#rm3 — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #rm3, aggregated by home.social.
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People have an implicit bias towards binary logic. Computers are great and all, but have you noticed they break and fail all the time? Binary logic is not the best system. "You are either with us or against us" is a fallacy, they are trying to trick you. 🚥🚦🚥🚦🚥🚦🚥🚦🚥🚦🚥🚦🚥🚦You use "real world logic" every day, and it's 3-valued. They tried binary traffic signals in the beginning but switched very quickly to 3
Also the Liar Paradox is solvable using a field extension which creates (like i^2 = -1) the complex truth value "I don't know"
which you should know
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People have an implicit bias towards binary logic. Computers are great and all, but have you noticed they break and fail all the time? Binary logic is not the best system. "You are either with us or against us" is a fallacy, they are trying to trick you. 🚥🚦🚥🚦🚥🚦🚥🚦🚥🚦🚥🚦🚥🚦You use "real world logic" every day, and it's 3-valued. They tried binary traffic signals in the beginning but switched very quickly to 3
Also the Liar Paradox is solvable using a field extension which creates (like i^2 = -1) the complex truth value "I don't know"
which you should know
-
People have an implicit bias towards binary logic. Computers are great and all, but have you noticed they break and fail all the time? Binary logic is not the best system. "You are either with us or against us" is a fallacy, they are trying to trick you. 🚥🚦🚥🚦🚥🚦🚥🚦🚥🚦🚥🚦🚥🚦You use "real world logic" every day, and it's 3-valued. They tried binary traffic signals in the beginning but switched very quickly to 3
Also the Liar Paradox is solvable using a field extension which creates (like i^2 = -1) the complex truth value "I don't know"
which you should know
-
People have an implicit bias towards binary logic. Computers are great and all, but have you noticed they break and fail all the time? Binary logic is not the best system. "You are either with us or against us" is a fallacy, they are trying to trick you. 🚥🚦🚥🚦🚥🚦🚥🚦🚥🚦🚥🚦🚥🚦You use "real world logic" every day, and it's 3-valued. They tried binary traffic signals in the beginning but switched very quickly to 3
Also the Liar Paradox is solvable using a field extension which creates (like i^2 = -1) the complex truth value "I don't know"
which you should know
-
People have an implicit bias towards binary logic. Computers are great and all, but have you noticed they break and fail all the time? Binary logic is not the best system. "You are either with us or against us" is a fallacy, they are trying to trick you. 🚥🚦🚥🚦🚥🚦🚥🚦🚥🚦🚥🚦🚥🚦You use "real world logic" every day, and it's 3-valued. They tried binary traffic signals in the beginning but switched very quickly to 3
Also the Liar Paradox is solvable using a field extension which creates (like i^2 = -1) the complex truth value "I don't know"
which you should know
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Boundaries. What's a bike? What's a motorcycle? If you put fins on a cat does that make it a fish?*
This is an excellent example of how binary choice breaks. I'm an avid bicyclist and putting pedals on a machine like that to make it into a bike is, yes, like putting fins on a cat
* Technically the answer is yes, and there are many videos of cats swimming underwater. Also you are a fish
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Boundaries. What's a bike? What's a motorcycle? If you put fins on a cat does that make it a fish?*
This is an excellent example of how binary choice breaks. I'm an avid bicyclist and putting pedals on a machine like that to make it into a bike is, yes, like putting fins on a cat
* Technically the answer is yes, and there are many videos of cats swimming underwater. Also you are a fish
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Boundaries. What's a bike? What's a motorcycle? If you put fins on a cat does that make it a fish?*
This is an excellent example of how binary choice breaks. I'm an avid bicyclist and putting pedals on a machine like that to make it into a bike is, yes, like putting fins on a cat
* Technically the answer is yes, and there are many videos of cats swimming underwater. Also you are a fish
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Boundaries. What's a bike? What's a motorcycle? If you put fins on a cat does that make it a fish?*
This is an excellent example of how binary choice breaks. I'm an avid bicyclist and putting pedals on a machine like that to make it into a bike is, yes, like putting fins on a cat
* Technically the answer is yes, and there are many videos of cats swimming underwater. Also you are a fish
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@MartinEscardo This is true. I'm suggesting that this is not just a computer engineering thing. I'm saying that at base, nature itself is non-binary, and we are non-binary, and we abstract things we don't understand into black and white distinctions to make them easier to understand. It's fast and efficient to ignore certain problems. There are still problems with binary logic.
