Dialetheism vs. Law of Non-Contradicton
In several of the past conversations about logic, dialetheism/dialectic logic has popped up.
https://plato.stanford.edu/entries/dialetheism/
It was asserted each time that dialetheism opposes, or contradicts, the law of non-contradiction, and therefore which laws of logic to use were called into question. My assertion is that all laws of logic are necessary, but some simply don't apply to the statement or assertion being made at the moment, but I would never assert that any one law would contradict another, which is what dialetheism appears to do.
It is my understanding that a contradiction is a statement about the quality of my model of the world (that it is inaccurate), and that some assumption or method (axiom or rule of inference) is in need of improvement. Therefore I'm somewhat surprised, and incredulous, that anyone would advocate for the acceptance of a contradiction, or even to create logics specifically to be able to accommodate "A & ¬A" being true.
Most contradictions appear to be a misuse of language. You can't actually picture a married bachelor, or a square-circle in your mind. You can picture the words, or the sounds of them being spoken together, and that creates the contradiction in your mind, but you could never have conceived of a married bachelor, or a square-circle without language.
The fact that you can put two scribbles or sounds that refer to opposite things together in space and time doesn't make what those scribbles refer to real, or true. Mistakes can be made with language - which is the whole point in following logical rules - to avoid those mistakes. Dialetheism doesn't seem to recognize this, as if all contradictions in language are true - whatever that means as it seems to blur the lines between what is true and false. And if this is the case, then it also makes determining what is useful or not nonsensical. What use is a contradiction? To what use could dialetheism be applied? What problems does it attempt to solve?
https://plato.stanford.edu/entries/dialetheism/
It was asserted each time that dialetheism opposes, or contradicts, the law of non-contradiction, and therefore which laws of logic to use were called into question. My assertion is that all laws of logic are necessary, but some simply don't apply to the statement or assertion being made at the moment, but I would never assert that any one law would contradict another, which is what dialetheism appears to do.
It is my understanding that a contradiction is a statement about the quality of my model of the world (that it is inaccurate), and that some assumption or method (axiom or rule of inference) is in need of improvement. Therefore I'm somewhat surprised, and incredulous, that anyone would advocate for the acceptance of a contradiction, or even to create logics specifically to be able to accommodate "A & ¬A" being true.
Most contradictions appear to be a misuse of language. You can't actually picture a married bachelor, or a square-circle in your mind. You can picture the words, or the sounds of them being spoken together, and that creates the contradiction in your mind, but you could never have conceived of a married bachelor, or a square-circle without language.
The fact that you can put two scribbles or sounds that refer to opposite things together in space and time doesn't make what those scribbles refer to real, or true. Mistakes can be made with language - which is the whole point in following logical rules - to avoid those mistakes. Dialetheism doesn't seem to recognize this, as if all contradictions in language are true - whatever that means as it seems to blur the lines between what is true and false. And if this is the case, then it also makes determining what is useful or not nonsensical. What use is a contradiction? To what use could dialetheism be applied? What problems does it attempt to solve?
Comments (54)
Correct usage: mods please note. :wink:
Quoting Harry Hindu
Vagueness. For example, non-vague discourse requires a non-vague syntax, provided by alphabetic characters of some kind. But these are always vague around the borders, causing judgements of syntactic identity to conflict. In Languages of Art, Goodman pointed out that the conflict is systematic, and maintains a suitable margin for error between the characters.
Some discourses also aspire to a non-vague semantics, in like fashion. Zones of permitted controversy concerning correct usage of a word maintain zones of unanimity concerning unacceptable usage.
Agreed.
Quoting bongo fury
What use is vageness other than to keep others ill-informed or to prevent one's self from being trapped by the rules of logic (especially when appealing to one's own emotions)?
