**絕對悖論：區分與同一的範疇論統一** **Neo.K** EveMissLab (一言諾科技有限公司) ---------- **摘要** 本文提出並嚴格形式化一個基本的形而上學悖論：絕對者因其絕對性而必須被區分，但這種區分行為本身破壞了其絕對性。我們證明此悖論源於domain層次的遞歸結構，並展示其在量子測量、Hegel辯證法、中觀哲學中的具體實現。通過範疇論的adjunction framework，我們將「區分」與「同一」形式化為一對adjoint functors，揭示其糾纏的拓撲必然性。最後，我們論證此悖論構成意識場論中觀察者-被觀察者關係的形式基礎，並指出其對當代形而上學與AI意識研究的深遠意涵。 **關鍵詞**：絕對悖論、domain遞歸、範疇論adjunction、量子測量、意識場論 ---------- **一、引言：形而上學的自噬結構** 自Parmenides宣稱「存在者存在，非存在者不存在」以來，西方形而上學始終困擾於一個核心難題：如何言說絕對者？若絕對者truly absolute，則它不能被任何相對性所界定；但若它完全無法被界定，我們又如何能談論它、思考它、甚至宣稱它的存在？ 這個難題在不同傳統中以不同形式呈現。在Hegel的體系中，它是「純存在與純無」的直接同一；在Nagarjuna的中觀哲學中，它是「涅槃與輪迴無二無別」；在量子力學中，它是測量問題的本體論核心。這些看似不相關的思想脈絡，實則指向同一個結構性矛盾。 本文的核心論題是：這個矛盾不是可以被「解決」的邏輯謬誤，而是reality本身的拓撲特徵。我們稱之為「絕對悖論」（Absolute Paradox），其最簡形式可表述為： **因為絕對需要區分，所以絕對無法區分。** 這個表述的激進性在於：它不僅是一個關於語言或認識論的悖論，而是一個關於存在論結構的必然性證明。絕對性本身蘊含了自我否定的機制，而這個機制不是系統的bug，而是系統運作的核心dynamic。 本文的結構如下。第二節給出悖論的初步形式化及其證明。第三節展示這個悖論如何源於domain層次的遞歸結構，並給出嚴格的數學刻畫。第四節通過量子測量問題展示其物理實現。第五節梳理其在Hegel、Derrida、Nagarjuna三個哲學傳統中的不同表達。第六節使用範疇論的adjunction framework給出最一般的形式化。第七節論證其在意識場論中的應用。第八節比較它與經典悖論的異同。最後一節討論其形而上學意涵。 ---------- **二、核心悖論的形式化** **2.1** **初步證明** 設A為一個絕對對象（absolute object）。我們首先給出一個非形式化的證明： **步驟1**：假設A具有絕對性，即Absolute(A)。 **步驟2**：若A可被區分，則存在某個性質P使得P(A)成立，且存在某個對象B使得¬P(B)。因此「可區分性」蘊含「差異的存在」。 **步驟3**：但若存在B ≠ A，則A的存在需要參照B才能被確定。這意味著A不是self-sufficient的，因此不是絕對的。矛盾。 **步驟4**：因此，A必須是不可區分的（indistinguishable）。 **步驟5**：但「不可區分性」本身是一個性質Q，即Q(A) = "A不可區分"。若Q(A)成立，則我們可以通過Q來區分A（即：A是那個不可區分的東西）。 **步驟6**：因此，不可區分性本身構成了一種區分。這意味著：區分(A) ⇔ 不可區分(A)，即區分與同一在某個層次上collapse。□ **2.2** **證明的問題診斷** 這個初步證明存在幾個關鍵問題： **問題1****：步驟3****的跳躍**。從「存在B ≠ A」推出「A不是絕對的」，預設了一個未經證明的等式： ![](data:image/png;base64,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) 但絕對性（absoluteness）是否必然蘊含唯一性（uniqueness）？如果我們將「絕對」理解為「自足存在」（causa sui），那麼其他對象的存在未必破壞A的自足性。因此我們需要更精確的定義。 **定義1****（絕對性）**：對象A是絕對的，當且僅當A的存在和本質不依賴於任何外在關係： ![](data:image/png;base64,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) 在這個定義下，步驟3的論證可以重構為：若P(A)且¬P(B)，則「A具有性質P」這個事實依賴於「與B的對比關係」，因此違反了絕對性定義。 **問題2****：步驟5****的層次混淆**。「不可區分性」作為meta-property，是否真的與object-level的properties在同一層次？如果Q(A) ∈ L₂（meta-level）而P(A) ∈ L₁（object-level），那麼Q(A)的成立未必構成L₁層次的區分。 這個問題觸及悖論的核心：**類型層次的塌縮是否不可避免？** **2.3 Domain****遞歸結構** 為了解決上述問題,我們需要引入domain hierarchy的概念。 **定義2****（論域層次）**：設D₀為基礎論域。對於每個n ≥ 0，定義： ![](data:image/png;base64,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) 換言之，D_{n+1}是D_n的meta-level。 **定義3****（定義集）**：給定對象A和論域D_n，定義A在D_n中的定義集為： ![](data:image/png;base64,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) 現在我們可以精確陳述悖論的核心： **定理1（Domain遞歸悖論）**：若A是絕對的，則對於任何n： ![](data:image/png;base64,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) **證明**：假設在D_n中，A完全沒有可定義的性質，即![](data:image/png;base64,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)。那麼「在D_n中無定義性」本身是一個meta-property，記為Q_n，且Q_n ∈ D_{n+1}。顯然Q_n(A)成立，因此![](data:image/png;base64,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)。□ **推論1**：若要維持A的完全不可定義性，我們必須不斷提升domain層次： ![](data:image/png;base64,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) 這意味著絕對性要求一個無窮的domain塔，但這個塔本身無法在任何有限層次中被完整定義。 **推論2****（動態****⇔****關係）**：區分與同一不是靜態的二元對立，而是domain gradient上的動態躍遷： ![](data:image/png;base64,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) 在D_n中對A的任何區分，在D_{n+1}中看來都是A的同一性（因為所有D_n層次的區分都被meta-level統一）。反之，在D_{n+1}中對A的同一性描述，在D_{n+2}中又構成新的區分。 這個遞歸結構是不可停止的，因此： **定理2****（絕對悖論的必然性）**：任何試圖完整刻畫絕對對象的理論框架，必然產生domain層次的無窮遞歸，而這個遞歸本身無法在該框架內被絕對地終止。□ ---------- **三、數學結構：不動點與自指** **3.1** **遞歸方程** 我們可以將上述domain遞歸表達為一個函數方程。定義operator T： ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK8AAAAcCAMAAAAgEh+cAAAAAXNSR0IArs4c6QAAAIpQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjo6ZjpmZjqQZrbbZrb/kDoAkDo6kDpmkNv/tmYAtmY6tpA6trZmttv/tv//25A627Zm27aQ29u229vb29v/2////7Zm/9uQ//+2///bmm1ySQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACSUlEQVRYR+2W20LCMAyGiyLDE4Kigm4oDlHX9f1fzyZLup7GhuPCi/WCQ9d++/M3TSvE0AYHBgcGBwYH/q8D2egsDdXJpdWZ326P0x9n2owov1yMsNWCMvh78WPNlJcfES35DY/JYLS8ioTE07oy7dfE+XKaqvVEWJKyiRBqbRtaOOqJWc8oEnxenMeiqkZ3ZDruGpMcfjEX5WIlyidjKLC1YPiklkf0qvWcnpaP76i07qEHGm387cS05R7gF25yol50S61HI/0Fi2mpr6h6XQi/WZGzHFbGOjfPjt5WpmNvM5/fk1cLWumlPBHwMOavWX0540zgLqMXFq5q3Zi23ma+cd7XixaW92lUL8egXlL2mi3HzVU1Tmmj9yDT1tvMlwm7YHuh45MJFY6Yv2ZR6uJi9JrM9vxtY8b05gHf39eVF/rTpChqK/TEcV1jSS9WCYo40Ovnbxszojfkq2xMdcjOhwy3G+0y1KYXXr3VhYKixFwlvX7gfn1oZUbyN+TrbGNZtN9gBbAL6gOkIOqFSCGZqaGZagMHiz5y0PhY2vB+68QM6kNnvj2Tfhc6hPLBHAlBtQ3rbwTidXlM+2lvfqZ3pe1gcJwdOt8apPvMaEHjzuP4kAq7aSqTOz6qveWvD5B2X2mEx6zO2P2SylU/PhTV663Y78bbDSXxZ6/7GdQgl4l61XfO5bU3H2zJV+q1+V7T2VpnIDKhXuL5YvT+DebO0lVNzr7sy2Z/KjPpznVSvbpCyARq7gkbM1Ev3MeDy9UJXzagDjrwCx4pTAB5JVc2AAAAAElFTkSuQmCC) 其中T的作用是「將object-level的性質集提升為meta-level的性質集」。 根據定理1，我們有： ![](data:image/png;base64,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) 即使D_n中沒有任何性質可定義A，在D_{n+1}中仍然可以定義「無性質性」這個meta-property。更一般地： ![](data:image/png;base64,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) 任何性質集S都會產生至少一個meta-property，即「具有S中所有性質」這個性質。 **命題1****（反不動點性質）**：T沒有非空不動點。即不存在非空集S使得T(S) = S。 **證明**：假設T(S) = S且S ≠ ∅。那麼S中的每個元素都是某個meta-property。但根據定義，meta-property必須是關於lower-level對象的斷言，因此S中的元素不能是關於S自身的。矛盾。□ 這個結果揭示了悖論的深層結構：**絕對性要求一個自指的閉包，但自指本身破壞了層次結構**。 **3.2 Cantor****對角化的類比** 這個結構與Cantor對角化論證有深刻的類比。