
The logic of Buddhist philosophy - gajju3588
http://aeon.co/magazine/world-views/logic-of-buddhist-philosophy/
======
throwaway13qf85
In case anyone is turned off by the expectation of wishy-washy flim-flam, it's
worth noting that Graham Priest may be a professor of philosophy, but is most
well known for his work in logic, particularly in non-standard logics (i.e.
not propositional or predicate logic) that allow non-boolean truth values, or
weaken or remove some of the axioms of classical logic.

I assume that what's relevant here will be his work on paraconsistent logics
(which allow contradictions) but I think an equally interesting line of work
is linear logics. It's of interest to computer scientists because of its
relationship to linear type theory (in the same way that the Curry-Howard
correspondence links type theory and classical logic) and because it has close
relationships with quantum computing.

In particular, you are not allowed to delete or duplicate
elements/propositions/types (corresponding to physical processes that cannot
arbitrarily create or destroy particles, the "no deletion theorem" and "no
cloning theorem" of quantum information theory), so functions of the type

    
    
      duplicate :: a -> (a, a)
    

and

    
    
      delete :: a -> ()
    

are not allowed in a linear type system. Practically, this means that many
operations can be optimized by the compiler to in-place mutations, because it
is guaranteed that there is only ever one reference to a particular object.

~~~
Retric
Fuzzy logic is a vary useful non boolean logic system.
[http://en.wikipedia.org/wiki/Fuzzy_logic](http://en.wikipedia.org/wiki/Fuzzy_logic)
In practice it's somewhat like neural net's but in a far more human readable
format and vary useful for things like washing machines that have lot's of
flakey sensors and little processing power. But the basic idea is statements
truth is percentage based. For example "this statement is true" would be 50%
true and there is no contradiction.

PS: Yet another 1960's discovery that keeps being renamed and rediscovered.

~~~
dj-wonk
Do you have personal, real-world examples of fuzzy logic being useful to you?
I find Bayesian statistics useful regularly; fuzzy logic not so much. What am
I missing?

~~~
Retric
The tradeoff between accuracy and speed. Real world devices ofen have tight
feedback loops and flakey sensors so you need something that aproximates
Bayesian logic without being bogged down.

The only real world example I have Persionaly used was a controller for a
hacked together hot tub, the basic problem was generally adapting a simple
program concept to both limited processing power and flakey data. You want to
write if temperature is > value instead you go if 70% sensors in area x say
temperature > value. You could try to find a better aproximation but the more
you calculate the longer it is until you can process more data. We also had
~380 bytes of RAM and 2000 bytes for sorce code so things needed to be simple.

Sure, you could try and find the actual energy in the hot tub water but that's
not needed, you really just want to know if the heater is on for to long with
the pump off then shutdown for safety otherwise shutdown if temperature is
probably to hot.

------
tel
_Central to his teachings is the view that things are ‘empty’ (sunya). This
does not mean that they are non-existent; only that they are what they are
because of how they relate to other things._

Immediately I thought of Category Theory as this statement is a not terrible
expression of what CT tries to teach. I'll immediately recommend the paper
Numbers Can Be Just What They Have To
([http://www.cwru.edu/artsci/phil/NumbersCanBeJustWhattheyHave...](http://www.cwru.edu/artsci/phil/NumbersCanBeJustWhattheyHaveTo.pdf))
for more exploration.

Briefly, while CT is usually "bootstrapped" off having a notion of objects
_and_ their relations, it becomes quickly obvious that focusing on the objects
themselves is useless—they are given no emphasis in CT and thus wither away to
being nothing at all. Instead, absolutely every interesting property of the
objects must be expressed in _the relations they take with other objects_.

This is formalized in the Yoneda Lemma which, in a not terrifically
generalized form, can be written

    
    
        forall a . (forall r . (a -> r) -> r) <-> a
    

which is to say "the collection of all ways to relate an object to other
objects is isomorphic to the object itself".

So what's the point? Well, as the paper linked above suggests, sometimes the
"intrinsic nature" of things makes them very difficult. We'd often like to
equate two things which "ought to be the same" but aren't because their
intrinsic nature differs. If you work in standard mathematics (set theory) you
run into this problem because everything is described as having an intrinsic
nature derived from sets. If you work in CT-based math you have no such issue
because objects fail to have intrinsic natures altogether. They only have
their "extrinsic" natures, their relations to other things.

~~~
dietrichepp
Haskellers may recognize (a -> r) -> r as a way to represent "a"... you'll see
that type signature in more than a few libraries.

~~~
gohrt
For what purpose? Surely the type checker doesn't recognize the equivalence.

    
    
        a1 :: a
        r1 :: r
    
        f :: a -> r
        f a1 = r1
    
        b :: (a -> r) -> r
        b f = f a1 -- == r1
    
    

but `a f` is ill-typed.

    
    
        m :: a -> (a -> r) -> r
        m a1 f = f a1  -- m === (flip ($)) === (flip id)
    
    

So it appears that `(a -> r) -> r` is a "co-value" that can be applied to a
function (resulting in the application of the function to the underlying vale
of type `a`, dual to the usual situation where functions are applied to
values.

~~~
tel
This is pretty much exactly correct. The common terminology is that `forall r
. (a -> r) -> r` is the Continuation Passing Style transformed version of `a`.
At the end of the day, `CPS a` is useful whenever CPS is, but also more often.

sometimes you see CPS (a.k.a. Church-encoded) forms of values in Haskell in
really tight inner loops as the compiler can optimize them better.

You also see a variant of it occurring in Free monad structures because it
allows you to re-associate the binds to make them much more efficient.

You also see it sometimes when making monads over categories other than
Hask—it lets you pretend you're working with a Hask monad (and thus use do
notation) for a while and only "pass through" the real category at fixed
points in time. This lets you, for instance, write a monad for Set even though
normally you couldn't due to the need for the Ord constraint.

------
joelmichael
Paradox is not really so alien to Western philosophy, as this article
initially suggests. It does end up referencing a number of modern Western
philosophers, but the idea is older than that. It's ironic he refers to
"Western orthodoxy" as being strictly anti-paradox, as traditional Christian
theology is full of official paradoxes; a major example would be the doctrine
that Jesus is simultaneously fully human and fully divine. Many were declared
anathema for refusing this and other paradoxical doctrines. So rather than
Western orthodoxy being unaware of paradox, it has insisted on it. The concept
of the dialectic also touches on this idea of reconciling apparent
contradictions, rather than defeating your opponent as one does in a debate,
and this idea originates not truly with Hegel but spans all the way back to
Socrates, and probably before.

