Ok, well, this is one of my favorite parts of the book. I really like this chapter and I think really
important things are going on in it, so I’m going to try and explain the source of my enthusiasm
about it.
So one thing that’s potentially a little puzzling right at the beginning of the chapter is that Hegel
talks indifferently and almost interchangeably about universality, negation, and mediation. So he
says things like in 112, the second paragraph, “The wealth of sense knowledge belongs to
perception, not to immediate certainty, for which it was only the source of instances. For only
perception contains negation. That is, difference or manifoldness within its own essence.” And
he talks about it in 115, about sensuous universality or the immediate unity of being and the
negative. And then again says “the universal is in its simplicity a mediated universal.”
Now I talked a little bit beforehand about the relation between determinate negation and
mediation, where I take mediation to be a matter of inference, material/consequential relations,
determinate negation to be a relation of material incompatibility, Aristotelian contrariety, which
will be a big topic here, and in particular I indicated that I take negation to be the more
fundamental notion, in part because, though I can’t catch Hegel saying this, it’s possible to
define inferential relations in terms of relations of determinate negation. That is, we can say that
‘Pedro is a mammal’ follows from ‘Pedro is a donkey’, because and in the sense that everything
incompatible with Pedro being a mammal is incompatible with him being a donkey. That’s a way
of going from a notion of material incompatibility to a notion of inference. P implies Q just in
case everything incompatible with Q is incompatible with P. So if we give Hegel a notion of
determinate negation as a sort of metaphysical primitive, he’s going to get a notion of mediation
out of it.
But what about universality? One of the big points of this chapter is to argue that coming out of
sense-certainty with an acknowledgement that determinate contentfulness requires universals,
some kind of generality, in particular sense universals, observable properties, ones that can be
applied immediately in the sense of immediacy of origin, that the application of these universals
was not the result of a process of inference, but a matter of observation, perception,
responsiveness in that way. One of the points of the chapter is to argue that in finding that the
presence or activity of sense universals is implicit in the idea of sensory episodes that have some
kind of determinate content we actually already have conceded a structure of negation that
universality implicitly involves a rich metaphysical fine structure of negation. I’m going to argue
that there’s two fundamental kinds of differences that Hegel sees as necessary for having any
kind of universality in play, having any notion of, well any notion of universality in play, and
he’s going to walk us through how we can elaborate five other senses of difference or negation
out of those fundamental two.
A different way of describing this same progression, a way that will turn out to be equivalent, is
that in the sense-certainty section, the contents we were talking about, not themselves thought of
as linguistic contents, but when we, as we have no choice, use language to try and specify these
contents, we use what’s Strawson in his book Individuals called a feature-placing language. So
feature-placing, when we say ‘It’s raining’ or ‘It’s fine’, because the language has a subjectpredicate structure, the surface structure of sentences like that is also subject-predicate, but you
can see that’s just the surface structure. The ‘it’ in ‘It’s raining’ or ‘It’s fine’ is not referring to
something. There’s not an object of which we’re predicating this universal. Rather it’s just a
feature. We’re saying ‘There is rain’, ‘There is sun’, ‘It’s sunny’, something like that. And we
say it exactly the same in German, ‘Es regnet’, and Strawson’s idea is that this is the most
primitive sort of contentfulness. In feature-placing you just characterize it. You’re just placing
this feature.
And Strawson, in Individuals, engaged in a self-describedly Kantian exercise in what he calls
reconstructive metaphysics, by contrast to descriptive metaphysics. He’s interested in how you
could move beyond feature-placing content to a subject and predicate, individual and property
structure, where you’ve still got the kind of universality you’ve got in feature-placing, those are
repeatables, contentful repeatables—to say it’s raining is different than to say it’s fine or it’s
sunny. Those are different. But now you add individuals, or particulars, or objects into the
picture and Strawson was concerned—well, what’s required to get those in the picture and
started thinking, well, this was his Kantian argument, you’re going to need something like space
and time to locate them in and you’re going to need the capacity to track those objects, to follow
them as they move through space.
And this is a line that his student and the young John McDowell’s best friend, Gareth Evans
elaborated in his work, saying really there’s two notions of space. He’s elaborating what
Strawson made of Kant in the Transcendental Aesthetic, Evans collaborating with Strawson
made of Kant, says it’s really two kind of space you’ve got to keep track of: ego-centric space,
located around you—how are things relative to you—and public space, the public space that
things move in. And you’ve got to be able to separate the effects of movement, in particular of
your movement, that is the relative change between egocentric space and public space, in order
to so much as have the idea of independent objects moving around in public space. You’ve got to
know the difference between what happens when you turn your head and what happens when an
object moves in public space, even though both of them involve shifts in how things are
relative— in egocentric space, for instance. and Evans is fascinated that this is a sub-conceptual
capacity at least in the sense that if your dog can catch a Frisbee, he’s got to have these
fundamental capacities of tracking objects, of mapping egocentric space onto public space, that
Evan’s Strawson’s Kant see as fundamental, but sub-conceptual capacities. So, all right, that’s a
little of what Sellars called being around in the neighborhood, neighboring bushes around the
Strawsonian idea of feature-placing language.
So Strawson in Individuals sets himself the task of trying to see what sort of practical capacities
knowers and agents would have to have to move from feature-placing consciousness to subject
and predicate consciousness, to consciousness of individuals as the subjects of properties, where
now we could say ‘This stone is warm and this stone is cold’. We move beyond the featureplacing, just ‘It’s sunny’ or ‘It’s rainy’.
And what Hegel is going to argue in the “Perception” chapter is that everything you need to
make that transition is already implicit in the feature-placing language, the feature-placing
contents, if you just realize that there’s two ways in which the features can differ. They can
either be merely different in the way in which night— ‘It’s night’ and ‘It’s raining’ are different.
Or they can be exclusively different, in the way in which ‘It’s night’ and ‘It’s day’ are different,
or ‘It’s raining’ and ‘It’s sunny’ are different.
He’s going to argue first that to see even the feature-placing things that we inherit from sensecertainty as determinately contentful, we’ve got to distinguish those two kinds of difference. And
then in I just think a tour de force of an argument, he argues give him that difference between
two kinds of differences and he’ll show how to build the full structure of objects and properties,
particulars and universals out of it. I’m going to just for purposes of short-hand call that structure
that’s beyond feature-placing, instead of calling a subject/predicate structure, I’m just going to
call it the Aristotelian categorial structure and I’ll say why I think that should be pinned on
Aristotle later in the development.
So Hegel’s got to show us that there’s a complex fine-structure to the notion of universality even
as it applies in feature-placing that is articulated by negation. So universality involves negation.
In the metaphysics that will explicitly be pursued in the science of logic, in this book,
determinate negation is a basic notion in terms of which we’re going to understand mediation,
that is inferential relations, and it’s the basic notion in terms of which we’re going to understand
universality. So although we can keep separate books on these notions, they’re intimately related
and this is the fundamental term.
Now I think maybe the easiest way into Hegel’s thought here is to think about the dawn of logic
in Aristotle, the dawn of the notion of formal logic. And this is something I know very little
about. My understanding of the history of philosophy basically starts with Descartes. I mean,
I’ve read these guys, I have views about them, but I don’t have the kind of control of them that
will let me, put me in a position really to stand behind things I say about guys any deader than
Descartes. But you know people who do and, in particular James Allen is one of the world’s
authorities on the origins of logic in Aristotle and downhill from there, so if you’re interested in
pursuing this, you can do so responsibly. Just don’t ask me. But let me say parenthetically, when
I was a graduate student, Gil Harman was notorious among the graduate students as the most
unhistorical philosopher it was possible to be. And this was on the basis of things like his advice
that it was a complete waste of time to read any philosophy written more than five years ago,
because if whatever was in the older stuff was important it would have been talked about in the
last five years and you should start with where the discussion is now, not where it was back then.
And it was only some years later that I realized this was a slander on him and that in fact
everything Harman did was rooted in his sense of the history of philosophy and grew out of his
reading of the history of philosophy. It was just that he believed it began with Quine. Anyway,
my sense is only driven slightly farther back to Descartes as well I’m confessing a shameful
truth.
Ok, but Aristotle, who room has it, started off with a distinction between two kinds of difference,
between contraries and contradictories. So contraries are things like square and circular,
universals that cannot apply to the same thing at the same time. Contradictories, like square and
not square, also cannot apply to the same thing at the same time, but each property only has one
contradictory, but it can have many contraries. So with red you only get not-red as the
contradictory, but it’s got all the other colors as contraries, red, green, and so on. And Aristotle
bequeathed us the square of opposition, relating contradictories, contraries, by negation and so
on. You’ve seen all this in baby logic courses. Some of you are probably teaching—well, we
probably don’t teach it, but at any rate you’re generally familiar with this.
