Common Philosophical Mistakes I – Abusing the Laws of Dialectic Logic

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26 Responses to Common Philosophical Mistakes I – Abusing the Laws of Dialectic Logic

  1. A great post, thanks Peter. I’m sure I’ve made many of these mistakes over the years.

    I appreciated this: “..it leads a great many people, even many of those who endorse and practice the mystic arts, to assume that for the Buddha’s view we would have to stop using our reason.” This is something that causes so many problems in spiritual circles, particularly New Age – the idea that you must stop thinking or that thinking is the enemy. And yet Buddhism is absolutely rational. There seems to be a difficulty in accepting that a philosophy could be both rational and mystical – as if they contradict one another. But as you show – they don’t!

    • PeterJ says:

      Yes, I know what you mean. It’s not just its opponents who see the dhamma as ‘illogical’. It took me some years to figure out how to reconcile it with classical logic, and in the end it is a quite simple task. But only after I read Whittaker and saw how clever was Aristotle.

  2. dondeg says:

    It seems cliche, but what about statements like “I am lying”, especially in the context of say Godel’s theorems? Personally, I am burnt out on the whole “self-reference” thing as found in the secondary literature like Hofstadter’s droning, monotonous and seemingly never-ending Godel, Escher, Bach, where people try to make something interesting out of iteration. Still, I wonder about such weird “third way” comments that are neither true nor false, nor true and false.

    Also, Pete, interesting take on logic and mysticism. I’m right in the middle of a series of posts that are building up to trying to show the inability of the mind to grasp experience; to try to come face to face with the idea of the “inscrutableness” at the base of experience. It is a weird exercise in logic as well, because the underlying device is to try to force the reader into accepting that something along the lines of Patanjali’s methods in the Yoga Sutra are the only logical reaction to the intrinsically inscrutable nature of our experience. It’s a tough set of pieces to write.

    Anyway, as usual, thanks for the interesting reading!

    Best,

    Don

    • PeterJ says:

      Thanks for the comment. That’ll be a tough series of posts, as you say. I’ll look forward to it. I know what you mean about self-reference and Hofstadter, although I really like his ‘strange loops’. As for Gödel, I am prone to mistakes when discussing him but have some ideas. Sometime I’ll post something on incompleteness, and hopefully you’ll check it over for me.

      • dondeg says:

        I’ll look forward to it, Pete. I am curious as to your take on these issues from your viewpoint. Also, please feel free to comment on my weird posts too! Best, Don.

  3. cabrogal says:

    Hi Peter.

    I guess the good news is that, taken individually, I can agree with almost every point in this post.

    The bad news is that I think the way you put them together muddies some issues more than clarifying them.

    The worse news is that, if I understand what you are trying to achieve in this post (indeed the whole blog), I think the muddiness carries through to your entire thesis (theses?), though it may just be that I am making incorrect assumptions about what you are driving at. Or that I am completely wrong.

    Rather than trying to be comprehensive (pretty hard within the context of a comment) I’ll simply give some examples that you may choose to use as talking points.

    Firstly, I can heartily agree that the world is full of false dichotomies, from ‘determinism/freewill’ to ‘for me/against me’ to ‘Labour/Conservative’. This sabotages many attempts at understanding and considerations of options so they should be identified and rejected wherever possible.

    True dichotomies need to be both exhaustive and exclusive. Without using these criteria it is easy to fall reflexively into a position one does not truly hold simply because the alternative offered seems ridiculous or repugnant. To come to define what you believe purely in terms of opposition to what others believe.

    If you hold to the validity of Hegelianism (I don’t) then it becomes even more important to select thesis and antithesis that begin as true dichotomies. It seems to me that most long-standing arguments between Hegelians hinge on this issue.

    But this is irrelevant to the formulation of statements of binary logic.

    The necessary contradictory pair in a binary logic statement is only in its predicate, not between the subject and predicate.

    So to evaluate the validity (rather than truth) of the statements “A dog is an animal” or “A dog is not an animal” it is not necessary to wonder whether a third option, say “artichoke”, exists nor whether the sets “dog” and “animal” partially overlap, but simply whether the categories “an animal” and “not an animal” are exhaustive and exclusive. If the predicate is well defined and can be validly divided at all, A and not-A will always fulfill these criteria. By definition.

    Category errors can confuse the issue somewhat, but not much.

