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modal_alt.html

<!DOCTYPE html>
<html>
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>Modal-Abhandlungen – Das Pompeji-Projekt</title>
    <base href="https://pompeii-project.org">
    <link rel="canonical" href="https://pompeii-project.org/modal.html">

    <meta name="description" content="Die modallogischen Abhandlungen (Versionen 1–5) – formale Beweise für die Trinität als notwendige Struktur einer monistischen Modalontologie. Mit interaktiven Tutorials.">
    <meta name="robots" content="index, follow">

    <meta property="og:title" content="Modal-Abhandlungen – Das Pompeji-Projekt">
    <meta property="og:description" content="Modallogische Beweise für die Trinität – Versionen 1–5 mit Tutorials.">
    <meta property="og:type" content="website">
    <meta property="og:url" content="https://pompeii-project.org/modal.html">
    <meta property="og:locale" content="de_DE">
    <meta property="og:locale:alternate" content="en_US">

    <style>
        * {
            margin: 0;
            padding: 0;
            box-sizing: border-box;
        }

        body {
            font-family: 'Georgia', 'Times New Roman', Times, serif;
            background-color: #f5f3ef;
            color: #2c2c2c;
            line-height: 1.7;
            padding: 2rem 1rem;
        }

        .container {
            max-width: 1000px;
            margin: 0 auto;
            background-color: #fffef7;
            padding: 2rem 2.5rem;
            border-radius: 16px;
            box-shadow: 0 8px 30px rgba(0,0,0,0.08);
            border: 1px solid #e0d6c8;
        }

        /* ===== HEADER ===== */
        .header-row {
            display: flex;
            justify-content: space-between;
            align-items: flex-start;
            flex-wrap: wrap;
            gap: 0.5rem 1rem;
            margin-bottom: 0.3rem;
        }

        .header-left {
            flex: 1;
        }

        .header-left h1 {
            font-size: 2rem;
            font-weight: normal;
            color: #2c2c2c;
            border-left: 6px solid #6b4f8a;
            padding-left: 1rem;
            margin-bottom: 0.2rem;
        }

        .lang-toggle {
            display: flex;
            gap: 0.3rem;
            background-color: #f0ede6;
            padding: 0.2rem;
            border-radius: 30px;
            border: 1px solid #d4cab8;
            flex-shrink: 0;
            margin-top: 0.2rem;
        }

        .lang-toggle button {
            background: none;
            border: none;
            padding: 0.2rem 0.8rem;
            border-radius: 30px;
            font-size: 0.75rem;
            font-family: inherit;
            cursor: pointer;
            color: #8b8b8b;
            transition: background-color 0.2s, color 0.2s;
        }

        .lang-toggle button.active {
            background-color: #6b4f8a;
            color: #fffef7;
        }

        .lang-toggle button:hover:not(.active) {
            background-color: #e0d6c8;
        }

        .back-link {
            display: inline-block;
            margin-bottom: 1.2rem;
            color: #6b4f8a;
            text-decoration: none;
            font-size: 0.9rem;
            border-bottom: 1px solid transparent;
            transition: border-color 0.2s;
        }

        .back-link:hover {
            border-bottom-color: #6b4f8a;
        }

        .subhead {
            font-size: 0.95rem;
            color: #6b6b6b;
            margin-bottom: 2rem;
            border-bottom: 1px solid #e0d6c8;
            padding-bottom: 0.8rem;
        }

        /* ===== LANGUAGE CONTAINERS ===== */
        .lang-de-container {
            display: block;
        }
        .lang-en-container {
            display: none;
        }

        body.lang-en .lang-de-container {
            display: none;
        }
        body.lang-en .lang-en-container {
            display: block;
        }

        /* ===== INTRO ===== */
        .intro-text {
            background-color: #f0ede6;
            padding: 1.5rem 2rem;
            border-radius: 10px;
            margin-bottom: 2.5rem;
            border-left: 4px solid #6b4f8a;
        }