There’s two main strategies that one could have for thinking about this difference between
contraries and contradictories. The tradition we grew up in, the tradition of modern mathematical
logic that starts with Frege, as codified by Russell and in particular on down to Tarski, so I’m
going to call this the Tarskian order of explanation, doesn’t start with the notion of properties. It
starts with the notion of objects and begins it’s thinking about logic with merely different
objects, a domain of objects about which all we know is which ones are the same and which ones
are different. They’re merely numerically different. It’s a domain of objects. And identifies
properties, to begin with, just with sets of objects. Red is its extension, a set of red objects.
Square is the set of square objects. And low and behold, our domain might have something that’s
both red and square. It’s in the intersection of those properties. Given that notion, we can define
a contradictory property. The contradictory property not-red is the property that’s exhibited by
all and only the objects that aren’t red.
(Writing on the board.) So we’ve got our domain with all of its merely different objects, you can
think of them as points, because points are all just alike except you can count them. We’ve got
this domain and we have a property of being red, it’s just the set of those, and not-red is the set
of everything that isn’t in there. And now we can say that something, say blue, is a contrary of
red in case it implies not-red. So we’re going to define contrariety from contradictoriness. We
use the notion of the complementary set of merely different objects to get a notion of formal
negation, which lets us define the contradictory property not red. And then we can say, well look
blue over here, every object that’s in that set is in the not-red set so it’s a contrary, whereas
square here—it doesn’t follow from being square that something is not-red. This one is square,
but it’s red, so square is not a contrary property to red. We’re building up a notion of contrariety
starting with merely distinct objects introducing a notion of formal negation to introduce the
notion of a contradictory and then treating contraries of a property P, Q counts as a contrary of
property P just in case Q implies not-P. That’s the way Tarskian model theory does things.
Let me say some more in the vicinity here. So Tarskian model theory has as the points of
evaluation, relational structures. And a relational structure is just a domain, and we’ll just worry
about the properties for now, a set of sets on it, which are understood as the extensions of
properties. Formal negation is defined—unlike any ordinary property—is defined by a function
or a constraint on interpretation that applies to all the points of the evaluation, all the relational
structures. It says no matter which relational structure you look at, no matter which domain and
which set of sets on that domain you look at, to be the contradictory of the property associated
with any one of these is to be the set that is the complement of that set in the domain. So
negation is a kind of function. From a point of evaluation, a relational structure, a predicate, it
gives you a way of constructing another predicate, which is its contradictory. And that works no
matter what point of evaluation you have. If you want to follow a contrary, if you want to follow
blue from one point of evaluation, from one relational structure to another, you’re not
automatically told how to do that. You’re what a contrary, let’s say you can follow red as having
a different domain in this relational structure than it has in this one, and the rule for contradictory
tells you how to compute the extension of its contradictory property not-red, and then it will tell
you what it is for some other extension in there to be the extension of a contrary property,
namely to be one that implies not-red, but it won’t tell you how to sort of follow the contraries
from one world to another.
This structure—I think of it as a bottom up structure, starting with the merely different objects,
going through formal negation to define contradictories, and then from there to contraries—this
is the one on which the Kripke/Lewis/Stalknaker possible worlds semantics is then built.
Possible worlds semantics differs from Tarskian model theory in a couple of essential ways. One
of them is that the points of evaluation are not thought of as relational structures anymore, but as
possible worlds. Now for a long time, people didn’t think that difference was a big difference.
And you’ll see a lot of fairly recent literature that ignores the distinction between possible worlds
and models.
One impassioned plea for keeping them separate is John Etchemendy’s book The Concept of
Logical Consequence, which argues that we don’t understand logical consequence precisely
because we’ve run together some model theoretic considerations and some possible worlds
considerations. Roughly, thinking of logical consequence on the one hand as consequence in all
models and on the other hand as consequence such that it’s impossible that the premises be true
and the conclusion not true. And he sees systematic argumentative slides between those two, he
argues, quite separate conceptions, where they come apart, you know, we don’t know what to
say.
But his is not the only such plea. I would say the fundamental difference between thinking in
terms of relational structures, as you do in Tarskian model theory, and thinking about possible
worlds, as you do in the possible worlds semantic framework, is that by definition relational
structures come with domains. You know what all the objects in the relational structure are—
they’re domain elements. On almost everybody’s conception of possible worlds, the actual world
is a possible world. But what’s its domain? I mean, you can by brute force say, “Well, it’s a
relational structure. God told me that I guess. So there must be domain elements so that
everything else is a matter of sets of those.” So David Lewis transcendentally deduces the
existence of fundamental particles and says what’s in his possible worlds is those fundamental
particles and all their mereological sums. Right, mereology is a less-commitive sort of set theory.
But possible worlds as initially conceived, they don’t come with domains. You can’t count
everything in a possible world. There’d be no definite totality of things in them.
Now, this is a bit of an excursus, but I think it’s worth it and if this is all old hat to you, think
about something interesting while I’m telling this story. So the modal revolution really came in
three waves. The first was Kripke’s furnishing of a complete semantics for all of the C. I. Lewis
axiomatic systems of modal logic by treating necessity- by introducing an accessibility operator
between possible worlds, treating necessity as truth in all accessible worlds, and possibility as
truth in some possible world, and then pointing out that if you varied the algebraic properties of
the accessibility relation you could get the different C. I. Lewis systems. You’d get S4 if you
treat the accessibility relation as transitive. You would get S5 if you treated it as reflexive,
transitive, and reflexive and so on. So he gave us a semantics for these modal logical systems
that had been studied axiomatically since 1912, when C. I. Lewis came up with them.
Parenthetically, Kripke was 14 when he did this, sent the proof in to Acta Philosophica Fennica,
a finished journal, which they say good thing about the internet is no one knows you’re a dog,
you know nobody knew he was a 14 year-old kid when he sent this thing in, they just knew he
had a proof, a bunch of proofs. So Kripke showed how to use possible worlds to give a complete
semantics for modal logic, indeed for every modal logic anybody really knew anything about at
the time, though we’ve found ones that you need something else for since. So but all that was
doing was interpreting modal operators in this framework, didn’t have anything to say about the
meanings of non-logical expressions.
In the second wave, and here there’s a lot of people one could mention, but David Lewis, Bob
Stalnaker, and, until his young life was cut short, Richard Montague used this framework to
extend Kripke’s results to give a semantics for non-logical expressions. And they said, well, we
could understand a property like red as semantically corresponding to a function from possible
worlds to sets of objects. So in each world there’s the set of red things. That’s the extension of
red in that world. But the property is the function that assigns to each world the set of red things
in it. It’s an intension, a function from points of evaluation, possible worlds, to extensions. David
Lewis, in his classic article “General Semantics” showed how this gave us a recipe for assigning
semantic interpretants with a power and precision that had hitherto been undreamed of.
(Writing on the board.) So in the possible worlds version of it, here we’ve got terms that are
assigned to objects at points of evaluation, because they’re extensions, and functions from points
of evaluation to extensions as their intension. So the term’ Barack Obama’ is assigned to as its
extension in this world Barack Obama and as it’s intension a function that in each world picks
out the individual who is Barack Obama if he exists in that world. Syntactically you can think of
a one-place predicate like walks as something that if you give it a singular term will give you
back a sentence. So if you give the predicate ‘walks’ ‘Barack Obama’ as its input it’ll give you
‘Barack Obama walks’, a sentence as its <word obscured by coughing>. And what these guys’
brilliant idea was how semantically what you should assign as the interpretant of a one-place
predicate is a function from the semantic interpretant of singular terms to the interpretant of
sentences. So a sentence is interpreted as the set of possible worlds in which it’s true. And the
term is assign a function from possible worlds to objects. So ‘walks’ is going to be a function
from functions from possible worlds to objects to sets of possible worlds.