    So the contradictory statements “red is salty” and “red is not salty” cannot be resolved logically (unless perhaps you are a synesthete), but adding the option “red is neither salty nor not salty” provides the answer.

    Where binary logic breaks down is not where the subject and predicate are from different categories, but where the predicate cannot be validly divided without destroying its essence. This is the case when it is a non-dualistic concept.

    Aristotle encountered some difficulties with binary logic when trying to resolve apparent paradoxes or oscillations (e.g. “This statement is untrue”) or when he had accidentally hidden non-dichotomous options within his predicate (as with “a sea battle will happen tomorrow”, in which he imbeds his confusion about determinism and free will within his concept of ‘will happen tomorrow’) but he didn’t run up against non-dualism because, prior to Plotinus, Hellenistic philosophy had no non-dualistic concepts (unless you count things like substance monism or mind-body monism – which is not really the same thing) or if it did there would seem to be no surviving record of anyone trying to come to grips with them, though the mystic-philosopher Anaximander may have been close. So they were free to develop a logic in which everything could be neatly divided into A and not-A.

    The Indians had no such luxury.

    Arguably from as early as the Rig Veda, but certainly by the time of the earliest Upanishads, Indian philosophers were trying to come to grips with notions that were inherently indivisible. Indeed, these concepts were often central to their philosophical musings.

    The Indians did develop a binary logic similar to that of the Greeks, but right from the start they recognised that it was inadequate for many of the tasks they sought to apply it to. Worse was that attempting to do so could easily cause them to lose focus on inherently slippery non-dualistic concepts (which evade formulation in natural language as they evade it with binary logic), thereby leading them into category errors or worse.

    Nagarjuna’s mis-named quadrilemma (because it was not originally formulated by Nagarjuna, nor is it a true example of four-value logic) is neither an application nor an extension of binary logic. It is a rejection of it. It is used not as an example of such logic but as a means of specifying its boundaries – of flagging territory into which it cannot validly stray.

    My reading of Indian philosophy is far from exhaustive but it is fairly extensive. I have never seen the quadrilemma applied positively. It is always used to negate. If you can find a relevant example of it being used to define or delineate a ‘thing’ – or of Aristotelian logicians applying the quadrilemma anywhere – then I will retract at least part of what I am claiming in this comment.

    It seems to me that you are trying to equate Indian and Greek logic and (perhaps) trying to argue that a complete metaphysics can be defined with reason and/or binary logic alone. I reject both of those claims.

    To attempt to equate Greek and Indian logic or to fold one into the other is, I believe, no more valid than the Dawkinists’ attempts to fold religion into science or the Creationists’ attempts to fold science into religion. To make one fit the other you must cut away at least some of its essential features. A mallet may be suitable for some of the tasks usually assigned a hammer and visa versa but one is not the other and to attempt to use it as such can damage the user or what he is using it on.

    As Kant showed, reason based metaphysics is always incomplete. There must be a non-phenomenal Ding an sich upon which phenomenal reason might stand without undermining itself. Reason cannot interrogate itself. The thing-in-itself is not a synthesis or unification of dualistic options but a transcendence of them.

    And as Hume showed, logic is inherently reductionist. Using it to generalise – as with inference – is unreliable at best and probably entirely invalid. You may be able to build an impressive looking pyramid by combining premises but you will never go beyond the premises themselves. You can’t ‘think’ outside your own mind.

    Russell and his ilk were right to reject metaphysics. While pursuing it may provide useful insights into some questions it is not a tool suitable to its task if that task is considered to be a comprehensive definition of reality or to evaluate any system that attempts to come to grips with it.

    I think Nagarjuna operated from the belief that a complete view of reality (albeit not a metaphysical one) can be ‘apprehended’, but not with reason. Zen, in particular, seeks to suspend the reason of the seeker with negation, paradox, koans or bashes on the bonce from a Roshi’s stick. It is the recognition that reality cannot be encompassed within rationalist metaphysics that makes Zen necessary. Nagarjuna is not showing you how to build reality from rationalism. He is telling you to let go of rationalism if you seek reality. Or at least to not insist that all of reality is the nail to rationalism’s hammer.

    Rationalist metaphysics will always be incomplete, so there will always be applications of it that are ‘extreme’ and invalid. Whether rationalist (or non-rationalist) metaphysics is even possible is probably a semantic question rather than an ontological or epistemological one.