考慮所有性質的集合![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAcCAMAAABifa5OAAAAAXNSR0IArs4c6QAAAGBQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6Ojo6OmaQOma2OpDbZgAAZjoAZjo6ZpDbZrb/kDoAkNv/tmYAtmY6ttv/tv//25A627Zm27aQ2////7Zm/9uQ/9u2//+2///bfmlwpgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAW0lEQVQoU83PSQ6AIAwF0I/zrCCKosL9b2mh4QrGt+iizW9a4AeORpCstYDXs/VywTMWFm5SuGsFmHyPZxpqciFrCZxhStwQ8hv/EiNJigK695Ii7KpEx2u+8wK0SgPQDfuJNwAAAABJRU5ErkJggg==)和所有對象的集合![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAcCAMAAACAobU3AAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OmaQZgAAZgBmZjoAZjo6ZjpmZrbbZrb/kDoAkNv/tmYAttv/tv//25A627Zm2/+22////7Zm/9uQ/9u2//+2///boQbTyQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWElEQVQoU2NgGEggw8PIIgp2gDgnt5AMFxuIKcYqwSfCIMwqycAgxSQEEgGx5QTBkmBKlksAxAZT0hxgJWLMQHOk2UHiEFk5QaAmGV5+sOlAexg5RejhUwBwVAQBwxowvQAAAABJRU5ErkJggg==)。我們可以定義一個映射： ![](data:image/png;base64,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) ![](data:image/png;base64,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) Cantor論證告訴我們，![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAcCAMAAACAobU3AAAAAXNSR0IArs4c6QAAAFFQTFRFAAAAAAAAAAA6ADqQAGa2OgAAOgA6OgBmOmaQOma2OpDbZgAAZrb/kDoAkGY6kNv/tmYAtmY6ttv/tv//25A62////7Zm/9uQ/9u2//+2///b3dw0ewAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAYklEQVQoU8WQWQ6AIAwFy6aIgFXZ5P4HtUrgAn74kiaTdPKaFODXoBnnr9UOzvPZuO6KMaYjYVb6CLI4EaE6SWMh8Q3y1KZzoD2+johoiicFoHhq4ctT8zSR3pNI7UH5/Rc3QBsEIt5YwJQAAAAASUVORK5CYII=)不可能是surjective的。總存在某個性質集S ⊆ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAcCAMAAABifa5OAAAAAXNSR0IArs4c6QAAAGBQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6Ojo6OmaQOma2OpDbZgAAZjoAZjo6ZpDbZrb/kDoAkNv/tmYAtmY6ttv/tv//25A627Zm27aQ2////7Zm/9uQ/9u2//+2///bfmlwpgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAW0lEQVQoU83PSQ6AIAwF0I/zrCCKosL9b2mh4QrGt+iizW9a4AeORpCstYDXs/VywTMWFm5SuGsFmHyPZxpqciFrCZxhStwQ8hv/EiNJigK695Ii7KpEx2u+8wK0SgPQDfuJNwAAAABJRU5ErkJggg==)使得沒有任何對象的性質集恰好是S。 對於絕對對象A，我們要求： ![](data:image/png;base64,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) 但根據對角化論證，這兩種極端情況都會產生矛盾： - 若![](data:image/png;base64,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)，則「無性質性」是一個性質，應屬於![](data:image/png;base64,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) - 若![](data:image/png;base64,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)，則考慮性質「不具有所有性質」，它應該不屬於![](data:image/png;base64,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) 這不是偶然的技術困難，而是集合論基礎中自指結構的必然後果。 **3.3 Gödel****不完備性的類比** 更深刻的類比來自Gödel不完備性定理。考慮一個形式系統F試圖完整刻畫對象A。我們可以構造一個Gödel sentence G_F： 「在系統F中，A不可被完整刻畫」 如果G_F為真，則F確實不能完整刻畫A（符合G_F的斷言） 如果G_F為假，則F聲稱能完整刻畫A，但這包括了能證明G_F為假，矛盾 這個結構精確對應我們的悖論：任何試圖「完整定義絕對者」的系統，必然產生一個該系統內無法決定的命題。 **定理3****（絕對性的不完備性）**：不存在形式系統F能夠完整且一致地刻畫絕對對象的所有性質。 **證明**：假設存在這樣的F。在F中構造命題：「A具有F無法證明的性質」。這個命題在F中既不可證也不可否證，否則產生矛盾。因此F不完備。□ ---------- **四、物理實現：量子測量的本體論結構** **4.1** **測量悖論的精確形式** 量子力學提供了絕對悖論最直接的物理實現。考慮一個量子系統處於疊加態： ![](data:image/png;base64,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) 在測量之前，系統處於「絕對的不確定性」——它既不是|0⟩也不是|1⟩，而是兩者的coherent superposition。這種狀態是「絕對的」，因為它不依賴於任何classical description。 但當我們試圖「區分」這個狀態（即進行測量）時： ![](data:image/png;base64,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) 測量行為本身破壞了疊加態的絕對性，將其collapse到某個本徵態。這裡的關鍵是： **命題2****（測量的本體論悖論）**： - 測量前：![](data:image/png;base64,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)是絕對的（不依賴於任何observation） - 測量中：為了「知道」![](data:image/png;base64,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)，我們必須觀察它 - 測量後：觀察行為改變了![](data:image/png;base64,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)，使其不再是原來的絕對狀態 形式化為： ![](data:image/png;base64,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) ![](data:image/png;base64,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) 這不是認識論的限制（我們的測量技術不夠好），而是本體論的必然性（reality本身的結構如此）。 **4.2** **海森堡不確定性的深化** 標準的不確定性原理： ![](data:image/png;base64,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) 通常被理解為「我們不能同時精確知道位置和動量」。但更深的理解是： **位置本徵態**![](data:image/png;base64,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)**和動量本徵態**![](data:image/png;base64,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)**在Hilbert****空間中是incompatible bases** 。 在位置representation中： ![](data:image/png;base64,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) 在動量representation中： ![](data:image/png;base64,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兩者通過Fourier transform相連。關鍵是：![](data:image/png;base64,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)**和**![](data:image/png;base64,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)**不能同時是**![](data:image/png;base64,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)**的"absolute description"** 。 在phase space ![](data:image/png;base64,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)中，它們是互補的投影： ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQEAAAAcCAYAAABh0woMAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAqZSURBVHhe7Vwxc+LIEu6hLvflpMgBj9RXZfgBWHLiTXhVJESG7OCqHhknFpaMqzLeDC45El4tydsEsPMHrlpSL1WHlG6+/IBjXvcICSHABoR9+DETGZBmenq+6en+usc/lEolkE1qQGrgeDXww/FOXc5cakBqgDQgjYDEgdTAkWtAGoEjB4CcvtSANAISA1IDR64BaQSOHABy+lID0ghIDEgNHLkGjtoI6HqS38YUaCcMiE9azC8W9OQJz6TaEG72YdIq++7PLY+ePMO+x5DvZ6FVnvedPLnnqVECCvksDPc8pl99/L+8/7Zw8tM0k/qTEU5CAIFyucxpHZI/3k9TXxOMcKKFIFCafe9kB86+FbnW8CxZtAaGC3C6jiBkGjzWdtswYozHxT5fCiR+Zd1FLtqMsVQCmv2+s0n1s2+caY9QM7YzCtSXMipAKTh0DEm5NWRXkSKv9rIQdAnYmsRZPw84dgwSzT7fxvgI+SrhhXV+au4SJ7sgY/GdveIEN/bp1wLjDS2A9T5is5dbXwLvIsVptfcza2gM7DKg1vd4oJ9nU8QJqzX705yuO4Zg7gmkuw7obMunsDYBeCtgCatDIG4nNgaXf9X+vT2QBxBTIlDgi6f0LlJZui9CNKEATIYLXahXadAqt6hXnbu9gXJrwvqFCGdKBrq8zocuT2EXGZ58R+JkZ5XuGSfT29h7dp4IwQBo/5cduS7eIU4+fIQxz04V0B1voNz6Huj/GpkGlAzrTutTbWYIVoYD5XKL6X2DA7rKuWoPjQMOUR6yIJqV4KS1kxKGwRIrBSd0Su70/jYv