A recent philosopher to argue with Plato -- someone who is frequently
thinking about the history of philosophy, but also the development of
mathematics and the long history of psychology -- add film, music, and
especially painting -- is Alain Badiou, whose 2006 Logic of Worlds
has inspired me to write this appreciation.
Plato famously hated the written word and saw real philosophy as
discussion. Yet philosophy sometimes finds a way to be a written text
that inspires a discussion in the reader -- the reader becomes the
discussion and enters in to the argument and thus gets to offer and
sort through good and bad hypotheses, not perhaps arriving at truth
but certainly engaged in looking for it. Plato’s dialogues are the
preeminent example of written work that can work this kind of alchemy
in the reader’s mind. Nietzsche and Kierkegaard sink and float many
kinds of ideas before the reader’s judgment and bring the excitement
of their thinking vividly and emotionally into play. Hegel and
Heidegger are modern masters who use a different technique, which is
something like bald arrogation, constructing vast landscapes of
thinking with let us say ‘made up’ words which -- if the reader will
begin reading them and taking them seriously -- soon provoke
objections and force the thinker to think. Badiou is a builder like
Hegel -- not a playwright or critic -- he is another writer who
attempts to weave a spell which will become absorbed and then provoke
thought.
Perhaps Socrates is behind all of these figures with his method of
cross-examination. Some say that Socrates only teaches negative
lessons and that he never concludes anything, but probably this is the
wrong way of looking at it. We have to take the Socratic project more
personally -- so the two lessons are not just ‘negative’ and
‘inconclusive,’ but: I don’t know what I think I know -- a kind of
humiliation and bitter knowledge; and, further, I actually do know
more than I thought (or something different from I what I thought) --
a kind of surprising understanding. Elenchus leads to disillusion --
uncovering one’s eyes -- as dialectic leads to recollection -- a
method whereby latent knowledge is recovered. The therapy or
recollection of dialectic is conversation -- acknowledging ignorance
drives the conversation -- not knowing makes us try to know -- and of
course Socrates and everyone else who begins to take part in
conversation already knows an enormous amount about life. Socrates is
certainly not an ‘ordinary language philosopher’ who sees anything
sacrosanct in a mere word, but is probably more an essentialist about
meaning, who sees everyday language as a ‘first draft’ of genuine
philosophical discourse -- we have to get some distance from everyday
life and try to dig deep to the foundations. Eventually we may
discover something like the underlying assumptions we are making when
we talk about things, which gives us a new chance to see things
clearly -- we are trying to get to the root form of our way of
projecting ideas into life, including ideas so basic that we can’t see
them because we are always using them.
Bitter, demoralizing personal defeats + deepening renewals from the
joy of practice
What I am talking about here is the Socratic-Platonic-Aristotelian
project of human excellence through practice of philosophical
engagement in every moment of life -- Socrates’ signal idea that the
unexamined life is not worth living for a human being.
Logic of Worlds is a 500+ page attempted demonstration of Socrates’
foundational claim for philosophy that “the unexamined life is not
worth living for a human being.”
Here are some steps in his thinking.
“Make yourself, patiently or impatiently, into the most irreplaceable
of beings.” Gide, Fruits of the Earth
Beginning question -- what are we thinking? What are we thinking
today? What are we thinking when we are not monitoring ourselves?
This appears to be the natural belief state. But this state is
brought about in keeping with the rule of an inculcated nature. And
the current inculcated nature negates that there is anything like
truth -- especially eternal truth -- it merely projects a screen over
an unexamined staging. But this is not enough -- Badiou is for
eternal truths, truths worth lots of trouble -- he says that there is
something demanded of us and this is “the Platonic gesture.”
So he begins by rejecting the idea that there are only bodies and
languages. The third term is truth -- there are truths. Truths may
not be eternal -- but a truth can be eternal in the sense that
believing it configures a present, so that a moment congeals and
comes to be. But again a real truth shines through its contexts and
instances as an invariant principle -- truths outlive the multiplicity of
worlds constructed of and recreated in them. So: examples from art,
mathematics, politics, love relations, histories and psychologies.
