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**1 - 2**of**2**### Gödel's Incompleteness Theorems: A Revolutionary View of the Nature of Mathematical Pursuits

"... The work of the mathematician Kurt Gödel changed the face of mathematics forever. His famous incompleteness theorem proved that any formalized system of mathematics would always contain statements that were undecidable, showing that there are certain inherent limitations to the way many mathematicia ..."

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The work of the mathematician Kurt Gödel changed the face of mathematics forever. His famous incompleteness theorem proved that any formalized system of mathematics would always contain statements that were undecidable, showing that there are certain inherent limitations to the way many mathematicians studies mathematics. This paper provides a history of the mathematical developments that laid the foundation for Gödel's work, describes the unique method used by Gödel to prove his famous incompleteness theorem, and discusses the farreaching mathematical implications thereof. 2 I.

### On Ontology and Realism in Mathematics * Outline

"... The paper is concerned with the way in which “ontology ” and “realism ” are to be interpreted and applied so as to give us a deeper philosophical understanding of mathematical theories and practice. Rather than argue for or against some particular realistic position, I shall be concerned with possib ..."

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The paper is concerned with the way in which “ontology ” and “realism ” are to be interpreted and applied so as to give us a deeper philosophical understanding of mathematical theories and practice. Rather than argue for or against some particular realistic position, I shall be concerned with possible coherent positions, their strengths and weaknesses. I shall also discuss related but different aspects of these problems. The terms in the title are the common thread that connects the various sections. The discussed topics range widely. Certain themes repeat in different sections, yet, for most part the sections (and sometimes the subsections) can be read separately Section 1 however states the basic position that informs the whole paper and, as such, should be read (it is not too long). The required technical knowledge varies, depending on the matter discussed. Aiming at a broader audience I have tried to keep the technical requirements at a minimum, or to supply a short overview. Material, which is elementary for some readers, may be far from elementary for others (my apologies to both). I also tried to supply information that may be of interest to everyone interested in these subjects.