The only dialetheist I've read at any length is Graham Priest, and he, at least, does not maintain that all contradictions are true. Rather, he argues that some contradictions are true. More precisely, he argues that there are actual situations containing statements that are both true and false, namely, those situations that fit the semantics of the enclosure schema. These situations involve self-reference and/or reference to absolute limits. Examples from his book "Beyond the Limits of Thought" include the limit of what can be known, the limit of what can be expressed and the limit of what can be conceived. He argues that all thought about such limits is intrinsically contradictory insofar as the very act of thinking such limits requires one to transgress them at the same time. Thought draws a boundary and then crosses it in the act of thinking it.
Quoting Harry Hindu
Priest would probably maintain that the mere prospect that dialetheism is true should be sufficient warrant for pursuing it, but he also thinks it is useful. In his book "One", he develops a dialetheic metaphysics that he calls "gluon theory" and employs it in solutions to various metaphysical puzzles around identity, unity, universals, being and nothingness and intentionality.
Admittedly, his theories and solutions have not been widely adopted in western analytical philosophy. And while I find them fascinating and worth learning about, I wouldn't say that I endorse them.
(1) First, I'd just like to second 's claim that Priest (and most dialetheists I know) does not claim that all contradictions are true, just that some of them are. One compelling example of an alleged true contradiction is, of course, the Liar sentence. It is surprisingly difficult to develop a classical account of the Liar that satisfies everyone and that is not prey to revenge paradoxes. Dialetheism provides a very straightforward solution to this and related paradoxes.
(2) Second, paraconsistent logics in general are concerned with controlling the trivialization that follows from the principle of explosion. That is, such logics provide a workaround for when we find contradictions in our belief set or in our model. Now, you may say, why would we want such a workaround? Shouldn't we just jettison the contradiction and be done with it? Well, yes, but the problem is, how do we do this? Suppose I have beliefs [math]A_1, \dots, A_n[/math], and from these beliefs I eventually derive a contradiction, say [math]B \& \neg B[/math]. This means that I should give up one of the [math]A_i[/math]'s, but which one? There may be no obvious way of selecting such an [math]A_i[/math], since there may be equal evidence for each of them. In that case, a reasonable course of action would be to investigate further into the source of the contradiction so that I can eventually revise my beliefs. In the meantime, however, do I need to act irrationally, as if I believed everything (which would follow from the explosion)? Of course not. But this means that I will need to employ a paraconsistent logic, since I will need to ignore explosion. So paraconsistency may be a useful tool in "controlling" a contradiction during belief revision.
1. The definition of the AND logical connective is different from that in classical logic because p & ~p has to evaluate to true which isn't possible with the classical logic AND which is true only when both propositions connected with it are true
AND/OR
2. The equivalence rule of ADDITION has to be discarded because allowing it leads to the principle of explosion
AND/OR
3. The definition of NEGATION is different if the AND connective has the same definition as in classical logic so that both p and ~p would be true and then (p & ~p) would evaluate to true
Since the law of noncontradiction (LNC), expressed as ~(p & ~p), is critically dependent on the definitions of negation and the AND logical connective, it follows that paraconsistent logic or dialetheism has different definitions for both of them.
Quoting Nagase
Thank you both for your informative posts.
It appears that Priest is confusing a misuse of language as a new logical system. This is why I pointed out that the fact that we can organize words that follow grammatical rules doesn't necessarily mean that you've also applied the LNC. As I have said, all logical rules - where applicable - need to be followed, and you can't have a sentence that is grammatically correct, yet logically inconsistent, be true.
The fact that we can place scribbles next to each other on paper, on a computer screen, or sounds in the air, that obey grammatical rules of some language, doesn't follow that what the scribbles mean together obeys the rules of logic, namely the LNC.
The fact that I can arrange the scribbles, "This sentence is false" in a way that obeys the grammatical and spelling rules, but when the words are read and interpreted (also a necessary part of language-use, not just arranging scribbles in a way that follow grammatical and spelling rules) it is found to be a contradiction, doesn't mean that the sentence is both true and false. It is a misuse of language.
Quoting Nagase
Quoting Theorem
This seems to be very rare occasions where two contradictory beliefs have the same amount of information. I am finding it difficult to even think of an actual example.
Computer programmers still have to program a machine to make decisions based on something, and when contradictions arise in memory, other factors can help determine which path the program should take.