I agree with the sentiment, however, that understanding paradox is extremely
important to a person's capability for nuance and understanding. If you insist
on a simplified internal consistency, you will end up sacrificing (and
demonizing) whole parts of your thought process rather than trying to
reconcile them as having some truth. It can be a process of self-
indoctrination purely to avoid the pain of confusion. Another way to think of
paradox is simply rejecting false dichotomies in favor of a more complex and
uncertain reality. I don't think the lesson here is to "break the chains of
Aristotelian logic" (God forbid) but rather, well, reconcile it with the idea
of paradox.

~~~
livingparadox
I would clarify that the "paradox" of being fully human and fully divine is an
apparent paradox, not an actual paradox. Most theologians I've come into
contact with hold to Jesus' nature being the intersection of all divine traits
and all human traits, allowing him to be both God and Man without
contradiction.

The confusion I think lies in the ambiguity of the word "fully". Its a paradox
if we take it to mean "100% of Jesus is human and 100% of Jesus if divine,
resulting in a total of 200% Jesus." But if it is clarified as "Jesus
possesses 100% of the qualifications required to be considered human and Jesus
possesses 100% of the qualifications required to be considered divine," then
the contradiction is gone.

~~~
septerr
Is there any statement/belief in Christian philosophy that

Human cannot be divine

or

Divine cannot be human?

If there is then the paradox does exist.

~~~
relampago
"Most assuredly, I say to you, he who believes in Me, the works that I do he
will do also; and greater works than these he will do, because I go to My
Father.”

------
Strilanc
I would have enjoyed this article if it dropped the Buddhism and kept the
math.

Alternate logics are interesting, but you tend to be able to reduce them into
each other in the same way that universal turing machines can simulate each
other. They don't add new functionality, they add succinctness. So it's really
strange to me to frame them as _totally different philosophies_.

For example, it is the case that self-referential statements don't always have
well-defined truth values and that allowing them to have values like {} and
{false,true} is a fruitful way to think about it. But this approach can be
grounded in two-valued logic (and vice versa), and it doesn't solve the
problem of self-reference (consider "This statement is not {}, is not {false},
is not {true}, is not {false,true}").

~~~
pera
> I would have enjoyed this article if it dropped the Buddhism and kept the
> math.

May I ask you why? Personally I enjoy reading about the origin of some
particular idea/philosophy, even when it's purely anecdotal.

~~~
alex-g
It's interesting, but the problem _I_ have with the presentation is that the
modern manifestation of this idea has nothing to do with Buddhism. While we
can maybe say that Buddhism came up with some similar-looking stuff, there's
no causal link, and the philosophical systems are not working within the same
paradigm. Like seeing a human face on the surface of Mars, this is an example
of coincidence more than any deep connection.

Well, OK, that's unfair, because Buddhism and formal logic are both human
endeavours, and have to deal with the same facts. But this disconnect is even
true with parts of Greek philosophy. "Atoms" as we understand them are very
different from "atoms" as Aristotle thought of them, even though there is a
historical connection. Today's chemists would do badly if they relied on
Aristotle for anything other than historical curiosity.

~~~
s_baby
>It's interesting, but the problem I have with the presentation is that the
modern manifestation of this idea has nothing to do with Buddhism. While we
can maybe say that Buddhism came up with some similar-looking stuff, there's
no causal link, and the philosophical systems are not working within the same
paradigm. Like seeing a human face on the surface of Mars, this is an example
of coincidence more than any deep connection.

Philosophies have been swapping ideas for thousands of years and it shows.
Take a look at thinkers like Plotinus for example. He lived in Alexandria back
when it was a multicultural metropolis hosting people from across the known
world. His philosophy uses ideas and language you would expect to find in
eastern traditions. Thanks to his extensive influence you will also find this
jargon in western philosophy, christianity, islam, etc... This might not seem
relevant to you. But if you know the historical connections between neo-
platonism and philosophy of math it might.

[http://en.wikipedia.org/wiki/Plotinus](http://en.wikipedia.org/wiki/Plotinus)

------
tel
If you only want to go partway to catuskoti, consider the intuitionistic logic
of Heyting and Brouwer. This is the actual form of logic which has the Curry-
Howard isomorphism with lambda calculus. In particular, it rejects PEM but not
PNC.

What does this world feel like? Well, let's assume we've formulated a
proposition. In type theory syntax we'd write the body of the proposition `B`
and give it a name `p` like so

    
    
        p : B
    

Here p is just a symbolic name and B is some formal language expression which
describes the proposition p.

It's important to note that while we've immediately written this proposition
but we've not established whether it is true or false. PEM would imply that
the state we are in currently is unstable—p must be either true or false
already!

Intuititionistic Logic, however, admits that the state of almost all
propositions is far closer to what p is now—neither proven nor refuted. This
neither-true-nor-false state is natural and only through a process of
communication and work can we move forward. For instance, we could construct a
proof of p

    
    
        p : B
        p = proof1   -- note how this looks like a typed program now
    

or we could construct a proof of its refutation

    
    
        notp : not B
        notp = proof2
    

But we might be incapable of either. It is unclear whether a program searching
through the space of possible proofs would ever terminate, one might note.

What's immediately nice about this system is that it can model internally the
notion of an independent statement—all statements are assumed independent
until proven otherwise even!

It also reflects the nature of (functional) programming (of a certain style)
where we define the type we're hoping to achieve and then work to create a
program satisfying that type.

Note finally that Intutionistic Logic still holds that PNC is true. In
particular, we can trivially prove the following proposition

    
    
        notPNC : forall prop . not (prop AND not prop)
        notPNC = /\_ -> \(p, np) -> np p    -- this is a legitimate proof term written in (System F) lambda calculus

------
wpietri
Very interesting.

It reminds me that I think an early start on programming made some Buddhist
concepts easier for me to get. In particular for me there's a strong
connection between using software to model the world and the Buddhist doctrine
of emptiness, the notion that nothing exists in its own right:
[https://suite.io/matthew-bingley/1z8s2kx](https://suite.io/matthew-
bingley/1z8s2kx)

I started coding young, and over time I gradually came to see that any
computational representation of the world was always false. The act of writing
software was always an editing of the real world, a discarding of everything
that wasn't apparently material to my particular purpose. Changing software
was sometimes a recognition of ignorance or fallibility, but often showed me
how changing purpose changed what the maximally useful model was.

Years of that experience, combined with things like Douglas Hofstadter's work,
made the apparent contradictions of Zen much easier for me to follow.

I think that also primed me to be ready for the Agile movement. Early on, I
had strong BDUF tendencies. But once I gave up believing that there was _one_
right model, _one_ right design, I lost my taste for BDUF. So when people
claimed we could keep our software as flexible as our understanding, that was
very exciting for me.

~~~
dj-wonk
In my experience, I have found that in some key Buddhist works that the
apparent contradiction is a literary device for learning. I don't think that
contradictions are intended to persist and represent a "finished" philosophy.

~~~
wpietri
Hm. I've seen some of that, for sure. But for me the contradictions also point
out the long-term weakness of taking conceptual frameworks too seriously. Our
conceptual models of the world, like our software models, are temporary
structures that we use for particular purposes. Eventually, we throw them all
away. The map is not the territory, and there is no perfect map, just the
right one for the moment.