Truths presuppose traces upon which they are based and which make them
possible -- traces imply an operative figure or subject for whom the
trace appears and is true.
Thus it becomes important to work through all the above ideas and
deploy them as the main parts of the exposition of human being that
Badiou is proposing to offer. Following Kant this is a kind of catalog
of the transcendental organization of the situations of being.
Following Hegel this is also a way of looking at human history.
Subsequently we are looking for a kind of algebra; for a kind of
logic; an ontology.
All this goes to bettering our understanding of what is meant by a
‘world’ -- a classical world is one in which the principles of
identity, non-contradiction and excluded middle holds -- a
non-standard world emerges from conflicted principles. As it turns
out, we have to be open to and in fact are constituted in virtual
infinities of worlds. Therefore ending and beginning again is
fundamental to the life process. There is a heroism and affirmative
joy in following through to a true completion. The desire to live,
the heroic sense, the power of self-discipline is the true weapon
against meaninglessness, but this sense has to be invented and lived
and redone. “We will only be consigned to the form of a disenchanted
animal for whom the commodity is the only reference point if we
consent to it. But we are shielded from this consent by the Idea, our
underlying making, the secret of the pure present.”
At the end of the text (in my edition p. 578), we get to this last denouement:
To live supposes that some trace has been given
To live supposes that some fidelity engenders a present
‘To live’ and ‘to live for an idea’ are identical
Several times in its life, every human is granted the possibility of living
Since it is possible, commencing and recommencing to live is the only imperative
Thus we have to contemplate the notion of unforeseeable change --
radical novelty -- something we did not and could not see -- the Event
-- moving from what was obvious and to an underlying pattern not
evident at the outset -- truths are denied or suppressed in the
ordinary condition -- the central aspect of truth is its exit to break
with an existing regime -- a breaking out which leads to a reordering.
The formal burden of the text and its 500+ page reasoning is an
end-run around the subject object dichotomy and all its attendant
biases, problems and confusions.
Logics of Worlds turns instead to category theory to model the domain
of appearing.
In general, a category can be understood as a structure of relations;
the identity of the objects thus structured is irrelevant, as long as
this structure of relations is preserved. Most significantly for
Badiou's project, however, it is also possible to use a special kind
of categorical structures, known as topoi, to model logical ones; for
instance, we can use topos theory to model algebraically all of the
axioms and relations of standard, classical propositional logic --
Grothendieck rescues Russell.
But then it is a further consequence of this categorical method that
the logics modeled need not be classical ones; indeed, we can use
topoi to model any number of non-classical logics, including
intuitionist and many-valued ones, to capture more of the ‘irrational’
lying within worlds constructed of traces -- e.g. non-classical logics
can uniformly be understood as determined by structures called
Heyting algebras (pp. 173-190).
Using this category-theoretical framework, Badiou can thus define the
underlying structures determining the "logic" or relations of
appearance -- the logic of worlds -- determining what is treated as
existent in each world, including various degrees of existence
correspondent to the degrees of truth allowed by that world's specific
categorical architecture. He terms the specific structure determining
these logical relationships and intensities of existence for a
particular world its "transcendental.”
The paradoxical structure of the event, the "evental site," the trace
that undergirds a world, is such that it is immediately possible for
it to be taken up in a variety of different ways, corresponding to
different degrees and intensities of change in the world. In the most
radical case, a subject's faithful tracing of the implications of the
structure of the evental site results in the element which was
formerly minimal in its degree of existence -- what had earlier
literally "in-existed" in that particular world, not counted, not
included in the count, being present in its being but completely
invisible to that particular world's logic -- suddenly to attain a
maximal degree of existence, bringing with it all the changes in the
existing structure that this implies (pp. 374-79). This is paradigm
change as Kuhn thinks of it and revolution as Marx thinks of it and
also of course the History of Being as Heidegger thinks of it -- an
overarching view of change emanating from beginnings…
In this sense the book is part of a project like Gödel’s (an author
Badiou often cites) who is trying to draw conclusions about what we
can do in our thinking and even regarding ‘being’ itself from
reflection on formalisms and limits of formal structures.