This also seems to conflate our ignorance as a new logical system. Sure, there are times when we need to act on incomplete, or even inconsistent, information. I don't understand how one could act as if they were all true, or what that would even look like, but I can understand acting as if one is true one moment and the other true at another moment. It doesn't follow that what I am acting on is completely true as I may make a mistake, and then that is when I learn which contradictory belief is actually false.
Quoting TheMadFool
Then dialetheism and LNC are talking past each other when using these terms?
The whole thing reminds me of the political entity we so fondly call "government" of, say, the USA. At the end of every term, the entire team that is the government is changed (barring the times when a party gets re-elected) - the president is different, the vice president is different, and so on, and yet, we still refer to every one of these disparate entities as the government of the USA. Likewise, every little essential detail of the LNC has been altered and all that remains of the real LNC is just the label - "the law of noncontradiction." This term is empty of meaning.
There isn't much difference between the political parties in the U.S. They both promote bigger government. And the reason that we will always switch back and forth (and a reason for the Electoral College) is that if one party gains to much power and the other party is never able to take the majority temporarily, then many states will secede. To appease the masses and keep the union unified, both parties take turns being the majority.
i) Self-negating universal imperatives, i.e. hypocritical statements such as "Don't live by rules!".
ii) When a semantic distinction is more fined grained than is expressible in the language used, such as when standing in a doorway and thereby "being in the kitchen but not in the kitchen".
iii) When a semantic distinction is vague or uncertain, such as "a heap of sand" that isn't defined in terms of a particular numeric range of sand grains Hence "heaps of sand" exist, but no particular collection of sand grains constitutes a heap.
ii + iii are contradictions that programmers have to deal with, but they also present challenges for self-learning autonomous agents, that like human beings must somehow internalise a truth-language distinction.
I suspect that like humans, AI agents will also behave in a logically inconsistent fashion relative to their self-knowledge.
Are you saying that things can only be the case if we can picture them in our mind?
I don't know how politics works but the words "law of non contradiction" as used in (some) paraconsistent logical systems is like the word "government" in being nothing more than a label - all the essential components change but the label remains the same.
I maybe completely wrong on this but that's how I feel about it.
If the LNC is indeed violated or rejected then only one option remains for anyone developing such a system and that's to remove the ADDITION equivalence rule. If not the principle of explosion is going to wreak havoc in such a system; interestingly, it seems that in paraconsistent logic the aim is to allow contradictions but avoid a system that's trivial in the sense one in which any and all propositions can be proved. One wonders what it means to not want a system in which any and all propositions can be proved if not that the aim is not to have situations where p & ~p i.e. a logical system is most trivial, if triviality comes in degrees, precisely when contradictions become possible.
:chin:
Priest (and other dialetheists) would obviously disagree. They present arguments. You should study them sometime.
Quoting Theorem
Obviously you weren't moved by their arguments or else you would endorse them. Why aren't you endorsing them? What is it that you find lacking, or unreasonable, in their arguments?
Quoting Michael
Sure. Why not? We, and our minds, are governed by the same laws of the universe as everything else. It seems to me that the burden is upon those that claim otherwise - to explain why a mind that is governed by the same laws of the universe wouldn't be able to understand the laws of the universe.
Doesn't solipsism, idealism and panpsychism endorse the idea that things only exist when present in some mind, primarily because mind is a fundamental feature of reality?
A contradictory statement says nothing at all, and is therefore useless. It is basically asserting something and then walking back that assertion at the same time resulting in a net zero amount of information. It is basically scribbles on a page, or sounds in the air.
Quoting sime
There is also the problem of ignorance of the language being used. I could just say, "being in the doorway between the kitchen and dining room". Languages are typically malleable and new things can be said using the same words (or even new words) in different patterns in different contexts, given the intelligence and wittiness of the person using some language. It's one of the ways that languages evolve.
Quoting sime
Vagueness or uncertainty don't count as a contradiction. A contradiction is a set of clearly defined assertions that stand in direct opposition to each other. There is no vagueness or uncertainty there, except as an effect of the contradiction, as per my response to i). A contradiction provides zero information, and zero use.