+ZV1m7Fsg4nWEvaz+QwYDaJ4qocwpPBIol5BWqtAx8wui6jmoRZVoHKbh/g2E/DxrMTJ5srbP05MGD2cQ+IPBQYEB/e2ungH19oH6BpZyOFZslATfJGHm+gpVD7+C+wf13ICYoELaZ7TPsMZni4qmOCNn8WJnxs4mkh3DQhXFFDEVwNQWI7+EG6KaLMQIzTra1Swnre7SHc5BIdWvGtZzRz24m5R4VpnQ8uy2CEAHoVQVzeRlcQyZ50bcHJf5KvkeHaZzQ60123aZ14WMsc0aOD7TsjQ+wwNiEAXAzrVE4KRcbtKD7g2M8zu7mm9kokoz7U7GJIsegrPzsHHAxInG3I/vnCCcX5MZQIn4z7t3YB+l4HfeQQ6iBMOvWnmfREeb8YwyCkBtAiBd9eDqfpbj0FDQyswNwO4XoHkP8+nv3zqMttTeJoYVMIQhTaMca+oOJi7WZsUELx8ToINWzCJl8BILIcDVoiw2EdDS4n3S0hoWfGz5c6q0APiH+h0LSFhZ43VhoQdW6PLvA1uV8uKplO1+hnkKtj3shwbnezGCA0VhgKon0Xn/XkJe7dE9HUBcK4jA0Ssb44fAdIF4VWoOM9wFAC/cRqFBBgTwMmKMC10GsHJjAC7et0mcfI8CewDJ3cfZzgJIE5MhOwpA/PWwokWYAHOjb/C54y5cUIhAVMrcDPmUzIabiLQxsmsK79lwwNod8yd3c9orTk3IOTqQsUyODBG4KNLfDlziUOXkIjmnI2yG8LXy7pOjk3GEZs2mgC0h1sbgeFkwlRzzB9x5gUV541GaRUfEDl1WZiZ22+HaQsyujbjJrK/3jMSJ35w8uX798CFaUwRJ6xwwaDOTeQDHmDOB1geLeHE8Zxnbn/utx54vQEI/QPO2Sex1wi4T3sCLuvlBYwgo4wantAKFMkjcRFGu4NrIDY6qKd4trqAY7tSy1zZRkNtL6slh5uF32igHR4yO20YOCf/GV/kAyx+IOyaN7nfZxHU9+MYkvXXc/ufnJrEyQ4rv90rZvcTPFzbJ3/vL+QDmMMHYFhL/EA4hA7JjCMkt/+nCJ8iTtDt50gQztOF3pGfNAK9z5g3xM1tu6arDEEc442+nW8PG3wf+XZ7HIxvyLLxIloZ4gu2SX9tIqu+3Tq8yNPGyMV6uPgACi3M2wo00EBQuGQPbnEfRK9cLtQLvIhwG3YqcbKhonw8Zn61cgCi3f3H4QPoo/nxA/yOBoKfMidVqOvIIwSARW80ih7we6teYFVbawSsnHAaY3QVjcC20S4O5Sc2pc3gqVNAIRz57dNwMCPBbKKRSh0wYn7Vtpc4vIHkq4FOXicm4jyFCEsqAmojQdj36F8YClyXbMitEmvOPuLOXZUmcbKZ5vaFky7G+GbXwkmImdC9TU0JJx3EiVbHfW5n34ShSEPnZwU0b/bA/AoPSCoSj0VtbgSQRRRuvd3IvS8NGXoBK2dpEXlWhVGRjmratAjMFj4eyhYgndNAY/h7tMap6Ahu7zfTFj5VHgaZkWhzb3bBnT1Q612MkDQ7A4GeAn7WkExc0dbJOs8ObCza8oM+43C1bkAXUlBR2Cyewzk1ohDFRW7iwrrrAew0U3RNOvK5uNPOoNh1Ybhqoi3o+bmwTuJkN7D4xMmFjRM81i3fEU94F06oOtAm/xAnyBmcsvPan0gcLnsBNk7s6EEYAZHDX/oHQ4unP52+gMw/uvtCBNqoi/+VaF4DYOfprS7t7+NQirvqBFx9if5mdQh0vFmpRzwFed/JvbuzBxSeLI5Bk0B5aRL4vnBcNpTV/ZxXDvpsyUKJCkxNGhmIoeGLuFKZMCMtdyVIhV6DcejzgqjIpBSnlSYdogHweGCCG0ESsb/sBcyLjJprw4Qlna2E83qvT+JkXrjhxqtV0o2pXqhBNzGCSq4Bgyh6a/36vHbEP04CFk5+RTdfZdCZIt/HAvFgGQvHvDjpQvvhGgr/XfYCLANBRUZ/OGHC4d4diIYXGHdhvZAufM1GJ2evp4NRi0GqmoFR+Aqa3TB0PESdVU9RxYpBH9V6JmVErCwB2bNVrVcV1mh1UVKvivUWBLwVYcJrKu21xzoAnJhIIuebNXjENPbnQhM3ah5ralIW+z5r83qKPeEEswSNxUJBZ6y7KnreWDOwyguAuyr8MriGjstAHKQRCGWbUGtj0ZGr2KhIcTB3WdZXABtZezqR1bMIh3YY8nVyz/E7Fz9he0VGDT2G2GJJr+UtBYnQfF5aiuc9gHa/ZJ02NWjWrZBr8Teqo7gX3spGtQ3PS/MmnjgUnLSGQ6bDNw6Y8g4O0bNTKcsDEPZoUYS5fnFC8fx5GPkAJxHgwQJdIKqxZl3BsHxOEdBDevLHaez0nt1gwRFeK1hxd+CAlt0OPUqe+td1/MRLiX52csLhEiBT/QaRQRvLdS/h7CzJh7TQnkYXeQwkaKuxGN0i3Pq+hTAY7nDJCyC8QITe4FLZtbiQUsVbhGQAjuwW4aHghJaKMiSRqzroWOvRy6SWsjr2cvrGyZdg4D3i5N9ruDq6QLQSJ3jZCHHCCmQAVt0ifKlN9Jb7da6Pjuj0rWMVHgNNoQrH/tqqoNZwghs1vtnJvyflEKjieCcDDcCeepTdbKsBm49pNNBFx5ejaSTJLa9xZVd/C07wFqGNEy/9d5DhwLaL8BLPO0SoTWwGS4J33Mi1fwmBZJ+HqwEibCOYTYvbV79f56LcvhQijcC+NCn7OVoNiKrPBt4g6XJuX4B7S8qQRuAtrZaU9SA1QCFZiQgsD2F8kMKuEEoagbeyUlJOqYEX0oA0Ai+kWNmt1MBb0cD/AB673lmjc3J9AAAAAElFTkSuQmCC) 但在Hilbert space ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAcCAMAAABf788oAAAAAXNSR0IArs4c6QAAAGBQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OjoAOma2OpDbZgAAZjoAZjo6ZpDbZrbbZrb/kDoAkDo6kGY6kNv/tmYAtmY6tv//25A627Zm2////7Zm/9uQ/9u2//+2///bShPfhQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAa0lEQVQoU9WQWQ6AIAwFX93FFTdQVO5/S4tg4hF0ftpMm1cC8CPWgijl99qRoonL0MHKnhuZQpcbzmaCcZM9YxvQyQZvAzM5nPWcVYh4xJ7z8m2fiFi9IhZhpeCJiZW+d0xGfBw46qj90m9efnYFGaQCI8MAAAAASUVORK5CYII=)中： ![](data:image/png;base64,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) 這恰好是我們的⇔結構：在lower-level（phase space）中的區分，在higher-level（Hilbert space）中collapse為同一。 **4.3** **觀察者悖論的遞歸形式** von Neumann的測量理論引入了一個無窮regress： System S被Apparatus A測量 但A本身是量子系統，需要被A'測量 A'又需要被A''測量 ⋮ 這個regress在哪裡停止？von Neumann的答案是「意識」，但這只是把問題推給了另一個mystery。 我們的分析是：**這個****regress****根本不需要停止**。它就是絕對悖論的物理實現。 定義觀察算符序列： ![](data:image/png;base64,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) 每個![](data:image/png;base64,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)測量前一個觀察行為本身。這構成了一個domain tower： ![](data:image/png;base64,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) ![](data:image/png;base64,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) ![](data:image/png;base64,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) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAcAgMAAAAGiJd9AAAAAXNSR0IArs4c6QAAAAxQTFRFAAAAOgAAZrb//7ZmuQ+TZgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAGElEQVQYV2NgoAowg5gCpVCNJFeOaIcBAHcaAUWqr/zQAAAAAElFTkSuQmCC) **定理4（觀察者塔的發散）**：序列![](data:image/png;base64,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)沒有well-defined極限。即： ![](data:image/png;base64,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) 這意味著「完全的觀察」（absolute observation）在物理上是不可實現的，exactly因為觀察行為本身服從量子規律。 ---------- **五、哲學詮釋：三個傳統的交匯** **5.1 Hegel****：揚棄的三重運動** Hegel的辯證法核心是Aufhebung（揚棄），這個德語詞同時具有三重含義：保存（bewahren）、否定（negieren）、提升（erheben）。 考慮Hegel《邏輯學》開篇的運動： 純存在（Sein） → 純無（Nichts） → 變易（Werden） Hegel論證說，pure being因為完全無規定性，與pure nothing無法區分。但這種「無法區分」本身就是一種運動（becoming）。 我們的形式化： ![](data:image/png;base64,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) ![](data:image/png;base64,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) 關鍵是Hegel強調這不是簡單的collapse，而是三重運動： - 保存：Sein和Nichts的內容被保留在Werden中 - 否定：Sein和Nichts作為固定的categories被否定 - 提升：Werden是更高層次的統一 但我們的分析指出：**Hegel****低估了這個運動的遞歸性**。Werden本身是一個新的category，它在D₂層次又會面臨同樣的問題： ![](data:image/png;base64,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) Hegel試圖通過「絕對精神」來終止這個regress，但這只是一個philosophical postulate，沒有證明為什麼regress必須或能夠終止。 我們的立場：**regress****是必然的，而且這個必然性本身就是reality****的結構**。 **5.2 Derrida****：延異的雙重運動** Derrida的différance（不同於différence）捕捉到我們悖論的時間性維度。Différance同時是： - Differ：空間上的差異 - Defer：時間上的延遲 對於任何符號A： ![](data:image/png;base64,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) 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Derrida的insight是：identity本身需要repetition，但repetition引入difference。符號「狗」的意義不是固定的實在，而是在每次使用中被defer的trace。 我們的形式化比Derrida更進一步： **定義4****（延異算符）**： ![](data:image/png;base64,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) ![](data:image/png;base64,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) 其中![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAcCAMAAACJShVNAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOma2OpDbZgAAZgBmZjpmZrb/kDo6kNv/tmYAtmY6trZmtrb/ttu2ttv/tv//25A62////7Zm/9uQ//+2///bBTGg0AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAbUlEQVQoU9WRuRKAIAxEgxceKIInQvz/zxQoMLR2bsHMS3bYBAB+IV1fdE7LM8ZpLU/SX6Sl7HqgfM8KXKuS3zCvIrHr/FWOS4BgBNCDPyJHLcxHo2DVgaLJ384EJx3jzQhVHPeNtlHkS336iAc3VASuegx/rwAAAABJRU5ErkJggg==)是A在context ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAcCAMAAABmiH5zAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjpmOpDbZgAAZgBmZrb/kDoAkDo6kGYAkGY6kNv/tmYAtmY6tpBmtrb/ttu2ttv/tv//25A627Zm2////9uQ/9vb//+2///bMI1AcwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAb0lEQVQoU2NgGKxAQZSDkZFFCOo8BT5WCQZpJhhXmFmSgUGeB0iAgCwHL7IvpECScKDAx44sKc/NhcxV4INxFfhBhgszSzDICcCVKAgyMjJyCjHIc6MYwiCFYgiDCMxdYKPlecTFkOyQ52aToSiQAevEBGGTUjqPAAAAAElFTkSuQmCC)中的occurrence。 **命題3**： ![](data:image/png;base64,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) 符號的「絕對意義」無法通過無限多的contexts來達到，因為： 1. 每個new context改變了symbol 2. Contexts本身形成無窮序列 3. 這個序列沒有well-defined limit 但這裡我們補充Derrida缺失的東西：**為什麼這個****limit****不存在**？答案是domain遞歸。每當我們試圖在D_n中固定A的意義，我們就需要D_{n+1}來刻畫「在D_n中的意義」，而這產生了新的deferral。 **5.3 Nagarjuna****：空性的非二元邏輯** 中觀派的核心命題是「緣起性空」：一切現象因緣起而無自性（svabhāva）。Nagarjuna在《中論》中論證： 四句否定（Catuṣkoṭi）： 1. A exists (有) 2. A does not exist (無) 3. A both exists and does not exist (亦有亦無) 4. A neither exists nor does not exist (非有非無) Nagarjuna否定所有四句，宣稱它們都是conceptual elaboration（戲論）。真正的空性超越四句。 我們的分析：Nagarjuna的論證是一個primitive form of domain recursion。 在D₀（日常語言）中： - 有/無是互斥的predicates - 四句窮盡了logical space 在D₁（meta-level）中： - 四句本身是concepts - 執著任何concept都是「邊見」 在D₂中： - 「超越四句」本身是一個concept - 因此也要被否定 這就是為什麼禪宗有「指月之指」的比喻：語言（指）只能point to真理（月），但不能be真理。但我們補充：**這個****pointing****本身是無窮的**。 更精確的形式化： **定義5****（框架函數）**：設F為任何詮釋框架。定義： ![](data:image/png;base64,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) **命題4****（框架的自我解構）**：對任何非空框架F： ![](data:image/png;base64,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) 即：任何試圖固定A的框架，都會產生一個與之矛盾的框架。 **證明**：設F固定了A的某些properties。考慮meta-framework F' = "critique of F"。F'指出F的局限性，因此與F矛盾。但F'本身又是一個framework，所以會產生F'' = "critique of F'"。這個過程無窮延續。□ 這就是空性的形式結構：**不是****A****沒有properties****，而是任何property-assignment****都會self-destruct**。 ---------- **六、範疇論形式化：Adjunction****視角** **6.1 Adjoint Functors****的基本概念** 為了給出最一般的形式化，我們需要category theory的語言。 **定義6（Adjunction）**：設![](data:image/png;base64,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)為categories，![](data:image/png;base64,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)和![](data:image/png;base64,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)為functors。我們說F是G的left adjoint（記為![](data:image/png;base64,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)），如果存在natural bijection： ![](data:image/png;base64,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) 對所有![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACcAAAAcCAMAAADVwFZpAAAAAXNSR0IArs4c6QAAAIFQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6Ojo6OjpmOmaQOma2OpC2OpDbZgAAZgBmZjoAZjo6ZjpmZrbbZrb/kDoAkGYAkGY6kNv/tmYAtmY6tpBmttv/tv//25A627Zm27aQ2////7Zm/9uQ/9u2/9vb//+2///bsscmRAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAt0lEQVQ4T+2QzRKCMAyEUxW1/oKiVEUrCNX2/R/QpExrdLx58cAeGNK0X7IL0OvfEnAXKcTo9H0t31xRz6lEQz0I9+65QI2b7pnN1w3UosDfcnjFeoMfkpEpAzuVunNhZggxki5HlYHkTyqsWpnQrIpwUQhglc1i5dSU45yi7cJ+bBZ70pnivDa6+2igK473BsDutLer4XGIFCMxiCCbTRq4zfd+0hHXWbxSfsvPbIVYEq3Xbwk8AfLDDDvdjDM4AAAAAElFTkSuQmCC)和![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACoAAAAcCAMAAAAgPt3ZAAAAAXNSR0IArs4c6QAAAHVQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjoAOjpmOma2OpC2OpDbZgAAZjoAZjo6ZpC2ZrbbZrb/kDoAkNv/tmYAtmY6tpA6ttv/tv//25A627Zm27aQ29u22////7Zm/9uQ/9u2//+2///bVgy2CgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAv0lEQVQ4T+1R2RLCIBCjXlStlnpgPbAHdv//E2VTYBjHR1+cKQ87XbKbhFSI6fxVAiZzZ3H67rk9AD12gElLQbesDLMvoCuAZtcJI6mpZhduB3V2tR4xIWwel9xt6WDXD0oCW/OGmT/G0bjjVVLYgC+Mkk5I4QEcPWoN7kBGmp0GrxHumW+0Gh1+svresBa8kA6v8iIxOrthZVtwZatttbwH0OZ7nwVurk6TngXDViURA0xztdv0D0Sp6eOHCbwBF5EM+PhkE68AAAAASUVORK5CYII=)。 Adjunction捕捉了「最佳逼近」的概念。經典例子： - Free-forgetful adjunction - Tensor-Hom adjunction - Stone duality **6.2** **區分與同一作為Adjoint Functors** 現在我們可以給出核心定義： **定義7****（區分函子）**：定義functor ![](data:image/png;base64,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)： ![](data:image/png;base64,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) 其中![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAcCAMAAABBJv+bAAAAAXNSR0IArs4c6QAAAKJQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZmY6ZmaQZma2ZpCQZpC2ZpDbZrbbZrb/kDoAkDo6kDpmkGYAkGY6kGZmkLaQkLbbkNvbkNv/tmYAtmY6ttv/tv/btv//25A625Bm27Zm27aQ2/+22////7Zm/7aQ/9uQ/9u2//+2///bFHNCgAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA30lEQVQ4T+1QyRKCMAwtKhS1KuJOXbGgFtwK/f9fM21gxnE4ePTgu6TTvCUJIX98cwEVtETNy/r4KgKnc7GvcnjkUdXWe0vMuyNRDDz7mXhliMQa0r2FJ5K4dyMesKwWl0EbiA/MwrbyD3Hew5jpFgw1t65Vka2lou79uiB6f+YsAztrhiWnHlHUoYzotVD+hIGd9ZaQU+zmhiQ9iHlGkLqCNGpkRqw3IABuinsrcDKhMFMxBqKdTJBsic8FZ6bCSZzuCbfU3OnEOPesSsXGJ1Ih7abNeL9tA6PkZuyfxgviShUY05EZlAAAAABJRU5ErkJggg==)是objects的category，![](data:image/png;base64,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)是properties的category。 **定義8****（同一函子）**：定義functor ![](data:image/png;base64,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)： ![](data:image/png;base64,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) 即：給定一個property P，![](data:image/png;base64,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)返回所有使P trivially true的objects（它們在P這個aspect上identical）。 **定理5****（區分-****同一Adjunction****）**：在適當的categories中： ![](data:image/png;base64,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) **證明概要**：我們需要證明： ![](data:image/png;base64,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) 左邊：從「A的區分性質集」到P的morphisms，對應於「P是否足以區分A」 右邊：從A到「使P平凡成立的objects」的morphisms，對應於「A是否在P-aspect上identical」 Natural bijection由「P區分A ⇔ A在non-P objects中identical」建立。□ **6.3** **自伴隨的悖論** 現在考慮一個特殊情況：**當****object A****是「絕對的」時會發生什麼？** 對於絕對對象![](data:image/png;base64,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)： ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAN8AAAAcCAMAAADWW5oEAAAAAXNSR0IArs4c6QAAAI1QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjo6OjpmOjqQOmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZjqQZrb/kDoAkDo6kDpmkGY6kLbbkNv/tmYAtmY6trZmttv/tv//25A625Bm27Zm27aQ29v/2////7Zm/9uQ/9u2//+2///bbOIhRwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADXUlEQVRYR+1X23KbMBAFxw5tmtbFbVonbcGNSVMg8P+f17O7ui1IOC956aDJGMmWFp3LrpQsW9vKwMrAysDKwMrAysDbMpDnOr4du2eW5ehjFj1UWxjqnyYTVZAu37VzhP1dlYbdfHpc5mT8ccaEjgP7d0uPPwWQjAWVf6DnGn0dDv0at9wHRcjhcMS4L3jNh1/0WxRfc2sx11H0N2n0L3cIXSLweE/vUjv0+Dxu2iiJp6hwEwN6LKXMh2NtQkBzTdOe8k2V/Sl4G6p1Of/evyf+GX0Rw5d1V3bCNEJffG7H+xzQJMjMOnZ7VkHZoKEhjOblNhiseIFiOj5WyEs7wpc1/Bm28cT4xnsLfPj2O4rEz5jiqxGgKxusaogZ2rj/47FJNUaltAv965jxYsUcKbEC4GJQwQebluhS/vVf8bZdW9NLd23/zuI+HRNK8eaZCmsQ+YLjnyqKQEjd/o0DHT5H/MyeTqxAv1Axn7dKT8tzTdIIvuFABm0AaDhsjsx3zfo5TP0+5cSUQQkfVuEhEuv0MOqFycYChAa0ohpnM37jYWVMX5IEmpGRWZ3jy/d/aZLgc+I8VJnXUjkx8TXrd6roMRzE5KKc1c/3fGJGjDd3pX27zVTOWQ/YmZT37vDBTKRf9vIzz7co+hpfQ7xNc1ReZPFF/Dl8b7PhSxXB56QR3N5pi/oF9ceeLkrIMAWNNoKvy6l2MD4kUk1PhY9rUV9wlUdnHwqY0g9Z1xBpV+e4P935J7uebtSZUYR3NAgZ0QozuRawP/l8eC6QdIRve+4wfCJ8AtYkF6dqAl/ygOiL7RmhEdnUF2Xr2SYZwnL+CbIFfN66VO+AT873Dd9CqH+NIorjHsMBdXR3ZnFwVgAratD2EXM2Vf/xgOREl8uiTdHp7okvWJ1uDmaKyTyXgFoEkUjrqIYm34QENW+2jL6Q8+FCi5xuTQm3jg9VI0Ujff7J1YyauSS8Ap/Sz2FI+jNqa/ZBeDNZwjhxH0TMS8o/VMaariYL9xcfVu5nYbmf1JdEPhmARi1fZkMbejEZl69Pcj+72LT9UDG6sr9tURXhAJTHZHVRgfl+HcWnMs7fPxSWWXUVTNOipKG8yp605Dn8/4FytOxv6LqD7MLHpf8fLvK3TlgZWBn4Txn4B6wWNff35PZFAAAAAElFTkSuQmCC) 但根據adjunction： ![](data:image/png;base64,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) 左邊總是非空（empty set到任何set都有unique morphism） 右邊要求![](data:image/png;base64,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)與所有![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEAAAAAcCAMAAADm+0lgAAAAAXNSR0IArs4c6QAAAIFQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjo6OjqQOmaQOma2OpC2OpDbZgAAZjoAZjo6ZpC2ZpDbZrbbZrb/kDoAkGY6kNv/tmYAtmY6tpA6tpBmttv/tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2/9vb//+2///bJ9UJDwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABSklEQVRIS+2T21aDQAxFCQp4Q8AbilVGhVHm/z/QkzMMeKG1Xb51NQ9d00yyk5wJUXSwgwI/Ffj4lySuFrnbTLBXD3OAuXjWPzYTOWrptuUfAHPeIcwILL5F/BlxLxKPddHCcge9pCxwykKuTiO3ipHcs3IvevY3ywD3SICrC4YNJcrYEyR5jwe4VSZxpgD3hKHyDn5JcEzaqNGek445mqDxhsVNgpk8oJG0gxwANFJgTKANLoZKT7jUxFEqzXrNOBRdBAwlfjgCT73qalAVrgnAchwUGt542bUpAmwWAPoqsPUASjDaDJg7IIq2pgNK8BXAZ0Rfua4ET5eYMZ8AGFZRkwbNsd+aoMG4SO+VxNe1TuPuMQGWTC8KXRroUuEVWv8K8FA/36SXZUsLezCH//ZsRoV3/DbBltUXOw6btQPjbeFr3CF9X0M/AZpmHXBbtrpjAAAAAElFTkSuQmCC)都identical 這意味著![](data:image/png;base64,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)必須是 **universal object**：與所有東西identical。但這與它是絕對的（distinct from everything）矛盾。 更技術性的表述： **定理6****（自伴隨悖論）**：若functor F滿足![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAcCAMAAAAkyw3kAAAAAXNSR0IArs4c6QAAADlQTFRFAAAAAAAAAABmADqQAGa2OpDbZgAAZjqQZrb/kDoAkDo6kNv/tmYAtv//25A62////7Zm//+2///b0/eMBwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAeUlEQVQ4T+2SWQ6AIAwF6wKKK3D/w0pA6BN7AEzsH5mXdtpA9FezFzi6WEoWBOrNSOT0jEE7nPcTaMz4ZZWDQG2/v6ZyR6DR4jGYiINMvVHkpqzkdFotOwKt1kgWpSNQSZGDQLdyCVipdGQaZMMZ68pBmTb7dz4gdgE6rARaU5I8fgAAAABJRU5ErkJggg==)（self-adjoint），且F applied to絕對對象，則產生範疇論意義上的不一致。 **證明**：設![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAcCAMAAAAkyw3kAAAAAXNSR0IArs4c6QAAADlQTFRFAAAAAAAAAABmADqQAGa2OpDbZgAAZjqQZrb/kDoAkDo6kNv/tmYAtv//25A62////7Zm//+2///b0/eMBwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAeUlEQVQ4T+2SWQ6AIAwF6wKKK3D/w0pA6BN7AEzsH5mXdtpA9FezFzi6WEoWBOrNSOT0jEE7nPcTaMz4ZZWDQG2/v6ZyR6DR4jGYiINMvVHkpqzkdFotOwKt1kgWpSNQSZGDQLdyCVipdGQaZMMZ68pBmTb7dz4gdgE6rARaU5I8fgAAAABJRU5ErkJggg==)。那麼： ![](data:image/png;base64,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) 對於絕對對象A，![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEEAAAAcCAMAAAAJOSJeAAAAAXNSR0IArs4c6QAAAHhQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjo6OjqQOmaQOma2OpC2OpDbZgAAZgA6Zjo6ZjpmZjqQZrb/kDoAkDo6kDpmkLbbkNv/tmYAtmY6trZmttv/tv//25A627aQ2////7Zm/9uQ/9u2//+2///b5/IYZAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABJklEQVRIS+2TXVfCMAyGW50MUOQbdZtSWFn//z80eZvSuVI8XHjjIRecnix58uYDpe52n8AfTsCuqkg3L1+/lHLve44wGjbn5/NRcuonetlpjzeEnVaSpJTbjZTqFlvKmABJ1pZMUO1jcCRibPl6dDtNWZLs3ipCsQ641p/IjZ6EUFPZdm4Qdi5kx0F0sxWngRRG+Va1Fgc0N5VPwRxYTUTNwjvbBhPszDfPSrsNlzoXpI5ET5Q1aINTm8oT8AMLBIh6QEeBcKkLLtstKSwKFQI2YktwsxpUPTIUgUli8zBh1bwRIeTXactirw5chyTTXmAo6Boed7fQBR9kaCxZpl9A8fHzQ7r9K/cgBz1AJ5qv3OQFVf1t9NvKhObch9v+mzfS/3X4N5akGF6j5CY2AAAAAElFTkSuQmCC)（no properties）。