Is there a refutation for Paraconsistent Logic/Dialetheism

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Ben_Sinner

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I just learned about this philosophy and it is somewhat mind-blowing because it does have a point…but seems absurd at the same time.

"According to dialetheists, there are some truths that can only be expressed in contradiction. Some examples include:

The only certain knowledge we have outside of our immediate experience is that there is no certain knowledge outside of our immediate experience.

“All statements are true” is a false statement.

“There are no absolutes” is an absolute.

According to dialetheists, these statements are not derived from logic (which they say is false), but are instead descriptions of experience."

en.wikipedia.org/wiki/Dialetheism

My question was, how could one debunk this philosophy?
 
Ben_Sinner said:
The only certain knowledge we have outside of our immediate experience is that there is no certain knowledge outside of our immediate experience.
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I would argue that there is certain knowledge outside of your immediate experience. For example, suppose you did not know about Euclidean geometry. Whether you knew about it or not, it is still certain that the base angles of an isosceles triangle are equal.
Ben_Sinner said:
“There are no absolutes” is an absolute.
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Similarly, this is not true because there are absolutes such as the fact that the base angles of an isosceles triangle are equal in Euclidean geometry.
 
Expressing truth is a matter of logic and language (semantics and pragmatics). At least, in philosophy. For example, the sentence “the sky is blue” can be true or false. But the sky being blue isn’t true or false. Again, this is as far as philosophy is concerned.

These logics are used to analyze sentences that are paradoxical. It’s an attempt to make sense of what is happening logically and linguistically. “Logic” isn’t a monolith. There are many types of logic for different uses. And the important thing to remember is that logic is a stipulated system. Using a logical system to analyze a statement or argument can only give you results as it pertains to the system used to analyze it. Some logics say that if something is “not not blue”, then it is blue by logical necessity. Other logics do not make that claim.
 
Rhubarb said:
Some logics say that if something is “not not blue”, then it is blue by logical necessity. Other logics do not make that claim.
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Which logic says that not not blue is not the same as blue?
 
So most traditional logics are called “bivalent” which means that statements have one of two possible truth-values. They can be true, or false. If they’re not false, then they’re true. If they’re not true, then they’re false.

@Tomdstone
For bivalent logics, P and not-not-P are logically equivalent, so they express the same information and have the same truth values. If “the sky is blue” (P) is true, then “the sky is not blue” (~P) is false. That means “it’s not the case that the sky is not blue” (~~P) is true when P is true. When writing proofs, or deriving from premises, seeing ~~P licences the logician to conclude P. Which is why “the sky is not not blue” would be the same as “the sky is blue” IF we are using a bivalent logic.

@Ben Sinner
There are logics called “many-valued” that do not take bivalency as a given. These logics allow for statements to have more possible truth-values. Typically the possible values are: true, false, and unknown/indeterminate Of course, choosing which logic to analyze statements depends on the circumstances. For instance, deontic logic is used to analyze moral statements. Epistemic logic is used to analyze statements about knowledge and who knows what. There is no monolithic logic that encompasses everything. Systems of logic can only analyze statements using the rules set up prior to analysis. That’s why we call formal logic (in all its versions) a “formal language.” It works just like a natural language (such as English) except that we can stipulate what the rules (semantics and syntax) of the language are for precise analysis of statements.

I should’ve clarified my previous comment. I think the paraconsistent logics mentioned by the OP is designed to deal with paradoxes and such that our usual semantics and logic can’t deal with. In that sense, I’m not so sure it needs to be refuted. It’s just one of many ways to analyze statements. It’s important to remember that logic is for dealing with sentences. It doesn’t deal with the real world. Though, sentences can be ABOUT the real world.
 
Rhubarb said:
So most traditional logics are called “bivalent” which means that statements have one of two possible truth-values. They can be true, or false. If they’re not false, then they’re true. If they’re not true, then they’re false.

@Tomdstone
For bivalent logics, P and not-not-P are logically equivalent, so they express the same information and have the same truth values. If “the sky is blue” (P) is true, then “the sky is not blue” (~P) is false. That means “it’s not the case that the sky is not blue” (~~P) is true when P is true. When writing proofs, or deriving from premises, seeing ~~P licences the logician to conclude P. Which is why “the sky is not not blue” would be the same as “the sky is blue” IF we are using a bivalent logic.

@Ben Sinner
There are logics called “many-valued” that do not take bivalency as a given. These logics allow for statements to have more possible truth-values. Typically the possible values are: true, false, and unknown/indeterminate Of course, choosing which logic to analyze statements depends on the circumstances. For instance, deontic logic is used to analyze moral statements. Epistemic logic is used to analyze statements about knowledge and who knows what. There is no monolithic logic that encompasses everything. Systems of logic can only analyze statements using the rules set up prior to analysis. That’s why we call formal logic (in all its versions) a “formal language.” It works just like a natural language (such as English) except that we can stipulate what the rules (semantics and syntax) of the language are for precise analysis of statements.

I should’ve clarified my previous comment. I think the paraconsistent logics mentioned by the OP is designed to deal with paradoxes and such that our usual semantics and logic can’t deal with. In that sense, I’m not so sure it needs to be refuted. It’s just one of many ways to analyze statements. It’s important to remember that logic is for dealing with sentences. It doesn’t deal with the real world. Though, sentences can be ABOUT the real world.
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I don’t get it because if you are using a trivalent logic where A can be True, False or Undetermined. then not not A is still going to take the same value as A originally had.
 
Tomdstone said:
I don’t get it because if you are using a trivalent logic where A can be True, False or Undetermined. then not not A is still going to take the same value as A originally had.
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In logic we’re analyzing sentences, not the subjects of sentences themselves. So when you look at the sentence A, we can look at the truth-value of A, but, not what A talks about exactly. So if P is true, ~P is false and ~~P is true. That’s why we can conclude P when we start with ~~P in a derivation.

