Ioana Simon | Universität Heidelberg (original) (raw)

Ioana Simon

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Papers by Ioana Simon

Research paper thumbnail of Is the Concept of Infinity Paradoxical?

In the introduction to his book The Infinite, A.W. Moore lists a number of apparent paradoxes tha... more In the introduction to his book The Infinite, A.W. Moore lists a number of apparent paradoxes that arise from the existence of infinity. This essay will examine these so-called paradoxes and attempt to defend infinity as a valid mathematical concept. This is done by clarifying that these so-called paradoxes are not truly paradoxical, they are merely examples in which human intuition of reality clashes with the mathematical concept of infinity. The counter-intuitiveness in Moore’s examples stem from three assumptions made by the human intuition. These three assumptions are identified and explained.

Research paper thumbnail of Comparing and Applying Rudolf Carnap's Theory of Frameworks to Mathematical Structuralism

In his essay "Empiricism, Semantics, and Ontology", Rudolf Carnap provides a theory of semantics ... more In his essay "Empiricism, Semantics, and Ontology", Rudolf Carnap provides a theory of semantics that permits someone to talk about abstract objects without necessarily committing to their existence. He does this through the use of what he calls "linguistic frameworks". There are striking similarities between this theory of frameworks and math- ematical structuralism. This essay will compare them, and apply Carnap’s theory to structuralism.

Research paper thumbnail of Is the Concept of Infinity Paradoxical?

In the introduction to his book The Infinite, A.W. Moore lists a number of apparent paradoxes tha... more In the introduction to his book The Infinite, A.W. Moore lists a number of apparent paradoxes that arise from the existence of infinity. This essay will examine these so-called paradoxes and attempt to defend infinity as a valid mathematical concept. This is done by clarifying that these so-called paradoxes are not truly paradoxical, they are merely examples in which human intuition of reality clashes with the mathematical concept of infinity. The counter-intuitiveness in Moore’s examples stem from three assumptions made by the human intuition. These three assumptions are identified and explained.

Research paper thumbnail of Comparing and Applying Rudolf Carnap's Theory of Frameworks to Mathematical Structuralism

In his essay "Empiricism, Semantics, and Ontology", Rudolf Carnap provides a theory of semantics ... more In his essay "Empiricism, Semantics, and Ontology", Rudolf Carnap provides a theory of semantics that permits someone to talk about abstract objects without necessarily committing to their existence. He does this through the use of what he calls "linguistic frameworks". There are striking similarities between this theory of frameworks and math- ematical structuralism. This essay will compare them, and apply Carnap’s theory to structuralism.

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