Did you know that SQL is one of the few computer languages to use 3-valued logic? Databases are highly exposed to the problems of inconsistent or missing information. But we can use binary logic to simulate 3-valued logic (MySQL uses the paraconsistent logic LP by Graham Priest, but you can use that to create a fully relevant implication as in RM3, it's just a longer expression)
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@MartinEscardo This is true. I'm suggesting that this is not just a computer engineering thing. I'm saying that at base, nature itself is non-binary, and we are non-binary, and we abstract things we don't understand into black and white distinctions to make them easier to understand. It's fast and efficient to ignore certain problems. There are still problems with binary logic.
Did you know that SQL is one of the few computer languages to use 3-valued logic? Databases are highly exposed to the problems of inconsistent or missing information. But we can use binary logic to simulate 3-valued logic (MySQL uses the paraconsistent logic LP by Graham Priest, but you can use that to create a fully relevant implication as in RM3, it's just a longer expression)
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@MartinEscardo This is true. I'm suggesting that this is not just a computer engineering thing. I'm saying that at base, nature itself is non-binary, and we are non-binary, and we abstract things we don't understand into black and white distinctions to make them easier to understand. It's fast and efficient to ignore certain problems. There are still problems with binary logic.
Did you know that SQL is one of the few computer languages to use 3-valued logic? Databases are highly exposed to the problems of inconsistent or missing information. But we can use binary logic to simulate 3-valued logic (MySQL uses the paraconsistent logic LP by Graham Priest, but you can use that to create a fully relevant implication as in RM3, it's just a longer expression)
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@MartinEscardo This is true. I'm suggesting that this is not just a computer engineering thing. I'm saying that at base, nature itself is non-binary, and we are non-binary, and we abstract things we don't understand into black and white distinctions to make them easier to understand. It's fast and efficient to ignore certain problems. There are still problems with binary logic.
Did you know that SQL is one of the few computer languages to use 3-valued logic? Databases are highly exposed to the problems of inconsistent or missing information. But we can use binary logic to simulate 3-valued logic (MySQL uses the paraconsistent logic LP by Graham Priest, but you can use that to create a fully relevant implication as in RM3, it's just a longer expression)
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@MartinEscardo This is true. I'm suggesting that this is not just a computer engineering thing. I'm saying that at base, nature itself is non-binary, and we are non-binary, and we abstract things we don't understand into black and white distinctions to make them easier to understand. It's fast and efficient to ignore certain problems. There are still problems with binary logic.
Did you know that SQL is one of the few computer languages to use 3-valued logic? Databases are highly exposed to the problems of inconsistent or missing information. But we can use binary logic to simulate 3-valued logic (MySQL uses the paraconsistent logic LP by Graham Priest, but you can use that to create a fully relevant implication as in RM3, it's just a longer expression)
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Sugihara monoids, RM3, infinite valued logic, and probability ...
Infinite-Valued Relevance Logic as a Probability Structure
Here’s a conceptual leap: if truth values form a bounded poset (e.g. real unit interval [0,1]), and conjunction, disjunction, and implication are operations preserving some form of ordering or residuation, you can begin to think of logic as probabilistic entailment.
Now, if we make the truth values correspond to probabilities (or credences), then:
A⇒B is strongest when the truth value of A is less than or equal to that of B.
This mimics conditional probability: P(B∣A) is highest when A almost implies B.
In fact, some researchers have developed algebraic models of conditional probability using residuated lattices or MV-algebras (multi-valued algebras from Łukasiewicz logic), and relevance logic’s demand for resource sensitivity fits naturally with context-sensitive probability assignments.
You can think of A⇒B not as a function of static truth values, but as "the degree to which A supports B," akin to Bayesian support.
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Sugihara monoids, RM3, infinite valued logic, and probability ...
Infinite-Valued Relevance Logic as a Probability Structure
Here’s a conceptual leap: if truth values form a bounded poset (e.g. real unit interval [0,1]), and conjunction, disjunction, and implication are operations preserving some form of ordering or residuation, you can begin to think of logic as probabilistic entailment.
Now, if we make the truth values correspond to probabilities (or credences), then:
A⇒B is strongest when the truth value of A is less than or equal to that of B.
This mimics conditional probability: P(B∣A) is highest when A almost implies B.
In fact, some researchers have developed algebraic models of conditional probability using residuated lattices or MV-algebras (multi-valued algebras from Łukasiewicz logic), and relevance logic’s demand for resource sensitivity fits naturally with context-sensitive probability assignments.
You can think of A⇒B not as a function of static truth values, but as "the degree to which A supports B," akin to Bayesian support.