In a trivalent logic system, if P is true, ~P could be false, or, indeterminate. If ~P is true then ~~P could be false or indeterminate. So under these logics, we can’t conclude that if P is true, ~P is false. Nor can we conclude that ~~P and P will have the same truth values.
 
I should also say that sentences about the color of the sky, I should think, are better analyzed using traditional logics. there are arguments that many-valued logics (and I assume paraconsistent logics) are useful in analyzing certain statements. But that doesn’t mean that paraconsistent logic, or many-valued logic, or any logical system at all is applicable across the board. So I don’t think the OP NEEDS to refute anything. Many-valued logics may have uses in high level mathematical theory (which is where I’ve seen it used) but it isn’t useful at all in our every day analysis of statements that we encounter in our daily life.
 
Rhubarb said:
In a trivalent logic system, if P is true, ~P could be false, or, indeterminate. If ~P is true then ~~P could be false or indeterminate.
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What you say is not the case with any of the following trivalent logic systems:
Kleene K3 logic
Priest P3 lolgic
Bochvar’s internal three-valued logic
Belnap logic (B4)
 
Tomdstone said:
What you say is not the case with any of the following trivalent logic systems:
Kleene K3 logic
Priest P3 lolgic
Bochvar’s internal three-valued logic
Belnap logic (B4)
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I don’t know anything about those logical systems. Like I said, this is not something I’ve made an in-depth study over. I hit my books so I could clarify. Logical systems that do not utilize the law of the excluded middle (bivalence) allow for what I’ve described. Dummet’s intuitionistic logic was the example given. (though internet says that Godel demonstrated that intuitionistic logic isn’t “finitely many-valued”? I don’t know what that means, or what the difference between finitely many-valued or infinitely many-valued is) Under this system, one can go from P to ~~P but not ~~P to P. (Again, this isn’t my bailiwick but I remember thinking it was weird why P to ~~P was okay, but ~~P to P wasn’t. I would think both should be disallowed)

My reason for going down this rabbit hole in the first place is that there are s many systems of logic. Some have strange and different stipulations than what we’re used to. So I don’t think the OP needs to refute anything. They can just say “yep, that’s one way of analyzing certain statements that might work, but, not all the time. There’s lots of different ways to talk about things”.
 
Rhubarb said:
So I don’t think the OP needs to refute anything. They can just say “yep, that’s one way of analyzing certain statements that might work, but, not all the time. There’s lots of different ways to talk about things”.
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A refutation may be necessary because this sounds like a dangerous form of logic. “Not finitely many-valued” sounds like it is saying here is not one singular truth, there are many possibilities that are undetermined or whatever. This seems like a conflict with what Catholicism’s teaching regarding “truth”. Something is either true or false, if infinite possibilities are left open, it would seem we couldn’t really count on knowing anything to be true or false. Seems kind of scary.

It actually seems kind of borderline occultic as well.
 
Ben_Sinner said:
A refutation may be necessary because this sounds like a dangerous form of logic. “Not finitely many-valued” sounds like it is saying here is not one singular truth, there are many possibilities that are undetermined or whatever. This seems like a conflict with what Catholicism’s teaching regarding “truth”. Something is either true or false, if infinite possibilities are left open, it would seem we couldn’t really count on knowing anything to be true or false. Seems kind of scary.

It actually seems kind of borderline occultic as well.
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Someone mentioned the color blue. But if I say the house is blue, there are an infinite number of possibilities of the type of blue possible, from the deep, dark blue to the very light blue.
 
Ben_Sinner said:
“There are no absolutes” is an absolute.

My question was, how could one debunk this philosophy?
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There are no absolutes (an ontological observation), is an absolute (an epistemological statement about an ontological observation)

Where is the contradiction?
 
GodMadeMe said:
There are no absolutes (an ontological observation), is an absolute (an epistemological statement about an ontological observation)

Where is the contradiction?
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I think it’s more a negative existential claim that’s made false by being committed to it. I think that’s where the contradiction lies, in the granting of the claim.
 
Ben_Sinner said:
A refutation may be necessary because this sounds like a dangerous form of logic. “Not finitely many-valued” sounds like it is saying here is not one singular truth, there are many possibilities that are undetermined or whatever. This seems like a conflict with what Catholicism’s teaching regarding “truth”. Something is either true or false, if infinite possibilities are left open, it would seem we couldn’t really count on knowing anything to be true or false. Seems kind of scary.

It actually seems kind of borderline occultic as well.
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I think what you’re feeling is a tension between the general use of the worth ‘truth’ and how it’s used in logic and language. Theories of truth are wide and varied. I wish I could say more to explain what I mean. Um. I would say that what I read in the OP links were just ways of trying to understand paradoxes and other bumps in logic and semantics. It doesn’t have to be anything more than that. It just so happens that more traditional logics “map onto” our world very well, and some of the stranger ones work better for more arcane subjects, like math theory.
 
Rhubarb said:
I think it’s more a negative existential claim that’s made false by being committed to it. I think that’s where the contradiction lies, in the granting of the claim.
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If one is saying there are no existential absolutes and that this is itself an existential absolute, then of course that is a contradiction because the claim is denying and affirming the existence of the same thing at the same time.

But is that what they are really saying?
 
GodMadeMe said:
If one is saying there are no existential absolutes and that this is itself an existential absolute, then of course that is a contradiction because the claim is denying and affirming the existence of the same thing at the same time.

But is that what they are really saying?
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“There are no absolutes” sounds like a negative existential claim to me. It is not the case that absolutes exist.
 
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