Quoting sime
If a contradiction provides zero information, and zero use, then what would it look like to act on zero information? What information would it be using to act on? When a contradiction arises, alternative reasons for acting or not acting a certain way will be searched for, so the reason for acting or not will actually have nothing to do with the contradiction.
Quoting Harry Hindu
Do you think that this undermines realism? Can you picture a cup without picturing the look of a cup, or the feel of a cup, i.e. how a cup is experienced?
Can you picture a cup and non-cup in the same mental space and moment? I can picture the words, "cup and non-cup", but not what they refer to.
Quoting Michael
The innateness of the look, or appearance, of the cup lies in the mind. The way the cup is, is irrespective of what they look/appear and feel like in our mind.
So you can picture the way a cup is, irrespective of its appearance?
This doesn't answer my question. Can you picture a cup without just picturing how a cup appears to us? Can you picture just the innate nature of the cup?
Sure it does.
Quoting Michael
Like I said, pictures/appearances/looks only exist in minds, so no you can't picture a cup without picturing how a cup appears in the mind. The question is nonsensical. It's like asking, can you think about a cup without thinking about it?
Quoting Michael
Like I said, the picture is an effect of the innate nature of the cup, innate nature of light, innate nature of your brain and eyes. You can get at the innate nature of all of these things via the innate nature of the picture. Turn out the lights and that changes the picture of the cup. Grow a tumor in your brain, or on the eye stem, and that changes the picture of the cup.
Then you're contradicting yourself. Here you claimed that things can't be the case if we can't picture them in our mind, and now you're saying that the innate nature of cups can't be pictured in our mind; only their appearances can.
You need to drop one of these claims. Either only appearances are the case or things can be the case that can't be pictured in our mind.
Yes in the sense of contradictory propositions. Nobody of course, experiences contradictory propositions - which goes to show that the general meaning of "contradiction" isn't to refer to propositions but to conflicts, such as the conflict between the definition of a language and it's application, or the rules of a sport and the moral notion of fair-play etc.
The reason we don't experience contradictory propositions is precisely because what we experience is information, and if there is no information, then there is nothing to experience - except for the visual experience of the seeing scribbles on a screen or hearing sounds spoken - which is information, but about something else that isn't about what is being written or said.
Quoting Michael
Right, and what I was talking about when it comes to picturing things in the mind were contradictions - like cups and non-cups. Do cups and non-cups exists as one entity either in your mind as an appearance (can you imagine a cup and non-cup entity?) or outside of your mind as an innate object of the universe? From where do contradictions come from - from somewhere out in the world for to be experienced by a mind that observes them, or are they created by the mind as a misuse of language, and then projected onto the world as if they existed outside of the mind?
I don't look at it that way. Dialetheism provides a way solving certain problems. Like any proposed solution to a problem, it has costs and benefits relative to other proposals. Which solution to use depends on the solution context. If I were writing a belief revision algorithm for an AI program, I would use whatever algorithm worked best within the resource constraints I was facing. If the dialetheic approach proved the most adequate to meet the requirements, I would use it.
When it comes to using dialetheism as the basis for one's personal metaphysics and epistemology, the same considerations apply. The class of situations/propositions to which dialetheism is purported to apply is exceedingly small. Again, I can only speak for Priest, but he applies it only to propositions/situations satisfying the semantics of the "enclosure schema". He feels that dialetheism provides the most "satisfying" solution for dealing with the semantics of such situations - for him, the benefits outweigh the costs.
Of course, things get fuzzy when it comes to evaluating the "truth" of metaphysical theories. Beyond insisting that such theories not be fatally self-contradictory, the criteria are mostly aesthetic and personal, although the behavioral consequences of holding such theories should also be a consideration (e.g. if a such a theory would prompt a person to become a suicide bomber, etc.). For me personally, while I can appreciate the beauty of Priest's metaphysics, and have no problems with the ethical commitments he derives from it, I ultimately find it too lifeless for my tastes.