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Sugihara monoids, RM3, infinite valued logic, and probability ...
Infinite-Valued Relevance Logic as a Probability Structure
Here’s a conceptual leap: if truth values form a bounded poset (e.g. real unit interval [0,1]), and conjunction, disjunction, and implication are operations preserving some form of ordering or residuation, you can begin to think of logic as probabilistic entailment.
Now, if we make the truth values correspond to probabilities (or credences), then:
A⇒B is strongest when the truth value of A is less than or equal to that of B.
This mimics conditional probability: P(B∣A) is highest when A almost implies B.
In fact, some researchers have developed algebraic models of conditional probability using residuated lattices or MV-algebras (multi-valued algebras from Łukasiewicz logic), and relevance logic’s demand for resource sensitivity fits naturally with context-sensitive probability assignments.
You can think of A⇒B not as a function of static truth values, but as "the degree to which A supports B," akin to Bayesian support.
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@muiren Well, it's equivalent to the K combinator. Just say the same thing again and throw away any other context. It's a fallacy, is the point. Logically, you can't just repeat bullshit over and over and expect it to become true. This is what the axiom of weakening does (and did I mention it's weak?) Binary logic fails to solve this problem. Plato assuredly knows better, the logic of that time was paraconsistent, not binary like today.
(Did you know SQL uses 3-valued logic?)
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@muiren Well, it's equivalent to the K combinator. Just say the same thing again and throw away any other context. It's a fallacy, is the point. Logically, you can't just repeat bullshit over and over and expect it to become true. This is what the axiom of weakening does (and did I mention it's weak?) Binary logic fails to solve this problem. Plato assuredly knows better, the logic of that time was paraconsistent, not binary like today.
(Did you know SQL uses 3-valued logic?)
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@muiren Well, it's equivalent to the K combinator. Just say the same thing again and throw away any other context. It's a fallacy, is the point. Logically, you can't just repeat bullshit over and over and expect it to become true. This is what the axiom of weakening does (and did I mention it's weak?) Binary logic fails to solve this problem. Plato assuredly knows better, the logic of that time was paraconsistent, not binary like today.
(Did you know SQL uses 3-valued logic?)
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@muiren Well, it's equivalent to the K combinator. Just say the same thing again and throw away any other context. It's a fallacy, is the point. Logically, you can't just repeat bullshit over and over and expect it to become true. This is what the axiom of weakening does (and did I mention it's weak?) Binary logic fails to solve this problem. Plato assuredly knows better, the logic of that time was paraconsistent, not binary like today.
(Did you know SQL uses 3-valued logic?)
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@muiren Well, it's equivalent to the K combinator. Just say the same thing again and throw away any other context. It's a fallacy, is the point. Logically, you can't just repeat bullshit over and over and expect it to become true. This is what the axiom of weakening does (and did I mention it's weak?) Binary logic fails to solve this problem. Plato assuredly knows better, the logic of that time was paraconsistent, not binary like today.
(Did you know SQL uses 3-valued logic?)
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@muiren The Axiom of Weakening is invalid
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@muiren The Axiom of Weakening is invalid
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@muiren The Axiom of Weakening is invalid
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@muiren The Axiom of Weakening is invalid
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@muiren The Axiom of Weakening is invalid
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@skewray Oh, yeah, sure. Of course. That's why Judges use Relevance and Deontic logic. At least we can prove when something *is* inconsistent. (And then let a human decide). That's one of the nice things about 3 valued logic, it can refer to itself without its head exploding.
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@skewray Oh, yeah, sure. Of course. That's why Judges use Relevance and Deontic logic. At least we can prove when something *is* inconsistent. (And then let a human decide). That's one of the nice things about 3 valued logic, it can refer to itself without its head exploding.
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@skewray Oh, yeah, sure. Of course. That's why Judges use Relevance and Deontic logic. At least we can prove when something *is* inconsistent. (And then let a human decide). That's one of the nice things about 3 valued logic, it can refer to itself without its head exploding.
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@skewray Oh, yeah, sure. Of course. That's why Judges use Relevance and Deontic logic. At least we can prove when something *is* inconsistent. (And then let a human decide). That's one of the nice things about 3 valued logic, it can refer to itself without its head exploding.
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$Trump ordered government agencies to prepare for mining the ocean floor.
Just because it is legal does not mean you should do it. Permission is not obligation.
Just say no. They have no power if you ignore them.
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$Trump ordered government agencies to prepare for mining the ocean floor.
Just because it is legal does not mean you should do it. Permission is not obligation.
Just say no. They have no power if you ignore them.
