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Lao Tsu's Tao Te Ching is full of paradoxes. Is paraconsistent logic sufficient to translate Tao Te Ching to formal logic?
To be specific, how can I get started with the following passage from J.Legge translation using ω-consistentcy theory?
The Tao that can be trodden is not the enduring and unchanging Tao. The name that can be named is not the enduring and unchanging name.
I know nothing about the Tao Te Ching, but the sentences you quote are not (logically) contradictory, or paradoxical:
The Tao that can be trodden is not the enduring and unchanging Tao.
Nothing paradoxical here, is there? Maybe the only enduring and unchanging Tao is one that people is prevented from trodding -- so as to avoid wear from all that trodding, and stay unchanged, say.
Suppose we introduce the following notation:
T: stands for the property of being a Tao EU: stands for the property of being enduring and unchanging R: stands for the property of being susceptible of being trodden
then your sentence can be rendered thus:
For all x, (Tx ^ Rx -> ~ EUx)
This is classical logic at its simplest.
[EDIT: As Mozibur suggests, one might want to argue that a path is, necessarily, susceptible of being trodden. I am not sure about that: consider a path inside a flooded mine, for instance. Anyway, if paths are to be practicable of necessity, then there is a contradiction in that sentence.]
The name that can be named is not the enduring and unchanging name.
Suppose that all names can be named. (Just like, for example, "Schiphol" is a name of my name.) If so, no name is enduring and unchanging. No paradox here either.
On the other hand, maybe there is an enduring and unchanging name, and that name has no name. This is semantically implausible, but not paradoxical.
Anyway, introducing the notation:
Nxy: stands for the relation of x being a name of y
We can say that a is a name iff there is an y such that Nay, and your second sentence can be rendered thus:
for all x (there is a y (Nxy) -> [there is z(Nzx) -> ~EUx])
Again classical, consistent logic.
Building on Schiphol's earlier answer, we can straightforwardly obtain what could be1 a perfectly adequate reading of what the Tao Te Ching is saying, in a hard-nosed analytic and falsificationalist framework.
The Tao that can be trodden is not the enduring and unchanging Tao.
Or contrapositive-ly: the Tao that is enduring and unchanging cannot be trodden. (Edited to add: in reference to Mozobar Ullah's comment on Schiphol's response, which points out that 'Tao' translates as 'path', which ought by definition to be treadable, this might also be rendered as 'no Tao is eternal and unchanging'; see below my commentary on 'names'.) If we suppose that:
then the theory of the Tao more or less trivializes in classical logic. However, if we weaken the second postulate above to say that "the enduring and unchanging Tao is worth emulating as much as possible", we obtain a philosophy of life that one should try to improve one's approximation of the true way, even if one cannot be sure of having achieved the perfect truth, or indeed even if capturing the perfect truth completely is impossible — to adopt a modus of trying always to be less wrong. This is an ethical prescription which is implicit even in somewhat popular readings of Christianity.
The name that can be named is not the enduring and unchanging name.
If we assume that a name must ipso facto be nameable, we may obtain a conservative interpretation that "no name is enduring and unchanging"; or perhaps "meanings in language shift". If we suppose that the first and last 'name' actually is meant to refer instead to an idea, obtaining the reading "The idea that can be named is not the enduring and unchanging idea', we obtain a thesis about how any idea which could be communicated in words, even in principle, is unstable in time and will shift.
In short, if these sentences are perfectly representative of the Tao Te Ching, it sounds as if they are only contradictory or paradoxical to a worldview which insists that a perfectly accurate representation of the state of affairs is attainable and expressible in language. It is unsurprising that a culture such as European culture, which has historically been substantially informed by revealed holy texts and afterwards believed that truth could be captured by pure reason, or even just a small amount of reasoning supplemented with a few careful observations, might reject such a premise out of hand. But at least since Popper and Wittgenstein, even (or perhaps especially) an analytic philosopher should be prepared not only to accept these notions as plausible, but perhaps even essentially correct.
[1] Of course, you should bear in mind that, like Schiphol, I have no expertise in the Tao Te Ching, and that while this is a possible and possibly fruitful interpretation, it may well not be the canonical interpretation. But I suppose, by the very nature of the Tao Te Ching, that there cannot be a canonical interpretation; or more precisely, that the interpretation of the Tao Te Ching which can be uttered is not the 'true' interpretation of the Tao Te Ching.