(Still writing on the board.) Now we also have operators that take one-place predicates and turn
them into one-place predicates. Those are adverbs like ‘slowly’ that turns ‘walks’ into ‘walks
slowly.’ And what Lewis saw is this general apparatus gives us a way to assign the right kind of
semantic interpretant to this. If we’re going to— I’ll just assume that we can follow objects from
world to world and so say this is interpreted by a function from objects to sets of possible worlds,
namely from the object to the set of possible worlds in which it has the property. Then to an
adverb like ‘slowly’ we have to assign a function from functions from objects to sets of possible
worlds to functions from objects to sets of possible worlds. The function from objects to sets of
possible worlds that assigns an object to a set of worlds in which it walks to the ones in which it
assigns it the set of objects in which it walks slowly. And now if you notice that semantically
adverbs come in two flavors, attributive and non-attributive adverbs. So if I buttered the toast
slowly, I buttered the toast. If I buttered the toast in the kitchen, I buttered the toast. But if I
buttered the toast in my imagination, it doesn’t follow that I buttered the toast. So some of these
transformations take you to properties such that it follows from the application of this that you
still have this property, and other ones it doesn’t. Well, now, when you semantically interpret
this adverb as a function from objects to sets of possible worlds to objects to sets of possible
worlds—to functions from sets of possible worlds, now you can actually represent this inferential
semantic difference between attributive and non-attributive adverbs. And no one had ever been
able to do semantics with that kind of power and precision before the late ‘60s when apparatus
came up. And Lewis called his article “General Semantics” because he said, you know it doesn’t
depend on what you take the semantic interpretants of these things to be. This apparatus is
general, or better neutral, between those. If you’re Michael Dummett, you think you should
semantically interpret singular terms not by objects but by sets of recognition conditions for
objects, the conditions under which he could recognize the ‘lark’ set. And he thinks that you
shouldn’t semantically interpret sentences by sets of possible worlds or by truth-conditions, but
by assertability conditions. Ok, that’s a philosophical disagreement, but this apparatus doesn’t
care about that difference, it says well then a Dummanian (?) adverb is going to semantically
interpreted by a function from functions from recognition conditions to assertability conditions to
functions recognition conditions to assertability conditions. So in “General Semantics”, Lewis
gives us a way of getting the power of this new intensional semantics no matter what we
semantically associate with these different kind of expressions. And that’s really when modern
formal semantics took off.
Ok, Hegel doesn’t note that. <Laughter> This happens— well, you’d be surprised, but he does,
but not that. But this second wave of the modal revolution was moving beyond Kripke’s
semantics for modal logical opperators to a semantics for any non-logical expressions and that
was a huge advance. The third wave of the modal revolution was initiated by “Naming and
Necessity” and taught us about a priority, necessity, and, this newfangled thing, metaphysical
necessity in a sense that we had never had before. My personal view is that was a bridge too far
and we should have stayed with the second wave, but that’s prejudice.
Ok, so what does all this have to do with Hegel? One way of thinking about the relation between
contraries and contradictories starts with merely different objects, understands properties as sets
of those merely different objects, so the properties are different if the objects that they’re sets of
are different—that’s how you individuate sets, just by what’s in them—then defines formal
negation by a complementary operation, so the contradictory of a property P, say red, is the
property that’s exhibited by all and only the objects that don’t exhibit red. And then you can
define contraries as something is a contrary, some property Q is a contrary of P if exhibiting Q
implies exhibiting non-P. So that’s all Tarski, made particularly precise and explicit in Tarskian
model theory, we build on top of that a possible worlds semantics and now what we do in the
possible worlds semantics is look at functions from points of evaluation to extensions which is
how we define negation. Negation is the same in all models. It means the same thing. You
compute the contradictory of a property the same way in all models. Well, you compute the
meaning of the adverb or the extension of the adverb the same in all models. Really, what the
second wave of the modal revolution was doing is extending the treatment that Tarski had given
to purely logical expressions to non-logical expressions. And now you could say something like
well there’s no world in which something is at the same time both red all over and blue all over.
That’s something you can say now in a way that in Tarskian model theory all you could do is
restrict the set of models in some completely arbitrary way, whereas now we say oh, that’s part
of the meaning of red and blue is that you track them across the worlds in such a way that
nothing ever had both of those whereas red and square are not like that
So this is a very powerful notion and you get a perfectly reasonable interpretation of contrariety
at the end of the day when you built up in this way. What Hegel has is a completely different
way of thinking about this relationship. He says start with the notion of contrary properties.
That’s the notion of determinate negation. Blue is a contrary of red. They stand in the relation of
determinate negation. Why is it determinate? Well, because it’s different from the way green
stands to red. They’re both contraries. Abstractly they have that in common, but they’re
determinately different. There’s more than one of them and you can pick out one of the
contraries—blue by contradistinction from green, so you can treat something as— Ok so if you
start with this notion of determinate negation which is a relation of Aristotelian contrariety,
where any property can have many contraries though it has only one contradictory—remember
we started with the notion of objects, built up contradictories, and eventually got to contraries in
the Tarskian and the Kripke/Lewis/Stalnaker (KLS) extension of the Tarskian model theoretic
apparatus—Hegel’s going to say well, what is formal negation, not-red? That’s what’s implied
by every contrary of red. So if something is blue, it follows that it’s not red. If it’s green, it
follows that it’s not red. The contradictory for Hegel is the minimum contrary, minimum in the
sense that it’s the one that’s implied by all the contraries. Furthermore, we can understand that
implication in terms of contrariety. Remember I said you can define P implying Q if everything
incompatible with Q is incompatible with P. So in terms of that notion of material
incompatibility we define contradictoriness. We’re doing this still at the level of properties. But
this is turning the Tarskian scheme on its head. We’re going from contrariety to contradictoriness
instead of the other way around. And from Hegel’s point of view, the notion of formal negation
has thrown away all the content, all the determinateness, because you’ve thrown away
everything that all the contraries don’t have in common. What all the contraries have in common
is just being not-red and, from that point of view, you can’t see the determinate differences
between them, the difference between green and blue and yellow and so on. So he’s going to say
formal negation is the poorest emptiest kind of negation. But furthermore, what he’s going to go
on to do next is build up the rest of the Aristotelian object-property structure, which the Tarskian
and KLS approach has a good story about, but he’s going to have a completely different order of
explanation. And that’s the story that we get in “Perception”. I haven’t said how that story goes
yet. But let me stop there for comments or questions so far.
So I’m saying that the way in is to think of the Aristotelian distinction between negation in the
sense of contraries, determinate negation, and negation in the sense of formal negation,
contradictoriness and see there’s two orders of explanation one could pursue. Aristotle doesn’t
pursue either one of them. He just treats these as two different things and looks at what we can
do with both of them, but the Tarskian order of explanation treats contradictoriness as prior,
explains it in terms of mere difference of domain objects, and the Hegelian one is going to take
determinate negation to be its primitive, semantically, logically, ontologically, and
metaphysically. It’s going to take that to be the primary notion. And just as we saw you can get
mediation out of that, you can get implication relations, so we can see you can get a notion of
formal negation. The contradictory is the minimum contrary in the sense of the one that’s
implied by all the contraries.
Jack: So we talked a couple weeks ago about how— Well, I asked about the argument for why
we should think that you can reduce content or mediation to determinate negation rather than
just— clearly you have to acknowledge that they necessitate each other but why we have to take
that further step of saying that it just consists of determinate negation. So I’m wondering if this is
what you take to be the argument and it’s something like an inference to the best explanation,
you know. Look at how much I can get out of starting with just one primitive.
Bob: I mean, he’s going to have a lot more things to say about negation as the metaphysical
essence of everything that there is—of thought and of being as well. But I think at the end of the
day is give me this and look how much I can build out of this one primitive. He’ll offer other
arguments, but you have to start somewhere and I think the things he needs to appeal to for those
arguments are all more controversial than the fact of this constructability that he’s going to do.
So I think the way of thinking of it is sort of implicit in the way I’ve presented it here—well,
we’ve got one familiar way of thinking about things, incorporated in the Tarskian picture, get
stereoscopic vision by thinking the same material through, taking another path through it, and
compare and contrast.
Student 1: Another question back from the dead. How does that tricky concept of sublation fit
into this? And I might ask to look at paragraph 113 more closely to figure that out.
Bob: Yeah, so far not at all. I mean, it’s going to be involved in— I mean, I will get to 113 and
when we can talk about it, but when I said Hegel’s going to argue that the whole Aristotelian
structure of objects and properties is implicit already in acknowledging a kind of generality even
at the feature-placing level that acknowledges that the universal, that universal, that kind of
generality is determinate in a sense that distinguishes these two kinds of difference, what he calls
mere or indifferent difference, like red and square are different in that sense, and exclusive
difference, that’s the determinate negation. Give him that, everything else is implicit in that.
That’s going to be an aufhebung, translated or labelled as sublation in the translation.
So ok. Let me say how this goes. Well, here’s a bit of commentary before I do this. Michael
Friedman, building on work by Jaakko Hintikka, has given us an astonishing revelation about
Kant, that essential features of the first critique come out of the years that Kant spent meditating
on the proof structure of Euclid’s elements in which he realized that there were a number of
conceptual arguments in Euclid’s Elements, arguments that could be reconstructed in a
syllogistic way or as we could put it, you know the syllogism seems outdated, that you could
represent with Venn diagrams inclusions and exclusions of concepts, but there was a class of
arguments that couldn’t be represented that way. These are, not by coincidences—well, these are
arguments like the argument that for any line segment there is a midpoint to it, which if you
think about Euclid, he says take some circles that have the end points as centers and they’ll
intersect in exactly two places—we’ve already proved that, Euclid says—and construct the line.
