Jeff Rubard
2010-02-06 19:07:06 UTC
Another World is Possible: Or, the Logic of Empire?
~ by jeffrubard on May 7, 2008.
I’m going to continue my series of logical profiles with Adam Kotsko,
author of the soon-to-be-released *Zizek and Theology* [now available
in Slovene]. Adam recently talked about the fortunes of Hardt and
Negri’s social theory, and I’ll take reopening that discussion as an
opportunity to unseal a thought I had about Empire about five years
ago (although when I explain, I expect some people will understand why
I never got around to offering it up). Perhaps unsurprisingly, I’ll be
talking about modal logic in this post: people unfamiliar with the
rudiments of possible-world models for modal languages can find out
about them in the third installment of my series on Montague Grammar.
The “simplest” modal logic is called K, for Saul Kripke; it’s not that
he discovered it, but that it naturally “falls out” from the structure
of Kripke models for normal modal logics (those closed under the rules
of modus ponens and “Necessitation”). The K axiom looks like this:
□(p->q) -> (□p -> □q)
In English, that reads “if it is necessarily so that p implies q, then
if it is necessarily so that p it is necessarily so that q”: it
expresses the principle that the necessity operator distributes over
the material conditional. This axiom is valid for any normal modal
frame: although different “accessibility relations” give different
modal logics, the K axiom is a part of every normal modal logic. It
generally isn’t regarded as being very interesting by itself, but
“back in the day” I wondered whether it might not have some
applicability to Hardt and Negri’s model of social life. How could
this possibly be? Well, modal logics can express a number of different
“intensional” concepts: in this case, I’m going to treat the necessity
operator as a deontic (logic of permission and obligation) operator
and as an epistemic (logic of belief and knowledge) operator.
As a deontic logic, K says if we are obligated to treat one state of
affairs as consequent upon another then an obligation to bring about
the antecedent state of affairs implies an obligation to bring about
the consequent state of affairs. I think there’s a certain point to
viewing that as a valid metaprinciple of social normativity, one which
is rather consonant with Hardt and Negri’s approach to extra-
governmental normativity deriving from the legal postivist Hans
Kelsen. When elements traditionally concentrated in state power have
recombined on a supranational level and diffused throughout social
formations, the question of what is to be done as a citizen of the
world order becomes rather complicated. But whatever obligations we
have as workers, intellectuals, city-dwellers or fellow-men, perhaps
they cannot but be subject (and us with them) to this basic principle
that conditional obligation (honoring a social norm however particular
or universal) implies conditional obligations (following through when
the antecedent condition occurs). But there’s more: we can reformulate
the K axiom in terms of possibility (the dual to necessity) as:
◊(p v q) -> (◊p v ◊q)
That’s “if it is possible that p or q, then it is possible that p or
it is possible that q”, and it’s an interesting way to view the
doxastic consequences of Negri and Hardt’s analysis, reading the
possibility operator as “it is believed that”. When they happen (as
opposed to when they get talked about and dissected), social trends
are really kind of disjunctive: nobody’s exactly sure what they’re
about, because in the nascent stage they exist at they could really be
about a couple of different things. But if we have a possible social
dichotomy (between conservative and progressive, atheist and
Christian, town and country, etc.) relevant to assessing the trend
we’re licensed to take the individual disjuncts as disjunctively
believable, which enables us to use the form of inference known as
“disjunctive syllogism”, where if “p or q” is true and we can prove a
proposition from either we’re (classically) entitled to assert it
outright.
Okay, if my credentials as a cod mathematical sociologist were in
question they aren’t any more, but what’s the connection to Empire?
