Paraconsistent Logic and Its Potential for Usefulness

Discussion in 'Consciousness & Science' started by Dan_LastName, Oct 6, 2018.

  1. Dan_LastName

    Dan_LastName Member

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    EDIT: It occurs to me that I should have started with my conclusions first, to help provide some context about why some of this dry "philosophy of logic" is important to me.

    Let me say that before I understood a little bit about paraconsistent logic, I was mostly of the mindset that any part of human experience that can't be understood through classical logic is somehow a deficient part of the human experience. Or, to put it another way, classical logic is the best way to consider experience, make decisions, etc, and for the murky parts of the human experience that don't seem to easily fit with classical logic, the pursuit of mankind should be in the direction of learning how to beat those murky parts into submission so that they will fit with classical logic, and in that way, humanity can continue improving. I think this is a common perspective, especially among folks on the atheist, materialist side of the spectrum.

    The beautiful thing about paraconsistent logic is that it provides a logically sound bridge from the rigors of classical logic into the murky territories of human experience that aren't readily understood in classical logic terms. So, I'm talking about mystical experiences, here, but also emotional experiences, confusing experiences, and some significant part of experience that seems to be beneath or alongside our logical faculties--call it the dream part or the subjunctive experience or the intuition or the deeper part or that intangible part that I don't have a name for. I think it's significant, but if you're deeply committed to classical logic, it can be difficult to even be aware of these deeper parts in any meaningful way.

    I saw a post from Alex in this sub-forum where he expressed a desire that at least some of the posts be practice oriented.
    I realize that my long post below is at least partly about my thoughts and what I've read.

    I would say that I've long held the intuitive suspicion that, somehow, thinking is itself a practice. I believe some eastern approaches to spiritual practice do make a point of identifying intellectual analysis to be a legitimate approach. Toward the end of my post below, I speculate on whether or not certain intellectual operations can themselves be considered to be a form of energy. It's an idea that's pleasing to me, and I think it's an idea that can help bridge the gap between thinking and doing.

    Learning about paraconsistent logic, for me, has the effect of making it easier to sink into a more enchanted, and less classically logical, experience of life.
     
    Last edited: Oct 7, 2018
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  2. Dan_LastName

    Dan_LastName Member

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    In classical logic, also known as Aristotelian logic, which is the default logic most of us probably use when we are being logical about things, the law of non-contradiction (LNC) is of the utmost importance.

    Among other things, the LNC means that if you’re reasoning about something, and you start off with a contradictory premise, you can prove anything from that contradictory premise, no matter how ridiculous.

    Source: https://en.wikipedia.org/wiki/Principle_of_explosion

    The idea that contradiction in the premises leads to “anything goes” in the conclusion is known as the principle of explosion. There is a little latin phrases that encapsulates the principle:

    Ex contradictione quodlibet
    From contradiction, anything follows

    The principle of explosion is one of the main arguments in favor of the absolute legitamacy of the LNC and classical logic in general.

    Today, alongside classical logic, we have paraconsistent logic. According to the Stanford Encyclopedia of Philosophy, the term ‘paraconsistent’ was coined by Miró Quesada at the Third Latin America Conference on Mathematical Logic in 1976.

    Paraconsistent logic is where you have a contradiction in your premises but it does not lead to explosion. Or, to put it another way, in paraconsisten logic, even if the available information is inconsistent, the consequence relation does not explode into triviality.

    Thus, paraconsistent logic accommodates inconsistency in a controlled way that treats inconsistent information as potentially informative.

    (Source: https://plato.stanford.edu/entries/logic-paraconsistent/)

    It’s uncertain what Miró Quesada meant by the name paraconsistent. The prefix “para” could mean ‘quasi’ (or ‘similar to, modelled on’) or it could mean ‘beyond’.

    For me, the significance of paraconsistent logic is that it gives logical support to the notion that some human experience can be understood in a way that is not exactly the same as classical, Aristotelian logic. Many people intuitively understand the idea that some experiences seem resistant to logical understanding, and, by extension, scientific understanding. But for me, if you don’t know about paraconsisten logic, it feels like when you say that, “oh, this experience or that quality of experience is beyond logical understanding,” it just seems like you’re stepping off the bedrock of classical reasoning, and why should we casually do that? Why would there be an impossible gap between classical logic and the human experience of contradiction, inconsistency, inexplicability, etc.

