Fermat’s last theorem proved in Hilbert arithmetic. I. From the proof by induction to the viewpoint of Hilbert arithmetic

In a previous paper, an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for “n = 3” has been known for a long time. It needs “Hilbert mathematics”, which is inherently complete unlike the usual “Gödel mathematics”, and based on “Hilbert arithmetic” to generalize Peano arithmetic in a way to unify it with the qubit Hilbert space of quantum information. An “epoché to infinity” (similar to Husserl’s “epoché to reality”) is necessary to map Hilbert arithmetic into Peano arithmetic in order to be relevant to Fermat’s age. Furthermore, the two linked semigroups originating from addition and multiplication and from the Peano axioms in the final analysis can be postulated algebraically as independent of each other in a “Hamilton” modification of arithmetic supposedly equivalent to Peano arithmetic. The inductive proof of FLT can be deduced absolutely precisely in that Hamilton arithmetic and the pransfered as a corollary in the standard Peano arithmetic furthermore in a way accessible in Fermat’s epoch and thus, to himself in principle. A future, second part of the paper is outlined, getting directed to an eventual proof of the case “n=3” based on the qubit Hilbert space and the Kochen-Specker theorem inferable from it

Space Programs Summary no. 37-38, volume IV FOR the period February 1, 1966 to March 31, 1966. Supporting research and advanced development

Supporting research in systems analysis, guidance and control, environmental simulation, space sciences, propulsion systems, and radio telecommunication

The Significance of Evidence-based Reasoning in Mathematics, Mathematics Education, Philosophy, and the Natural Sciences

In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. The second yields a strong, finitary, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically computable Tarskian truth values to the formulas of PA under the interpretation. We situate our investigation within a broad analysis of quantification vis a vis: * Hilbert's epsilon-calculus * Goedel's omega-consistency * The Law of the Excluded Middle * Hilbert's omega-Rule * An Algorithmic omega-Rule * Gentzen's Rule of Infinite Induction * Rosser's Rule C * Markov's Principle * The Church-Turing Thesis * Aristotle's particularisation * Wittgenstein's perspective of constructive mathematics * An evidence-based perspective of quantification. By showing how these are formally inter-related, we highlight the fragility of both the persisting, theistic, classical/Platonic interpretation of quantification grounded in Hilbert's epsilon-calculus; and the persisting, atheistic, constructive/Intuitionistic interpretation of quantification rooted in Brouwer's belief that the Law of the Excluded Middle is non-finitary. We then consider some consequences for mathematics, mathematics education, philosophy, and the natural sciences, of an agnostic, evidence-based, finitary interpretation of quantification that challenges classical paradigms in all these disciplines

Kant in English: An Index

Kant in English: An Index / By Daniel Fidel Ferrer. ©Daniel Fidel Ferrer, 2017. Pages 1 to 2675. Includes bibliographical references. Index. 1. Ontology. 2. Metaphysics. 3. Philosophy, German. 4. Thought and thinking. 5. Kant, Immanuel, 1724-1804. 6. Practice (Philosophy). 7. Philosophy and civilization. 8). Kant, Immanuel, 1724-1804 -- Wörterbuch. 9. Kant, Immanuel, 1724-1804 -- Concordances. 10. Kant, Immanuel, 1724-1804 -- 1889-1976 – Indexes. I. Ferrer, Daniel Fidel, 1952-. MOTTO As a famous motto calls us back to Kant, Otto Liebmann’s writes (Kant and His Epigones of 1865): “Also muss auf Kant zurückgegangen werden.” “Therefore, must return to Kant.” Table of Contents 1). Preface and Introduction. 2. Background on Kant’s Philosophy (hermeneutical historical situation). 3). Main Index (pages, 25 to 2676). Preface and Introduction Total words indexed: 58,928; for the 12 volumes that are in the MAIN INDEX are indexed: pages 1 to 7321. This monograph by Daniel Fidel Ferrer is 2676 pages in total. The following is a machine index of 12 volumes written by Immanuel Kant and translated from German into English. Everything is indexed including the text, title pages, preface, notes, editorials, glossary, indexes, biographical notes, and even some typos. No stop words or words removed from this index. There are some German words in the text, bibliographies, and in the glossaries (also included in Main Index). Titles in English of Kant’s writings for this index (pages 1 to 7321). Anthropology, History, and Education [Starts on page 1 Correspondence [Starts on page 313 Critique of Pure Reason [Starts page 971 Critique of the Power of Judgment [Starts on page 1771 Lectures on Logic [Starts on page 2247 Lectures on Metaphysics [Starts on page 2991 Notes and Fragments [Starts on page 3670 Opus Postumum [Starts on page 4374 Practical Philosophy [Starts on page 4741 Religion and Rational Theology [Starts on page 5446 Theoretical Philosophy after 1781 [Starts on page 5990 Theoretical Philosophy, 1755-1770 [Starts on page 6541 Universal Natural History and Theory of the Heavens or An Essay on the Constitution and the Mechanical Origin of the Entire Structure of the Universe Based on Newtonian Principles [Starts on page 7162 The whole single file which includes all of these books ends on page 7321. 12 volumes are pages 1 to 7321. These actual texts of these books by Kant are not include here because of copyright. This is only an index of these 7321 pages by Immanuel Kant. There are some German words in the text and in the glossaries, etc. Searching this Main Index. Please note the German words that start with umlauts are at the end of the index because of machine sorting of the words. Starting with the German word “ße” on page 2674 page of this book (see in Main Index). Use the FIND FUNCTION for all examples of the words or names you are searching. Examples from the Main Index mendacium, 5171, 5329, 5389 mendation, 220 mendax, 2702, 2800 mended, 360 Mendel, 416, 925, 965 Mendelian, 2212 Mendels, 345, 363, 417, 458, 560, 572, 588, 926, 928, 929 MENDELSSOHN, 925 Mendelssohn, 8, 9, 19, 98, 99, 100, 101

