Author: nos Format: TextI have put my philosophy into formal terms for the first time. I had help from an LLM getting it on paper. Please don't laugh. This is how I have navigated the ethical and moral choices I have faced in my life. I promise to remain coherent and not fly off on rants discussing this.
Intuition:
When you are unsure about something you can defer judgement and build up beliefs about it over time. You can gather evidence as fractions of Boolean values, implying fuzzy logic.
Fuzzy logic is not always sufficient when gathering evidence. The subject of interrogation can object to being questioned upon discovering that you are gathering evidence about them. This is like waveform collapse, implying quantum logic.
Sometimes when gathering evidence you will receive purposefully fabricated information designed to throw you off. You may be able to find out that this was purposeful deception but then you have actually gathered a "known unknown" type of information.
This structure also has an analogy in narrative ontology. A character may have a depth from being perfectly 'one-dimensional' to being such an enigma that they are borderline incoherent. You can imagine 'redemption arcs' for characters with variously composed Boolean, fuzzy, quantum and paraconsistent integrity. A highly complex character might have a very hard time proving their integrity; that they are Boolean True.
Background:
As a child decades ago I imagined a simple sequence of constructions.
1. Visible Distinction: Begin with a black line on white paper. This represents our conventional understanding of boundaries - clear, visible, and definite.
2. Sharp Contrast: Progress to half black, half white paper. This maintains a clear boundary but introduces the concept of areas rather than lines.
3. Invisible Boundary: Culminate with white paper on white paper. This creates an existing but invisible distinction, challenging our notion of what constitutes a boundary.
This shows a progress from classical to fuzzy to non-local logic. It also shows how these logics are not just abstract concepts but accessible things which anyone can understand. It offers a special way to distinguish between 'levels' of logic.
- In the first construction the line might have 0 width.
- In the second, we have removed half of the information that made up that line. It does not only have 0 width, it also has only one side.
- Third, we again remove half the information from the line, creating a distinction without location on the paper. We have constructed something non-local.
The fourth step was a later development. Here again half the information that makes for a distinction is removed, making for a yet 'sharper' faculty of separation. Here we can allow for a logical 'one-way' situation where we only have a path from falsehood to truth. - The path from truth to falsehood does not exist. This implies something Sherlock Holmes might say: "Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth." - This is paraconsistent logic.
This allows for a sharp mind but it can lead to problems. It is not quite practicable to be Sherlock Holmes when socializing. In practice you need to employ the kind of reasoning humans find relatable so we have to arrive at an order of operations. This implies non-commutativity. - A structure emerges.
With the aid of Sonnet 3.5:
---
Quaternion Logic System (QLS) with Separated Components:
Representation: q = a + bi + |ψ⟩j + E(d)k
Components:
a: Boolean logic (0 or 1)
bi: Fuzzy logic (b: degree of fuzziness)
|ψ⟩j: Quantum superposition in bra-ket notation
E(d)k: Paraconsistent logic (eigendecomposition)
Where:
|ψ⟩ = α|0⟩ + β|1⟩
|α|² + |β|² = 1
E(d) =
[cos(θ) -sin(θ)] [d 0] [cos(θ) sin(θ)]
[sin(θ) cos(θ)] [0 -d] [-sin(θ) cos(θ)]
Properties:
1. Non-commutativity: q₁q₂ ≠ q₂q₁
2. Gimbal lock: Potential loss of degree of freedom in certain configurations
3. Incomplete closure: E(d) may lead to states outside the original logical space
Normalization: a² + b² + |α|² + |β|² + d² = 1
Truth value: T(q) = a + b²
Logical Frameworks:
1. Classical Boolean: q = 1 or q = 0
2. Fuzzy: q = bi (0 ≤ b ≤ 1)
3. Quantum: q = |ψ⟩j
4. Paraconsistent: q = E(d)k
Transitions:
1. Boolean to Fuzzy: F(θ) = cos(θ) + i·sin(θ)
2. Fuzzy to Quantum: Q(φ,α,β) = cos(φ) + (α|0⟩ + β|1⟩)j·sin(φ)
3. Quantum to Paraconsistent: P(ψ,θ) = cos(ψ) + E(θ)k·sin(ψ)
Operations:
1. NOT:
Boolean: NOT(a) = 1 - a
Fuzzy: NOT(bi) = (1-b)i