Hardt and Negri celebrate the growth of new constellations of social
power; and in this they are following Foucault’s insistence that the
experiments and control of the disciplinary apparatus positively
created the space of modern life, rather than being mere shackles to
be thrown off. But if the multitude is going to be navigating by way
of tacit “negotiated orders”, what they are able to reasonably believe
about the social world they are operating in is going to be
exceptionally fragmentary and prone to change. Back then I would think
of emerging cultural tropes, interactional patterns, and political
arrangements as “K-pulses”, where people were automatically reasoning
along these lines. (This all probably had something to do with knowing
a woman named K., who was very stimulating along a number of axes —
lots of statements were “K-valid” that other people might handle
differently.)
I guess being on top of things, or trying to, has always been like
that; but I thought that Hardt and Negri’s enthusiasm was perhaps ill-
placed because of a historical sequence that occurred to me. There was
of course the Holy Roman Empire, which many viewed as neither holy,
nor Roman, nor an Empire, but it was followed by the German Empire,
which implemented efficient bureaucracy in conjunction with political
repression, and it seemed to me for a while that was followed by
Empire — the Nazi regime, the character of which perhaps has to be
viewed as a seriously defective and perennially tempting response to
modernity rather than a visitation of diabolical evil. The Nazis had
no real values of any kind, even nationalistic ones: renaming Berlin
“Germania” wouldn’t have been much of an expression of Deutschtum.
They were in love with technology and science, and those medieval
anachronisms for the people and ancient bacchanales for the elite
which mass production and mass media made simultaneously possible.
Perhaps that was a little bit the dream of a spirit-seer; I was
certainly seeing spirits at the time. But expecting that technological
progress and social change are failure-proof indices of social justice
shouldn’t be axiomatic.
----
The possibility of /modally licenced/ inference!
The possibility of /modally licenced/ inference!
That's what this [abstractum] is.
To-wit: *Sine* K's /divisionés/ of frame + world into
"normal" [cheaply bought inferences legitimated by "simple" frame-
conditions] and "non-normal" [where a *conceptión* of a /
surreptitously/ non-modal inference such as 'strict inference' drives
a "step-wise" analysis of the frames of S2 symbolized by an *abstract*
mathematical condition requiring "further analysis" in-principle-or-in-
practice.] *Like that*.
~ by jeffrubard on May 7, 2008.
I’m going to continue my series of logical profiles with Adam Kotsko,
author of the soon-to-be-released *Zizek and Theology* [now available
in Slovene]. Adam recently talked about the fortunes of Hardt and
Negri’s social theory, and I’ll take reopening that discussion as an
opportunity to unseal a thought I had about Empire about five years
ago (although when I explain, I expect some people will understand why
I never got around to offering it up). Perhaps unsurprisingly, I’ll be
talking about modal logic in this post: people unfamiliar with the
rudiments of possible-world models for modal languages can find out
about them in the third installment of my series on Montague Grammar.
The “simplest” modal logic is called K, for Saul Kripke; it’s not that
he discovered it, but that it naturally “falls out” from the structure
of Kripke models for normal modal logics (those closed under the rules
of modus ponens and “Necessitation”). The K axiom looks like this:
□(p->q) -> (□p -> □q)
In English, that reads “if it is necessarily so that p implies q, then
if it is necessarily so that p it is necessarily so that q”: it
expresses the principle that the necessity operator distributes over
the material conditional. This axiom is valid for any normal modal
frame: although different “accessibility relations” give different
modal logics, the K axiom is a part of every normal modal logic. It
generally isn’t regarded as being very interesting by itself, but
“back in the day” I wondered whether it might not have some
applicability to Hardt and Negri’s model of social life. How could
this possibly be? Well, modal logics can express a number of different
“intensional” concepts: in this case, I’m going to treat the necessity
operator as a deontic (logic of permission and obligation) operator
and as an epistemic (logic of belief and knowledge) operator.