    To construct a complete metaphysics with reason (or anything else) is a contradiction in terms from the perspective of Buddhism. Constructions are inherently conditioned and subject to anicca. They can never encompass reality. Perhaps that is why the Buddha was so reluctant to answer metaphysical questions.

    There can be no extremes in non-dualism. Nor can there be dichotomies upon which logic might operate. It will always remain beyond the bounds of reason.

  4. PeterJ says:

    Well, there you go. Thanks for a very interesting response, but I could hardly agree less with much of it. I don’t know where to start on so many issues at once.

    Let go of rationalism? How is a rational person supposed to do this? Letting go of computation is the trick.

    You comments about subject and predicate seem a bit muddled. You say, “The necessary contradictory pair in a binary logic statement is only in its predicate, not between the subject and predicate.” Are you sure you mean this? I do not understand it. For Aristotle the contradiction is contained in modification of the copula ( ‘is’ and ‘is-not’).

    You say, “So to evaluate the validity (rather than truth) of the statements “A dog is an animal” or “A dog is not an animal” it is not necessary to wonder whether a third option, say “artichoke”, exists nor whether the sets “dog” and “animal” partially overlap, but simply whether the categories “an animal” and “not an animal” are exhaustive and exclusive. If the predicate is well defined and can be validly divided at all, A and not-A will always fulfill these criteria. By definition.”

    On this we agree completely.

    Your view of Hellenistic philosophy contradicts that of Heidegger, and I would agree with him. The dualistic approach that becomes a characteristic this philosophy would be the dumbing-down of an earlier tradition.

    I would say that Nagarjuna is definitely an example of binary logic put to good use. The identification and rejection of Aristotelian contradictions is the basis for his argument.

    I cannot see why you think a complete metaphysics is impossible. What’s wrong with Nagarjuna’s? .

    You say, “I think Nagarjuna operated from the belief that a complete view of reality (albeit not a metaphysical one) can be ‘apprehended’, but not with reason. Zen, in particular, seeks to suspend the reason of the seeker with negation, paradox, koans or bashes on the bonce from a Roshi’s stick.”

    Quite so. But Nagarjuna wrote his proof for people to read and understand, It was not an attempt to make them apprehend reality, but to gain a logical understanding of it. Second best. sure, but it’s a start, and a great help to the practitioner. . . .

    You then say, “It is the recognition that reality cannot be encompassed within rationalist metaphysics that makes Zen necessary.”

    Not so. It can be so encompassed. But it cannot be properly understood or verified, and certainly cannot be known, as a metaphysical theory. A theory is never knowledge. Check out the patriarchs of Zen and you’ll find some very good metaphysicians.

    You say” So the contradictory statements “red is salty” and “red is not salty” cannot be resolved logically (unless perhaps you are a synesthete), but adding the option “red is neither salty nor not salty” provides the answer.”

    This is not a true contradictory pair, which is why there is another option. Neither statement is true, so the laws of logic are irrelevant here.

    You say, “To attempt to equate Greek and Indian logic or to fold one into the other is, I believe, no more valid than the Dawkinists’ attempts to fold religion into science or the Creationists’ attempts to fold science into religion. To make one fit the other you must cut away at least some of its essential features.”

    Why? In metaphysics nondualism is an interpretation of logical results, not an abandonment of those results or even a modification to the method. .
    .
    You say,” Rationalist metaphysics will always be incomplete, so there will always be applications of it that are ‘extreme’ and invalid.” Why must it be incomplete? Mine seems complete enough.

    “To construct a complete metaphysics with reason (or anything else) is a contradiction in terms from the perspective of Buddhism.”

    This is not quite right. To describe or imagine the world completely in the language of our conceptual categories would be impossible. But we can get around this for a theory, as Kant shows. We just need to include a phenomenon that he describes as ‘not an instance of a category’. Problem solved. For logic we only need tokens.

    You say, “Constructions are inherently conditioned and subject to anicca. They can never encompass reality. Perhaps that is why the Buddha was so reluctant to answer metaphysical questions.”

    Exactly. We had to wait for Nagarjuna to explain this reluctance. But a complete metaphysical scheme may still, nevertheless, encompass reality. Check out the Abhidhamma pitaka. It deals with all phenomenon without exception.

    You say, “There can be no extremes in non-dualism. Nor can there be dichotomies upon which logic might operate. It will always remain beyond the bounds of reason.”