    The thing about classical, Aristotelian logic is that it’s extremely powerful and useful. For the most part, most of our understanding of materials is explainable with classical logic, which is extremely important for manipulating our environments, building things, advancing technologically, and for at least attempting to make changes in social organization. I think the ancient Greeks, and later the French, the Americans, etc tried to use reasoning to justify the overthrow of monarchy as an organizing principle and to usher in some version of representative democracy.

    The thing about getting into the human experience side of things, though, is that humans tend to be inconsist and we think, feel, talk, and act in contradictory ways, at least some of the time. So I think it can be speculated that, in practice, human experience and behavior is understandable in a perhaps more profitable way through the lense of paraconsistent logic.

    For me, thinking about paraconsisten logic makes me feel like I can now relax some part of me that is very hung up in the energy of classical logic.

    Oh, I should say that it seems possible to—as a metaphor—think of classical logic as being somehow inter-related to energy. Perhaps it has an energy to it as it works in human minds. After all, the logical thinking of people has worked in conjunction with our physical ability to manipulate the environment, and it requires energy to manipulate the environement. Might logical thinking be an energy somehow? (Or, at the very least, might it be productive to at least think that idea as a metaphor?)

    And perhaps paraconsistent logic is of a different kind of energy, metaphorically.

    So, in closing, paraconsistent logic feels like some kind of intellectual validation that could help me get the cold, hard stick of logic out of my butt. It’s been there for too damn long.

    I’ll probably have to learn the more technical aspects of paraconsistent logic, and see if I can figure out how those technical aspects map over to my and/or our human experience.

    I want to find a copy of Graham Priest’s book Beyond the Limits of Thought, where he gets deep into the topic, for less than $30, but am having no luck.

    Edited: fixed a couple typos and deleted a couple weak sentences.
     
  3. David Bailey

    David Bailey Administrator

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    Thanks for that, wonderful account! Unfortunately, I became disillusioned with logic many years ago. In the 1980's there was a period when AI was hyped to the rafters, before everyone shuffled off because it didn't achieve much (sounds familiar...). A favourite idea back then was that everything should be based of first order predicate calculus. This was a variant on Aristotelian logic which included variables, for example:

    mother(X,Y) if parent(X,Y) & female(X)

    This translates as
    X is the mother of Y if X is the parent of Y and X is female.

    This could be turned into actual computer code, and was all the rage for a while. However it seemed to get horribly gummed up in practice. There was a suggestion that the ideal test are would be law, so you came up with expressions like

    stolen(X,Y) if not (owns(X,Y)) & moves(X,Y)

    X has stolen Y if X does not own Y and X moves Y

    However, simple real world examples end up need an endless set of complications. If X is a student and Y is a bicycle, then we need something like

    stolen(X,Y) if not (owns(X,Y)) & moves(X,Y,D) & D<M

    This caters for the situation in which bikes are left on top of each other, and you need to move other bikes to get at yours! M is some maximum distance that you should move a bike which is not yours. Already things are getting complicated, but if this were to be used in legal software it would also need to handle:

    1) Cases where someone might grab a bike to go and get help after an accident.

    2) Cases where someone might accidentally grab the wrong bike.

    3) The case where a road repair man moved a bike a distance > M in order to dig a hole in the road!

    etc etc.

    I became convinced that logic is a very poor way to describe human knowledge.

    David
     
  4. Dan_LastName

    Dan_LastName Member

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    Thanks for the reply, David. I think we're on the same page with Aristotelian logic. It is a poor way to describe some aspects of knowledge and experience. I believe that Graham Priest, the most visible champion of paraconsistent logic, seems to consider that paraconsistent logic can help provide insight into those aspects where Aristotelian logic fails. I want to learn more about when and how to map paraconsistent logic to experience.
     
  5. David Bailey

    David Bailey Administrator

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    Maybe you are right, but there have been a few attempts to use modified logics in AI, without I think much success.

    Take Fuzzy Logic(FL), where adjectives like tall get interpreted so that a 6ft man would have a tallness of 0.9 (say) whereas a man a few inches shorter would get a figure of 0.5 (say). The trouble is, I think, that when someone uses an adjective like 'tall' they are expressing something else. A woman who says, "Bill is a tall man" may be expressing a sexual appreciation for example - she might not say it about an equally tall ugly man! Or indeed it may be used for comparison purposes only - as I did in the previous sentence. A lot of human language uses words like that, and they are obviously troublesome for AI language comprehension.

