
The Outer Limits of Reason: A look at paradoxes in language - dnetesn
http://mitp.nautil.us/feature/148/the-outer-limits-of-reason
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leoc
Before you even get to self-reference there are the
[https://en.wikipedia.org/wiki/Paradoxes_of_material_implicat...](https://en.wikipedia.org/wiki/Paradoxes_of_material_implication)
: ~(A & ~B) is a very poor approximation of 'if A then B' once you leave the
world of statements about mathematics. Graham Priest's /Introduction to Non-
Classical Logic/
[http://www.cambridge.org/ie/academic/subjects/philosophy/phi...](http://www.cambridge.org/ie/academic/subjects/philosophy/philosophy-
science/introduction-non-classical-logic-if-2nd-edition) is great (as is his
lecturing on the subject: Priest really ought to do a MOOC...)

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skybrian
These paradoxes seem to be tied to not distinguishing between correlation and
causation? True statements are perfectly correlated with all other true
statements, and material implication doesn't distinguish between them even if
they have different causes.

When reasoning informally we do try to distinguish between correlation and
causation.

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woodandsteel
Good article. I would just like to add that this whole question of linguistic
paradoxes is important for a fundamental debate in Western philosophy.

This has to do with the basic relation between language and reality. In one
view, reality is such that it can be perfectly described by an appropriate set
of precise philosophical concepts. In the other view, this is impossible, and
language is just a tool that the human mind has developed that can only
imperfectly describe reality.

Russell was the twentieth century's leading advocate of the perfect language
view. His student Wittgenstein started out there, but later changed to the
latter view. And in fact, most of the major philosophers of the last hundred
years or so have held the language-as-imperfect-tool view.

I am interested in this question partly because if you start with the perfect
language view, then for political philosophy you end up with something like
Plato's philosopher-king. On the other hand, the imperfect tool view leads to
something more like liberal democracy. And indeed, I think it is not an
accident that Pragmatism, an imperfect-tool philosophy, developed in the
United States.

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chris_st
Good points.

I may have misunderstood the article, but I'm a little surprised the author
didn't write about Russell's inability to accept Gödel's Incompleteness proof.
This made _mathematics_ not fit in the "[it] is such that it can be perfectly
described by an appropriate set of precise philosophical concepts". So I
guess, if he held that philosophical opinion about reality, it would be hard
to accept it about math.

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woodandsteel
Haha, I wasn't aware of that story, and yes, it fits right in with what I'm
saying.

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chris_st
I have always liked, "We have to believe in free will -- we have no other
choice."

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cobbzilla
one of my favorite paradoxes is Buridan's Bridge [1]

"Socrates wants to cross a river and comes to a bridge guarded by Plato.

Plato: Socrates, if in the first proposition which you utter, you speak the
truth, I will permit you to cross. But surely, if you speak falsely, I shall
throw you into the water.

Socrates: You will throw me into the water."

[1]
[https://en.wikipedia.org/wiki/Buridan%27s_bridge](https://en.wikipedia.org/wiki/Buridan%27s_bridge)

~~~
prmph
A "solution" to this paradox: Truth and falsehood only apply to past or on-
going situations. No one can foretell he future, so the truth value of
predictions is undefined