    Nondualism is perfectly reasonable. It is only that we cannot understand or know what lies beyond concepts by the use of our intellect. Nevertheless, we can still treat it as a well defined phenomenon for logical purposes. Logic doesn’t care what its symbols stand for.

    Hell. We’d better not keep going at such length. I felt you made some very good points here but clearly we have very different ideas. As yet I see not reason to alter my view but I don’t mind being pushed.

    Best
    Pete

    .

    • cabrogal says:

      I guess trying to argue rationally against rationalism is a bit of a fools errand. From the outside it looks like just another circular meme – like biblical Christianity. If you define reality according to what is rational then yes, it is all resolvable via rationalism. It is ‘complete’ in the sense that a perfect circle is complete. But does drawing a perfect circle necessarily mean you have enclosed anything? Or is logic more like Russell on mathematics? All reducible to tautology.

      To me reality is not something to be worked out. It is something to be lived. Or just to be. So from where I sit, empiricism refutes rationalism more effectively than visa-versa – though I trust neither as stand-alone filters of existence. They both produce blind spots and that’s where non-duality is.

      It’s not all phenomenological you know. Not by a long shot. If you have ‘experienced’ non-duality in a manner even remotely like my own you would know it is not subject to knowing, understanding or logic. You must leave them behind. It just is. And it’s real alright. More real than subjectivity or objectivity.

      • PeterJ says:

        It’s okay, cobrogal, your last paragraph is unnecessary here. Of course it is true. But it has no bearing on the problem. I’m not suggesting that logic allows us to know the truth. I’m suggesting that it allows us to construct a complete theory. That is, a set of terms and theorems that describe the world. But yes, a theory is not knowledge. There is no suggestion that logical analysis would be a substitute for ‘walking the walk’.

        The point is simply that logic and experience coincide. What we discover in experience would be what we can expect to discover given the conclusions of metaphysical analysis.

        I may be claiming a bit less than you think I’m claiming. I’m not saying anything original.

      • cabrogal says:

        I guess our differences may be mainly semantic. I can agree with you by sufficiently restricting the definition of ‘the world’ but by the time I’ve done that I can see little point to the exercise of describing it. There are things that can never be described with natural language or logic (e.g. http://en.wikipedia.org/wiki/The_Void_(philosophy) – which Aristotle denied existed), so if you exclude them from ‘the world’ you have made a start on making your assertion true.

        If logic and experience coincide I would suggest it is because logic is being used to condition experience. The druids ‘knew’ from induction that the appropriate ceremonies during the winter solstice would bring back the sun, so they performed them. Lo and behold, the sun always came back. Logic again matches experience perfectly.

        Deductive logic is more robust than induction but, as Wittgenstein points out, all it describes is itself.

        A couple of examples.

        Dogs are animals.
        Fido is a dog.
        Therefore Fido is an animal.

        All that really says is that you have chosen to define ‘dogs’ as a subset of ‘animals’ in a manner that places Fido within that subset. You are merely describing where you have drawn some lines.

        Or how about:
        I think therefore I am.

        Descartes begins with the assumption there is an ‘I’ doing the thinking and draws the conclusion that therefore there is an ‘I’. It’s just question begging.

        The Buddha acknowledged there is thought but did not assume a thinker lay behind it. He did not beg the question and was never able to conclude that an ‘I’ exists at all. Hence anatta.

        Anatta may be justifiable with logic, as is ‘I’, but all logic can really describe are the starting assumptions of the logician. And if you approach experience with those same assumptions in all likelihood what you experience will comply with your logic.

        So really all you are talking about is yourself.
        And there is no self. 😉

    • cabrogal says:

      Oops. I just checked.

      Russell derived his assertion that maths is tautology from Wittgenstein’s claim that logic is tautological. I had thought it was the other way around.

  5. PeterJ says:

    Sorry, but I don’t see your objection. I’m certainly not disagreeing with anything said by the Buddha. Sure, there are things that cannot be described by natural language, or any language. It is even debatable whether anything at all can be so described. The point is that all metaphysical positions give rise to contradictions except Nagarjuna’s. We can see this as a meaningless discovery or an important one, but the logical conclusion stands. To say that it is meaningless, on the grounds of the limits of logic, would seem perverse to me, and it would mean abandoning rational philosophy. As it is, logic is vital for checking the plausibility of our premises and axioms.