Thus it is reasonable for Buddhists to advocate the end of Buddhism. E.g.:
[http://www.shambhalasun.com/index.php?option=content&task=vi...](http://www.shambhalasun.com/index.php?option=content&task=view&id=2903Itemid=247)

------
noisy_boy
For the benefit of non-Hindi/Sanskrit speakers: the pronunciation of
"catuskoti" starts with "ch" (as in "chat") and not as in "cat". "chaet" is
the prefix signifying "four".

------
tremols
Much of the mysticism and misunderstandings about indian philosophy comes from
a very bad habit in the translation of indian works where some words are left
untranslated as to give them a magical-religious cool sounding sanskrit aura.

If koti means corner, there is no reason that 'koti' should appear in a
translation instead of corner otherwise you are giving it a special importance
that distracts from the text's true meaning. Almost every translation of
indian philosophy suffers from this fetish for the sanskrit language and as
beautiful as sanskrit is, it shouldn't contaminate the purpose of a
translation.

~~~
1stop
I was under the impression this was done because the english translation loses
some meaning or context.

The idea that every concept can be translated is probably a false one. Ideas
are built on cultures, cultures are described by language you can't change one
without changing another. So when describing an idea generated by a culture,
using a secondary idea and secondary culture, you will lose things.

That is why (for example) nirvana, has a bunch of translations: awakening,
calmness, relief, void/voidless, the light, nothingness, or (my favourite)
phew. Because we don't have the context to properly describe that in the west
(latin-germanic based languages), so we need a bunch of other concepts that
kind of point at it.

~~~
kazagistar
If a concept cannot be translated between languages, it seems likely that it
cannot be translated properly between people either. Or do you mean directly
translated? The concept of nirvana is ill defined if you cannot directly
describe it, and can only point at it.

~~~
1stop
ill defined in one language, doesn't mean ill defined in another.

I'm saying language and culture are inextricably linked. And not 100%
compatible with all other languages and cultures.

------
nabla9
Henk Barendregt (known for his work in lambda calculus and type theory) has
good explanation of the apparent contradictions in tetra lemma.

Buddhist Phenomenology - 1.7 Explaining apparent contradictions:

[http://www.cs.ru.nl/~henk/BP/bp1.html#SECTION000270000000000...](http://www.cs.ru.nl/~henk/BP/bp1.html#SECTION00027000000000000000)

In other words: And Now for Something Completely Different...

------
logicchains
The logic of Buddhist philosophy: emotional attachment to and/or desire of
impermanent things has the potential to result in dissatisfaction, as
impermanent things are impermanent. It's hardly rocket science. Desire
nothing, and you'll never never feel the dissatisfaction of not getting what
you want. Be attached to nothing, and you'll never feel the pain of losing
something.

Some quotes by emperor Marcus Aurelius, of the Stoics, expressing a similar
idea:

"You have power over your mind - not over outside events. Realize this, and
you will find strength."

"If you are distressed by anything external, the pain is not due to the thing
itself, but to your estimate of it; and this you have the power to revoke at
any moment."

~~~
xmonkee
This is a rather gross oversimplification. What you state is true, and is in
fact the essence of the first 2 noble truths, but that's hardly the meat of
"the logic of buddhism". The hardest attachment is that to the self, and the
hardest realization is that the self itself is impermanent. To have the "right
view" of the self, one has to understand the illusory nature of phenomena and
the paradoxial nature of awareness itself. Awareness, is one of those things
about which none of the following can be said: 1) that is exists, 2) that is
doesn't exist, 3) that is both exists and doesn't exist, and 4) that is
neither exists nor doesn't exist.

Buddhism is very simple, but at the same time it can take "many lifetimes" to
achieve true understanding of it.

~~~
logicchains
The illusory nature of the self can also be explained relatively simply to
anyone who's familiar with the justification problem[1]. What 'is' the self
and what 'is not' the self? That requires a metric for deciding. But that
metric in turn requires another metric to determine its validity, and so on ad
infinitum. The concept of self is thus arbitrary, and hence logically
meaningless. Wittgenstein expresses this idea far better than I do here, in
his Tractatus[2].

This equally applies to all phenomena; any attempt to divide anything up into
'things' is ultimately arbitrary, as it relies on ultimately unsubstantiated
metrics, and hence is without meaning.

1\.
[http://en.wikipedia.org/wiki/Regress_argument](http://en.wikipedia.org/wiki/Regress_argument)
2\.
[http://philosurfical.open.ac.uk/tractatus/tabs.html](http://philosurfical.open.ac.uk/tractatus/tabs.html)

~~~
orasis
Explaining the illusory nature of the self isn't important. _seeing_ , in real
time, the illusory nature of the self is what brings liberation.

------
gambiting
This made me think of an interesting way I have heard some people answer the
question "if God is omnipotent, then can he create a rock so heavy he wouldn't
be able to lift it and then lift it? If yes, he is not omnipotent, if no, he
is not omnipotent!" with a logical leap also hard to comprehend to western
minds - he can do both, and that's why he is considered omnipotent. He doesn't
need to follow human logic, hence the third option - creating a rock too heavy
to lift and lifting it.

I am completely non-religious,but as a logical riddle it always fascinated me
that there could be a "third" option.

~~~
thyrsus
A rock too heavy to lift would be a rock inside the event horizon of a black
hole, if one can stipulate that the rock still "exists".

My own attitude toward paradoxes concerning God is that understanding is a
gift - awesome in its comprehension of the universe from big bang to Planck
length scale interactions. Nonetheless, the understanding given to us as
finite beings will be incomplete and approximate. If we avoid every other end,
dementia will eventually remove what little understanding we have. I hold that
rejection of the gift of understanding - e.g., the six day materialist
biblical interpretation - is a grave error. Nonetheless, I hold that entities
(or sets of relations) exist for which I will never have a consistent or
correct rational model - and that one of those is God. Other instances are my
fellow humans, and even myself. It should go without saying, ignorance does
not preclude fascination with, delight in, nor love for those beings.

------
zenogais
"An abhorrence of contradiction has been high orthodoxy in the West for more
than 2,000 years."

Not necessarily so, just a particular branch of western thinking and tradition
now widely called the analytic tradition. GWF Hegel and Karl Marx had
philosophies that deeply and profoundly embraced contradictions. Neither tried
to abolish them, but instead to embrace them. To quote Marx in "Capital Volume
1":

"This is, in general, the way in which real contradictions are resolved. For
instance, it is a contradiction to depict one body as constantly falling
towards another and at the same time flying away from it. The ellipse is a
form of motion within which this contradiction is both realized and resolved"

In other words, contradictions are not resolved but given room to move within
forms. This was a move deeply influenced by Hegel, whose Logic embraced
contradictions and sought to sublate them in higher forms.

