Some Varieties of Superparadox. The implications of dynamic contradiction, the characteristic form of breakdown of breakdown of sense to which self-reference is prone

The Problem of the Paradoxes came to the fore in philosophy and mathematics with the discovery of Russell's Paradox in 1901. It is the "forgotten" intellectual-scientific problem of the Twentieth Century, because for more than sixty years a pretence was maintained, by a consensus of logicians, that the problem had been "solved"

A critique of Tractarian semantics

This is a critique of the principal claims made within Ludwig Wittgenstein\u27s Tractatus Logico-Philosophicus. It traces the development of his thought from the time he dictated the pre-Tractarian Notes on Logic to Russell up until about 1932 when he began work on the Philosophical Grammar. The influence exercised upon him by Frege, Russell and Moore are considered at length. Chapter one examines Moore\u27s relational theory of judgment which Wittgenstein apparently accepted upon his arrival at Cambridge in 1911. From Moore Wittgenstein would inherit one of the fundamental metaphysical theses of the Tractatus, namely, that the world consists of facts rather than things. Wittgenstein\u27s attempt to overcome the relational theory\u27s inability to account for falsehood, negation, and the possibility of truly ascribing false beliefs to others would herald some of the principal theses of Tractarian semantics: that propositional signs must exhibit bipolarity, that a distinction must be drawn between Sinn and Bedeutung, and that a distinction holds between what can be said and what can only be shown. Chapter Two examines how these theses are sharpened by considering the influence of Frege and the manner in which Wittgenstein disposes of Russell\u27s Paradox. considerable attention is given to the issue of whether Frege is to be interpreted as a semantic Platonist. It is argued that he is not, and that Tractarian semantics shores up the problematic features of Frege\u27s philosophy which make it susceptible to the paradox. From Frege Wittgenstein derives the idea that all representation requires a structured medium. The chapter concludes by considering how this entails the falsehood of semantic Platonism. Chapter Three studies Wittgenstein\u27s argument for logical atomism and gives it a favorable assessment. The influence of Russell\u27s conception of logical analysis is considered. The chapter concludes by showing the way Wittgenstein\u27s thesis that there must be simple subsistent objects depends upon the truth of his Grundgedanke, i.e., the claim that the logical constants are not referring terms. Chapter Four examines the argument for the Grundgedanke, and defends it against criticism based upon phenomenological considerations for objectifying negativity. It is demonstrated that Wittgenstein\u27s view entails that a distinction must be drawn between propositions possessing sense and those that are senseless but no less a part of our language. Chapter Five examines Wittgenstein\u27s claim that the essence of a proposition consists in a propositional sign\u27s projective relation to the world, and it considers the Tractarian analysis of propositional attitude ascriptions. It is argued that the analysis of these sorts of sentences forms the principal problem with the Tractatus. The chapter includes a discussion of why the Color Exclusion Problem need not be considered problematic for the author of the Tractatus, and it defends the realistic interpretation given of the Tractatus throughout the dissertation against criticisms arising from a consideration of Wittgenstein\u27s remarks on solipsism

The Principle Of Excluded Middle Then And Now: Aristotle And Principia Mathematica

The prevailing truth-functional logic of the twentieth century, it is argued, is incapable of expressing the subtlety and richness of Aristotle's Principle of Excluded Middle, and hence cannot but misinterpret it. Furthermore, the manner in which truth-functional logic expresses its own Principle of Excluded Middle is less than satisfactory in its application to mathematics. Finally, there are glimpses of the "realism" which is the metaphysics demanded by twentieth century logic, with the remarkable consequent that Classical logic is a particularly inept instrument to analyze those philosophies which stand opposed to the "realism" it demands

Properties

Panorama aggiornato delle principali teorie filosofiche su propriet\ue0 e relazioni intese come universal

A Quasi-Fregean Solution to ‘The Concept Horse’ Paradox

In this paper I offer a conceptually tighter, quasi-Fregean solution to the concept horse paradox based on the idea that the unterfallen relation is asymmetrical. The solution is conceptually tighter in the sense that it retains the Fregean principle of separating sharply between concepts and objects, it retains Frege’s conclusion that the sentence ‘the concept horse is not a concept’ is true, but does not violate our intuitions on the matter. The solution is only ‘quasi’- Fregean in the sense that it rejects Frege’s claims about the ontological import of natural language and his analysis thereof

Propositions and Paradoxes.

Propositions are more than the bearers of truth and the meanings of sentences: they are also the objects of an array of attitudes including belief, desire, hope, and fear. This variety of roles leads to a variety of paradoxes, most of which have been sorely neglected. Arguing that existing work on these paradoxes is either too heavy-handed or too specific in its focus to be fully satisfactory, I develop a basic intensional logic and pursue and compare three strategies for addressing the paradoxes, one employing truth-value gaps, one restricting propositional quantification, and one restricting our ability to have attitudes like belief and desire. This results in four distinct resolutions of the paradoxes, all but one of which are novel and all of which receive novel and general implementations. While resolving the paradoxes is of course the ultimate goal, I do not here argue that any one of the resolutions is superior. These paradoxes have been so little studied that my primary goal is only to identify the most fundamental costs and benefits of the various approaches one can take to addressing them. Each resolution I develop has significant drawbacks, which I argue highlight tensions between the different roles propositions play. Past researchers have skirted these tensions, and the issues raised by these paradoxes more generally, by focusing on non-propositional paradoxes, such as the most familiar forms of the Liar paradox. At the least, then, I hope this dissertation establishes that the propositional paradoxes deserve attention not only because of their consequences for intensional logic, but also because of their consequences for our understanding of content, truth, quantification, and a host of mental attitudes.Ph.D.PhilosophyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89611/1/dtuck_1.pd

solutions in the origins of Math

i. a poetic solution of the Goldbach Conjecture; ii. several responses to the Epimenides Paradox; iii. the volitional solution to Russell's Paradox