        .intro-text p {
            margin-bottom: 0.8rem;
        }

        .intro-text p:last-child {
            margin-bottom: 0;
        }

        /* ===== VERSION GRID ===== */
        .version-grid {
            display: grid;
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        <!-- ===== BACK LINK ===== -->
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            <a href="./" class="back-link">← Back to the entry page</a>
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        <!-- ===== HEADER ===== -->
        <div class="header-row">
            <div class="header-left">
                <div class="lang-de-container">
                    <h1>📐 Modal-Abhandlungen</h1>
                </div>
                <div class="lang-en-container">
                    <h1>📐 Modal Treatises</h1>
                </div>
            </div>
            <div class="lang-toggle" role="group" aria-label="Sprache umschalten">
                <button id="langDe" class="active" aria-pressed="true">🇩🇪 DE</button>
                <button id="langEn" aria-pressed="false">🇬🇧 EN</button>
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        </div>

        <div class="subhead">
            <div class="lang-de-container">
                Die Trinität als notwendige Struktur einer monistischen Modalontologie<br>
                <span style="font-size:0.85rem; color:#8b8b8b;">Modallogische Beweisführung – Versionen 1–5</span>
            </div>
            <div class="lang-en-container">
                The Trinity as a Necessary Structure of a Monistic Modal Ontology<br>
                <span style="font-size:0.85rem; color:#8b8b8b;">Modal-logical proof – Versions 1–5</span>
            </div>
        </div>

        <!-- ===== INTRO ===== -->
        <div class="intro-text">
            <div class="lang-de-container">
                <p><strong>Was ist das?</strong></p>
                <p>
                    Die <strong>modallogischen Abhandlungen</strong> beweisen formal, dass unter den Axiomen des Monismus,
                    der Existenz einer möglichen Welt und weiterer metaphysischer Annahmen eine <strong>trinitarische Struktur</strong>
                    aus <strong>Ursprung (U)</strong>, <strong>Totalität (T)</strong> und <strong>Selbsterkenntnis (S)</strong>
                    notwendig folgt.
                </p>
                <p>
                    Die Abhandlungen sind <strong>keine Gottesbeweise</strong> im klassischen Sinne. Sie zeigen:
                    <em>Wenn Sie die Axiome akzeptieren, dann folgt die Trinitätsstruktur logisch zwingend.</em>
                </p>
                <p>
                    <strong>Fünf Versionen</strong> dokumentieren die Entwicklung der Beweisstrategie – von der ersten
                    Skizze bis zur finalen Fassung mit vollständiger formaler Analyse.
                </p>
                <p style="margin-top:0.8rem; font-style:italic; color:#6b4f8a;">
                    📖 Die Versionen 1–5 sind in Deutsch und Englisch verfügbar – als PDF, EPUB, DOCX und TeX.
                </p>
            </div>

            <div class="lang-en-container">
                <p><strong>What is this?</strong></p>
                <p>
                    The <strong>modal-logical treatises</strong> formally prove that under the axioms of monism,
                    the existence of a possible world, and further metaphysical assumptions, a <strong>Trinitarian structure</strong>
                    of <strong>Origin (U)</strong>, <strong>Totality (T)</strong>, and <strong>Self-Knowledge (S)</strong>
                    necessarily follows.
                </p>
                <p>
                    The treatises are <strong>not proofs of God</strong> in the classical sense. They show:
                    <em>If you accept the axioms, then the Trinitarian structure follows logically and necessarily.</em>
                </p>
                <p>
                    <strong>Five versions</strong> document the development of the proof strategy – from the first
                    sketch to the final version with complete formal analysis.
                </p>
                <p style="margin-top:0.8rem; font-style:italic; color:#6b4f8a;">
                    📖 Versions 1–5 are available in German and English – as PDF, EPUB, DOCX, Tex and MD.
                </p>
            </div>
        </div>

