Abstract
Universals are usually considered to be universal properties. Since tropes are particular properties, if there are only tropes, there are no universals. However, universals might be thought of not only as common properties, but also as common aspects (“determinable universals”) and common wholes (“concrete universals”). The existence of these two latter concepts of universals is fully compatible with the assumption that all properties are particular. This observation makes possible three different trope theories, which accept tropes and no universals, tropes and determinable universals and tropes and concrete universals.
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Notes
Perhaps others meanings of “abstract” can be obtained from this one with the help of auxiliary premises following from particular theories. However, I cannot analyze this now.
If such “abstract entities” as sets or numbers are abstract in this sense, it is not because of their being outside the spatiotemporal world, but their dependency on other beings—presumably on set members and counted things. Again, this topic cannot be analyzed here.
An attempt to define a similar general ontological relation was carried out by J. Perzanowski (1996); however, his “ontological connection” differs in a number of ways from inherence as just defined.
It is interesting that both transcendent realism and the theory of “free” tropes takes properties as absolutely concrete, that is, independent entities. They differ in that for the former takes them as universals, whereas the latter as particulars.
See, for example, De ente et essentia III; In I Sent., d. 19, q. 1 a. 1.
The crucial texts are: “Foreword” to the Phenomenology of Mind, “Introduction” to the Lectures on the History of Philosophy, some paragraphs in the Encyclopedia and––the most important––the third book of Science of Logic. Some of these texts were glossed by J. Royce (1892).
N. Lossky (1951) has noted the similarity between the idea of concrete universal and the principle of the philosophy of pan-unity.
I owe this interesting remark to an anonymous reviewer of Axiomathes.
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Acknowledgements
This paper was supported by Foundation for Polish Science (FNP). I am indebted to Jerzy Szymura (Jagiellonian University, Poland), Anna-Sofia Maurin (Lund University, Sweden) and an anonymous reviewer of Axiomathes for reading and criticizing early versions of this paper. Jarosław Olesiak (Jagiellonian University) and Elwira and Tadeusz Bucki kindly helped me in brushing up my English.
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Rojek, P. Three Trope Theories. Axiomathes 18, 359–377 (2008). https://doi.org/10.1007/s10516-008-9036-1
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DOI: https://doi.org/10.1007/s10516-008-9036-1