-- ? --
thinking about the history of philosophy, but also the development of
mathematics and the long history of psychology -- add film, music, and
especially painting -- is Alain Badiou, whose 2006 Logic of Worlds
has inspired me to write this appreciation.
Plato famously hated the written word and saw real philosophy as
discussion. Yet philosophy sometimes finds a way to be a written text
that inspires a discussion in the reader -- the reader becomes the
discussion and enters in to the argument and thus gets to offer and
sort through good and bad hypotheses, not perhaps arriving at truth
but certainly engaged in looking for it. Plato’s dialogues are the
preeminent example of written work that can work this kind of alchemy
in the reader’s mind. Nietzsche and Kierkegaard sink and float many
kinds of ideas before the reader’s judgment and bring the excitement
of their thinking vividly and emotionally into play. Hegel and
Heidegger are modern masters who use a different technique, which is
something like bald arrogation, constructing vast landscapes of
thinking with let us say ‘made up’ words which -- if the reader will
begin reading them and taking them seriously -- soon provoke
objections and force the thinker to think. Badiou is a builder like
Hegel -- not a playwright or critic -- he is another writer who
attempts to weave a spell which will become absorbed and then provoke
thought.
Perhaps Socrates is behind all of these figures with his method of
cross-examination. Some say that Socrates only teaches negative
lessons and that he never concludes anything, but probably this is the
wrong way of looking at it. We have to take the Socratic project more
personally -- so the two lessons are not just ‘negative’ and
‘inconclusive,’ but: I don’t know what I think I know -- a kind of
humiliation and bitter knowledge; and, further, I actually do know
more than I thought (or something different from I what I thought) --
a kind of surprising understanding. Elenchus leads to disillusion --
uncovering one’s eyes -- as dialectic leads to recollection -- a
method whereby latent knowledge is recovered. The therapy or
recollection of dialectic is conversation -- acknowledging ignorance
drives the conversation -- not knowing makes us try to know -- and of
course Socrates and everyone else who begins to take part in
conversation already knows an enormous amount about life. Socrates is
certainly not an ‘ordinary language philosopher’ who sees anything
sacrosanct in a mere word, but is probably more an essentialist about
meaning, who sees everyday language as a ‘first draft’ of genuine
philosophical discourse -- we have to get some distance from everyday
life and try to dig deep to the foundations. Eventually we may
discover something like the underlying assumptions we are making when
we talk about things, which gives us a new chance to see things
clearly -- we are trying to get to the root form of our way of
projecting ideas into life, including ideas so basic that we can’t see
them because we are always using them.
Bitter, demoralizing personal defeats + deepening renewals from the
joy of practice
What I am talking about here is the Socratic-Platonic-Aristotelian
project of human excellence through practice of philosophical
engagement in every moment of life -- Socrates’ signal idea that the
unexamined life is not worth living for a human being.
Logic of Worlds is a 500+ page attempted demonstration of Socrates’
foundational claim for philosophy that “the unexamined life is not
worth living for a human being.”
Here are some steps in his thinking.
“Make yourself, patiently or impatiently, into the most irreplaceable
of beings.” Gide, Fruits of the Earth
Beginning question -- what are we thinking? What are we thinking
today? What are we thinking when we are not monitoring ourselves?
This appears to be the natural belief state. But this state is
brought about in keeping with the rule of an inculcated nature. And
the current inculcated nature negates that there is anything like
truth -- especially eternal truth -- it merely projects a screen over
an unexamined staging. But this is not enough -- Badiou is for
eternal truths, truths worth lots of trouble -- he says that there is
something demanded of us and this is “the Platonic gesture.”
So he begins by rejecting the idea that there are only bodies and
languages. The third term is truth -- there are truths. Truths may
not be eternal -- but a truth can be eternal in the sense that
believing it configures a present, so that a moment congeals and
comes to be. But again a real truth shines through its contexts and
instances as an invariant principle -- truths outlive the multiplicity of
worlds constructed of and recreated in them. So: examples from art,
mathematics, politics, love relations, histories and psychologies.