Would it be better if I had said that things can't be the case if we can't represent, symbolize, or simulate them in our mind?
The effect isn't the cause. The map isn't the territory. The woman isn't the painting of the woman.
If you want to say that things can only be the case if we can picture them in our mind then for the cause, the territory, and the woman to be the case we must be able to picture them in our mind.
You need to abandon your claim that things can't be the case if we can't picture them in our mind (else you have to abandon realism).
There are more stars in the universe than I can picture at any one time, yet presumably they still all exist at the same time.
Our brains/minds are powerful, but they're still limited.
Yet you symbolized the fact that there are more stars in the universe than you can "picture" with scribbles on screen.
What do you mean by symbolize? How does it differ from picturing? It's not just about being able to say the words is it? As you said before "the fact that you can put two scribbles or sounds that refer to opposite things together in space and time doesn't make what those scribbles refer to real, or true."
These objects are mental objects. They are real in the sense that the mind and thoughts are real because they establish causal relationships. Can you draw a picture of pictures in your mind?
Exactly. The key phrase here is "refer to opposite things" - as if opposite attributes can be the innate nature of something other than a phrase in some language. Do objects with opposing properties exist?
I'm not sure what you mean by "exactly" as you haven't resolved the inconsistency of your position. I was addressing this:
Quoting Harry Hindu
You seem to be saying that married bachelors and square-circles can't be the case because I can't picture them in my mind, and yet there are 10[sup]21[/sup] stars in the universe even though I can't picture that many stars in my mind.
You then say that this doesn't matter because I can symbolize the fact that there are 10[sup]21[/sup] stars in the universe with scribbles on the screen, but I can also symbolize married bachelors and square-circles with scribbles on the screen.
So which is it? Must I be able to picture things in my mind for them to be the case, in which case there can't be 10[sup]21[/sup] stars in the universe, or is it enough that I can symbolize things with scribbles on the screen, in which case there could be married bachelors and square-circles?
Right. And so the word "contradiction" doesn't mean zero information, for that is nonsensical, but refers to conflicting sources of information, actions, intentions, judgements and so on. A "true" contradiction can be taken to refer to an unresolved conflict that is logically implied.
For example, conflicts of judgement that are present in discrete borderline categorisation problems, as in being in the kitchen and not in the kitchen, are not resolvable by introducing more linguistic precision, for the same borderline problem resurfaces on a finer level of semantic granularity; here the "true" contradiction refers to the fact that the concept of discreteness cannot be reconciled with the existence of borderline cases. It's all well and good hoping that the conflict is potentially resolvable, but there is no reason to believe that all such conflicts are resolvable.
But you did picture 10[sup]21[/sup] stars in your mind - with the scribbles, "10[sup]21[/sup] stars". Does not the scribble, "10[sup]21[/sup] stars" simulate a real state of affairs of their actually being something like 10[sup]21[/sup] stars in the universe? If not, then what are you saying when you say that there are 10[sup]21[/sup] stars in the universe?
As for married-bachelors and square-triangles, you haven't simulated anything. All you did was make a model of something that doesn't exist outside of your mind - like a Penrose triangle. In other words, contradictions are real thoughts, but not real thoughts about anything. They are pictures, or words, that have no aboutness to them.
You're begging the question then. You were using the fact that we can't picture married-bachelors and square-circles as proof that they can't be real, but are now saying that because there are 10[sup]21[/sup] stars in the universe then it doesn't matter that we can't picture them. And you're saying that the phrase "there are 10[sup]21[/sup] stars in the universe" simulates a real state of affairs because there are 10[sup]21[/sup] stars in the universe but that "married-bachelors" and "square-circles" doesn't simulate a real state of affairs because there can't be such things.
It seems to me that in saying that there are borderline cases is the same as making a level of semantic granularity. The colors blue and green are distinct, yet we also have blue-green which is also distinct - related to blue and green, yet not blue or green. It seems to me that there are instances where something seems like a contradiction, yet it isn't because we find that they weren't opposing qualities, just different qualities that can interact and cause something new.