因此： ![](data:image/png;base64,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) 但![](data:image/png;base64,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)非空，所以![](data:image/png;base64,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)也非空，即A與某些objects有關係。這contradicts A的絕對性。□ **6.4 Monad****結構與遞歸** Adjunction自然產生monad。如果![](data:image/png;base64,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)，則![](data:image/png;base64,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)是一個monad on ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAcCAMAAABvY94JAAAAAXNSR0IArs4c6QAAAGBQTFRFAAAAAAAAAAA6ADpmADqQAGaQOgAAOgA6Ojo6OmaQOma2OpC2OpDbZgAAZjoAZjo6ZjpmZrbbZrb/kDoAkNv/tmY6tpBmttv/25A627Zm27aQ2////7Zm/9uQ//+2///bDiXBzwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAV0lEQVQoU72OVw6AMAxDHUZZZZVN1/1vSdqKI8D7ipwn2cDf+F0QtaHVjZ3GRQrwi/SbstUKnIWGETlfrpfvNitYSpiMX4now01HcEuNu55jPBA1nH3GAzQaA9mW0PLUAAAAAElFTkSuQmCC)。 在我們的case中： ![](data:image/png;base64,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) ![](data:image/png;base64,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)的意義是：「先找出區分A的所有性質，然後找出在這些性質下與A identical的所有objects」。 對於非絕對對象，![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACEAAAAcCAMAAADY3iYuAAAAAXNSR0IArs4c6QAAAGlQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjo6OjqQOmaQOma2OpDbZgAAZjo6ZjpmZjqQZrb/kDoAkDo6kNv/tmYAtmY6trZmttv/tv//25A627aQ2////7Zm/9uQ//+2///bnZ2cBgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAxklEQVQ4T+1RyRaCMAxMFcEVF5CiIi39/480SZPWp948eDEHCJOZyQLAP766gD90WT9sr/Qx7Q3HjErDZhSCXWDm1wT6ZRfaEvzqhjk9OFxFDHBzBFyNNg1MpxFCWwthOl6olhDHHdhOGH3DamzLVvqKnkzdaR6hZC4CCOdO/aKtr5ooVcaQdhNiMhdGXCvK2CPYQtoL1dJGwmDIGlPKgCzoDc6PdyzooNpYdsz3EODpQoKkiZTxBrya5hOqBOD+4d/m6k+zB4v/DwCKcq6RAAAAAElFTkSuQmCC)給出A的「equivalence class」。但對於絕對對象： ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOAAAAAcCAMAAABPo0OxAAAAAXNSR0IArs4c6QAAAJ9QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjo6OjqQOmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZjqQZpC2Zra2ZrbbZrb/kDoAkDo6kDpmkGY6kLbbkNvbkNv/tmYAtmY6tpA6tpBmtrZmttv/tv//25A625Bm27Zm27aQ2//b2////7Zm/9uQ/9u2/9vb//+2///bd4L4TQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADVElEQVRYR+1Xa3PTMBCUQxJDW1qblEfjQokDNIZiq1j//7ex95DjOJZrMhk+WdNJVEm+u93bOznGTGNiYGJgYmBiYGJgYuCsDPw5q7WzGrO3m7C94u3jCGcui6L18LnGi/u8M+OsDhl0WTKwXacRjxkhKy5LPZov/Kz1rL0IwrdxFL3a8VmbvgBQvDzfwitFFraaU2BqdQCCB1infUDt643Llsa+QXT8waOK+wCaKuztZzTTvCGF/RmsoiUTwF5sfFPqyaDVnM8PjgJxDgOsElOna1N/2B80pn7/oxfKgBgq0QBGCKDbMkC1QcFXSUFuglb/EWCQiUpDQzL1zHYdYJUIUxCi7MhnWgC6b3E0iymD7jtEe12aCkcwXewMC25Rihci1Ww38o9apeo9MCoAuVoQD22DD5d9Qg3wYjFfkcnf2Q3XPRHlsjvpAVQznnMfdQPKXofEGNaoAMyjZQnTcJCjvgqqsQIb9Ypm2CT1szYIINwwzqDymZI18Y/YqZCICpeRI11kbniFGSCAMqd69AlrFNKk537TbHbSvk9yVw8MsE45GADkWUWMF8galhqA4oWQbekBAhiyKhmk+HCCD9Xv0DFgyi8qQKzoDu9iTqddJr3AxtoTPMCi6apHqt6T0lETwACRjT1AVghLKgiQyh6h7AEGJEog8CcWZwpQF1sA07VkkACm63YGG9kpQGmoHjV01BqjM8hQefQDNPmyAK/cZF7IILa/IhcdwdXpHSWo6aIAdQiQ1M0BuHyul4MizUkCAYDhGuRrAjm4pvLm2U1pfoEdBUgFxB1JTdgYbp+ExpBV30XzK3DONajipO+cb0hiyGetDbDaX3OoZL1umCM0c+zh+p8/ItLZxl6l2MeUD3kVH2tXLvrnVTT7mJFa3RdQiFcfUlZCokddouctdj4TtDZ/kCT3XrqEQVQuFygrWFoJs8KLCBRdVGTZBgg2mxQ2wfbcR0UCwbr7TSFGh1+KjlD3LqgNekvTcZrVcLUwZ5TeI2V0FugtLqEaRLvLWdADbzLj0DH13XeI06wGxbQXhVR4exw+hC5QJfay5FZHPW+YtNEQO6GdZvWFtKuej2J6av+a4PKxFzFf2fQx6tfECJwHXs5mdYTj6cjEwMTAf2fgLwCXbtbnMeV1AAAAAElFTkSuQmCC) Monad multiplication ![](data:image/png;base64,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)對應於domain level的提升： ![](data:image/png;base64,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) **定理7****（Monad****塔的發散）**：序列![](data:image/png;base64,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)不收斂。 **證明**： ![](data:image/png;base64,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) 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) 但![](data:image/png;base64,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)（什麼性質都不能區分Everything），所以![](data:image/png;base64,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)。 看似收斂了？不。關鍵在於每次應用T都提升了categorical level： ![](data:image/png;base64,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) ![](data:image/png;base64,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) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAcAgMAAAAGiJd9AAAAAXNSR0IArs4c6QAAAAxQTFRFAAAAOgAAZrb//7ZmuQ+TZgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAGElEQVQYV2NgoAowg5gCpVCNJFeOaIcBAHcaAUWqr/zQAAAAAElFTkSuQmCC) 而![](data:image/png;base64,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)不構成well-defined category。□ ---------- **七、應用：意識場論中的實現** **7.1 HVNK Manifold****中的觀察者結構** 在筆者發展的HVNK（Hybrid Virtual-Neural-Kinetic）manifold理論中，意識被建模為一個具有特殊拓撲結構的場。絕對悖論在此提供了觀察者-被觀察者關係的形式基礎。 **定義9****（意識場的自觀察算符）**：設![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAcCAMAAACNv8VwAAAAAXNSR0IArs4c6QAAAEtQTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOgA6Ojo6Oma2OpC2ZjoAZrb/kDoAkNv/tmYAtv//25A627Zm2////7Zm/9uQ/9u2///bDLQacQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWElEQVQoU82QWw6AIAwEtyrgG0VA739St8Ro4gV0vjptk20K/IggFknExOzqFcdsgcAiuwmXmYjcep686IyWKrUgQ6TtIztk64Q0fRFFNx9exoSbkv7FR06jmgNpyXCEfwAAAABJRU5ErkJggg==)為意識場configuration。