According to realist structuralism, mathematical objects are places in abstract structures. We argue that in spite of its many attractions, realist structuralism must be rejected. For, first, mathematical structures typically contain intra-structurally indiscernible places. Second, any account of place-identity available to the realist structuralist entails that intra-structurally indiscernible places are identical. Since for her mathematical singular terms denote places in structures, she would have to say, for example, that 1 = − 1 in the group (Z, +). We call this (...) the identity problem and conclude that nominalism is presently the safest route for the structuralist. (shrink)

In the present study, cross-modal (i.e., across sensory modalities such as smell and sound) iconicity (i.e., resemblance) and indexicality (i.e., contiguity) in lexical sensory and emotional signs in Finnish Sign Language will be considered from an articulatory perspective (i.e., the production of signs). Such cross-modal iconicity has not been extensively studied previously, so here, with the help of cognitive semiotics, I aim to carefully describe the cross-modal patterns observed across 118 signs, including 60 sensory signs and 58 emotional signs. The (...) analysis is framed within the theoretical model of Semiotic Hierarchy, which entails a non-reductionist view of meaning. In addition, a pheno-methodological triangulation will be applied: phenomenology (first-person method), literature of phenomenological and semiotic descriptions (second-person perspective) and experimental findings (third-person perspective). The results of this analysis show that (a) 71 of the 118 sensory and emotional signs are cross-modally indexical, (b) only 10 of the 71 signs can be regarded as cross-modally iconic, (c) cross-modal iconicity is highly diagrammatic, (d) iconicity and indexicality are highly integrated, and (e) articulatory feedback matters in the formation of semiotic patterns. This study contributes to our understanding of cross-modal iconicity in signed languages, as well as studies in semiotic systems more generally. (shrink)