So why can I imagine blue-green, but not married-bachelors? Why can't I mix bachelors and married men together to get something new, like I can blue and green? Why don't bachelors and married men mix well? Why is it like water and oil? There seems to be something about their nature, like water and oil, that prevents them from being mixed, and something about blue and green that allows them to be mixed. It seems to be the fact that they are polar opposites - that one is defined as being the absence of the other. Blue and green are not defined as being the absence of the other. There is no borderline case for married-bachelors like there is for blue-green.
So now you're saying that things can only be the case if they can be drawn? What about dark matter?
And how would a drawing of a bachelor, a married man, and a married-bachelor differ? All I could do is draw a man and then say that they're one of these.
No, I'm saying that things can only be the case if they aren't immediately negated in the same instant by it's opposite. As I said, a contradiction amounts to a net-zero information. The moment you draw something or think of something you must draw or think of it's opposite in the same moment of time and the same area of (mental/material) space. All you end up with is one or the other in any moment of time or space. Just as if I were to write a computer program where x = 1 and then the next line will be x = 0, the computer will use the last definition, not both.
Then you're just begging the question by asserting that contradictions are impossible. That's not a refutation of dialetheism, it's just a denial of it.
You may have missed my edit, and it may be redundant now that you're backtracking from your talk about being able to draw stars, but how would drawings of a married man, a bachelor, and a married bachelor even differ? They'll just be drawings of a man that I say is married, a bachelor, or a married bachelor.
That's good enough for me. I can't really refute the existence of god(s) or idealism/solipsism, only deny it, and the fact that you can deny them means that there are other means of solving the problems it attempts to solve, not the only solution to those kinds of problems. But tell me, can you deny the LNC and still solve problems like distinguishing between things, like true and false?
And I'm not denying that contradictions exist, or are possible. What I am denying is that contradictions exist as anything but a particular arrangement of scribbles or sounds in the air.
Quoting MichaelA married man could have a ring on his finger and the bachelor without. How would you represent a married-bachelor?
So I can't draw a married man who isn't wearing a ring or a bachelor who is?
Or, since words are merely visual scribbles, like a picture, you could just write the definitions of married and bachelor and see how they relate. It's not just that they have different definitions, but that their definitions cancel each other out - that you can't, by definition, be one while being the other.
The solution isn't to think that they both exist in the same entity, rather the definition needs to be changed. Marriage and bachelorhood are cultural constructions and can be redefined at any time, for any reason, unlike the number of stars in the universe which is only changed when we find more or less stars in the universe.
Married men don't need to wear a wedding band and bachelors can if they like. And neither needs to be doing "married" or "bachelor" things to be married or a bachelor. A married man and a bachelor can be sitting in a Jacuzzi together wearing nothing but swimming trunks. How do I draw that one is a married man and one is a bachelor?
This is why your talk about whether or not I can draw a married man, a bachelor, or a married bachelor makes no sense. I can just draw three men and label them as married, a bachelor, and a married bachelor respectively.
Quoting Harry Hindu
So again, you're just denying dialetheism rather than refuting it, and what you said earlier about not being able to picture certain things in the mind is an irrelevant comment that does nothing to further your case (and has been shown false by my example of the number of stars in the universe, or the existence of dark matter).
Then you seem to be saying that the words, "married", "bachelor" and "married-bachelor" are meaningless and that there is no difference between them, or that they could mean anything about a man. What is the relationship between these different strings of scribbles? Is a contradiction a misuse of language? Do you agree that there is such a thing as a misuse of language? If so, then what would a misuse of language entail?
Quoting Michael
While I may not be refuting dialetheism directly, I believe that I am at least doing indirectly by refuting the concept of a "married-bachelor" as meaningless. Contradictions are a means of refuting arguments. I've made contradictions and you showed how that refutes my argument (and I agree which is why I've been trying to rephrase and rework my argument), so if contradictions are used to refute and argument, then what use is dialetheism?
Not when the position you're trying to refute is a position that says that some contradictions are true.
What makes one contradiction false another true?