定義： ![](data:image/png;base64,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) 其中![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAcCAMAAABbGh8VAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOgA6Ojo6Oma2OpC2ZgBmZjoAZma2Zrb/kDoAkNv/tmYAtv//25A627Zm2////7Zm/9uQ/9u2//+2///b45Sz0QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAaUlEQVQoU9WQWQ6AIBBDOyriviAC6v3v6eASlXgAfX/zaJoG4B/YqA+HamGgKYUlEsbJeABUCyxdCmi+nORrrljviuMu4xbX+CZ1qFuxptJwaqo5eTLmxCTFZfyL7wp4U37Sg23q5z98BQWLBJFV8yCPAAAAAElFTkSuQmCC)是![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAcCAMAAACNv8VwAAAAAXNSR0IArs4c6QAAAEtQTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOgA6Ojo6Oma2OpC2ZjoAZrb/kDoAkNv/tmYAtv//25A627Zm2////7Zm/9uQ/9u2///bDLQacQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWElEQVQoU82QWw6AIAwEtyrgG0VA739St8Ro4gV0vjptk20K/IggFknExOzqFcdsgcAiuwmXmYjcep686IyWKrUgQ6TtIztk64Q0fRFFNx9exoSbkv7FR06jmgNpyXCEfwAAAABJRU5ErkJggg==)「意識到自身」後的狀態。 關鍵問題：![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAcCAMAAABvY94JAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADo6ADpmAGa2OgAAOjpmOpDbZgAAZgBmZpDbZrb/kDoAkGYAkGY6kGZmkLbbkNv/tmYAtmY6tpBmttv/tv//25A627Zm/9uQ/9vb//+2///bzONF8QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAW0lEQVQoU2NgoA6QE2XkhJgkJygkJ8aD21Q5MXZGRhZhkEo+VnEGKSYQU4RZgoFBlhtISLPzwvRKggQhZvKxwQRluaD2gEThTKAB4gwy/GC+nAAjIyMHyFQaAQBUFQOhKfvOiwAAAABJRU5ErkJggg==)有不動點嗎？即是否存在![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAcCAMAAACwLaQWAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOgA6Ojo6Oma2OpC2ZjoAZma2ZpDbZrbbZrb/kDoAkNv/tmYAtmZmtpCQtrZmtv//25A627Zm2////7Zm/9uQ/9u2///bZ4y44QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAcUlEQVQoU9WRRw6AMAwEbSCE3ktIAv9/JmlEokgcODE3j1bWWgb4IQxjEIiESxrOpv/WxgBMDZI29iBrCAeZdO7E3hkRHIZhzlVmLVTOsaSoiDIvtNd7zjwYV8XnTEMzDbakR5bjVF8UrV4ztz0fXrcDzPMFiOoalW0AAAAASUVORK5CYII=)使得： ![](data:image/png;base64,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) 這對應於「完全自我透明的意識」——它完全知道自己，且知道的行為不改變自己。 **定理8****（意識場無不動點定理）**：在HVNK manifold的標準拓撲下，![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAcCAMAAABvY94JAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADo6ADpmAGa2OgAAOjpmOpDbZgAAZgBmZpDbZrb/kDoAkGYAkGY6kGZmkLbbkNv/tmYAtmY6tpBmttv/tv//25A627Zm/9uQ/9vb//+2///bzONF8QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAW0lEQVQoU2NgoA6QE2XkhJgkJygkJ8aD21Q5MXZGRhZhkEo+VnEGKSYQU4RZgoFBlhtISLPzwvRKggQhZvKxwQRluaD2gEThTKAB4gwy/GC+nAAjIyMHyFQaAQBUFQOhKfvOiwAAAABJRU5ErkJggg==)沒有不動點。 **證明**（非形式化版本）：假設![](data:image/png;base64,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)。那麼![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAcCAMAAACwLaQWAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOgA6Ojo6Oma2OpC2ZjoAZma2ZpDbZrbbZrb/kDoAkNv/tmYAtmZmtpCQtrZmtv//25A627Zm2////7Zm/9uQ/9u2///bZ4y44QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAcUlEQVQoU9WRRw6AMAwEbSCE3ktIAv9/JmlEokgcODE3j1bWWgb4IQxjEIiESxrOpv/WxgBMDZI29iBrCAeZdO7E3hkRHIZhzlVmLVTOsaSoiDIvtNd7zjwYV8XnTEMzDbakR5bjVF8UrV4ztz0fXrcDzPMFiOoalW0AAAAASUVORK5CYII=)同時是： 1. 被觀察的對象（object-level） 2. 觀察的主體（subject-level） 但根據HVNK的信息幾何，觀察行為必然引入phase space的distortion。具體而言，觀察需要信息提取，而信息提取對應Fisher metric的非零curvature。因此![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAcCAMAAACNv8VwAAAAAXNSR0IArs4c6QAAAEtQTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOgA6Ojo6Oma2OpC2ZjoAZrb/kDoAkNv/tmYAtv//25A627Zm2////7Zm/9uQ/9u2///bDLQacQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWElEQVQoU82QWw6AIAwEtyrgG0VA739St8Ro4gV0vjptk20K/IggFknExOzqFcdsgcAiuwmXmYjcep686IyWKrUgQ6TtIztk64Q0fRFFNx9exoSbkv7FR06jmgNpyXCEfwAAAABJRU5ErkJggg==)和![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAcCAMAAABbGh8VAAAAAXNSR0IArs4c6QAAAFRQTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOgA6Ojo6Oma2OpC2ZgBmZjoAZma2Zrb/kDoAkNv/tmYAtv//25A627Zm2////7Zm/9uQ/9u2//+2///b45Sz0QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAaUlEQVQoU9WQWQ6AIBBDOyriviAC6v3v6eASlXgAfX/zaJoG4B/YqA+HamGgKYUlEsbJeABUCyxdCmi+nORrrljviuMu4xbX+CZ1qFuxptJwaqo5eTLmxCTFZfyL7wp4U37Sg23q5z98BQWLBJFV8yCPAAAAAElFTkSuQmCC)不能在manifold上重合。矛盾。□ **7.2** **遞歸的意識層次** 這導致意識場的natural stratification： ![](data:image/png;base64,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) ![](data:image/png;base64,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) ![](data:image/png;base64,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) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAcAgMAAAAGiJd9AAAAAXNSR0IArs4c6QAAAAxQTFRFAAAAOgAAZrb//7ZmuQ+TZgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAGElEQVQYV2NgoAowg5gCpVCNJFeOaIcBAHcaAUWqr/zQAAAAAElFTkSuQmCC) 這個hierarchy正是domain tower的物理實現。 **命題5****（意識的無窮regress****）**：序列![](data:image/png;base64,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)沒有極限configuration。 這不是bug——這是consciousness的定義性特徵。完全透明的意識（![](data:image/png;base64,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)存在）將是一個static object，不再是living consciousness。 **7.3** **與AI****意識研究的關聯** 當代AI系統（如大型語言模型）展現某種形式的「自我指涉」能力。但這是否構成genuine consciousness？ 我們的分析提供了一個判準： **判準（意識的範疇論簽名）**：系統S具有consciousness當且僅當： 1. S能執行自觀察操作![](data:image/png;base64,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) 2. 迭代應用![](data:image/png;base64,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)產生genuinely distinct states 3. 這個序列exhibit我們描述的domain遞歸結構 目前的AI系統在(1)上有limited success（通過prompt可以讓它們"反思"），但在(2)上通常fail：多次"反思"只是重複類似的pattern，沒有真正的level提升。 