    Personally, I don't believe AI will ever achieve that much.

    David
     
  6. Dan_LastName

    Dan_LastName Member

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    Hi David,

    I agree with you about fuzzy logic. It doesn't have a lot of power at the end of the day. I found a quick article about mathematical fuzzy logic (MFL in the article) and paraconsistent logic:

    Source: https://pdfs.semanticscholar.org/6deb/e7251b8414446fcc2916f972b2fa33965154.pdf

    The main thing about paraconsistent logic is that, when using it, a person can let some contradictions exist in the process in a way that doesn't ruin the whole operation.

    It seems like a useful approach for thinking about human experience and behavior, because humans feel, think, and act in contradictory ways, at least some of the time.

    Out of curiosity, do you know of any experiments in AI where the developers tried to let the AI software contradict itself without returning an error?

    Graham Priest, the champion of paraconsistent logic, uses an example from database operations. He says that databases can have contradictory data, but can still be worked with in a way that doesn't lead to complete system failure.
     
  7. David Bailey

    David Bailey Administrator

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    I think the only way to tell would be to think of an interesting example, and then try to see how it would be treated.

    I suspect that analogous to FL, the concept of 'contradiction' used by the PL would not be a close match to what people really mean by contradictory evidence.

    I don't - I worked on a PROLOG implementation many years ago (1980's), and I got to see a fair few 'AI' programs, and wasn't impressed - I was pretty sure the hype would come to nothing, and it did! I am almost certain the current AI hype will end up the same way. Back then there were big discussions about the ethics of AI, how many people would become redundant, etc etc.

    Real self-driving cars that could drive anywhere a human could, would clearly need AI, and it is looking less and less likely that that will happen.

    David
     
  8. Dan_LastName

    Dan_LastName Member

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    I think you hit the nail on the head where you're drilling down to what they mean by "contradiction." Obviously, contradiction has a specific meaning in formal logic, but I still need to figure out if it really maps over to contradictory human beliefs, expressions, actions, etc. For now, it works for me to let the formal meaning of contradiction and the real world meaning be loosely associated with each other, without forcing them to be exactly the same.

    I finally ordered Priest's book Beyond the Limits of Thought. I think it will help me understand some of the technical aspects to a greater degree. I also want to drill into the relevant Stanford Encyclopedia articles, though they are slow going.
     
  9. Dan_LastName

    Dan_LastName Member

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    I found some examples of contradictions from the SEP article on paraconsistent logic.

    1. Bohr’s theory of the atom. According to Bohr's theory, an electron orbits the nucleus of the atom without radiating energy. However, according to Maxwell’s equations, which formed an integral part of the theory, an electron which is accelerating in orbit must radiate energy. Hence Bohr’s account of the behaviour of the atom was inconsistent. Yet, patently, not everything concerning the behavior of electrons was inferred from it, nor should it have been. Hence, whatever inference mechanism it was that underlay it, this must have been paraconsistent (Brown & Priest 2015).

    2. The liar paradox. Consider the sentence: ‘This sentence is not true’. There are two options: either the sentence is true or it is not. Suppose it is true. Then what it says is the case. Hence the sentence is not true. Suppose, on the other hand, it is not true. This is what it says. Hence the sentence is true. In either case it is both true and not true.

    3. Natural languages. In linguistics, it has been observed that normal lexical features are preserved even in inconsistent contexts. For example, words like ‘near’ have spatial connotations that are not disturbed even when dealing with impossible objects (McGinnis 2013):

    If I tell you that I painted a spherical cube brown, you take its exterior to be brown …, and if I am inside it, you know I am not near it. (Chomsky 1995: 20)

    Hence, if natural language can be said to have a logic, paraconsistent logics could be a candidate for formalizing it.

    4. Automated reasoning. Consider a computer which stores a large amount of information, as in Belnap 1992. While the computer stores the information, it is also used to operate on it, and, crucially, to infer from it. Now it is quite common for the computer to contain inconsistent information, because of mistakes by the data entry operators or because of multiple sourcing. Hence, even if steps are taken to get rid of contradictions when they are found, an underlying paraconsistent logic is desirable if hidden contradictions are not to generate spurious answers to queries.