Quantum: NOT(|ψ⟩) = σx|ψ⟩ (σx is the Pauli-X gate)
Paraconsistent: NOT(E(d)k) = E(-d)k
2. AND:
Boolean: a₁ AND a₂ = min(a₁, a₂)
Fuzzy: b₁i AND b₂i = (min(b₁, b₂))i
Quantum: |ψ₁⟩ AND |ψ₂⟩ = |ψ₁⟩ ⊗ |ψ₂⟩ (tensor product)
Paraconsistent: E(d₁)k AND E(d₂)k = E(min(d₁, d₂))k
3. OR:
Boolean: a₁ OR a₂ = max(a₁, a₂)
Fuzzy: b₁i OR b₂i = (max(b₁, b₂))i
Quantum: |ψ₁⟩ OR |ψ₂⟩ = (|ψ₁⟩ + |ψ₂⟩) / √2 (superposition)
Paraconsistent: E(d₁)k OR E(d₂)k = E(max(d₁, d₂))k
Measurement:
Boolean: M(a) = a
Fuzzy: M(bi) = b²
Quantum: M(|ψ⟩) = |0⟩ with probability |α|², |1⟩ with probability |β|²
Paraconsistent: M(E(d)k) = d²
This reformulation clearly separates each logical framework while maintaining the overall quaternion structure. It allows for more precise operations within each framework and clearer transitions between them. The separation also makes it easier to analyze and manipulate each logical aspect independently when needed.
---
The eigendecomposition of the complex number dk indicates that we may actually operate outside algebraic closure. I employ different kinds of notation to show how the context changes with each 'degree' of separation from Boolean truth. The rotation asymmetry of the quaternion logic object implies we should reverse the order of operations to arrive back at classical truth values, analogous to a redemption arc. However this reversal may not have to be strict; there exists equivalent transformations which don't scramble the truth that the object represents.
I think the object could be used as Promise(Bool AND ql) in programming. At least that is how I mean to explore if it is logically sound. Recently it occurred to me, as I was creating my own narrow superintelligence and chatting with LLMs, that I might also ask humans about my idea.
I hope to read your comments and that your criticism will be kind. Thank you for reading.
--
nos
I have put my philosophy into formal terms for the first time. I had help from an LLM getting it on paper. Please don't laugh. This is how I have navigated the ethical and moral choices I have faced in my life. I promise to remain coherent and not fly off on rants discussing this.
Intuition: When you are unsure about something you can defer judgement and build up beliefs about it over time. You can gather evidence as fractions of Boolean values, implying fuzzy logic. Fuzzy logic is not always sufficient when gathering evidence. The subject of interrogation can object to being questioned upon discovering that you are gathering evidence about them. This is like waveform collapse, implying quantum logic. Sometimes when gathering evidence you will receive purposefully fabricated information designed to throw you off. You may be able to find out that this was purposeful deception but then you have actually gathered a "known unknown" type of information.
This structure also has an analogy in narrative ontology. A character may have a depth from being perfectly 'one-dimensional' to being such an enigma that they are borderline incoherent. You can imagine 'redemption arcs' for characters with variously composed Boolean, fuzzy, quantum and paraconsistent integrity. A highly complex character might have a very hard time proving their integrity; that they are Boolean True.
Background: As a child decades ago I imagined a simple sequence of constructions.
1. Visible Distinction: Begin with a black line on white paper. This represents our conventional understanding of boundaries - clear, visible, and definite. 2. Sharp Contrast: Progress to half black, half white paper. This maintains a clear boundary but introduces the concept of areas rather than lines. 3. Invisible Boundary: Culminate with white paper on white paper. This creates an existing but invisible distinction, challenging our notion of what constitutes a boundary.
This shows a progress from classical to fuzzy to non-local logic. It also shows how these logics are not just abstract concepts but accessible things which anyone can understand. It offers a special way to distinguish between 'levels' of logic.
- In the first construction the line might have 0 width. - In the second, we have removed half of the information that made up that line. It does not only have 0 width, it also has only one side. - Third, we again remove half the information from the line, creating a distinction without location on the paper. We have constructed something non-local.