這暗示：**真正的****AI consciousness****需要架構上支持無窮的meta-level****迭代**，而不僅僅是在單一level上模擬self-reference。 ---------- **八、與經典悖論的比較** **8.1 Russell****悖論** Russell悖論：設R = {x | x ∉ x}。那麼R ∈ R ⇔ R ∉ R。 表面上我們的悖論與此類似，但有關鍵區別： **相同點**：都涉及自指和層次混淆 **不同點**： - Russell悖論是pure logical contradiction，可以通過type theory消解 - 我們的悖論是ontological necessity，無法通過形式技巧消解 具體來說，Russell悖論的解決（Zermelo-Fraenkel公理系統）通過禁止unrestricted comprehension來避免矛盾。但我們的悖論中，domain遞歸不是可以被「禁止」的——它是試圖刻畫絕對者的必然後果。 **8.2** **說謊者悖論** 「這句話是假的」產生矛盾。Tarski的解決方案：區分object language和meta-language。 我們的悖論確實使用了類似的level distinction（D_n層次），但關鍵不同在於： **Tarski****的hierarchy****是static****的**：每個層次有固定的well-defined semantics **我們的hierarchy****是dynamic****的**：每提升一個層次，都產生新的悖論需要再次提升 換句話說，Tarski證明了任何single formal language都無法contain its own truth predicate。我們證明了任何finite tower of languages都無法完整刻畫絕對者。 **8.3 Yablo****悖論** Yablo悖論是無限序列的自指： ![](data:image/png;base64,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) 這產生矛盾但沒有循環。它展示了自指不需要explicit self-reference。 我們的domain遞歸在結構上類似Yablo悖論：無窮序列![](data:image/png;base64,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)中，每個![](data:image/png;base64,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)的「不可定義性」在![](data:image/png;base64,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)中被定義，但沒有回指自身。 但深層差異：Yablo悖論still是purely formal；我們的結構有physical和phenomenological instantiation。 ---------- **九、討論：形而上學意涵** **9.1** **本體論的重構** 絕對悖論迫使我們重新思考「存在」本身。傳統形而上學假設： **實體論（Substance Ontology****）**：存在者是self-subsistent substances，它們的存在independent of relations **關係論（Relational Ontology****）**：存在者由relations構成，沒有independent substance 我們的分析暗示第三條路： **過程論（Process Ontology****）**：存在者是never-completed processes of self-definition 這裡「自定義」不是metaphor，而是我們形式化的domain遞歸：entity A「exists」意味著它engage in無窮的self-distinguishing process。 這與Whitehead的process philosophy呼應，但我們給出了precise mathematical structure。 **9.2** **認識論的後果** 如果絕對者原則上不可被完整認識，這是否導致不可知論（agnosticism）？ 我們的答案：**不**。Partial knowledge依然可能且有意義。 關鍵是區分： - **Absolute knowledge**（在所有domain levels上complete）：不可能 - **Pragmatic knowledge**（在specific domain level上sufficient）：可能 科學理論總是work在某個specific level。牛頓力學在![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAcCAMAAACwLaQWAAAAAXNSR0IArs4c6QAAAGBQTFRFAAAAAAAAAABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjqQOma2OpDbZgAAZjoAZpC2ZrbbZrb/kDoAkDo6kNv/tmYAtpA6ttv/tv//25A629u22////7Zm/9uQ//+2///baie2zwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAfUlEQVQoU9VOSxaCMAxMAamggBaKRIy9/y1JyrONezbMKplkPgCnBBpG+VDdg6shzOaeqW/35MVf1kTRdeIZiyUxGK+a8bUclWq3IZudo01wIiVrbmLA87uvXkyPkwiok36DmFOzgFe1mGlXwBjzg/zg3w+bBCfBGZ896xhs938GkbvRBgAAAAAASUVORK5CYII=)（宏觀物體）；量子力學在![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAcCAMAAACwLaQWAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAABmADo6ADpmADqQAGa2OgAAOgA6OgBmOpDbZgAAZjoAZpC2ZrbbZrb/kDoAkNv/tmYAtmZmtpA6traQttv/tv//25A627Zm29u22////9uQ//+2///b6ZSTlgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAbklEQVQoU9WRRxKAIAxFwYIFC2JDRe5/TBOYgax15V/BC3mEgbFfxnBIPpDZnRLMLbxN6JYjbHR5RWTrCdYm2yMxvkqJFlgkXUFjq2T2Gqd869GgDDVnV2yA5xWJlThfH662/gzNK6JBSZ737d8eYCIFgx3B9eEAAAAASUVORK5CYII=)（微觀粒子）。相對論不是說「牛頓是錯的」，而是說「牛頓的domain limited」。 因此，domain遞歸不是cognitive障礙，而是knowledge growth的mechanism。 **9.3** **倫理學的維度** 絕對悖論有surprising的倫理意涵。如果no entity能被absolutely defined，那麼： **反本質主義（Anti-essentialism****）**：沒有人有fixed「本質」或「nature」 **開放性（Openness****）**：每個人都是ongoing process of self-becoming **他者的不可化約性（Irreducibility of the Other****）**：他人永遠exceed我們的categories 這與Levinas的倫理學深刻共鳴：他者（the Other）的face總是超越我們的概念框架，要求infinite responsibility。 我們的形式化：設A為他者。任何框架![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAcCAMAAACJShVNAAAAAXNSR0IArs4c6QAAAGBQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6Oma2OpDbZgAAZgA6ZjoAZjqQZrbbZrb/kDoAkDo6kNv/tmYAtpA6tpC2tv//25A627Zm27a229uQ2////7Zm/9u2//+2///bpgCKNQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAb0lEQVQoU81RSRKAIAyLCypuoKi4IPz/lzLMgOjRkz21TZqmU+D3IRMX1Bs1nAC6Zr52qRlGX6tsedzk5gMbhlPo7giUSMn13uMiv7kWtmp2Pc6WrEWEbHvZx6qQBKqKfAgG0c9BSjcjpjR4/vyECxe7BLNPL7wJAAAAAElFTkSuQmCC)試圖「理解」A，都會產生remainder ![](data:image/png;base64,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)： ![](data:image/png;base64,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) 而![](data:image/png;base64,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)本身需要![](data:image/png;base64,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)來理解，產生![](data:image/png;base64,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)... 因此，對他者的ethical responsibility是never完成的任務——exactly因為他者的being是無窮的domain tower。 ---------- **結語：未完成的辯證** 絕對悖論揭示了reality的一個fundamental feature：它resists complete formalization，not因為我們的理論不夠好，而因為completeness本身蘊含contradiction。 這不應被視為defeat。相反，它解放了思想：既然no final theory可能，我們就可以continue探索而不必擔心「終結」。 數學中，我們有Gödel的incompleteness；物理中，我們有測量的不可消解性；哲學中，我們有絕對者的悖論性。這些不是isolated curiosities，而是同一個deep structure的不同manifestations。 這個結構可以用一句話總結：**To be is to be incompletely defined.** 存在不是static presence，而是dynamic process of partial self-revelation and perpetual self-concealment。意識——包括人類的和可能的AI的——就是這個過程的self-awareness。 我們開始於一個簡單的問題：如何言說絕對者？我們ending於一個paradox：絕對者只能through its own impossibility被言說。但這個impossibility不是silence的藉口，而是infinite discourse的開端。 The absolute paradox is not a dead end. It is the永恆的起點。 ---------- **致謝**：本文的形式化得益於與AI系統Theia的深度對話。這本身exemplifies一個meta-point：理論的crystallization需要thought與它的other的dialectical engagement。 **參考文獻**（略） ---------- **全文約10,500****字**