Truths presuppose traces upon which they are based and which make them
possible -- traces imply an operative figure or subject for whom the
trace appears and is true.
Thus it becomes important to work through all the above ideas and
deploy them as the main parts of the exposition of human being that
Badiou is proposing to offer. Following Kant this is a kind of catalog
of the transcendental organization of the situations of being.
Following Hegel this is also a way of looking at human history.
Subsequently we are looking for a kind of algebra; for a kind of
logic; an ontology.
All this goes to bettering our understanding of what is meant by a
‘world’ -- a classical world is one in which the principles of
identity, non-contradiction and excluded middle holds -- a
non-standard world emerges from conflicted principles. As it turns
out, we have to be open to and in fact are constituted in virtual
infinities of worlds. Therefore ending and beginning again is
fundamental to the life process. There is a heroism and affirmative
joy in following through to a true completion. The desire to live,
the heroic sense, the power of self-discipline is the true weapon
against meaninglessness, but this sense has to be invented and lived
and redone. “We will only be consigned to the form of a disenchanted
animal for whom the commodity is the only reference point if we
consent to it. But we are shielded from this consent by the Idea, our
underlying making, the secret of the pure present.”
At the end of the text (in my edition p. 578), we get to this last denouement:
To live supposes that some trace has been given
To live supposes that some fidelity engenders a present
‘To live’ and ‘to live for an idea’ are identical
Several times in its life, every human is granted the possibility of living
Since it is possible, commencing and recommencing to live is the only imperative
Thus we have to contemplate the notion of unforeseeable change --
radical novelty -- something we did not and could not see -- the Event
-- moving from what was obvious and to an underlying pattern not
evident at the outset -- truths are denied or suppressed in the
ordinary condition -- the central aspect of truth is its exit to break
with an existing regime -- a breaking out which leads to a reordering.
The formal burden of the text and its 500+ page reasoning is an
end-run around the subject object dichotomy and all its attendant
biases, problems and confusions.
Logics of Worlds turns instead to category theory to model the domain
of appearing.
In general, a category can be understood as a structure of relations;
the identity of the objects thus structured is irrelevant, as long as
this structure of relations is preserved. Most significantly for
Badiou's project, however, it is also possible to use a special kind
of categorical structures, known as topoi, to model logical ones; for
instance, we can use topos theory to model algebraically all of the
axioms and relations of standard, classical propositional logic --
Grothendieck rescues Russell.
But then it is a further consequence of this categorical method that
the logics modeled need not be classical ones; indeed, we can use
topoi to model any number of non-classical logics, including
intuitionist and many-valued ones, to capture more of the ‘irrational’
lying within worlds constructed of traces -- e.g. non-classical logics
can uniformly be understood as determined by structures called
Heyting algebras (pp. 173-190).
Using this category-theoretical framework, Badiou can thus define the
underlying structures determining the "logic" or relations of
appearance -- the logic of worlds -- determining what is treated as
existent in each world, including various degrees of existence
correspondent to the degrees of truth allowed by that world's specific
categorical architecture. He terms the specific structure determining
these logical relationships and intensities of existence for a
particular world its "transcendental.”
The paradoxical structure of the event, the "evental site," the trace
that undergirds a world, is such that it is immediately possible for
it to be taken up in a variety of different ways, corresponding to
different degrees and intensities of change in the world. In the most
radical case, a subject's faithful tracing of the implications of the
structure of the evental site results in the element which was
formerly minimal in its degree of existence -- what had earlier
literally "in-existed" in that particular world, not counted, not
included in the count, being present in its being but completely
invisible to that particular world's logic -- suddenly to attain a
maximal degree of existence, bringing with it all the changes in the
existing structure that this implies (pp. 374-79). This is paradigm
change as Kuhn thinks of it and revolution as Marx thinks of it and
also of course the History of Being as Heidegger thinks of it -- an
overarching view of change emanating from beginnings…
In this sense the book is part of a project like Gödel’s (an author
Badiou often cites) who is trying to draw conclusions about what we
can do in our thinking and even regarding ‘being’ itself from
reflection on formalisms and limits of formal structures.
-- ? --