That line will be, we will show, perpendicular, but it will also, we’re going to show, bisect the
segment. You can always perform these constructions, so there always is a midpoint of two lines.
That’s not an argument that you can reconstruct in syllogistic terms. It’s not an argument that
you can represent in terms of Venn diagrams. Kant says, well it’s a matter of construction, rather
than extracting conceptual inference or consequences. You’re constructing the midpoint. And
that’s the way of course that infinite totalities come into geometry, because if every— if we can
perform this construction on every segment, we can bisect it, then we can bisect the half and we
can bisect that, and we can, by this construction, determine an infinite totality. So these notions
of arguments of infinity and by construction, those are not conceptual arguments. You don’t get
them by logic. You get them some other way. And Kant’s name for how you get them is
synthesis. Synthesis, some of it’s conceptual and some of it’s not. Some of it’s intuitive
synthesis. Now what— so, people had known that it was specifically by looking at argument in
Euclid’s elements that Kant had come to think of the intellect as having this non-conceptual,
constructive element, which was the only grip we have on infinity. You have to construct these
things synthetically in intuition. It’s not a matter of the concepts.
What Hintikka realized is that these are exactly the arguments that involve iterated, alternating
quantifiers. For all..., there exists.... For every line segment there is a center point. That’s what
you can’t represent in a Venn diagram, a relation between two sets such that for every point in
this one there is a point in this one such that.... That the Venn diagram isn’t set for. Traditional
logic couldn’t handle that. We needed to introduce, Frege needed to introduce quantifiers in
order to get arguments that involved these alternating quantifiers, but particularly the for
all...there exists... So this is why traditional logic couldn’t handle instances like ‘If someone
admires everyone, then someone admires himself’, to see that that was a good inference. Ok, so
look, Kant realized that the expressive power of traditional logic didn’t extend to exactly the
things that we would add the expressive power to represent with quantificational logic. So he put
something else in there—synthesis.
Now what Friedman realized is that what Kant was doing is exactly like an alternate form of
quantificational reasoning, one that uses Skolem functions, due to the logician Skolem. (Writing
on the board.) And what he realized is that these tough inferences that involve alternating
quantifiers <coughing and turning pages obscures words> two universals or two existentials
becomes collapsible into one and just have an ordinary pair of stuff. It’s these alternating ones
where new stuff happens. Instead of saying that, you could just have a function which goes from
one of these and gives you this one. This says “for every f, there is a g”, but if you had a function
such that if you gave it an f, it would give you a g as the consequence, you could do everything
that you can do with these alternating quantifiers, you could do that with Skolem functions
instead. And furthermore, the Skolem functions do it by—what?—by constructing this one. They
determine the particular. This just says there is one, but the Skolem function actually gives you
one. It’s a way of constructing them. And what Friedman realizes in the second chapter of his
book on Kant and the exact sciences is Skolem functions are exactly what Kant’s intuitive
syntheses do. It’s the same conceptual apparatus. He not only saw in Euclid’s elements that there
was a class of arguments that couldn’t be represented in traditional logic, he came up with a
construction in intuition method that basically was Skolem functions which are expressively as
powerful as our quantificational apparatus.
If I’d had an idea like that about Kant I would die and go to heaven. That would be it. I think the
scales fall from our eyes when we see this, but what I want to say is in the wake of this Friedman
and Hintikka sequential discovery and sort reconstrual of what’s going on we see that the twenty
years that Kant spent thinking about the proof structure of Euclid’s elements yielded this
incredible result. Well, that’s the same way Hegel concentrated on Aristotle on contraries and
contradictories. And I think what he came up with from that is no less remarkable than what
Kant came up with, which it’s taken us two hundred years to see exactly what it was, but you
know that’s the way it goes when you make these big moves. And I think something of that order
of magnitude came out of Hegel’s meditations on Aristotle here, specifically on contraries and
contradictories. So, I don’t know, I’ll stop there. This is again a bit of a byway, but yeah.
Anyway I recommend the Friedman chapter.
Ok. Here’s the way I think Hegel’s story goes and I’d like us to get sort of clear on how that
works as I’m telling the story and then we’ll go read some of the passages and try and catch him
saying these things. So how is it that this whole Aristotelian structure of objects characterized by
properties, and I still haven’t justified calling it that yet, is implicit in the difference between
these two kinds of differences, or the difference between these two kinds of negation? Well, we
start off with the idea that what makes a property the determinate property that it is the relations
of exclusive difference that it stands in to other ones, that a property is the determinate property
that it is because of its position in the space of contraries.
That’s already to say that universality, being a determinate property, is articulated by relations of
negation, of exclusive negation. And, I mean I should say the terms Hegel uses for these.
‘Exclusive difference’ is ‘ausschließender Unterschied’. That’s literally exclusive—
ausschließen is to rule out and it’s probably worth keeping in mind that the term for drawing a
consequence in German is ‘schließen’ and an inference is a ‘Schluß’, which is the result of doing
that. But ausschließen, ruling out, it’s ausschließende, difference. That’s the exclusive
difference. And he says it’s mere, bloße, or indifferent, gleichgültige, difference is the kind of
difference that there is between red and square, where they’re not contraries. All right, but it’s
these modally robust exclusive differences that determine, that articulate the contents of
determinate properties or universals. Hegel will invoke, in other places, the Spinozistic doctrine
“Omnis determinatio est negatio”, “All determination is negation”. Something’s determined
insofar as it has a limit, beyond it it’s not. That’s what it is to be determinate. And he’s adding to
Spinoza’s doctrine—yeah, and that’s exclusive negation, not mere negation. But there’s already
a sense in which the identity of a property consists in its differences from other properties. Its
unity, its self-relation, he’ll say, not entirely helpfully, depends on its relation to other things;
indeed, consists in. What it is, consists in its relation to other things. And one of the overarching
intellectual tasks that he set himself is to try and understand this kind of identity that consists in
differences. And what we see here is his exploring the fine structure of those differences.
So we said if we start with exclusive difference, we’ve seen we can get material consequences
and we’ve seen we can get contradictories. We can get merely formal negation out of exclusive
negation. And here we get a category, determinate properties or universals, officially all we’ve
got is sense universals, coming out of sense certainty, whose identity consists in their exclusive
differences from each other. That’s the first level. But now when we ask, well what do you mean
by exclusive differences? What is the difference between exclusive difference and mere
differences? Well, we see there has to be a unit of account. Exclusive differences are those that
one unit can’t have both of, whereas mere differences are ones that one unit of account can have
both of. Implicit in the distinction between exclusive and indifferent difference is the idea of a
unit of account, which is going to be objects, particulars, things, thinghood in general he says
here. But without that unit of account you can’t make sense of that difference between two kinds
of difference. I mean, you can just think of them as, again, points of evaluation, but one point of
evaluation can’t have two exclusively different properties associated with it, but it can have two
merely indifferent ones. Only if you’ve got those points of evaluation or units of account can you
make sense of that difference between two kinds of differences. Well, those units of account are
categorially different from properties. Properties we can only make sense of as an ontological
category by their relation to something that isn’t properties but is a unit of account for keeping
track of the exclusive or mere difference between properties. So here’s a second sense in which
the identity of the property consists in its difference. Now it’s the difference categorially, the
inter-categorial difference between properties and objects. We started off with the intracategorial difference, exclusive differences between properties, but now that we see that those
come in the two flavors, exclusive and indifferent, we’ve got to acknowledge something that
isn’t a property, but is a unit of account for them.
Now let’s think about those units of account for a minute. They by the very process by which we
have uncovered them, extracted what was implicit in the idea of a difference between these two
kinds of difference, they can stand in two different kinds of relations to properties. On the one
hand, they are what Hegel will call the also or the medium in which properties that are only
indifferently different are associated. So ‘The salt is white and it’s cubical and it’s tart’, that’s the
also, being the medium of indifferently different, merely different, compatibly different
properties. But it’s equally essential to being an object that they’re the units of account that
exclude exclusively different properties. That is, because I’m host to white, I can’t be host to red
and black and so on. Because I’m host to cubical, I can’t be host to spherical and so on. So on the
one hand there’s a principle of inclusion of properties and on the other hand a principle of
exclusion of properties. To be an object you’ve got to play both those roles. That difference
between two relations that the objects can have to properties, that’s essential to what it is to be an
object, that it stands in an inclusive also relation to some properties and an exclusive relation to
other properties. That difference between its two kinds of relation to properties is of the essence
of what it is to be an object or a particular.