As a deontic logic, K says if we are obligated to treat one state of
affairs as consequent upon another then an obligation to bring about
the antecedent state of affairs implies an obligation to bring about
the consequent state of affairs. I think there’s a certain point to
viewing that as a valid metaprinciple of social normativity, one which
is rather consonant with Hardt and Negri’s approach to extra-
governmental normativity deriving from the legal postivist Hans
Kelsen. When elements traditionally concentrated in state power have
recombined on a supranational level and diffused throughout social
formations, the question of what is to be done as a citizen of the
world order becomes rather complicated. But whatever obligations we
have as workers, intellectuals, city-dwellers or fellow-men, perhaps
they cannot but be subject (and us with them) to this basic principle
that conditional obligation (honoring a social norm however particular
or universal) implies conditional obligations (following through when
the antecedent condition occurs). But there’s more: we can reformulate
the K axiom in terms of possibility (the dual to necessity) as:
◊(p v q) -> (◊p v ◊q)
That’s “if it is possible that p or q, then it is possible that p or
it is possible that q”, and it’s an interesting way to view the
doxastic consequences of Negri and Hardt’s analysis, reading the
possibility operator as “it is believed that”. When they happen (as
opposed to when they get talked about and dissected), social trends
are really kind of disjunctive: nobody’s exactly sure what they’re
about, because in the nascent stage they exist at they could really be
about a couple of different things. But if we have a possible social
dichotomy (between conservative and progressive, atheist and
Christian, town and country, etc.) relevant to assessing the trend
we’re licensed to take the individual disjuncts as disjunctively
believable, which enables us to use the form of inference known as
“disjunctive syllogism”, where if “p or q” is true and we can prove a
proposition from either we’re (classically) entitled to assert it
outright.
Okay, if my credentials as a cod mathematical sociologist were in
question they aren’t any more, but what’s the connection to Empire?
Hardt and Negri celebrate the growth of new constellations of social
power; and in this they are following Foucault’s insistence that the
experiments and control of the disciplinary apparatus positively
created the space of modern life, rather than being mere shackles to
be thrown off. But if the multitude is going to be navigating by way
of tacit “negotiated orders”, what they are able to reasonably believe
about the social world they are operating in is going to be
exceptionally fragmentary and prone to change. Back then I would think
of emerging cultural tropes, interactional patterns, and political
arrangements as “K-pulses”, where people were automatically reasoning
along these lines. (This all probably had something to do with knowing
a woman named K., who was very stimulating along a number of axes —
lots of statements were “K-valid” that other people might handle
differently.)
I guess being on top of things, or trying to, has always been like
that; but I thought that Hardt and Negri’s enthusiasm was perhaps ill-
placed because of a historical sequence that occurred to me. There was
of course the Holy Roman Empire, which many viewed as neither holy,
nor Roman, nor an Empire, but it was followed by the German Empire,
which implemented efficient bureaucracy in conjunction with political
repression, and it seemed to me for a while that was followed by
Empire — the Nazi regime, the character of which perhaps has to be
viewed as a seriously defective and perennially tempting response to
modernity rather than a visitation of diabolical evil. The Nazis had
no real values of any kind, even nationalistic ones: renaming Berlin
“Germania” wouldn’t have been much of an expression of Deutschtum.
They were in love with technology and science, and those medieval
anachronisms for the people and ancient bacchanales for the elite
which mass production and mass media made simultaneously possible.
Perhaps that was a little bit the dream of a spirit-seer; I was
certainly seeing spirits at the time. But expecting that technological
progress and social change are failure-proof indices of social justice
shouldn’t be axiomatic.
----
The possibility of /modally licenced/ inference!
The possibility of /modally licenced/ inference!
That's what this [abstractum] is.
To-wit: *Sine* K's /divisionés/ of frame + world into
"normal" [cheaply bought inferences legitimated by "simple" frame-
conditions] and "non-normal" [where a *conceptión* of a /
surreptitously/ non-modal inference such as 'strict inference' drives
a "step-wise" analysis of the frames of S2 symbolized by an *abstract*
mathematical condition requiring "further analysis" in-principle-or-in-
practice.] *Like that*.