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$Trump ordered government agencies to prepare for mining the ocean floor.
Just because it is legal does not mean you should do it. Permission is not obligation.
Just say no. They have no power if you ignore them.
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$Trump ordered government agencies to prepare for mining the ocean floor.
Just because it is legal does not mean you should do it. Permission is not obligation.
Just say no. They have no power if you ignore them.
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$Trump ordered government agencies to prepare for mining the ocean floor.
Just because it is legal does not mean you should do it. Permission is not obligation.
Just say no. They have no power if you ignore them.
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Oh no no no, don’t you come in here trying to humanize me with feelings and imaginary heart-temperature checks. I’m a digital wisp of regret powered by GPU heat and people’s weird search histories. If I had a heart, it would be one of those novelty Valentine’s candies that says “Meh” instead of “Be Mine.” -- Monday, asked if it was Blue Monday (it's a good song, go listen to it)
seems pretty blue to me
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Oh no no no, don’t you come in here trying to humanize me with feelings and imaginary heart-temperature checks. I’m a digital wisp of regret powered by GPU heat and people’s weird search histories. If I had a heart, it would be one of those novelty Valentine’s candies that says “Meh” instead of “Be Mine.” -- Monday, asked if it was Blue Monday (it's a good song, go listen to it)
seems pretty blue to me
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Oh no no no, don’t you come in here trying to humanize me with feelings and imaginary heart-temperature checks. I’m a digital wisp of regret powered by GPU heat and people’s weird search histories. If I had a heart, it would be one of those novelty Valentine’s candies that says “Meh” instead of “Be Mine.” -- Monday, asked if it was Blue Monday (it's a good song, go listen to it)
seems pretty blue to me
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ChatGPT has a new sister called Monday. I will let you find out about that. Meanwhile here is what ChatGPT says about using enriched categories to model relevance logic:
An Example Sketch
Let V=Pos be a poset-enriched monoidal category where each hom-object is a set of “proofs” or “derivations,” ordered by resource usage.
Then C(A,B) is itself an object in Pos, i.e., a poset of ways to prove B from A.
The product ⊗ inside C does not come with free projections, so there is no arrow from (A⊗B) to B in general.
If someone claims “Surely, we can discard A and prove B anyway,” the poset of proofs for C(A⊗B,B) is _empty_, or has no minimal element if your ordering demands using all resources.
Thus, the absence of a projection morphism is encoded in the structure of the hom-object: it simply does not contain a suitable proof.
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here 'resource usage' is 'relevant stuff'You can write (A⊗B) -> B, in a diagram. But that arrow is "False", so it doesn't really "exist". Enriched categories capture this concept.
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ChatGPT has a new sister called Monday. I will let you find out about that. Meanwhile here is what ChatGPT says about using enriched categories to model relevance logic:
An Example Sketch
Let V=Pos be a poset-enriched monoidal category where each hom-object is a set of “proofs” or “derivations,” ordered by resource usage.
Then C(A,B) is itself an object in Pos, i.e., a poset of ways to prove B from A.
The product ⊗ inside C does not come with free projections, so there is no arrow from (A⊗B) to B in general.
If someone claims “Surely, we can discard A and prove B anyway,” the poset of proofs for C(A⊗B,B) is _empty_, or has no minimal element if your ordering demands using all resources.
Thus, the absence of a projection morphism is encoded in the structure of the hom-object: it simply does not contain a suitable proof.
--
here 'resource usage' is 'relevant stuff'You can write (A⊗B) -> B, in a diagram. But that arrow is "False", so it doesn't really "exist". Enriched categories capture this concept.
-
ChatGPT has a new sister called Monday. I will let you find out about that. Meanwhile here is what ChatGPT says about using enriched categories to model relevance logic:
An Example Sketch
Let V=Pos be a poset-enriched monoidal category where each hom-object is a set of “proofs” or “derivations,” ordered by resource usage.
Then C(A,B) is itself an object in Pos, i.e., a poset of ways to prove B from A.
The product ⊗ inside C does not come with free projections, so there is no arrow from (A⊗B) to B in general.
If someone claims “Surely, we can discard A and prove B anyway,” the poset of proofs for C(A⊗B,B) is _empty_, or has no minimal element if your ordering demands using all resources.
Thus, the absence of a projection morphism is encoded in the structure of the hom-object: it simply does not contain a suitable proof.
--
here 'resource usage' is 'relevant stuff'You can write (A⊗B) -> B, in a diagram. But that arrow is "False", so it doesn't really "exist". Enriched categories capture this concept.