So not only is it essential categorially to objects that they be related to properties, but
furthermore that they have these two different and opposed relations to properties is essential to
what it is to be an object or a particular. So now we’ve got the intra-categorial differences,
exclusive differences among properties, in virtue of which they’re determinately contentful; the
inter-categorial difference between objects and properties, in virtue of which properties are what
they are an objects are what they are; and we’ve got the difference within the object, within the
category of objects now in two different relations that it stands to properties, which is an
essential part of being of the category it is, of being an object. Now we can turn the crank one
more time. And this is an argument that Hegel takes from Aristotle. We said we can construct
from the notion of contrariety, from the notion of exclusive difference or determinate negation,
we can construct the notion of formal negation by throwing away all the determinate differences
between the contraries of something. So we can construct the idea of a contradictory of a
property, of one that is, Hegel says, its opposite. And we do that just the way, I mean it’s another
path through the same— exploiting the same structure, just the way that the, well just by
reversing the way that the Tarskian order of explanation looked at these things. So the opposite
of a property is the property that’s had by all and only the objects that don’t have that property.
So we can get red, we can get to non-red. Non-red just is the property that’s exhibited by all the
objects that don’t exhibit red.
That’s the opposite of a property. What’s the opposite of an object? We have this symmetrical
relation between objects and properties. The object has a bunch of properties. The property is
true of a bunch of objects. We can define the opposite, the contradictory, of a property in this
way. We have a property that applies to some objects and its opposite is the property that applies
to all and only the other objects, the ones that that property doesn’t apply to. So what would the
contradictory, the opposite of an object be? It would be an object that had all and only the
properties that the first object doesn’t have. But what Aristotle already noticed is: there is no
such thing. Because all the properties that a given object doesn’t have aren’t compatible with one
another. They include things that are contraries of each other as well as things that are contraries
of the objects they have here. So, my right thumb has the property of not being identical with
Mozart. And it also has the property of not being identical with the phone that’s sitting on the
table here. So the object that was the opposite of my thumb would have to be the property of
being identical to Mozart and identical to the phone that’s sitting there, but it can’t have those.
Those are exclusively different properties. Because of the way contraries work, objects can’t
have opposites. Now that’s an inter-categorial asymmetry between objects and properties, which
is a necessary feature of, in part constitutive of, the identity of those ontological categories, that
properties have opposites and objects don’t. That’s another way of thinking about the relation
between contrariety and contradictoriness. Hegel spent years thinking about this difference in
Aristotle and the Dawn of Logic. And what we get is this result. If we start with this distinction
between exclusive and mere difference, we can see that implicit in it is this fine structure of
different kinds of identity and difference, different kinds of constructed negation. We can say
objects and properties are in a certain sense categorially opposites of each other. They differ
from each other in this constitutive way, namely that properties has opposites and objects don’t.
That’s a category defining difference between objects and properties. To be an object, the
identity of thinghood in general, as he says, consists in part, but essentially and necessarily in
being different from properties in that it doesn’t have opposites. That turns out to be necessary
for it to play the role of a unit of account for properties. That isn’t obvious when you just think
about feature-placing.
‘It’s fine’ and ‘it’s night’. ‘It’s raining’ and ‘it’s night’. Those three different properties stand in
the two different kinds of difference to each other. ‘Fine’ and ‘rainy’ are exclusively different,
‘fine’ and ‘night’ indifferently different, ‘raining’ and ‘night’ indifferently different. In that
already is the identity of these two categories, the properties and the units of account for the
properties, whose difference as ontological categories is constituted in part by this exclusive
inter-categorial difference between them, namely that the one has contradictories and the other
doesn’t. It because Aristotle saw that already that I call this structure of objects and properties
Aristotelian. He was the first one to think through what it was about. Well, it’s this structure that
starts with exclusive differences between properties as what the identity of the property consists
in is its difference from its intra-categorial others, its exclusive difference. You can think of it as
being the property it is as its position in the space of contraries. If, in the contemporary literature
on the metaphysics of properties, if you identify properties by the nomological relations they
stand in to other properties this is an instance of that kind of view, because these contrarieties are
modally robust, they’re nomological relations. So that’s the first kind of identity and difference,
just within the category of properties.
But then we see that the difference between the exclusive difference and mere difference requires
an inter-categorial difference—it requires units of account for these things—and that that intercategorial difference, that’s equally essential to what it is to be a property. It’s to be in this inter-
categorial relation to things that are not properties, that are exclusively different from properties
in a quite different sense than the sense in which contraries are exclusively different from one
another. And when we think about these units of account and the relations that they stand in to
the properties, we see that they stand in two quite different and opposed exclusive relations to
properties: one of inclusion, the also, and one of exclusion. They’re units for both of those. And
the difference between those relations between objects and properties, the difference between
those is essential to the identity of objects as objects, as the kind of things that they are. And then
we see that it follows from all of this that while properties can have contradictories, objects can’t,
that these categories are asymmetric with respect to negations in yet a different way, that the
identity of these ontological categories depends on this difference between them, depends on, is
articulated, necessarily involves this difference. This is an order of explanation starting from
exclusive difference of properties that gets us the full Aristotelian structure of objects and
properties. It’s the converse, in a certain way, of the Tarskian order of explanation that is the
foundation of modern logic and semantics, that starts with mere differences of objects,
understand properties as different in terms of the mere differences of the objects they apply to,
defines contradictoriness and formal negation by complementation within the domain and then
defines contrariety in terms of implying the contradictory, and then builds in the modal character
of these things once we go up to the KLS superstructure on the Tarskian structure. That’s one
way of thinking about it. Hegel’s got a completely different metaphysical path through these
ontological structures, one that builds the modality in at the base instead of having it come way
at the end when we impose restrictions on what logically possible worlds are metaphysically or
nomologically possible, that we never imposed on the model theoretic things. So this is the
structure, this is I’m claiming the way he wants us to think about objects and properties. This is
the order in which we extract different features of the fine structure of the relations of negation
that are implicit in the idea of universality tout cour. There are all these different, more
complicated kinds of difference that we can build out of that fundamental difference between
two kinds of difference, between indifferent and exclusive difference. Now we’ve got the
categorial difference between objects and properties; we’ve got the difference between the two
kinds of relations between objects and properties, the inclusive and the exclusive one; we’ve got
this difference of contradictories and no contradictories. All of these are kinds of identity through
difference within the same category and across categories. We build all of them out of the basic
ones and, he says, those basic ones I already gave you at the end of sense-certainty. We looking
on could see that you were already committed to making this distinction just in seeing what’s
expressed by feature-placing language as determinate only insofar as you could distinguish these
two kinds of distinction. So this is the conceptual structure he wants us to grasp and it’s the
background for all of the [?] things that he says here trying to find a language to say these.
Student 2: I’m just wondering, on what grounds are we characterizing this as a metaphysical
claim? So why not limit it to the epistemological at this point?
Bob: Well, the “Perception” chapter has got the structure of an introduction in which he reminds
us what we were getting from the previous chapter and sort of tells us where we’re going to end
up. And then the three experiences of consciousness understanding itself as perceiving, that is
understanding itself as applying sense universals which are immediate and as immediate are still
conceived of as independent of their relations to anything else. You can’t have that, but that’s the
conception. We get the three experiences of it and then a concluding thing that sums up and
points us to the next one. The middle, the second of those experiences of perceiving
consciousness, says “Can’t I help myself by going epistemological here?” I mean specifically
what it’s doing is saying “I’m just a simple caveman. I can’t understand this identity consisting
in differences. Maybe the identity is there ontologically and the differences are just epistemic.”
No, turns out that won’t work. “Maybe the differences are there ontologically and I’m unifying
these things epistemically.” No, that isn’t going to work. We’re going to have to say, well
ontologically objects and properties have identity and difference and our thoughts must too, but
if that’s true, if they have the same structure, how is error possible? Oh, don’t know yet, but
we’ll find out going on. So I mean, the question you ask is up in the air. What is this a structure
of? But it’s going to end up being the structure of both of them. And you know he’s going to
need a term for what structure— determinate ways the world can be and determinate thoughts
about it have to share and everything he said here is going to be amphibious between those.
When all the dust has settled in the science of logic, he says, well this is the structure of logic, so
it’s the structure of being and of thought. You know, philosophers need to be very careful when
they’re giving an irritated response to somebody who really is missing the point that they’ve
gotten and we have this sort of horrible history of Plato’s irritated response when someone asked
him, “Where are these forms anyway?” “Oh they’re laid up in heaven.” If you’re silly enough to
ask that question, then you’re silly enough to accept this answer. And suddenly we have NeoPlatonism and they say, “Ah, yes! But where is this heaven in which these things are laid out?”