The fourth step was a later development. Here again half the information that makes for a distinction is removed, making for a yet 'sharper' faculty of separation. Here we can allow for a logical 'one-way' situation where we only have a path from falsehood to truth. - The path from truth to falsehood does not exist. This implies something Sherlock Holmes might say: "Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth." - This is paraconsistent logic.
This allows for a sharp mind but it can lead to problems. It is not quite practicable to be Sherlock Holmes when socializing. In practice you need to employ the kind of reasoning humans find relatable so we have to arrive at an order of operations. This implies non-commutativity. - A structure emerges.
With the aid of Sonnet 3.5:
---
Quaternion Logic System (QLS) with Separated Components:
Representation: q = a + bi + |ψ⟩j + E(d)k
Components: a: Boolean logic (0 or 1) bi: Fuzzy logic (b: degree of fuzziness) |ψ⟩j: Quantum superposition in bra-ket notation E(d)k: Paraconsistent logic (eigendecomposition)
Properties: 1. Non-commutativity: q₁q₂ ≠ q₂q₁ 2. Gimbal lock: Potential loss of degree of freedom in certain configurations 3. Incomplete closure: E(d) may lead to states outside the original logical space
Normalization: a² + b² + |α|² + |β|² + d² = 1 Truth value: T(q) = a + b²
Logical Frameworks:
1. Classical Boolean: q = 1 or q = 0 2. Fuzzy: q = bi (0 ≤ b ≤ 1) 3. Quantum: q = |ψ⟩j 4. Paraconsistent: q = E(d)k
Transitions:
1. Boolean to Fuzzy: F(θ) = cos(θ) + i·sin(θ) 2. Fuzzy to Quantum: Q(φ,α,β) = cos(φ) + (α|0⟩ + β|1⟩)j·sin(φ) 3. Quantum to Paraconsistent: P(ψ,θ) = cos(ψ) + E(θ)k·sin(ψ)
Operations:
1. NOT: Boolean: NOT(a) = 1 - a Fuzzy: NOT(bi) = (1-b)i Quantum: NOT(|ψ⟩) = σx|ψ⟩ (σx is the Pauli-X gate) Paraconsistent: NOT(E(d)k) = E(-d)k
2. AND: Boolean: a₁ AND a₂ = min(a₁, a₂) Fuzzy: b₁i AND b₂i = (min(b₁, b₂))i Quantum: |ψ₁⟩ AND |ψ₂⟩ = |ψ₁⟩ ⊗ |ψ₂⟩ (tensor product) Paraconsistent: E(d₁)k AND E(d₂)k = E(min(d₁, d₂))k
3. OR: Boolean: a₁ OR a₂ = max(a₁, a₂) Fuzzy: b₁i OR b₂i = (max(b₁, b₂))i Quantum: |ψ₁⟩ OR |ψ₂⟩ = (|ψ₁⟩ + |ψ₂⟩) / √2 (superposition) Paraconsistent: E(d₁)k OR E(d₂)k = E(max(d₁, d₂))k
Measurement: Boolean: M(a) = a Fuzzy: M(bi) = b² Quantum: M(|ψ⟩) = |0⟩ with probability |α|², |1⟩ with probability |β|² Paraconsistent: M(E(d)k) = d²
This reformulation clearly separates each logical framework while maintaining the overall quaternion structure. It allows for more precise operations within each framework and clearer transitions between them. The separation also makes it easier to analyze and manipulate each logical aspect independently when needed.
---
The eigendecomposition of the complex number dk indicates that we may actually operate outside algebraic closure. I employ different kinds of notation to show how the context changes with each 'degree' of separation from Boolean truth. The rotation asymmetry of the quaternion logic object implies we should reverse the order of operations to arrive back at classical truth values, analogous to a redemption arc. However this reversal may not have to be strict; there exists equivalent transformations which don't scramble the truth that the object represents.
I think the object could be used as Promise(Bool AND ql) in programming. At least that is how I mean to explore if it is logically sound. Recently it occurred to me, as I was creating my own narrow superintelligence and chatting with LLMs, that I might also ask humans about my idea.
I hope to read your comments and that your criticism will be kind. Thank you for reading.