~~~
vidarh
In Marx case - at least in your example - he is not using "contradiction" in a
formal logic sense. He is using it in the sense of the contradicting forces of
_dialectical contradictions_.

Marx specifically used different terms when referring to contradictions of
formal logic.

~~~
grifpete
Exactly. (just posted same point.) Even those 'dialectical contradictions' are
perhaps better described as opposing forces that set in train a dialectical
resolution.

------
simondedalus
nagarjuna's point is not that contradiction or many-valued logic can be
tolerated. nagarjuna, who is addressing a specific set of buddhist logicians,
is finding paradoxes in logic in an attempt to break those logicians clinging
to logic, and (somewhat presciently in the history of buddhism) suddenly
enlighten them. he, like most buddhists, is not making any ontological or
metaphysical claims whatsoever.

it's similar to kant's antimonies. he is not trying to assert contradiction
exists, he is trying to point out why we need to countenance ideas like a
distinction between noumina and phenomena. or like zeno's paradoxes, which
have a rhetorical purpose: to confirm zeno's teacher parmenides's claim that
the universe is one undifferentiated whole. see also plotinus, who does
roughly the same thing (any real ontological difficulty posed by the paradox
of plurality is uninteresting to them; they have a thesis and their statement
of the paradox is for a purpose).

incidentally, i don't mean to slag graham priest too much. after all, j.c.
beall was my logic professor, and i'll always fondly remember how he
introduces every new step in a proof by saying, slowly, "now holllld on, what
about (etc)." the dialetheists will always hold a place in my heart. that
said, i think godel did about all that need be done with the liar's paradox,
and we ought to be wittgensteinians regarding language in the first place
(words mean what they do in virtue of their being used by agents for a
purpose; you cannot fully enumerate representational content of an utterance
solely in virtue of its shape. all utterances are context sensitive. for more,
see the almost unreadable but spot on work of charles travis, e.g. unshadowed
thought).

[http://www.thezensite.com/ZenEssays/Nagarjuna/Nagarjuna_and_...](http://www.thezensite.com/ZenEssays/Nagarjuna/Nagarjuna_and_Skillful_Means.htm)

[http://homepages.uconn.edu/~jcb02005/](http://homepages.uconn.edu/~jcb02005/)

[http://www.amazon.com/Unshadowed-Thought-Representation-
Lang...](http://www.amazon.com/Unshadowed-Thought-Representation-
Language/dp/067400339X)

------
shawndumas
An "abhorrence of contradiction" is necessary for him to even begin to express
his having eschewed his former "parochialism". To have said, "abhorrence of
contradiction" he has demonstrated an abhorrence of contradiction -- in the
very act of making his declaration.

The Principle of Non-Contradiction (PNC) means that every word in the sentence
"The line is straight" has a specific meaning. 'The' does not mean 'any',
'all', or 'no'. 'Line' does not mean 'dandelion' or 'doughnut'. 'Is' does not
mean 'is not'. 'Straight' does not mean 'white', or anything else. Each word
has a definite meaning. In order to have a definite meaning, a word must not
only mean something, it must also not mean something. 'Line' means 'line', but
it also does not mean 'not-line' — or 'dog', 'sunrise', or 'monkey'.

If 'line' were to mean everything, it would mean nothing; and no one,
including him, would have the foggiest idea what he means when he says the
word 'line'. PNC means that each word, to have a meaning, must also not mean
something. And so; anyone who argues against an "abhorrence of contradiction"
must use PNC for that statement to even mean anything, thus undercutting his
own argument.

\----

"There exist, indeed, certain general principles founded in the very nature of
language, by which the use of symbols, which are but the elements of
scientific language, is determined. To a certain extent these elements are
arbitrary. Their interpretation is purely conventional: we are permitted to
employ them in whatever sense we please. But this permission is limited by two
indispensable conditions, first, that from the sense once conventionally
established we never, in the same process of reasoning, depart; secondly, that
the laws by which the process is conducted be founded exclusively upon the
above fixed sense or meaning of the symbols employed."

—George Boole, An Investigation of the Laws of Thought

~~~
dllthomas
I don't see that _every_ violation of the principle of noncontradiction
trivially leaves _definitions_ meaningless. Suggesting that a principle
shouldn't be taken to hold in general doesn't mean that you have to violate
the principle at every opportunity, just that there is some place it is (in
whatever sense) correct to violate the principle. Of course, under traditional
logics, accepting a contradiction leaves everything provable - but we're
dealing with nontraditional logics that _may_ have other ways of dealing with
that.

~~~
shawndumas
by ' _every_ violation' do you mean ' _any_ violation', ' _no_ violation', '
_blue_ violation'...

by 'every _violation_ ' do you mean 'every _observance_ ', 'every _miss-fire_
', 'every _monkey_ '...

you see, apart from the law of non-contradiction language is impossible.

~~~
GnarlinBrando
That's just being difficult. The real world does work that way. Take poltical
labels for example, liberal, conservative, et al have totally different
meanings for different people. Contradictions do exist, just externalizing
them in a formal system is lazy.

~~~
dllthomas
I don't think linguistic ambiguity - while clearly something that exists - is
the same thing as what is under discussion in this post.

------
ableal
(Just a quick note, don't have time for more now.)

 _" The great lodestar of the German Enlightenment, Immanuel Kant, said that
there are things one cannot experience (noumena), and that we cannot talk
about such things. He also explained why this is so: our concepts apply only
to things we can experience. Clearly, he is in the same fix as Nagarjuna. So
are two of the greatest 20th-century Western philosophers. Ludwig Wittgenstein
claimed that many things can be shown but not said, and wrote a whole book
(the Tractatus), explaining what and why."_

The jump from Kant to Wittgenstein elides the step that was Schopenhauer, who
did look East and said some cogent things.