    5. Belief revision. (The study of rationally revising beliefs in the light of new evidence.) Notoriously, people have inconsistent beliefs. They may even be rational in doing so. For example, a person may write a book, after much intensive research, in which they claim A, B, C, D, etc. But that person may also believe very deeply that no book contains only truths. So, in addition to believing A, B, C, D, etc, they also believe NOT A, B, C, D, etc. If people are able to revise their beliefs, they are typically in a state of contradictory belief first.

    Source: https://plato.stanford.edu/entries/logic-paraconsistent/
     
  10. David Bailey

    David Bailey Administrator

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    I am quite busy at the moment, so I certainly do not want to get into personally exploring PL, but I was hoping that you would show how PL can be used in cases such as the ones you cited. As I indicated, I am fairly sceptical of what these modified logics can achieve - but feel free to surprise me!

    Obviously the simplest example is the liar paradox. Now when a human thinks about that sentence, I think his natural reaction is to pop up to a meta-level and contemplate the fact that sentences can be internally inconsistent - and of course, Gödel too things a whole load further! Is there any evidence that a computer program based on PL can manage some of that?

    The QM example would also be good, but I suspect a program would need a shed load of physical knowledge and intuition before it could handle that!

    I think that example illustrates another problem with logic - it thins problems down and loses all the context, but that is not the way humans work. Einstein said that he reached the idea of Relativity by trying to imagine actually travelling at the speed of light - alongside a light beam. He didn't just ponder the inconsistency that light always travels at the same speed, even though the earth is moving and changing direction as it orbits the sun.

    He made his deductions by reference to the context of the contradiction.

    David
     
    Last edited: Oct 9, 2018 at 1:12 AM
  11. Dan_LastName

    Dan_LastName Member

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    Thanks again, David. I appreciate all of your replies. In terms of my ability to go into more detail on PL as it applies to computer science, I'm not going to be able to push further into that territory. I don't have the training or experience to speak to that beyond what's in the examples above.

    The reason I have become interested in PL is that I intuitively feel like it helps me relax a bit. I think I get very hung up on classical logic. I like to listen to Skeptiko and some other podcasts that look at psi, paranormal, consciousness, ufos, etc. because they are interesting topics, but I get frustrated by many of the viewpoints that are shared in these fields. I have been very conflicted for a long time about what I think and feel about things and all of that song and dance. I have tried to push my own perspective on things as far as I can go using my understanding of classical logic, and I just ended up with all kinds of paradoxes and self-referential loops and a not-very satisfying, cold, disenchanted experience.

    This topic of contradiction, especially, has captured my imagination and my spirit. If individuals truly do contradict themselves (and I know that's a big IF in light of the fact that I haven't really defined contradiction), I think we could then say that the universe contradicts itself, in the form of people contradicting themselves. And if the universe contradicts itself in this small way, it begs the question of what other ways might the universe contradict itself. I know this isn't a knew idea, but it's a beautiful idea to me, and it leaves open the possibility for all sorts of mystery in the universe.

    When I was a kid, I was a faithful Christian in a family full of faithful Christians. In my teen years and into college, I moved away into atheism and agnosticism. I think I have relied on my understanding of classical logic as a replacement for whatever that early faith developed in me. However, I've never been able to move away from classical logic as I previously moved away from Christianity. To me, casually tossing aside classical logic is akin to going back to my childhood faith, and I can't or won't do that. PL seems like a move in a more satisfying direction for me, and I feel there is great potential for enchantment that comes along with it.
     
  12. Wormwood

    Wormwood Member

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    Using hard cold logic, and hard cold logic only is really for the robots and cannot be successfully squared with the human experience. Feelings, emotions, and mystical experiences are just as valid as mathematics. I’d even be willing to state that they may be more valid in a number of ways, although they are not always totally distinct and separate from mathematical logic, depending upon perspective of course.
     
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  13. David Bailey

    David Bailey Administrator

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    Well I started out as a Christian, just as you did, and became an atheist while at university. I still tend to call myself an atheist, because I define being an atheist as not believing in any specific version of God - Christian, Islamic, etc.

    Interestingly other people often leave Christianity for rather vaguer reasons. My brother and his wife simply decided that church services were boring (which they usually are). Of course, if they really believed that not believing would send them to hell, they would accept the boredom, but yet again a non-logical argument worked for them!

    I came to realise that there was something wrong with straight forward materialism very slowly. The failure of AI in the 1980's was one step along that direction. Somehow various mathematicians managed to persuade a lot of other people that mathematical logic was 'obviously' the way to express computerised thinking processes. I was amazed how wrong they were and how empty this idea proved to be. It doesn't seem to be part of the new enthusiasm for AI, though it is not clear to me what new fad has replaced it!