Taking literally in the preface to The Science of Logic Hegel sort of asking himself on behalf of
some Wittgensteinian creatness [?] straight man “So what is this structure? What kind of thing is
this anyway?” He says, “Ah, it’s the structure of God’s thought before the creation,” before there
was a distinction between being and thought is the idea. Well, if you find that helpful, then he’s
glad he said it and if not, don’t take it too literally. Atheist that he is, he doesn’t believe in
creation and so on. So yeah, it’s a new kind of, it’s of a sui generis category, which he will call
indifferently logical, philosophical, or speculative structure, and it has these aspects, ontological
and epistemic. But I mean, I think it’s helpful obviously in the way I presented it to lay it
alongside— Well, I mean is the Tarskian order of explanation an ontological— I mean, that’s a
logical and a semantic way of thinking about things, but you better believe people take it
metaphysically seriously, mostly these days under the heading of Humean metaphysics, and
thereon hangs a different tale, but people certainly do think, well, if that’s the structure of what
we can mean, then that must be the structure of the way things are. Or other people will say,
“Oh, no, no, that’s a bad inference. You can’t read your ontology off of our semantics.”
Ok, well, why don’t we take a twenty minute break and come back at five minutes of the hour
and we’ll look at some actual text to see this going <word obscured by people getting up>.
Ok, well, let’s look at some of the passages and see how much sense they make in the light of the
story that I was telling. The introduction is really up through paragraph 116, is the introduction,
so that’s mostly what I’m going to be looking at first, but I’m going to be jumping around in it.
So in 114, he introduces the idea that the identity of the properties depends on their determinate
differences from one another. So he says, “…if the many determinate properties were strictly
indifferent (gleichgültig) to one another, if they were simply and solely self-related...” That’s a
way he’s talking about unity, about identity, about the one as opposed to the many. “...if they
were simply and solely self-related, they would not be determinate; for they are only determinate
insofar as they differentiate themselves from one another…” That’s unterscheiden. “...and relate
themselves to others as their opposites.” Als entgegengesetzte. “Yet; as thus opposed”
(entgegensetzung) “...as thus opposed to one another they cannot be together in the simple unity
of their medium, which is just as essential to them as negation...” So you’ve got the exclusive
differences between them—that’s the first difference that their identity consists in. “Yet; as thus
opposed to one another they cannot be together in the simple unity of their medium...” Their
medium is thinghood in general, the particulars that exhibit them. “...which is just as essential to
them as negation.” They can’t be together in it if they’re opposed. If they’re exclusively
different, that precisely means they can’t be exhibited by the same object. And yet, that kind of
unity, being in an Also, is as essential as their negations from one another are. So we’ve got a
relatively complex structure. “...the differentiation”—that’s unterscheidung, rather than
unterschied that would be different—”...the differentiation of the properties, in so far as it...is
exclusive,” ausschließende “each property negating the others, thus falls outside of this simple
medium...”, the medium being the objects. So he says you’ve got to think of the property as
having these two kinds of relations—its intra-categorial relations of exclusive difference to other
properties and its inter-categorial relation to the simple medium, the one, the thing, and yet it’s
relation to the thing is just such that the thing excludes all those other properties, all the ones that
are contraries of it.
Again in 114, “if the many determinate properties...” Yeah, ok, all right. So then 114 continues,
“The One”—objects—”is the moment of negation; it is itself quite simply a relation of self to
self and it excludes an other; and it is that by which ‘thinghood’ is determined as a Thing.” So
this is just saying that its role as a unit of account for exclusions, for exclusive differences, is
essential to what it is for it to be one thing. Two things can have incompatible properties, but one
thing can’t. So its identity as one thing essentially depends on its excluding some of the
properties that it doesn’t have. Some of them it simply doesn’t have and others it excludes—the
ones that are contraries of ones that it has. Still in 114, “Negation is inherent in a property as a
determinateness which is immediately one with the immediacy of being”—now that’s because
we’re talking about sense universals, so observable properties, ones that we can apply not as a
product of and inference—”an immediacy which, through this unity with negation, is
universality.” Now remember I quoted him saying the richness of content belongs to perception,
not to sense certainty, not to immediate certainty, because only here is the content mixed with
negation. And now we’re finding out mixed with negation is a very crude way of describing the
intricately articulated structure that he’s got. “As a One, however, the determinateness is set free
from this unity with its opposite, and exists in and for itself.” So it is a unity and what we’ve got
to understand is the multifarious ways in which having the identity you do, being the unity that
you are as an object depends on all of these contrasts, some of them exclusive, but even the
exclusive differences have different kinds. The way the object excludes other properties is
different from the way properties exclude other properties. The way the object is exclusively
distinguished from properties in general—properties in general have opposites; it doesn’t—all of
those are different.
Here I thought it was useful to jump ahead a little. In 120, which is in the middle of the second
experience of consciousness conceiving itself as understanding, he says, “...these diverse aspects
for which consciousness accepts responsibility are specifically determined. White is white only
in opposition to black, and so on, and the Thing is a One precisely by being opposed to others.
But it is not as a One that it excludes others from itself...it is through its determinateness”—its
properties— “that the thing excludes others. Things are therefore in and for themselves
indeterminate; they have properties by which they distinguish themselves from one another.” I
think this is a way of saying that objects are merely different from one another—they don’t have
contraries, as well as not have contradictories—but their mere difference from one another,
which is what makes them have the kind of unity that they do, consists in them having the
specifically determined properties that they do, namely in excluding properties that are the
contraries of those properties.
So in 113, before those passages in 114 I was reading, he says the sense universal is a universal
immediacy and I’m saying that just means it’s a sense universal. And 113 continues, “the
medium in which these determinacies permeate each other in that universality as a simple
unity...but without making contact with each other…” This is what later he’ll call the Also, all
these indifferent properties that are properties of one and the same object are in it without
interfering with one another. Its being cubical doesn’t interfere with its being white or its being
tart, because those are all merely different. So he says they permeate each other in that
universality. Now here the universality is the medium of one object and what it’s universal over
is all of the properties, merely indifferent properties, that it’s got. It’s universal relative to those
properties.
Hegel does not, as far as I can see, distinguish here between properties as repeatables and
properties as tropes. I think I mentioned that, for no very good reason, the recent literature has
taken to using the word ‘trope’ for individual property instances, as opposed to properties that
can have many instances. Ok, so when he says that it’s universal, that it’s the universality, the
one object that has these many properties is a universality, a universal medium with respect to
them, one might want to know, well is that a bunch of property tropes? Or is that a bunch of
property repeatables that it’s universal with respect to? And I can’t pin him down as answering
that question one way or another.
Ok, “...for it is precisely through participation in this universality that each is on its own
indifferent to the others.” Each is, on its own, the property that it is. It’s indifferent to the
others—they can be co-exemplified. As it has turned out, “this abstract universal medium, which
can be called ‘thinghood’ itself…is nothing other than” what in the previous section we called
“the here and now…” Ok, part of the background to this is that in spite of the huge differences
that there were between the Early Modern, pre-Kantian philosophers and the medievals—less
than some people think. Former colleague Joe Camp has a very interesting article called
“Descartes, the Last Scholastic”—all of them used basically Aristotelian principles of identity
and individuation. Kant was the first one, because of his study of Newton, to use spatio-temporal
principles to identify and individuate ordinary objects, to think of them as identified and
individuated by their spatio-temporal location. That shift, from thinking about essence and
accident to thinking about spatio-temporal principles of identity and individuation, vastly
important in Kant—that’s why the aesthetic plays the role that it does—and Hegel is here saying,
well look the reason the Here and Now played the role that they did in sense certainty already,
we can now see the successor, sort of more filled-in notion of that is the pure thinghood. And
he’s thinking of the things as being what were individuated by Here and Now, but he says
they’re individuated by their properties. “This abstract universal medium, which can be called
thinghood itself is none other than the here and now, namely, as a simple ensemble of the many.”
It’s a one in which the many are unified.
Ok, a couple of things from 114 that I think are still elaborating this picture I described. He
identifies his topic. He says, as it turned out, “In this relationship, it is merely the character of
positive universality which is at first observed and developed…” So we’re just looking to unpack
the notion of universality. And he says, already in 114, “This simple medium is not merely an
“also”,”—the Also of the many indifferently different properties— “an indifferent unity,” he
says, “it is also a “one”, an excluding unity.” So here are the two aspects of objecthood, as
inclusive relative to merely different properties and exclusive relative to exclusively different
properties. In all of these things, I’ve been talking about the topic as being understanding unity as
consisting in differences of different kinds. And we can already see that’s not just a vague
slogan: identity consists in differences. Yes, he would accept that, but we’re seeing there’s a
much more articulated structure of differences that he thinks the identity of an object or property
consists in. He also will use the term for the kind of identity that consists in its differences—he’ll
talk about it as the negation of the negation. The negation it’s the negation of is the differences
that constitute the unity and it’s the negation of them in that it’s a unity created out of those
differences. I think you don’t get anywhere in thinking about Hegel if you think there’s some one
principle of the negation of the negation or of identity out of difference. Already just in talking
about perceptible objects we see that there are many kinds of negation, many kinds of difference,
and many kinds of identities formed out of them and an intricate, indissoluble structure of all of
those. So just rehearsing these slogans—negation of the negation, identity through difference—
that isn’t going to get you there. You’ve got to look at the fine structure of different kinds of
differences, all of which, he’s claiming, can be elaborated from those two fundamental kinds of
difference—mere difference and exclusive difference.