    The non-existence of the self would be an empirical fact,. but it is also a conclusion of logic. Hegel uses logic to arrive at his view of the world as a ‘spiritual unity’. Nagarjuna uses it to show the same. (Not that he would use the same language). Kant likewise. This shows the value of logical analysis. If logical analysis is useless then we might as well pick our metaphysical view out of a hat. .

    Logic is empty of meaning, as you say. But once we assign referents to its terms, as we do in metaphysics and physics, it becomes full of meaning. The statements ‘x is in y’ and x is-not in y’ may or may not be a contradiction. It would depend on the referents for x and y. If we say that x = marmalade and y = cupboard then we have a dialectical contradiction and can use logic to help guide our search for breakfast.

    Your objections would seem to render the proof of Nagarjuna worthless. But this was clearly not his opinion.

    I think the problem here may be that a term in logic can stand for a thing but does not have to fully describe it. Tao cannot be described except negatively, but this is good enough for its use as a logical term. And in any case all formal systems need at least one undefined term. So our inability to fully describe a thing does not prevent us from using it as a term for a logical argument. The point is that logic can prove Tao. What it cannot do is give us any real sense of what we have proved. I discuss this at length somewhere. Logic can show us where to look, but it cannot take us there. In more traditional terms, logic might tell us who fired the arrow and where from, and it might tell us how to go about curing the wound, but we can agree that it won’t do anything to cure it.

  6. SamL says:

    I too would be interested to know how a thoroughgoing Aristotlean would deal with sentences like: “this sentence is false”

    By the law of the excluded middle it’s either true or false, and both options are self-contradictory.

    So either the excluded middle or LNC has to go in this case. (I’d suggest excluded middle) (Or perhaps we could argue that it’s just not the sort of sentence which can be true or false, like “stop that!”)

    Re waves and particles, certainly it is not the case that an electron has to be either a wave or a particle. We now know that it is something else which is neither wave nor particle, but which behaves like a particle in some scenarios and like a wave in others. But it is true that being a particle implies not being a wave, and that being a wave implies not being a particle. What is not true is that ‘wave’ and ‘particle’ are mutually exhaustive options for things like electrons.

    Similarly with materialism and idealism, you are quite right when you say that the negation of materialism is not-materialism, and this is not the same as idealism. But idealism does imply not-materialism, and materialism does imply not-idealism. So they are mutually exclusive, but not mutually exhaustive. There could be something else which is neither materialism nor idealism which implies both are false (dualism, for example).

    I don’t think there’s anyone who’s thought seriously about metaphysics who fails to appreciate this. If people sometimes sound like they’re treating them as the only options on the table, this likely has nothing to do with them believing that this is some sort of logically necessary bifurcation, but with them believing that other options are no longer credible, or fail to contrast significantly with either of them, or something else.

    Sam

    • PeterJ says:

      Hi Sam. Thanks for the comment.

      I’m not interested in sentences such as ‘This sentence is false’. It is not a dialectic thesis so might as well be ‘This sentence does not have a truth-value’. or ‘This sentence is meaningless’ or ‘This elephant is false’.

      Materialism and idealism are both dualism by my definition, so I wouldn’t go along with your solution. But yes, there is nothing to prevent there being alternatives.

      You say that you don’t think there’s anyone who’s thought seriously about metaphysics who fails to appreciate this (‘this’ being the point about dilemmas not being true dilemmas). I would disagree completely on this one. I can think of only a tiny handful of people who appreciate it. Most philosophers just get stuck in a muddle of category-errors and end up thinking that metaphysics is hopeless. It is a point not well understood even in mysticism.

      If the nondual view of the world is correct then we would expect to be able to show what Nagarjuna shows, viz. that all other views are logically flawed. So logic, reality, experience, metaphysics, science and rationalism all agree. Take any approach we like and we end up at the same place. As long as we use logic correctly. .

      • SamL says:

        I’m not quite sure what you mean by ‘dualism’ when you say that materialism and idealism are versions of it — they are both forms of type monism, which says that ultimately there is only one kind of thing, while dualism says there are two fundamental kinds. Perhaps you are using ‘dualism’ differently to how it normally is. It would help me to understand what you’re getting at here if you could explain that?

        “You say that you don’t think there’s anyone who’s thought seriously about metaphysics who fails to appreciate this (‘this’ being the point about dilemmas not being true dilemmas). I would disagree completely on this one.”