~~~
KrisAndrew
Wittgenstein would say that the Buddha and Schopenhauer were playing a quite
similar language-game.

~~~
ableal
He might say that, but I think "language-game" is not quite the right take.

Anyways, to shore up my impression I looked up "Schopenhauer eastern
philosophy" and hit a few things. The "Schopenhauer and Buddhism" piece by
Peter Abelson ( at [http://ccbs.ntu.edu.tw/FULLTEXT/JR-
PHIL/peter2.htm](http://ccbs.ntu.edu.tw/FULLTEXT/JR-PHIL/peter2.htm) ) seems
good:

 _" When the tenets of Buddhism became known in Europe during the third and
fourth decade of the nineteenth century, Arthur Schopenhauer was delighted
with the affinity they showed to his own philosophy. Having completed his main
work Die Welt als Wille und Vorstellung as early as 1818, he considered it an
entirely new (and thus pure) expression of the wisdom once taught by the
Buddha."_

I would have been gladder if the original article, by a professional
philosopher, which I am not, had said something about this.

------
dj-wonk
I can appreciate the depth of research behind the article. The many-valued
notions of logic are quite helpful. Here's are two ways that I would distill
the message for different audiences.

1\. A computer science audience: Not all sentences have a computable boolean
truth value. Here's why. To find the truth value of the sentence "This
sentence is false.", you have to figure out the truth value of the following
statement (call it X1): "Whether or not this sentence is false depends on if
X1 is true or false." Put that way, you can immediately see the circularity in
computation. From a computer science perspective, there is no terminating
condition. The function will never complete, so there is no computable boolean
truth value.

2\. To an educated, but non-technical, audience: Just because a sentence
asserts something doesn't mean there is any guarantee of the result being
"truth" or "falsehood". The truth value of this "This sentence is false." is
simply "undecidable" or "ineffable" \-- pick a word. So, just live with the
fact that not everything is true or false. Note: I'm _not_ saying that the
statement is really one or the other but we just can't figure out which (as in
Schrödinger's cat); I'm saying that neither "true" or "false" makes any sense
for that kind of self-referential sentence.

This really isn't mind-blowing. Many articles write up these "paradoxes" as if
they are insurmountable. They aren't.

All of this said, I think many philosophical writings, especially Buddhist
writings, use contradiction as way of promoting thinking and careful
decomposition of the essence of things. In short, complex things consist of
parts that vary over time. So their components or transient values can seem to
change or stand in contradiction.

There is no contradiction in Dickens writing "It was the best of times and it
was the worst of times." in my opinion. This is just a literary device to show
contrast eloquently, because saying "In some regards, it was the best of
times. In other regards, it was the worst of times." is not as memorable or
striking.

~~~
virtualwhys
> In short, complex things consist of parts that vary over time. So their
> components or transient values can seem to change or stand in contradiction.

Forgot something, one's self is also transient. Given that the observer itself
is constantly changing, mind blowing is possible.

------
anuraj
Sankara (8th century CE) talks about two types of truth - 1) Kevala Satya
(Absolute Truth) and 2) Vyavaharika Satya (Relative Truth) - He also says that
people who are not one with the Absolute truth (One with God - liberated) can
only discern the Relative Truth. He called this state - Maya (illusion). Looks
like he was talking similar to Gorampa. To be noted is Sankara was extremely
knowledgeable about Budhist thought - and is often called Abhinava Budha (Neo
Budha) and was instrumental in propagating Neo Hinduism based on Adwaita (Non
Duality) defeating the Budhist schools of the day using their own arguments.

------
doxcf434
It's interesting that the west would write off eastern philosophy, as though
the eastern philosophers were unaware of the seeming contradictions and that
there may be a deeper reason for that.

~~~
feralmoan
I think by extension of the Platonic school of thought Western culture has
become deeply ingrained in dichotomous thinking applying such constraints to
all areas of life (beyond simple science and logic), whereas Eastern non-
dualism supposes all things (existentially) being equal. Neither West or
Eastern philosophies do a very good job of describing each others domain space
and yet they share many similar concepts. Karma (Theoretical) vs Causality
(Empirical) is a basic example - they're exactly the same but few Westerners
and particularly those in academic circles would admit to such a thing as it
undermines Western status quo.

------
jotux
I'm going to go meta here and say the hn discussion here is just fantastic.
This is the reason I frequent hn and I wish more submissions would spur
discussions of this quality.

~~~
visarga
Yes, guys, where have you all come from? There is just tech and politics talk
for months, and then suddenly, religion and philosophy pops out - and everyone
is talking at a very high level. How come?

------
logfromblammo
Silly Buddhists. Everyone knows that there are nine possible logic values:
false, true, unknown, uninitialized, irrelevant, indeterminate, weak false,
weak true, and high impedance. Didn't Siddharta read the IEEE 1164 standard?

------
ap22213
Could someone explain why Priest, in discussing the 'four corners', presents
the Hasse diagram with {F} at the bottom? Why would it not be {}? I'm not too
familiar with posets, but it seems the order matters, right?

~~~
throwaway13qf85
Intuitively, it is to indicate degree of 'truthiness'. Certainly false {F} is
less truthy than either both true and false {T,F} and neither true nor false
{}, which are in turn less truthy than certainly true {T}. The Hasse diagram
indicates that there is no relationship between {} and {T,F} in terms of level
of truthiness.

More mathematically, you can think of the Hasse diagram as a lattice, with the
meet and join operations being AND and OR. For example, we are used to
thinking of the expression

    
    
      p AND q
    

as being true if p is true and q is true. But what if we have four values: {},
{T}, {F} and {T,F}? The Hasse diagram tells us how to interpret expression
like this - p AND q is the meet (greatest lower bound) of p and q, and p OR q
is the join (least upper bound) of p and q. So for example,

    
    
      {F} AND {T}   = {F}
      {F} OR  {T}   = {T}
    
      {F} AND {}    = {F}
      {F} AND {T,F} = {F}
      {F} OR  {}    = { }
      {F} OR  {T,F} = {T,F}
    
      {T} OR  {T,F} = {T}
      {T} OR  {}    = {T}
    
      { } OR  {T,F} = {T} // I think..!
      { } AND {T,F} = {F}
      { } OR  { }   = { }
      { } AND { }   = { }
    

The Hasse diagram in the article makes sure that expressions like this agree
with our intuition in the cases where we have intuition for what the result
should be, and give us a way to interpret expressions consistently when our
intuitions fail us.

We're used to seeing Hasse diagrams for subsets of a set S used to indicate
inclusion, in which case you would have {} < {F}, but you can have a valid
poset structure that's not based on inclusion.

------
dpweb
Nature is to have no nature, taken literally that is a contradiction, but
isn't it possible that is not meant to be taken literally, but to illustrate
for instance that everything we hold dear is really just a construct. What we
call "nature" isn't true essence but our interpretation of what we think
essence is?

Jesus for instance freely admitted he taught in parables, and so everything
was not to be taken word for word literally. Doesn't make it any less true,
but when interpreted literally you can come to some incorrect conclusions.

------
arh68
Seems like statements can have both verity (truthiness) and falsity in varying
quantities. They might sum to 0, 1, or anything at all. Whether a statement
has _meaning_ seems important, too. '2020 will be a rainy year.' does not have
meaning (yet). Pretty soon, though, the universe will reach a certain point
where that statement starts to accumulate verity & falsity. Maybe 2020 will be
a peak monsoon season in the Eastern Hemisphere; verity++. Maybe it'll be a
record drought in North America, too; falsity++. This is not a 1-dimensional
spectrum.

Seems like meaning is some sort of vector norm over || < verity, falsity > ||.
It should be easy to imagine scenarios all across this unit square for '2020
will be rainy': (0,0) is now, (1,0) means lots of agreed-to raining
everywhere, ( .9, .9) is crazy weather, and ( .2, 1) means it was mostly dry
that year.

This seems heavily reliant on _human interpretation_ , but trying to extract
"intrinsic truthiness" will always rely upon some global context telling you
what the rules are. '2 = 3' is absolutely true, depending on what you think
the rules are.

'Correctness' seems to correspond to (verity - falsity), which is why ( .9,
.9) is certainly _meaningful_ but doesn't improve on the correctness of saying
2020 is rainy.

I have a haunting feeling GEB talks about this, though I never finished
reading yet.

------
wwweston
> If something is ineffable, i, it is certainly neither true nor false.

Wouldn't it instead be the case that it's simply not expressible inside a
given formalism (or other form of expression)?