Kant in English: An Index

Kant in English: An Index / By Daniel Fidel Ferrer. ©Daniel Fidel Ferrer, 2017. Pages 1 to 2675. Includes bibliographical references. Index. 1. Ontology. 2. Metaphysics. 3. Philosophy, German. 4. Thought and thinking. 5. Kant, Immanuel, 1724-1804. 6. Practice (Philosophy). 7. Philosophy and civilization. 8). Kant, Immanuel, 1724-1804 -- Wörterbuch. 9. Kant, Immanuel, 1724-1804 -- Concordances. 10. Kant, Immanuel, 1724-1804 -- 1889-1976 – Indexes. I. Ferrer, Daniel Fidel, 1952-. MOTTO As a famous motto calls us back to Kant, Otto Liebmann’s writes (Kant and His Epigones of 1865): “Also muss auf Kant zurückgegangen werden.” “Therefore, must return to Kant.” Table of Contents 1). Preface and Introduction. 2. Background on Kant’s Philosophy (hermeneutical historical situation). 3). Main Index (pages, 25 to 2676). Preface and Introduction Total words indexed: 58,928; for the 12 volumes that are in the MAIN INDEX are indexed: pages 1 to 7321. This monograph by Daniel Fidel Ferrer is 2676 pages in total. The following is a machine index of 12 volumes written by Immanuel Kant and translated from German into English. Everything is indexed including the text, title pages, preface, notes, editorials, glossary, indexes, biographical notes, and even some typos. No stop words or words removed from this index. There are some German words in the text, bibliographies, and in the glossaries (also included in Main Index). Titles in English of Kant’s writings for this index (pages 1 to 7321). Anthropology, History, and Education [Starts on page 1 Correspondence [Starts on page 313 Critique of Pure Reason [Starts page 971 Critique of the Power of Judgment [Starts on page 1771 Lectures on Logic [Starts on page 2247 Lectures on Metaphysics [Starts on page 2991 Notes and Fragments [Starts on page 3670 Opus Postumum [Starts on page 4374 Practical Philosophy [Starts on page 4741 Religion and Rational Theology [Starts on page 5446 Theoretical Philosophy after 1781 [Starts on page 5990 Theoretical Philosophy, 1755-1770 [Starts on page 6541 Universal Natural History and Theory of the Heavens or An Essay on the Constitution and the Mechanical Origin of the Entire Structure of the Universe Based on Newtonian Principles [Starts on page 7162 The whole single file which includes all of these books ends on page 7321. 12 volumes are pages 1 to 7321. These actual texts of these books by Kant are not include here because of copyright. This is only an index of these 7321 pages by Immanuel Kant. There are some German words in the text and in the glossaries, etc. Searching this Main Index. Please note the German words that start with umlauts are at the end of the index because of machine sorting of the words. Starting with the German word “ße” on page 2674 page of this book (see in Main Index). Use the FIND FUNCTION for all examples of the words or names you are searching. Examples from the Main Index mendacium, 5171, 5329, 5389 mendation, 220 mendax, 2702, 2800 mended, 360 Mendel, 416, 925, 965 Mendelian, 2212 Mendels, 345, 363, 417, 458, 560, 572, 588, 926, 928, 929 MENDELSSOHN, 925 Mendelssohn, 8, 9, 19, 98, 99, 100, 101