        To be clear: the point I was making was that no-one thinks materialism and idealism are mutually exhaustive in any strict logical sense (i.e. they don’t think each is logically equivalent to the negation of the other). It was not a point about dilemmas in general. (Again though, there are not, generally, widespread assumptions about dilemmas as such — some dilemmas are genuine dilemmas, some are artificial, some are based on semantic mistakes, and some depend on false information, etc etc.)

        I don’t think you can dismiss self-referential paradoxes anything like as easily as you want to. “This elephant is false” is clearly not truth-apt (because truth or falsity is a property of propositions, not elephants), but the others are genuine problems for anyone who believes that both the law of non-contradiction and the excluded middle are laws of logic, since they provide clear examples in which both cannot hold. (Whether or not you’re interested in them is rather beside the point.)

        “This sentence is false” is clearly not a category error: it applies the truth-predicate to a proposition, which is exactly the domain of application for the truth-predicate. What makes it paradoxical is not any sort of category error, but its negative self-reference. People have tried to build watertight semantic criteria which prevent this kind of self-reference (e.g. Russell and Whitehead’s Principia Mathematica) but these systematically fail (part the power of the incompleteness theorem is that it shows how these efforts *have to* fail).

        So pending some account of why “this sentence is false” is not truth-apt, we’re left with an important class of counter-examples to the claim that both the law of non-contradiction and the excluded middle are universally truth (i.e. that they’re laws).

        Sam

  7. PeterJ says:

    I’m sorry Sam, but I cannot agree, The sentence ‘This sentence is false’ is meaningless. What is supposed to be false? How can this sentence have a truth-value? If I disagree and make the counter-claim ‘This sentence is-not false’, then how can we decide which is correct? Obviously we cannot. ‘This sentence is undecidable’ becomes an option. But, of course. the phrase ‘this sentence’ does not have a truth-value. It cannot be true or false, anymore than can an elephant. For a statement to be subject to the LEM it must be a legitimate dialectical thesis. ‘This sentence’ is not a proposition and cannot be true or false.

    The dualism thing is to do with the scope of the idea. You’re probably using it to mean mind-matter dualism, as is most common, while I am using to mean metaphysical dualism. From a non-dual perspective monism IS dualism. This would be why Al-Halaj tells us that it would be incorrect to say ‘God is One’. This would be dualism, since it implies a testifier apart from God. That is, it implies two things. Likewise materialism posits not just matter, but also space, time, motion, change, process, and some would say an observer capable of observing the matter. Idealism (of the kind that is the target here) is clearly dualism, since it depends on a dualism of subject and object. This is why non-dualism is not called monism. It is very a different idea.

    I take the point about Russell but we do not have to do metaphysics as he did. His method is doomed to failure. He makes exactly the mistake that we need to avoid. George Spencer Brown solved R’s famous problem, as R acknowledges, and he did it by introducing the idea of nondualism. This allows us to construct a system that does not fall foul of the incompleteness theorem or Russell’s paradox.

  8. SamL says:

    “The sentence ‘This sentence is false’ is meaningless. What is supposed to be false? How can this sentence have a truth-value? If I disagree and make the counter-claim ‘This sentence is-not false’, then how can we decide which is correct? Obviously we cannot. ‘This sentence is undecidable’ becomes an option. But, of course. the phrase ‘this sentence’ does not have a truth-value. It cannot be true or false, anymore than can an elephant. For a statement to be subject to the LEM it must be a legitimate dialectical thesis. ‘This sentence’ is not a proposition and cannot be true or false.”

    The sentence “this sentence is false” is what is supposed to be false. The fact that ‘this sentence’ is a term which only refers when it’s in the context of a sentence is irrelevant. By your logic, “this sentence is written in English” would be meaningless (but it’s meaningful and true) and “this sentence contains 3 letters” would also be meaningless (but it’s meaningful and false).

    Re what you’re calling ‘nondualism’ I think you are attributing positions to people which they do not hold. You seem to be hinting at the problem of the one and the many, but it’s not quite clear how either materialism or idealism relate to this problem. (Idealism and materialism concern the character of reality, while the One and the Many concerns its division, or its unity, or its multiplicity, or its unexpressible unity, or its unexpressible multiplicity, or whatever.) I wrote something about ontological nihilism recently which may or may not touch on what you’re getting at: http://theplatopus.com/2014/07/28/considering-ontological-nihilism/

    Sam

  9. PeterJ says:

    I fear we are different planets, Sam.

