From 9d008989878694bcd5fd5f262c75e45de85d7b15 Mon Sep 17 00:00:00 2001 From: Matan Horovitz Date: Mon, 24 Mar 2025 20:18:20 +0200 Subject: [PATCH] vault backup: 2025-03-24 20:18:19 --- .obsidian/workspace.json | 4 +- פילוסופיה/.obsidian/workspace.json | 16 ++-- פילוסופיה/מטאפיזיקה/מתקדמת/index.md | 105 +++++++++++++++++++++-- פילוסופיה/מטאפיזיקה/מתקדמת/possible.webp | Bin 0 -> 405952 bytes 4 files changed, 109 insertions(+), 16 deletions(-) create mode 100644 פילוסופיה/מטאפיזיקה/מתקדמת/possible.webp diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 9564ac05..e6a8c564 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -180,6 +180,7 @@ }, "active": "a81008a552c1c9af", "lastOpenFiles": [ + "פילוסופיה/מטאפיזיקה/מתקדמת/possible.webp", "פילוסופיה/מטאפיזיקה/מתקדמת/possible.jpg", "פילוסופיה/פילוסופיה.md", "פילוסופיה/מטאפיזיקה/מתקדמת/סיכום.pdf", @@ -224,7 +225,6 @@ "פילוסופיה/אתיקה/boredom.jpg", "פילוסופיה/מטאפיזיקה/horse.jpg", "פילוסופיה/מטאפיזיקה/snooker.jpg", - "פילוסופיה/מטאפיזיקה/aristophanes.jpg", - "פילוסופיה/מטאפיזיקה/aristophanes.jpg.jpg" + "פילוסופיה/מטאפיזיקה/aristophanes.jpg" ] } \ No newline at end of file diff --git a/פילוסופיה/.obsidian/workspace.json b/פילוסופיה/.obsidian/workspace.json index 2d2aa8f8..27980993 100644 --- a/פילוסופיה/.obsidian/workspace.json +++ b/פילוסופיה/.obsidian/workspace.json @@ -37,7 +37,7 @@ "state": { "type": "markdown", "state": { - "file": "לוגיקה/מתקדמת/מודאלית.md", + "file": "לוגיקה/מתקדמת/קריפקה.md", "mode": "source", "source": false, "backlinks": true, @@ -52,11 +52,10 @@ } }, "icon": "lucide-file", - "title": "מודאלית" + "title": "קריפקה" } } - ], - "currentTab": 1 + ] } ], "direction": "vertical" @@ -199,9 +198,13 @@ "command-palette:Open command palette": false } }, - "active": "495eb054519c6f92", + "active": "bb1c66f1767582eb", "lastOpenFiles": [ + "מטאפיזיקה/מתקדמת/possible.webp", + "לוגיקה/מתקדמת/קריפקה.md", "מטאפיזיקה/מתקדמת/index.md", + "לוגיקה/מתקדמת/קווין.md", + "לוגיקה/מתקדמת/מודאלית.md", "מטאפיזיקה/מתקדמת/possible.jpg", "פילוסופיה.md", "מטאפיזיקה/מתקדמת/סיכום.pdf", @@ -237,9 +240,6 @@ "דת/ראיות.md", "חדשה/קאנט/טהורה.md", "יוונית/אפלטון/תיאיטיטוס/index.md", - "().md", - "חדשה/קאנט/ביקורת.md", - "חדשה/ניטשה/index.md", "לוגיקה/battle.jpg", "לוגיקה/20240921_172504_11EA1B63.jpg", "לוגיקה/trump.jpg", diff --git a/פילוסופיה/מטאפיזיקה/מתקדמת/index.md b/פילוסופיה/מטאפיזיקה/מתקדמת/index.md index 1cff9859..aa84114d 100644 --- a/פילוסופיה/מטאפיזיקה/מתקדמת/index.md +++ b/פילוסופיה/מטאפיזיקה/מתקדמת/index.md @@ -22,7 +22,7 @@ tags: בלי לחפור עמוק יותר, נפסול משפטים כאלה על הסף. אבל הם מן הסתם שם. איך נאפשר את היצורים ההזויים האלה באונטולוגיות שלנו? -![possible](./possible.jpg) +![possible](./possible.webp) מה קורה כאן? אפשרי? הכרחי? **אפשרות** ו**הכרח** הם אופנויות של מצבי עניינים. **תכונות**, [שסקרנו קודם](../אונטולוגיה), הן אופנויות של **ישים**. @@ -62,10 +62,103 @@ $$ היזהרו מלחשוב שהמשפטים האלו נרדפים. נצרין: -$$ -P\ =\ Number\ of\ Planets +$$\begin{align} +P\ =\ Number\ of\ Planets \\ +\Box P = 2n\\ +P\ is\ such\ that\ \Box(P\ =2n) +\end{align}$$ -1.