So in 117 he says, “I now further perceive the property as determinate, as contrasted with another
and as excluding it”. So that was our first point. “I thus in fact did not apprehend the objective
essence”—well, the essence of objects—”correctly when I determined it as a community with
others…” That is, as an Also, as a medium in which indifferent properties can be. And in terms
“of the determinateness of the property, I must in fact break up the continuity into pieces”—the
community into pieces—”and posit the objective essences”—the essence of objects—”as an
excluding One...” So we got the object as an Also and the object as One—again the exclusive
difference between those two roles with respect to properties that are essential to the identity of
particulars or objects as such. And he says, “In the broken up One I find many such properties
which do not affect one another but which are instead indifferent to each other.”
Ok and in 115 he says, “...the Thing as the truth of perception”—he elsewhere calls it the Thing
with many properties—”reaches its culmination to the extent that it is necessary to develop it
here.” So here’s everything that we have extracted as implicit in the notion of universality in the
form of the Thing of many properties and it is the “indifferent passive universality, the Also of
the many properties of rather ‘matters’“—so that’s the Also—the “negation generally as simple;
that is the One, the excluding of contrasting properties—that’s the other side of objects as
exclusive—”and the many properties themselves” identified by their standing in relations both of
exclusive difference to some properties and of indifferent difference to others, which is “the
relation of the first two moments”. So that difference of two kinds of difference of properties is
reflected in the difference between the object as Also and the object as excluding the One, so just
as we can think of the object as the relation between those two roles, we can think of the
properties as the relation between the two kinds of relations of difference that they stand in to
other properties. The “negation as it relates itself to the indifferent element”—that’s the object—
”and extends itself within it is a range of differences;”—that the many properties in the Also—
”the point of…individuality in the medium of enduring existence radiating out into multiplicity.”
And now here I think the “radiating out” means this is its role in excluding, this penumbra of
contrary properties, this cloud of uninstantiated contrary properties that we can think of as
surrounding every instantiated property. Those are all the ones that are repelled by it and that are
not in the object. And there’s the others that are indifferent, that are not repelled by it because
they’re not in this cloud of contraries around it. And what we’re going to find in the next section,
where he’s worried about the supersensible world behind the sensible world, the one he’s really
going to be worrying about is all of those uninstantiated possibilities, the ones that are excluded,
in virtue of which the ones that are instantiated are the things they are—where are they? They’re
not instantiated in the things and yet they’re essential to those properties being what they are and
so to the object being what they are. Ask where they are that’s not right, but how are we to think
of their presence, their activity in this thing.
Ok, so I think every piece of the story that I was telling we see in those passages from 113 to 115
really and those are the ones where he’s not—where he’s just telling us how it is, this is where
we’re going, I’m speaking in the order of exposition of the book to you the phenomenological
consciousness, haven’t yet seen how any of this emerges in the experience of the phenomenal
consciousness, the consciousness that understands itself as perceiving the thing of many
properties. That will get three experiences, three movements of experience, in the sense of
movements of experience, experience of error and so on that we saw in the introduction. So next
I’ll say something about those three movements of experience, but let me stop here. At this point
the hope is that you can understand what he’s saying in this sometimes extravagant language as
talking about this other order of metaphysical explanation of the Aristotelian structure of things
of many properties.
Ok, well, the three experiences go like this. And let me say, I don’t have a really good story
about why it’s just these three, why in this order, how they come out of one another. I think I
understand the picture we’re supposed to get, that we get in those introductory paragraphs and in
the concluding one. Exactly how these experiences give rise to one another is much less clear to
me. So I’m going to give it my best shot, but I don’t think it’s that satisfactory. What I am
confident of is, the first of them involves consciousness conceiving itself, understanding itself,
under the categories of perception, of perceiving consciousness—that is, taking itself to be
applying sense universals, which are immediate, both immediate in the sense of immediacy of
origin, which they really are, and in the sense of immediacy as independence of relation to other
things, as being self-contained or autonomous, and that’s the one that you can’t have. What it’s
going to be experiencing are manifestations of the fact that the identities of everything it
perceives are intelligible only in terms of their relations of multifarious kinds of multifarious
other things, of properties to other properties, of properties to objects, of objects to those
properties of objects to other objects. And the first of those experiences, which is just the long
paragraph 117, is perceiving consciousness being bemused because it seizes on unity and that
dissolves into multiplicity and when it asks, well what is the identity of these multiple items, that
identity dissolves into further multiplicities. Furthermore, these are negations, oppositions. It just
doesn’t understand what’s going on. So that first experience is realizing that there’s an issue,
realizing that universality is fraught with negation, is articulated by negation. It doesn’t know
how, yet, and it doesn’t understand how that can be. But it’s still seeing these as objectively in
the things and the properties.
In the second experience of consciousness, it tries out the strategy of—and I mean, I will go back
and look in more detail at that first one; this is just the overview—it tries out the strategy of
assigning identity and difference to different poles of the intensional axis. So it starts with
objective unity and subjective diversity. The way things are is just the way things are but I see all
these differences in it. And the second one as objective diversity which I unify. Now these
correspond to Kantian and Shelleyan schemes. So the second one—Kant says, unity is
everywhere and always the product of the intellect. What sense delivers is a manifold of intuition
and any unification of it is the result of our activity. Namely, our synthetic activity. Unity is the
product of intellectual activity. That’s what the understanding does: it unifies things. And
because he thinks the mind is best known to itself, he thinks what we’ve done we should be able
to understand and analyze. So we ought to be able to analyze these unities, since they’re our
products. This is Kant now.
I call the other scheme Shelleyan because of this passage in his poem Adonis. He says, “The One
remains, the many change and pass;/ Heaven’s light forever shines, Earth’s shadows fly;/ Life,
like a dome of many-coloured glass,/ Stains the white radiance of Eternity.” So we’ve got the
white radiance of Eternity, Heaven’s light that shines forever, and life is this dome of multi-
colored glass that breaks it up, stains it with colors, and gives us this multi-colored appearance.
So that’s the opposite of the Kantian picture—the white radiance of Eternity is unified until it
gets to our jumbled, colored pieces of glass that create this other view.
Now whether thinking about this epistemologically or ontologically, this was a battle that was
fought out with the British absolute idealists between Bradley and Russell just before the turn of
the century. Russell, in his characteristic style, says the question is whether the universe is to be
conceived of as a bucket of shot or as a bowl of jelly. If it’s a bucket of shot then you’ve got to
pick up—he’s thinking of shotgun shot, so that’s all these little BBs—you’ve got to pick up
some of them and keep them from rolling out of your hand. You’ve got to keep them together,
but you can pick up different ones. Or if it’s the bowl of jelly you’ve got to carve something out
of it with a spoon, out of the goo, and where those distinctions are made that will be your
contribution. Again, thought of ontologically this was the view that Russell was giving us a
metaphor for. And in contemporary analytic metaphysics you’ve got your goo universe and your
atomistic universe too. This is still going on or going around again on the merry-go-round,
depending on how you think it. Bradley’s way of putting this, which Russell took over, was to
distinguish between internal and external relations. Internal relations are—the paradigm is
relations between the parts of a thing—they’re the relations without which the thing wouldn’t be
the thing that it is. And the external relations are the relations that are not essential to its being
the thing that it is. So paradigmatically, in the example F.H. Bradley uses, the relation between
the rungs and the rails of a ladder are internal relations. If you separate the rungs from the rails,
you don’t have a ladder any more. A ladder is rails related to rungs in a ladder-like way. The
relation between the ladder and the wall that it’s leaning up against—that’s an external relation.
You can have the same ladder leaning up against a different wall. But the relation among its
parts, rungs to rails, that’s internal to it. And in characteristic, late 19th century metaphysical
fashion the two options available were absolute idealism, all relations are internal relations, and
Russellian atomism, all relations are external relations. One of the ways the American
pragmatists sometimes conceived themselves was saying, there, there. There really are some
internal relations and some external relations. You know, don’t go berserk with this. And
Russell’s friend Whitehead coined the name the fallacy of lost contrast with this as a paradigm
instance of that. So look the distinction between internal and external relations in the case of the
ladder makes perfect sense, as a distinction, but now if you say all there is, in principle, in the
universe is internal relations, the distinction with external relations that was necessary to make
the notion of internal relations coherent is gone—fallacy of lost contrast. And by the way, you,
Russell, are in the same position. You can’t say, “Well yes that’s foolish. They’re really all the
relations there are external relations.” Again, fallacy of lost contrast. This was their way of
talking about what earlier generations would have talked about as essential or accidental, but
now in the mode of relations. This is Bradley’s way of being a holist. It’s put in literary form in
Wordsworth’s [Note: this is actually by Tennyson] Flower in the Crannied Wall, when he says,
“Ah, but for me to really understand this part of the universe I would actually have to understand
everything.” It’s relation to a butterfly in China, that’s really internal to this flower in the
crannied wall. That was what Bradley was giving philosophical voice to and Russell, no, the
atomism on the other side, talking about what were essential relations and what were not—
they’re all essential; no, none of them are essential.