    ‘This sentence’ is not a sentence by any normal grammatical rules. How can it be true or false? It is not a proposition. How can anyone think is could have a truth-value? Why create these unnecessary complexities? We could say, ‘This sentence is true AND false’, or, ‘This sentence is NOT a sentence’. We can say anything we like. If it is not a legitimate dialectical thesis then the laws of logic become irrelevant.

    In short, I cannot see any way to assign a truth-value to the words ‘This sentence’, and see no need to complicate the issues by assuming we can. The sentence, ‘This sentence is false’ is simply meaningless, It’s like saying, ‘This word is spelt incorrectly’.

    I’m not sure what to make of ontological nihilism. ( I read your post). The various forms make varying degrees of sense to me,. If it means that nothing exists independently, or in the way we usually think it does, then this would be fine by me. However, I would never call it nihilism. Clearly there is something that is real, even if ‘exists’ might not be quite the word to describe it.

    To say that it exists would be dualism since we are denying its non-existence. That is, we would be adopting an extreme position. (Like materialism or idealism). .

    One-Many is only a problem if we assume they form a true contradictory pair for the dialectic. The problem evaporates if we do not. This was the message of the essay. A problem still remains,. but it is not the same problem and it is not intractable. From a technical perspective nondualism simply means endorsing compatibilism as the solution for all metaphysical problems, and I am proposing that this presents no logical difficulties. I struggle to see a reason for complicating the issues any further. But I am not known for explanatory powers so may be explaining my thoughts poorly. I don’t have students to practice on, which is a mixed blessing.

    • SamL says:

      Sorry to press this, but it’s kind of critical —

      Your confusing these:

      1. “this sentence” is false.

      and:

      2. this sentence is false.

      1 is a category error, because a simple term can’t be true or false. But the appearance of ‘this sentence’ in 2 refers to the whole sentence: “this sentence is false”. To see the point, notice that these are different:

      3. “This sentence” has 12 letters.

      4. This sentence has 12 letters.

      3 is true, because “this sentence” has 12 letters, and 4 is false, because “this sentence has 12 letters” does not have 12 letters.

      Sam

  10. PeterJ says:

    Press away. Perhaps you’re right. I don’t think so, but then I wouldn’t.

    But no, no confusion. It seems we agree that the two words “This sentence” does not constitute a sentence. In this case ‘This sentence is false’, is just a muddle of meaningless words.

    That is, if 1 is a category-error, as you suggest, then 2 obviously embodies the same error. The negation must be external to the subject. Otherwise we could have, ‘This true sentence is false’, or, ‘This sentence is longer than it looks’. First one makes a proposition, and then one makes a truth claim about it. The proposition cannot actually be identical with the truth claim, as in ‘This claim is false’. What claim?

    As it happens I don’t see this as critical whichever way it comes out. As far as I can tell the point I’m making about logic and metaphysics would be unaffected by any mistakes made by Aristotle. I’m not saying that we have to use his logic, only that physics and metaphysics work out just fine if we use it as he specifies.

    So I’d say never mind all this stuff about confusingly contrived statements, let’s just solve metaphysics so that it makes sense according to our reason.

    • SamL says:

      I think this stuff is rather important, actually, particularly in relation to what you have to say about Nagarjuna. You’re probably aware that the reading you’re putting on Nagarjuna is fairly unorthodox. That’s fine, but it will need some defense, which I’m not convinced that you offer.

      You’re saying, as far as I can tell, that a perfectly clear reading can be put on Nagarjuna using classical logic, and what’s more, that the system presented by Nagarjuna thus-interpreted is true. So there’s two claims there.

      You say: “Nagarjuna’s argument refutes all four possible answers to all dialectical metaphysical questions.” I presume you’re referring to one of the catsukoti. But this seems strange to me, because to accept that a catsukoti refutes four possible answers is to grant the possibility of (A and ~A) and ~(A or ~A), which is to reject classical logic. The best effort I’ve ever seen to make sense of this is to appeal to a dual semantic context: so when I say (A and ~A), it would mean “A is true in one sense and false in another.” (I may be misinterpreting you here — I find it difficult, because while you make reference to ‘Nagarjuna’s argument’ throughout you never go into what this argument actually is in any concrete terms. I, for one, would be interested in reading a post in which you did so.)

