth, and that addressing this question is challenging