~~~
wyager
That is absolutely the case. If something is "ineffable", it's probably
logically ill-defined, and we should treat anyone who tries to use something
"ineffable" in formal argument as a mystic spouting hogwash.

~~~
muhuk
This seems like a valid argument to me. Could one of the downvoters perhaps
care to point out the errors in it. Or is it just because of the word
'hogwash'?

~~~
wyager
I'm very concerned at the number of people on HN who seem to have bought into
this religious mysticism disguised as math. That's one of the oldest tricks in
the book.

~~~
muhuk
But logic is subjective and reason is impotent. What is the purpose of
philosophy other than to protect us from acquiring knowledge about reality?
We'd be defenseless without faith and mysticism.

------
awakened
"The only correct view is the absence of all views." \- Thich Nhat Hanh (Thay)

~~~
vram22
That statement is false :)

------
kalaya
If you want to learn more about this catuskoti, meaning ‘four corners’
theories there are another one threekoti, meaning ‘three corners’ you need to
check Prof. Nalin de silva's works. [http://kalaya.org/](http://kalaya.org/)

Unfortunately foreigners most of his work is in sinhala. And only foreigners
learn that language is germans,russians,chines and japanes diplomats.

------
smithy44
Could the 'easterners' point be the avoidance of reification and the
limitation and mental trapping that involves? For example, we say we see a
tornado. But there is no essence of the tornado, no 'thing' there.. it is a
perceptual grouping of a set and series of events. Nevertheless, functionally
there very much is a tornado. 'It' has its conditions, states, and results.
(But there is only the wind...) (And in some visions of physics, this goes all
the way down to the vacuum.) Renaming for clarity of action is useful, but no
new substances are generated by the act. (One doesn't have to think in terms
of the objects in someone else's code nor in terms of the lumped matter
discipline.) So if one can think outside of the perceptually given externally,
how much more so might it be useful to do so in relation to internals, i.e.
'my anger'.

------
weatherlight
I can't remember the last time I read an an article and it's discussion on HN
that I enjoyed this much.

------
wyager
How the hell are there this many people here who buy this hogwash?

>Nagarjuna often runs through the four cases of the catuskoti. In some places,
moreover, he clearly states that there are situations in which none of the
four applies. They don’t cover the status of an enlightened person after
death, for example.

Are you kidding me? This article isn't even about formalizing non-boolean
logic. It's thinly veiled religious propaganda, artificially ascribing
mathematical formality to a mystical religion.

And yes, statements are either true or false. If you can't say a statement
will be either true or false (you don't have to know which one), the statement
is ill-defined. Non-binary logical systems are useful only insofar as they
allow us to model uncertainty, not because they reflect the nature of reality.

~~~
muhuk
"The truth or falsehood of all of man’s conclusions, inferences, thought and
knowledge rests on the truth or falsehood of his definitions." \- Ayn Rand

------
novalis78
Its strange that he brings Nagarjuna in when discussion sunnyata as this was
already clearly spelled out in the sutta's themselves. Two books that discuss
this very well are [http://www.amazon.com/Concept-Reality-Early-Buddhist-
Thought...](http://www.amazon.com/Concept-Reality-Early-Buddhist-
Thought/dp/9552401364) and [http://www.amazon.com/The-Magic-Mind-Exposition-
Kalakarama/d...](http://www.amazon.com/The-Magic-Mind-Exposition-
Kalakarama/dp/9552401356)

------
vram22
Interesting thread, though I could not understand all of it (tongue in cheek).
I'm going to lighten up the mood a bit by posting this link to a blog post I
wrote a while ago - Bhaskaracharya and the man who found zero:

[http://jugad2.blogspot.in/2010/06/bhaskaracharya-and-man-
who...](http://jugad2.blogspot.in/2010/06/bhaskaracharya-and-man-who-found-
zero.html)

------
grifpete
The bizarre states uncovered by quantum mechanics resulted in a million
popular works trying to distill quantum reality into a world in which multiple
states could coincide even at the macro level. We know that this is true at
quantum scale, it has been a little harder to swallow at the level of everyday
reality.

------
jqm
This is an awesome article.

So much of our daily life in the west rests directly on fundamental
assumptions we make about reality. I believe it's mind expanding to have those
base assumptions challenged from time to time.

------
transfire
It is amazing how tangled men can get in their own thoughts and words. The
concept of ineffable is nonsense from the outset. By the definition given, if
something were truly ineffable, not a word has been spoken about it. What is
being contorted here is the difference between the limitations of words to
describe an experience, which is the Buddhist ineffable, and the idea of the
unassailable noumena, which is the Reality that might be outside of any
experience we can have. There is also nothing mysterious or limiting about
Western logic. A statement is either true or false; or it is a contradiction
(which generally means a premise was false), or indeterminate (which simply
means that no one knows which it is).

------
kirab
This is nice. I'm wondering how much our restricted thought environment (x can
only be true or false) has hindered our development in the last thousands of
years?

~~~
wfn
I'm wondering how much Aristotle's metaphysics of essence may have hindered
certain paths of thought. :) You must admit, his base system is powerful and
ever-penetrating (Descartes is probably a very good example, but it's only one
of the more obvious ones...)

Of course it's easy to say things like that, and harder to come up with a
consistent (pun intended) metaphysical system on your own self. :)

~~~
vram22
Speaking of Descartes, I've always thought that the famous quote supposed to
be by him, i.e. "I think, therefore I am":

[http://en.wikipedia.org/wiki/Cogito_ergo_sum](http://en.wikipedia.org/wiki/Cogito_ergo_sum)

is (vaguely? :) wrong. Shouldn't it be: "I am, therefore I (can) think"?

~~~
wfn
Hmm. I don't think so, but, feel free to expand your opinion (why do you think
it should be "I am, therefore I (can) think"? Maybe you have an interesting
point to make?)

Re: etymology, it's pretty much "think => exist."

Re: conceptual level: well, one of the texts where this whole concept/causal-
chain is introduced is in his "Meditations on First Philosophy"[1], in
particular, in Meditation 2.

Very (very) roughly (and from bad memory), the idea is that one can first
start casting into doubt everything that there is (skepticism as a method)
(this is Meditation 1.) When you abstract enough times, you can start doubting
even the certainty of things which may seem true in themselves (this latter
notion is an endless field of debate in itself; see e.g. Quine's "Two Dogmas
of Empiricism"[2]) - cliche example is "2+2=4."