        <!-- ===== VERSIONEN ===== -->
        <div class="version-grid">

            <!-- V1 -->
            <div class="version-card">
                <span class="version-badge v1">Version 1</span>
                <div class="lang-de-container">
                    <div class="version-title">Die Trinität als notwendige Struktur einer monistischen Modalontologie</div>
                    <div class="version-sub">Erste systematische Fassung</div>
                    <div class="version-desc">
                        Eine streng formalisierte modallogische Untersuchung mit sechs Axiomen.
                        Der Beweis wird im System S5 geführt.
                    </div>
                </div>
                <div class="lang-en-container">
                    <div class="version-title">The Trinity as a Necessary Structure of a Monistic Modal Ontology</div>
                    <div class="version-sub">First systematic version</div>
                    <div class="version-desc">
                        A strictly formalized modal-logical investigation with six axioms.
                        The proof is conducted in system S5.
                    </div>
                </div>
                <div class="btn-group">
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal.pdf" class="primary">PDF DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modaleng.pdf">PDF EN</a>
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                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal.docx">DOCX DE</a>
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                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal.tex">TeX DE</a>
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                </div>
            </div>

            <!-- V2 -->
            <div class="version-card">
                <span class="version-badge v2">Version 2</span>
                <div class="lang-de-container">
                    <div class="version-title">Minimalistische, grenzwertbasierte Version</div>
                    <div class="version-sub">Mit nur zwei Axiomen</div>
                    <div class="version-desc">
                        Diese Version kommt mit nur zwei Axiomen aus: Monismus (A1) und Existenz einer möglichen Welt (A4).
                        U, T und S werden als Grenzwerte eines offenen Intervalls verstanden.
                    </div>
                </div>
                <div class="lang-en-container">
                    <div class="version-title">Minimalist, Limit-Based Version</div>
                    <div class="version-sub">With only two axioms</div>
                    <div class="version-desc">
                        This version uses only two axioms: Monism (A1) and Existence of a possible world (A4).
                        U, T, and S are understood as limits of an open interval.
                    </div>
                </div>
                <div class="btn-group">
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2.pdf" class="v2-primary">PDF DE</a>
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                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2.epub">EPUB DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2eng.epub">EPUB EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2.docx">DOCX DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2eng.docx">DOCX EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2.tex">TeX DE</a>
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                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2.md">MD DE</a>
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                </div>
            </div>

            <!-- V3 -->
            <div class="version-card">
                <span class="version-badge v3">Version 3</span>
                <div class="lang-de-container">
                    <div class="version-title">Finale Version</div>
                    <div class="version-sub">Mit vier Axiomen und transzendentalen Brücken</div>
                    <div class="version-desc">
                        Die finale Version der Abhandlung. Sie verwendet vier Axiome: Monismus (A1), Existenz einer Welt (A4),
                        Transzendentale Brücke (A11) und Erfahrbarkeit ↔ Realisierung (A12).
                    </div>
                </div>
                <div class="lang-en-container">
                    <div class="version-title">Final Version</div>
                    <div class="version-sub">With four axioms and transcendental bridges</div>
                    <div class="version-desc">
                        The final version of the treatise. It uses four axioms: Monism (A1), Existence of a World (A4),
                        Transcendental Bridge (A11), and Experience ↔ Realization (A12).
                    </div>
                </div>
                <div class="btn-group">
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal3.pdf" class="v3-primary">PDF DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal3eng.pdf">PDF EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal3.epub">EPUB DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal3eng.epub">EPUB EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal3.docx">DOCX DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal3eng.docx">DOCX EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal3.tex">TeX DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal3eng.tex">TeX EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal3.md">MD DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal3eng.md">MD EN</a>
                </div>
            </div>