      Now, the reason why all this stuff about paradoxes of self-reference is important is because they motivate non-classical approaches to logic, and these approaches offer another way of putting a consistent reading on Nagarjuna (a la Graham Priest, as I’m sure you’re aware). In my view these seem to offer a better reading, as they make things relatively clear (though nothing is very clear when it comes to Nagarjuna) and don’t rely on ad hoc semantic hypotheses.

      It’s strange, because sometimes it seems like you’re hinting at something which can pretty well be expressed just by abandoning classical logic. So when you say “One-Many is only a problem if we assume they form a true contradictory pair for the dialectic. The problem evaporates if we do not.” I don’t quite understand what you’re saying. As I see it, here are the exhaustive options to the question of the unification of reality:

      1. one
      2. many (i.e. more than one)
      3. none
      4. the question doesn’t make sense

      Do you agree that those are exhaustive? If not, then you’re not doing classical logic. If we waive that and say “all these answers are false”, that that doesn’t make the problem evaporate at all — it just formally ignores it. (What’s more, what we’d actually like are some *reasons* why each is false.)

      So back to “this sentence is false.” Let’s take your examples:

      1. This true sentence is false.
      2. This sentence is longer than it looks.

      There’s nothing wrong with either of these. 1 parses to “this sentence is both true and false”, which is false, and 2 may be true or false, depending on what you mean by “longer than it looks”. So I’m not seeing what you’re issue is. If you can see that “this sentence has twelve letters” is meaningful and false, then you can see how ‘this sentence’ can refer to the whole sentence it is embedded in.

      “‘This claim is false’. What claim?” Err, that claim!

      Sam

      • PeterJ says:

        It’s very strange. I place an interpretation on Nagarjuna by which he makes sense, by which his philosophy would be consistent with the Buddha’s teachings, as well as with Aristotle, by which there is a real purpose behind his proof, by which his result is secure, and that solves all metaphysical problems once and for all. And you prefer a different interpretation by which the status quo is preserved and we’re back where we started with Plato and a muddle of dilemmas. And all because of some trick of language by which it is possible to confuse the issues. It’s as if any lengths should be gone to avoid conceding any ground to mysticism.

        I see his four-way proof as positioning two dialectical theses orthogonal to each other. Firstly, the truth is not this or that, and, secondly, it is not both or neither. I have great difficulty turning this into a complicated logical problem. Besides , it is N’s result that is important, not his method. Is his result trustworthy? If so then metaphysics is solved. So why worry about lying Cretans and meaningless self-references?

        A relevant book would be Spencer Brown’s ‘Laws of Form;. He turns the argument into mathematics and introduces imaginary values into ordinary logic to make the structure work, and by so doing solves Russell’s paradox. I’m suggesting that the imaginary values are unnecessary, but both our approaches would do Nagarjuna justice and work equally well. .

        Do you know Nagarjuna’s doctrine of two truths? It is the doctrine that explains Lao Tsu’s remark, ‘True words seem paradoxical’. They seem paradoxical for the reasons you give, that it is possible to completely confuse the logical issues and see a contradiction where there is none. Perhaps Francis Bradley’s proof in his ‘Appearance and Reality’ would be more to your liking, since (if I remember right) he does not bother with the ‘both/neither’ part of the proof and thus his argument is more simple and more clearly a use of ordinary logic. .

        It is true that we have a choice of how to respond to Nagarjuna. It is possible to dismiss his proof and argue that metaphysics is intractable. I just cannot see why anyone would do this. It is not possible to gainsay his result, and it is only because Priest, Routley and Melhuish reject it (or used to) that they get in such a muddle and end up with an incomprehensible universe.

        It would be a shame if one lying fictional Cretan forever prevented us from making progress in metaphysics.

  11. PeterJ says:

    Sam – I’m going to be taking this post down since I have tidied it up and submitted it for publication and it shouldn’t be here as well, or not at the moment. If it is rejected I’ll reinstate it. In case you want to go on discussing this I’ll replace the text with a note and leave the comment section up.

    • SamL says:

      Nah don’t worry about it, I’ve said everything I want say and the weekend beckons 😉

      • PeterJ says:

        Fair enough. The message I take away is that your objections are at least possible, and that I need to be able to deal with them more decisively. Thanks for making them. and have a good weekend.

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