
How Robert Nozick put a purple prose bomb under analytical philosophy - diodorus
https://aeon.co/ideas/how-robert-nozick-put-a-purple-prose-bomb-under-analytical-philosophy
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danharaj
Jean-Yves Girard, a great logician, also has a lot of quarrels to pick with
analytic philosophy. His prose is idiosyncratic, lyrical and definitely at
odds with the dryness of "logic of the 20th century". If you like the idea of
an energetic approach to reconceptualize philosophy, in particular the
philosophy of logic, I recommend reading Girard's work. The Blind Spot:
Lectures on Logic is an organized survey of logic starting with Hilbert's
formalism and ending up in the operator algebras of Geometry of Interaction.
Along the way, Girard's combative, highly opinionated and witty commentary
ceaselessly entertains and engages.

Perhaps what is most striking about Girard in contrast to Nozick is how he
manages to be very rigorous and artful simultaneously. Something as abstract
of logic becomes a living creature when Girard talks about it. To see logic
this way is to expect it to flourish in subordination to the rest of human
experience, not languish in its own obscure enclave, ceaselessly chasing its
own tail, reducing the alluring to the banal.

~~~
igravious
Energetic though it may be, and notwithstanding Girard's brilliance, I doubt
that I could consider a quirky treatise on proof theory to be a
_philosophical_ text.

And one can be rigorous without resorting to formulae.

~~~
neel_k
Girard is French, and The Blind Spot is best understood as a piece of
continental philosophy, not analytic.

The short version is that back in the late 60s, Althusser suggested that
fields of knowledge inherently have "a blind spot" \-- his idea was that every
field of knowledge has to resort to structuring/organizational principles
which cannot be properly articulated within the field of knowledge itself.
Jacques-Alain Miller applied this idea to logic, arguing that the Fregean
definition of equality (and hence number) exhibits precisely this kind of
problem. Namely, Frege defined zero as the extension of the predicate "not
equal to itself", and so Frege implicitly excludes the subject from logic, as
Lacan had defined "subject" as the non-self-identical.

However, Alain Badiou objected very strongly against the extension of
Althusser's ideas to logic. He thinks that science and mathematics can
generate definitively true, objective, non-political knowledge, and so while
blind spots can occur in daily ("ideological") life, they cannot occur in
science.

Girard is essentially making an argument against Badiou and in favor of
Miller. Because Girard is Girard, he never explicitly mentions any of these
people in his lectures. This way, he can laugh at those of us who were too
ill-informed to catch the fact that the TITLE of his lectures is a direct
reference to Althusser.

Anyway, Girard begins with Lorenzen's idea that a proof can be understood as a
dialogue between a proponent and a refuter, and the observation that the
continuation-passing-style translation embedding classical logic into
intuitionistic logic doesn't require that the answer type of the continuation
be the empty type. He observes that these two ideas fit together in Krivine-
style realizability models of classical logic: every formula can be
interpreted as a set of proofs and refutations, and the interaction of a proof
with a refutation yields a behaviour in the answer type. As a programmer, I
think of the answer type as the runtime system of a programming language. The
Krivine construction ensures that every proof -- every program -- both
respects the invariants of the answer type/runtime system, and can never
observe them.

So the runtime system of a programming language exhibits the essential
structure of an Althusserian blind spot, and so via Curry-Howard so must
logic.

I don't claim to understand the implications of all this, but I find the idea
of bringing continental philosophy into the foundations of logic in a really
serious, technically profitable way to be very exciting.

~~~
danharaj
> He observes that these two ideas fit together in Krivine-style realizability
> models of classical logic: every formula can be interpreted as a set of
> proofs and refutations, and the interaction of a proof with a refutation
> yields a behaviour in the answer type.

I've wanted to see this paradigm implemented in the Isbell envelope of a
category, whose objects are pairs of a presheaf and copresheaf T, E and a
natural transformation from T(-) x E(--) ~> Hom(-,--) . I think it would be
really striking if the answer type could be Hom itself, which I like to think
of as a formalisation of the turnstile |- by itself.

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Wissmania
"Philosophers, he posited, would be better off if they stopped trying to prove
things like scientists, an impulse he believed led thinkers to overlook how
philosophy might stimulate the ‘mind’s excitement and sensuality’. Rather,
they ought to limit themselves to explaining how a system of thought is
possible."

Can someone explain what this last sentence means?

~~~
bobwaycott
In simplest terms that don't depend too heavily on philosophical references or
terminology, I believe he means the philosophical task shouldn't be to prove a
thing _is_ or _isn 't_, but that a thing _could be_ —that a set of plausible
explanations exist or could exist to provide enough convincing power that a
given system of thought or a different state of affairs is not _impossible_ to
conceive of or consider capable of existing.

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DaggerDagger
Wow, this is great. So he took philosophy out of the normative, positivist,
Hegelian world it was stuck in, pointlessly proving useless esoteric questions
of logic, and applied it phenomenologically to the broad experience of human
experience and reality. Anybody know anything I should read besides Nozick
along this vein?

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RodericDay
Yeah, Karl Marx.

The Communist Manifesto and Capital are both good, but I personally think
Marx's Inferno by William Clare Roberts is great.

~~~
ue_
I don't know if it's just me, but I consider Capital more of an economic text
than a philosophical one. That's Marx in political economist mode. And from
what (albeit little) I've read of Nozick I much prefer Marx and continental
philosophy as a whole (though I'm just beginning).

The Manifesto draws varying opinions even within Communist circles; arguably
Engels' "The Principles of Communism" is a more gentle text.

~~~
bobwaycott
This is definitely a common thought, and has long been considered the proper
way to read Marx. You should check out _Marx 's Inferno_ for an
interesting—and, I've long thought, more accurate—take otherwise.

~~~
ue_
I've heard about it before, though I haven't checked it out. I'll take a look,
thanks.