Say there's a deceitful daemon: each time the thought "2+2" is produced, the
daemon "intercepts" the answer and produces a "5". (Yes, I'm saying that
Descartes may be one of the originators of the concept of a MitM, ha!) (Also,
this doesn't work so well with mathematics, since again, one could say that
mathematical statements are "analytically true", and it's simply not true that
one may mistake a "5" for a "4". But imagine something more mundane: each time
you think if there is a god, the daemon deceives you into thinking there isn't
one; whatnot.)

So now you generalize the doubt process enough to start doubting whether
_anything_ exists, what-so-ever. The point is not so much in thinking that
there isn't anything, but in removing _certainty_ from usual ontological
assumptions (what (kinds of) things exist.)

So now you're not certain if there is an "I": you are able to doubt it.

But then Descartes says that this very process of certainty-removal requires
an operation (he doesn't use these words, did I say this is extremely rough):
namely, the "doubt" itself. "Doubts are to be had."

Or, if you will (and closer to D. (I think)): if an evil daemon can cast into
doubt even the existence of your own self - it it can deceive everything, etc.
- there needs to be a something to be deceived. Or at the very least, _the
process of deception (or: of doubt) does happen_ (if you want to cast
everything into doubt.)

So if you doubt that anything exists and hence can not be certain of anything,
then it so happens that this requires doubt "to happen." Hence "doubt exists."
(He also says (I think) that, basically, "clearly since I am doubting right
now, _doubt does happen_ ". A kind of phenomenological argument, which doesn't
really stick with me, fwiw. He then starts using the notion of "clear and
distinct perception", and that's where things go downhill imho (Meditation 3,
a (kind of circular) proof of God, etc.) But I have few qualms about
Meditation 2, and this includes cogito ergo sum.)

(You could say that the only thing one can be certain of is that "there are
thoughts" (not an "I"). I would agree with this. "Thinking exists." And since
"thinking" would be, well, thinking this thought, it is certain that "thinking
exists.")

 _edited to include two paragraphs (this+next one):_ So now we (hopefully)
have something that exists for certain; thoughts exist (or somesuch.)
Descartes claims a bit more: this entity that does the thinking (there does
need to be an agent which thinks those thoughts (is what he assumes, I guess))
- let us just say it is "I", who does the thinking/doubting - when we trace
back the process by which we concluded that we are certain that it exists -
involves us discovering that thinking/doubting definitely does take place.
Hence "I think; I exist."

(I suppose you could have a concept of an "I" that is simply instrumental
(doesn't have independent substance (oof, this is dangerous/slippery
territory)): thoughts can have relations, and related thoughts can be seen as
"bundles", and this process producing continuing interrelated bundles is "the
I doing the thinking." But, I'm not sure of this at all. Maybe D. would say
that the deceiving daemon needs to deceive something, if it does actually do
any deceiving; and if this does happen, then this "something" which is being
deceived is (let us call it an) "I".)

Now, to go from cogito ergo sum to proof of God and subsequent re-
establishment of certainty about the whole world - that is something else. And
I don't think that he does a very good job at it. (And this is "usually",
"generally" agreed upon.)

[1]:
[https://en.wikisource.org/wiki/Meditations_on_First_Philosop...](https://en.wikisource.org/wiki/Meditations_on_First_Philosophy)
\- which btw is an easier read than you might think, if you're curious enough!

[2]:
[http://www.ditext.com/quine/quine.html](http://www.ditext.com/quine/quine.html)

~~~
vram22
>Hmm. I don't think so, but, feel free to expand your opinion (why do you
think it should be "I am, therefore I (can) think"? Maybe you have an
interesting point to make?)

I did say "vaguely". Let me think about it a bit and then reply later tonight.

~~~
vram22
Ok, here's my attempt at an answer:

Take his statement: "I think, therefore I am."

My guess is that the way people interpret it is like this: Descartes is saying
that he (notices that he) thinks, wbich (to him) implies that he must exist.

The statement can be broken down like this:

A, therefore B where A = "I think" and B = "I am".

But if you look at it like this: the "I am" part is asserting that he exists,
which according to him is a logical implication of "I think". But his
asserting "_I_ think" itself implies that his "I" exists (whether it thinks or
not). So the "I think" is like saying "I exist" (and am also thinking - my
emphasis is on the "I"). So it seems like he is already assuming something is
true ("I" exist/am), on the left side of the sentence, what he is trying to
prove ("I am"), on the right side of the sentence. Note the difference in the
two uses of quotes in the last sentence. Hope I've made my thinking :) clear.

~~~
wfn
Thanks for this. :)

Indeed, I think I actually mostly agree with you. See my longer comment /
explication of Descartes' argument (if it's an argument) above: I personally
(also) think that "I think" already presupposes too much. What one _might_ be
able to argue is a lesser version of the thing, though:

thinking, therefore, existing. ("thought exists" (whatever that actually
means!))

> So it seems like he is already assuming something is true ("I" exist/am), on
> the left side of the sentence, what he is trying to prove ("I am"), on the
> right side of the sentence.

..so yeah, I think that the only safe thing for him to say at that point would
have been "thoughts exist." Maybe this does sound lame, but in the context of
Descartes' _Meditations_ , it's about discovering that even though you can
doubt everything, this does require (the process of ) doubting as such.

Or: I can be deceived about everything there is in the world (so e.g. in
actuality, there is no world as such); but _who_ is being deceived? At the
very least, there is (some kind of) thought happening. One _might_ say that
doubting requires an agent, etc., but really, this is already debatable.

But in short: you're right, if one were to establish "I exist" (with an "I"
having certain desirable properties), one could then say "I think", and _that_
would have been less murky, indeed!

Problem is, poor Descartes is not sure that he "exists":

indeed, for him (and this is partly to do with the whole mentality present in
Rationalism, and with the start of Modern philosophy (many people hold him to
be the father of it)) _thinking comes before existing_. You will find many
parallels of the latter around, scattered in various places; cf. "god thinks
itself into being", etc.

He kind of articulates one of the foundations of Rationalism as in the
epistemology: thought shall be the ultimate and _primary_ criterion for truth.

But again, I agree, however, I would say that he _could_ have stated a lesser
version of his point (while not reversing the logical implication arrow):
"thoughts exist."

However, to go from _that_ to re-establishment of certainty about the whole
wide world would have been _even more tough_ (and he was already having a hard
time!) In summary, I think I understand where he's coming from, but one could
say that his project (a kind foundationalist epistemology) had been doomed
from the very beginning!

> Hope I've made my thinking :) clear.

Yeah, I think that was clear! Forgive me for my verbosity, and thanks for the
explanation. I think it makes sense, and fwiw, I agree with the general gist
of it.

~~~
vram22
No problem, and you're welcome. I agree that he could have asserted a lesser
version, such as "thoughts exist", as you say. Interesting points, and good
discussion, thanks!

