The Russell‐Myhill paradox targeting the structuralist view of proposition in classical higher‐order logic is blocked by implementing restrictions associated with an ordinary account of predicativity. However, it has been shown that these restrictions are not safe: “revenge” versions of the paradox show the inconsistency of the structuralist view in what is ordinarily regarded as a predicative setting. This result has been interpreted as suggesting an expressive limitation of the structuralist view. In this paper, I argue otherwise. There is a metaphysical sense in which structured propositions presuppose properties appearing as their constituents. I use this idea to elaborate a more thoroughgoing understanding of predicativity. In this way, the structuralist has the resources to interpret revenge paradoxes as a byproduct of impredicativity and coherently block them by means of a more subtle regimentation on how properties are defined.
The article argues that the logicism through which Russell approached Kant’s antinomies possessed a distinct character, determined by: a) discovery of paradoxes, and b) theory of types as finding ways to solve them. The paper demonstrates both the strengths and weaknesses of Russell’s logicism regarding his approach to...
This volume presents a dialectic-idealist overview of natural language and natural (non-artificial) thinking. Pauli Pylkkö’s view is thoroughly non-classical and takes ambiguity and contradictoriness as vital and inalienable properties of all speaking and thinking. The main function of a sentence is to change the meani...
This article argues that Russell's paradox can be solved by amending the theory in a zigzag fashion. The first part of the article sets out several reasons why this kind of revision to Frege's system is preferable to other solutions. More specifically, we argue that the extensionality function implicitly described by F...
Ludovica Conti· Teorema. Revista Internacion...· 0 citations
A rigorous analysis of the paradoxes of apophatic theology, revealing its deep logical structure and challenging inconsistencies.
In this book, Piotr Urbanczyk delves into the theory known as negative, or apophatic, theology where God is completely ineffable and unknowable. This doctrine, however, presents a paradox:...
P. Urbańczyk· 0 citations
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