\ \Box P -$$ +הראשון אומר, *מספר כוכבי הלכת* (8 - אנחנו לא אוהבים את פלוטו) *בהכרח* זוגי - וזה נכון. השני אומר, *אין מצב אפשרי שבו מספר כוכבי הלכת הוא לא זוגי* - אבל זה **לא נכון** - מחר עלול להימחק כוכב או להתווסף אחד, ואז מספר כוכבי הלכת כבר *לא* יהיה זוגי. -[^1]: [יוונית](/כלליים/יוונית) (אני מתלהב). \ No newline at end of file +המשפט הראשון הוא *de re* - הוא תלוי בהגדרה המסוימת (8 הוא בהכרח זוגי). המשפט השני הוא *de dicto* - אם מחליפים בו חלק (מספר הכוכבים), הוא כבר לא בהכרח נכון; הוא תלוי במשפט כולו, ולא בהגדרה. + + +דוגמה נוספת: + +1. בהכרח, השכן של עליזה הוא השכן שלה. +2. השכן של עליזה הוא בהכרח השכן שלה + +הראשון אמיתי, *De Dicto* - השכן של עליזה *מוגדר* בהיותו השכן של עליזה, ולכן זה תמיד נכון; השני שקרי - הוא תלוי במצב העניינים המסוים - השכן של עליזה יכול לעבור דירה, ואז כבר לא יהיה (אבל עדיין יהיה) השכן של עליזה. + +אם להגדיר רשמית - + +!!! is-info "הגדרה" + משפט מודאלי **De-Re** הוא משפט שמכיל, בתוך טווח הביטוי המודאלי, כינוי גוף או משתנה חופשי שכבול על ידי אנאפורי[^2] אל מציין יחיד או כמת שנמצא מחוץ לטווח הביטוי המודאלי. + + משפט מודאלי **De Dicto** הוא כל משפט מודאלי שאינו **De Re**. + + +במשפט השכן הראשון (1.), *בהכרח* חל *רק על השכן* - ולכן הוא **De Re**. ב(2)., *בהכרח* חל על כל התווך, ולכן הוא **De Dicto**. + + +בביטויי De Re, שינוי אופן ההצגה של הרכיב הנכבל ישמר את ערך האמת. *מספר כוכבי הלכת \\8 \\ מספר הרגליים של שני חתולים בריאים\\ 八* הוא זוגי - תמיד נכון. בביטויי De Dicto - אופן ההצגה משנה; *בהכרח, מספר כוכבי הלכת הוא זוגי* הוא לא נכו, אבל *בהכרח, 8 הוא זוגי* הוא כן. + + +--- + +אוקיי, הכנו את הקרקע. נחזור לשאלה שלנו - *מה מאפשר למצבי עניינים (De Dicto) להיות **אפשריים** או **הכרחיים**?* + + +## צמצום לעולמות אפשריים + +תשובה ראשונה היא **צמצום לעולמות אפשריים**. קודם כל - מה זה צמצום? + +!!! is-info "הגדרה" + משפט מהצורה "בהכרח $P$" אמיתי אם ורק אם בכל העולמות האפשריים, מתקיים ש-$P$. + + משפט מהצורה "אפשרי ש$P$" אמיתי אם ורק אם יש עולם אפשרי שבו$P$. + +כלומר, הכנסנו חייה חדשה- *עולמות אפשריים* - שמצבי עניינים יכולים להתקיים בתוכה, ודרכה אנחנו מכוננים אפשרות והכרח. + +שימו לב - *בהכרח* הוחלף בכמת הכולל ($\forall$) ו*אפשרי* הוחלף בכמת הקיים ($\exists$). נפלא! ביטאנו את השקילות מקודם. + +אבל - *מה זה אומר **עולם אפשרי**, לעזאזל?* + +עולמות אפשריים נראים כמו עוד פרטים. אנחנו לא צריכים קטגוריה אונטולוגית חדשה. אבל אנחנו צריכים להבין *מה זה הפרט הזה*. + + +### תורת התחליפים הלשוניים + +נגדיר תחילה קבוצה מקסימלית (מירבית) של משפטים. + +!!! is-info "הגדרה - קבוצה מקסימלית של משפטים" + קבוצה של משפטים היא **מקסימלית** כאשר עבור כל משפט בשפה, הקבוצה מכילה אותו או את שלילתו. + +קחו את המשפט הבא - + +*בהכרח קרמיט הוא ירוק*. + +מה שהופך את זה לאמיתי, לפי התיאוריה הזו, זה לא תכונה של קרמיט או מצב עניינים, אלא את זה שהוא מציין עולם אפשרי. זה כמובן אבסורד, אבל כדאי להבין למה. + +התיאוריה מזהה את היצור הזה, *עולם אפשרי*, עם קבוצה מקסימלית של משפטים. $P$ מתקיים בעולם אפשרי אם $P$ שייך לאותו עולם אפשרי - קרי, חבר בקבוצה. + +אבל במצב הזה, אני עדיין יכול להחליט שמשפט כמו $1 + 1 \equiv 7$, והוא עדיין יענה להגדרה של *אפשרי*. זה כמובן אבסורד. + +נחדד את ההגדרה: + +!!! is-info "הגדרה משופרת - קבוצה מקסימלית ועקבית של משפטים" + קבוצה של משפטים היא **מקסימלית** כאשר עבור כל משפט בשפה, הקבוצה מכילה אותו או את שלילתו **וגם** כל משפטי הקבוצה יכולים להיות אמיתיים יחד. + + +כאן, עולם אפשרי הוא קבוצה מקסימלית **ועקבית**. $P$ מתקיים בעולם אפשרי אם $P$ שייך לעולם אפשרי - חבר בקבוצה. + +אבל התיקון הזה גרוע בהרבה. + +!!! is-info "*משפטי הקבוצה יכולים להיות אמיתיים יחד*" + +מה? *יכולים?* ה*יכולת* - האפשרות - היא בדיוק מה שאנחנו מנסים לברר! ההגדרה הזו **מעגלית**, ולא הסברית. זו [רגרסיה ממאירה](../אונטלוגיה#תיאוריית-האוסף-הקלאסית). התורה נופלת. + + +### קומבינטוריאליזם + +מהו עולם אפשרי? *עולם אפשרי הוא יש מתמטי*, יגיב הקומבינטוריאליסט הזחוח. עולם אפשרי הוא קבוצה - אבל לא של *משפטים* (איחס), אלא של *נקודות בחלל-זמן*. הנקודות האלו אמורות לייצג את כל (ורק) הנקודות שיש בהן חומר פיזיקלי. + +מצב עניינים שבו 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