------
novalis78
That's quite fascinating - reading the Pali canon as a teenager I got so used
to the catuskoti.

------
javert
His argument is self-defeating. Ultimately, it amounts to: "There is no such
thing as truth." But that is a statement about the truth.

The law of noncontradiction is one of several axioms that are presupposed by
any proposition. Such axioms can't be "proven," because any proof would
presume their correctness, but it is proper to accept them.

------
e12e
Very interesting article -- I'm only surprised Gödel didn't make an
appearance.

------
EGreg
Do you think the Buddha borrowed some of his philosophy from the Stoics?

~~~
orasis
Its very important to understand, that unlike most Western philosophers, the
Buddha's philosophy came as a side effect of his meditation and realization.

When you realize the non-dual nature of reality, that the split between
subject and object is an illusion, your entire conception of reality changes
radically. This realization, which is beyond concepts, allows the generation
of ideas that are completely outside "normal" frames of thinking.

This present moment is not conceptual, it is real.

------
pepon
Can some enlightened soul give me a TL;DR version of this text?? :D

~~~
andreasvc
It is possible to give a rigorous mathematical definition of a logic that
deals with contradictions and propositions that cannot be assigned a truth
value. This has parallels with traditions in Buddhism and helps resolve
paradoxes which are problematic for traditional Western logic (e.g., "this
sentence is false").

~~~
pepon
Thanks a lot!! It looked like interesting but I am way too busy for such a
long text.

~~~
dodders
But not too busy to read HN and post questions, it would seem...

------
funky_lambda
Does anyone know any good books with similar stuff in it?

------
wfn
jaxytee: fyi, you are shadowbanned; there's no contact info on your profile,
and your previous comments suggest no reason for the shadowbanning.

------
Uncompetative
Well that was amazingly well-written and informative...

------
personZ
Fascinating essay. I enjoy and appreciate the references to Buddhist
("Eastern") philosophies given that the paradoxical thinking is what most of
us attribute to it.

What is the catch with Aeon? There don't seem to be ads, paywalls,
subscriptions, or other monetizing strategies, but the content seems
fantastic. Is it charitable intellectualism?

~~~
grifpete
I LOVE the fact that you can download to read later!

------
javert
But the Law of Non-Contradiction does hold.

And it's very easy to save the PEM if you distinguish the value of a
proposition (true or false) and the cognitive status of the proposition
(certain, probable, possible, or arbitrary).

Moreover, to exist is to have a particular identity, to have a nature, to be
something.

Thus, all of this work is utter hogwash. The professor who wrote this IS
practicing mysticism and irrationality. He ought to be shunned by all actual
philosophers.

If this kind of thinking were to get "popular," Western civilization and
science would collapse into skepticism and religion would take over again.
Just as happened in the Middle Ages and at the end of the Islamic Golden Age
(in the latter case, there never was a recovery).

~~~
mcguire
" _Moreover, to exist is to have a particular identity, to have a nature, to
be something._ "

Tweet! Assuming the conclusion! 10 yard penalty, return the sliotar to first
base.

~~~
muhuk
Can something exist without identity?

Can something exist yet have no nature?

Can something exist without being (anything)?

~~~
mcguire
Let me start by pointing to to
[https://news.ycombinator.com/item?id=7715277](https://news.ycombinator.com/item?id=7715277).

How do you know something exists?

Because you can see it.

So you don't know that something exists, you only know that your sense
impressions have been triggered. How do you know its nature?

Because of what you see.

So you don't know anything about its nature, only about its relationship with
your sensory apparatus. (Hey, I may have just invented category theory!)

How can something exist...?

Don't look at me, man. It's all probability waves as far as I can tell.

Note: I don't really, actually, myself, buy into this form of epistemology and
metaphysics, so I may have the arguments badly. On the other hand, those are
major topics that have a lot of diverse implications. They cannot simply be
dismissed by assertion.

~~~
muhuk
By your logic, that you didn't own but used nevertheless:

You don't know I asked those questions, you only know that your sense
impressions have been triggered.

Similarly my eyes sent some signals to my brain and after processing them I
have concluded that you have replied to my comment. But wait! I don't really
know you replied me, do I?

Since my senses are unreliable and I don't have any other means to interact
with reality but my senses, my mind is impotent to deal with reality. What
else can I do but go through my life hallucinating and doubting myself or
inventing fantasies to keep my sanity.

\-----

When you look at the moon (at the right time) you see circle. Then you can
decide the moon is circular. Your senses are working just fine, so is your
brain. It's your limited knowledge that leads you to wrong conclusions. As you
observe and learn more, you integrate more and more concepts and you can
eventually arrive to the point that moon is indeed a somewhat spherical
object.

Or you can conclude that your senses are lying to you and reality cannot be
known. Then you'd never go further than "looks circular, but know knows,
right?".

------
dusklight
This article is kinda missing the point. The "empty" is the undefined. That
which has yet to exist, or never will. There is that which is uncountable, for
example the number of corners in a circle. Just because it is a contradiction
doesn't mean it is wrong -- maybe your models are wrong. The usefulness of
eastern philosophy is to free yourself of preconceived ideas. I think it is
obviously clear to everyone today that there are modes of thought that are far
inferior to logic. I think it would be supremely arrogant to presume that
logic is the best mode of thought that humanity will ever come up with. To try
to shoehorn everything to fit into a logical framework feels akin to epicycles
to me.

~~~
andreasvc
Maybe it is missing your pet theory, but the article has a definite point and
Priest argues it at length. You seem not to have grasped the article because
you refer to logic as something singular that should not be deemed superior to
other modes of thought, while the article demonstrates there are many
different, mathematically rigorous conceptions of logic. Epicycles are a non-
sequitur here, because there is not a particular proposition that you set out
to prove with whatever explanation you can find. Rather the goal is to find a
logic that does not break down when presented with paradoxes.

~~~
dusklight
There can be an infinite number of different rigorous conceptions of logic,
while at the same time there are also an infinite number of modes of thought
outside of logic .. we know the ones like instinct, superstition, and religion
that are considered inferior to logic. Is it possible for there to exist a
mode of thought yet to be found or invented that is better?

~~~
andreasvc
I wouldn't say we "know the ones like instinct, superstition, and religion
[...] are considered inferior to logic". They are not comparable, unless you
formulate criteria for what is better, and then you can easily bias the
comparison towards one or the other.

If there exist an infinite number of modes of thought as you posit, then yes
it is possible that the best one is not among the ones we know of now.

I don't really think of it this way though, because logic is not supposed to
give us something new, not supposed to give surprising conclusions. Logic
formalizes the steps you can take to arrive at valid conclusions. However,
what constitutes valid conclusions is ultimately based on our intuitions, it
is what the logic is founded on (comparable to how mathematics is ultimately
based on accepting axioms).