            <!-- V4 -->
            <div class="version-card">
                <span class="version-badge v4">Version 4</span>
                <div class="lang-de-container">
                    <div class="version-title">Vollständige Analyse</div>
                    <div class="version-sub">Teil I–III: Nicht-Ableitbarkeit, Beweis, Einordnung</div>
                    <div class="version-desc">
                        Diese Version vereint alle vorangegangenen Erkenntnisse: Teil I zeigt die Nicht-Ableitbarkeit in
                        reinem S5, Teil II den Beweis im erweiterten System S5+SP, Teil III die metatheoretische Einordnung.
                    </div>
                </div>
                <div class="lang-en-container">
                    <div class="version-title">Complete Analysis</div>
                    <div class="version-sub">Part I–III: Non-derivability, Proof, Classification</div>
                    <div class="version-desc">
                        This version unites all previous insights: Part I shows non-derivability in pure S5,
                        Part II the proof in the extended system S5+SP, Part III the metatheoretical classification.
                    </div>
                </div>
                <div class="btn-group">
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal4.pdf" class="v4-primary">PDF DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal4eng.pdf">PDF EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal4.epub">EPUB DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal4eng.epub">EPUB EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal4.docx">DOCX DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal4eng.docx">DOCX EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal4.tex">TeX DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal4eng.tex">TeX EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal4.md">MD DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal4eng.md">MD EN</a>
                </div>
            </div>

            <!-- V5 -->
            <div class="version-card">
                <span class="version-badge v5">Version 5</span>
                <div class="lang-de-container">
                    <div class="version-title">Finale Version mit vollständiger formaler Analyse</div>
                    <div class="version-sub">Teil I–IV: Vollständige Axiome, Ableitungen, Konsistenz</div>
                    <div class="version-desc">
                        Die finale Version fasst die gesamte Entwicklung zusammen. Teil IV bietet eine vollständige formale
                        Analyse: alle Axiome, vollständige Ableitungen der Theoreme und ein Konsistenzbeweis des erweiterten
                        Systems S5+SP mittels kanonischer Modellstruktur.
                    </div>
                </div>
                <div class="lang-en-container">
                    <div class="version-title">Final Version with Complete Formal Analysis</div>
                    <div class="version-sub">Part I–IV: Complete Axioms, Derivations, Consistency</div>
                    <div class="version-desc">
                        The final version summarizes the entire development. Part IV provides a complete formal
                        analysis: all axioms, complete derivations of the theorems, and a consistency proof of the extended
                        system S5+SP by means of a canonical model structure.
                    </div>
                </div>
                <div class="btn-group">
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal5.pdf" class="v5-primary">PDF DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal5eng.pdf">PDF EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal5.epub">EPUB DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal5eng.epub">EPUB EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal5.docx">DOCX DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal5eng.docx">DOCX EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal5.tex">TeX DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal5eng.tex">TeX EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal5.md">MD DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal5eng.md">MD EN</a>
                </div>
            </div>

        </div>

        <!-- ===== TUTORIALS ===== -->
        <div class="tutorial-section">
            <div class="lang-de-container">
                <h3>📖 Interaktive Tutorials</h3>
                <p style="font-size:0.9rem; color:#4a4a4a; margin-bottom:0.5rem;">
                    Die Tutorials führen Schritt für Schritt durch die Beweisführung – mit Erklärungen, Formeln und
                    Verständnisfragen. Ideal für alle, die die Abhandlungen nicht nur lesen, sondern verstehen wollen.
                </p>
            </div>
            <div class="lang-en-container">
                <h3>📖 Interactive Tutorials</h3>
                <p style="font-size:0.9rem; color:#4a4a4a; margin-bottom:0.5rem;">
                    The tutorials guide you step by step through the proof – with explanations, formulas, and
                    comprehension questions. Ideal for anyone who wants to understand the treatises, not just read them.
                </p>
            </div>

            <div class="tutorial-grid">

                <div class="tutorial-card">
                    <div class="tut-title">📐 Version 1</div>
                    <div class="lang-de-container">
                        <div class="tut-desc">Erste systematische Fassung – sechs Axiome, S5-Beweis</div>
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