    If you want to immerse yourself in a wealth of information that really blows away the idea of materialism, I recommend "Irreducible Mind", which is now fairly cheap on a Kindle.

    David
     
  14. Dan_LastName

    Dan_LastName Member

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    This is well said. The only thing that I get hung up on, is why isn't their a way for classical logic to accurately describe its own edge or limits and can classical logic, or some other form of logic, be used to shed light on the nature of feelings, emotions, mystical experience, etc.

    Western culture has obviously turned its back on "non-logical" experience in formal ways--you can't fight a parking ticket by claiming a higher power told you it was okay to park there in a mystical vision. I think it would be very helpful to be able to bring some technical perspective to the non-logical experiences, and I believe that's something paraconsistent logic can help with.
     
  15. Dan_LastName

    Dan_LastName Member

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    Thanks for bringing up materialism, it got me thinking that materialism would be aligned with classical logic and "not-materialism" would be aligned with paraconsistent logic, at least loosely.

    From the perspective of someone committed to classical logic (aka materialists), the claims of mystics, experiencers, spiritual believers, etc amount to contradictions, and paraconsistent logic is a good tool for looking at experience that includes contradiction. Paraconsistent logic is defined as a kind of logic that is able to tolerate contradiction in its premises.

    Strictly speaking:
    "There is life after death" is a contradiction from the perspective of classical logic.
    "There is a reality beyond this reality" is a contradiction from the perspective of classical logic.
    "It's 7:30 AM right now, and of course there's no such thing as time" is a contradiction from the perspective of classical logic.
    "Only people are conscious, and consciousness exists outside of people" is a contradiction from the perspective of classical logic.
    "I can see the future" is a contradiction from the perspective of classical logic.
    "I can see things that are beyond my field of vision" is a contradiction from the perspective of classical logic.
     
  16. Vortex

    Vortex Member

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    In fact, none of the statements above is inconsistent from the point of the classical logic, as long as the person making them makes some necessary clarifications - or just talk / write more precisely.

    For example, statement "there is life after death" is perfectly logically coherent if formulated more precisely: "there is life of the mind after death of the body": mind and body are different entities, and there is no fundamental contradiction in stating that they can exist separately. The insistence that there is a contradiction may exist only because of some common habits of the natural language usage - in this case, the one that assosiates words "life" and "death" only with physiological functioning of the body, and thus wrongly assumes that BOTH "life" and "death" words in the life-after-death statement means bodily conditions. Yet, in fact, "life" and "death", as any other natural language words (and phrases composed of them), have a wide range of situation-context-and-intent-dependent meanings.
     
    Last edited: Oct 10, 2018 at 10:44 AM
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  17. Vortex

    Vortex Member

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    Other examples being reformulated for clarity, and perfectly logically consistent after such a reformulation:

    "There is another (or greater) reality beyond this reality".
    "It's 7:30 AM right now in the pragmatically useful description model of "physicality", yet there's no such thing as time in the absolute, non-descriptive sense".
    "Only living beings manifest consciousness in the limited individual form, yet the fundamental universal source of consciousness exists outside of any living being".
    "I can perceive the future by the means of perception that are beyond sensory abilities of the body".
    "I can perceive things that are beyond sensory abilities of the body in the moment of perception by the means that are beyond sensory abilities of the body".
     
    Last edited: Oct 10, 2018 at 11:01 AM
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  18. Dan_LastName

    Dan_LastName Member

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    Thanks for the responses, Vortex. You have given much food for thought. I'm wondering if you have any thoughts about people contradicting themselves in other ways, like saying there is such a thing as a round square. Or, another one that I think is interesting is how, when in the process of shifting beliefs about any given topic, people may hold contradictory beliefs for a period of time. What I'm trying to ask is, do you think people contradict themselves in other ways?
     
  19. Dan_LastName

    Dan_LastName Member

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    I was thinking more about this point, and I think I will modify my earlier idea about materialism being aligned with classical logic and "not-materialism" being aligned with paraconsistent logic.

    I would say instead that:

    1. Most (or all) materialists are committed to classical logic as the best tool to use to understand the universe and the human experience.
    2. Some (but not all) non-materials are committed to classical logic as the best tool to use to understand the universe and the human experience.

    Do you think this is accurate?
     

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