Quine in ‘Two Dogmas of Empiricism’ says, “Meaning is what essence becomes when it’s
divorced from the thing and attached to the word.” And I think this is a deeply resonant passage.
He’s looking at semantics, theory of meaning, and saying, “You know, we may think this debate
about buckets of shot and bowls of jelly is really old-fashioned and we know better than to worry
about that, but a debate of exactly the same structure is happening in semantics, where the
holists, like me Quine by the way, say all semantic relations are internal relations. The meaning
of something is a matter of its role in the whole web of belief—its relation to everything else, all
those relations are equally essential to it. You can’t make an analytic/synthetic distinction. That
would be the distinction between semantic internal relations and semantic external relations.
That just is the analytic synthetic distinction.” And he’s saying, no they’re all equally analytic,
equally synthetic. They’re all reacting to that, people like Fodor say, “No, there are these, glassy
essences, these atomic units of meaning and what we have to do is put them together in various
ways.” But Quine was indicating that there are parallel issues, either on the side of ontology or
on the side of semantics. “Meaning is what essence becomes when it’s detached sic from the
thing and attached to the word.” The very same sorts of disputes come up.
Hegel is going to claim to leap over this whole structure of debate in both of its forms, but
worrying about the relation between them and this middle experience, second experience of
consciousness understanding itself as perceiving consciousness, is his first shot across the bow,
his first effort to say, “Look, neither the Kantian mind is the source of all unity nor the Shelleyan
life is the dome of many colored glass refracting the white radiance of eternity—neither of those
is going to do justice to the intricate ways in which identity and difference are interdigitated and
articulated, both on the side of determinate facts—the fact that something has properties—and on
the side of the thoughts that express those facts. So I mean it is only the opening salvo in this but
it’s an important thing.
The third—I’ll also come back to talk about that in more detail insofar as I have time, if not it’ll
be in the notes. The third experience is a very interesting one and particularly interesting in the
light of subsequent philosophical developments, a lot have escaped your attention but I often
think of stuff that happened later as casting light on the earlier thing. The third strategy that
perceiving consciousness tries out in order to make sense of identity and difference says really
this talk about different properties, exclusively different properties, is talk about the relations
among objects. To have different properties is to be related to two different objects. We can
understand all of this in terms of mere differences of objects and of relations between objects.
Now this view has a lot in common with what I called the Tarskian order of explanation, but
there’s more to it than that. The diversity that makes an object determinate is thought about as
exclusively consisting in its relation to other objects. And there’s going to be a kernel of the truth
in this. This is the third experience which is going to take us to the “Force and Understanding”
chapter. There’s a holist truth in there that isn’t yet explicit, but what I want to emphasize is this
is a Tractarian conception. Noticeably in the Tractatus there aren’t monadic properties. What
would it be for them to be different? The Tractatus has merely different elementary objects and
merely different relations among those objects. To talk about a property in the Tractatus is to talk
about different relations to objects. You’re always abstracting from some multiadic property and,
of course notoriously, every elementary object can stand in every relation to every other
elementary object. That is, there is no relation of contrariety or exclusive difference among the
properties that are emergent from these relations among objects. Every combination is logically
possible and there is no other sort of modality than the logical in the Tractatus. Now probably not
coincidentally, it seems to have been when he was working on his lectures on color that
Wittgenstein decisively moved away from his Tractarian conception. If colors weren’t
elementary features, what were? And yet it seemed to be an essential feature of them that they
stood in these contrariety relations that the Tractatus had no room for. And it was in starting to
think about those that he moved into the Blue and Brown Book middle period.
Anyway, the claim I want to make is that this third experience of consciousness, the strategy that
dissolves there is a recognizably Tractarian strategy that’s going to use relations among objects
to stand in for the properties as a way—the hope is—of reconciling the identity of objects as
standing in—well, as being determinate, but instead of thinking that as having many properties,
it’s thinking of it as standing in relations to many objects. That’s the strategy.
Ok. Well, we’ve got time to look at least at the first one of these and maybe more. So, this is all
in paragraph 117, but I think there’s three moves and we have to sort of decide what’s up with it
by looking at those three moves. So the first one is, “The object which I apprehend presents itself
purely as a One…” So we start with experience of the unity, the identity—we’ve got the One
there. “…but I also perceive in it a property which is universal, and which thereby transcends the
singularity of the object.” It’s a universal. It can apply to more than one thing. So maybe that
does tell against it being a trope that we’ve got. “On account of the universality of the property, I
must rather take the objective essence to be on the whole a community.” Now this is actually not
the way I would have used his language, given what he says in 114/115. I would have thought
that what made me see the object as a community was seeing that it had more than one property,
that it had merely different properties in it. But maybe he’s saying here that’s a consequence of
identifying this property. Its being at least merely different from the others makes me see the
One as a community. If not, what he’s saying by seeing the One as a community is it’s being
grouped into a community by the universal. We’ve got this repeatable property that characterizes
it and that’s creating a relation between this object and all the other objects that share that
property. That’s, I would say, not to see it as a community, but as a member of a community. So
I mean that reading follows better from seeing it as just one universal, one property, but then it’s
a little awkward. He should say he sees it as a member of a community there. So ok, but that’s
the first move.
The second move— “I now further perceive the property to be determinate, opposed to another
and excluding it.” So he’s started, the object that I see there’s this universal thing in it, that was
what I learned from sense certainty. Now I see that it’s determinate and what that means is
excluding others. But now that’s going to mean, that’s going to show that it was incorrect to
think of the property as just unifying its instances, putting them into a community. That’s an
inclusion, seeing the property as including. Now I’m seeing it as excluding as well and how am I
to understand the relation between those two things?
And then the third move, “In the broken up One I find many such properties which do not affect
one another but are mutually indifferent.” So, all right, this I think is saying—it’s only now that
he’s got the multiplicity of properties, so the universal was seeing the object as falling into a
group, into a community of other like-propertied things. So at the previous stage it was noticed
that each property instantiated by a particular object excludes the instantiation by that object of
many others, and now it’s noticed that the object also includes many such excluding properties.
So to continue the passage, so now it, the object, is a universal common medium. So we’ve gone
from thinking of the universal as creating a community to thinking of the object as “a universal
common medium in which many properties are present as sensuous universalities”—observable
properties—”each existing on its own account and, as determinate, excluding the others.” But
now, how can it both be existing on its own account, be just the property that it is, and be
determinate only in virtue of excluding the others? Well, since it’s true of properties that, quote:
“Only when it belongs to a One is it a property, and only in relation to others is it determinate.”
That’s the conclusion of its experience here. Those are two essential features of properties that it
can’t see how to get together. It has to be related to an object, but it has to be related to these
properties in an exclusive way as well.
So, I mean, I’m inclined to see that as merely setting the problem. It’s noticing these features
which in 113 through 115 he’s told us how to think about, how he wants us to think about them,
and here we just see, well, the phenomenal consciousness over whose shoulder we’re looking
can’t do that. So let’s look a little more closely at the second strategy, the second experience,
which is 118 to 120. Well, I’ve said a lot about this, so let me just read some of it. In 118, “for
consciousness it has thereby been determined just how its perceiving is essentially composed,
namely,…not as a simple pure act of apprehending”—it was still supposed to be immediate
universality—”but rather as being in itself an act of apprehending at the same time taking a
reflective turn into itself from out of the True.”—Because it’s finding these opposed aspects in
what it’s doing. It’s not just taking it in anymore.—”This return of consciousness into itself
which immediately blends itself into that pure apprehending”—he’s saying, well what I’m
immediately apprehending is the thing of many properties, but again how can that be? The pure
apprehending and these other…—”has been shown…to be essential to the act of perceiving”—
well, sorry, I’m... “This return of consciousness into itself which immediate blends itself into that
pure apprehending, for…it’s been shown…to be essential to the act of perceiving”—that
reflective return into itself alters the true. Well, remember the emergence of the second new true
object at the end of the introduction. The new true object, the alteration that occurs, is what I
took to be the way things were in themselves, now shows up merely as the way they were for
me, for consciousness. And he’s now realized, oh, there’s more to this apparently simple
apprehending than just that. I’m doing something. I’m distinguishing the thing from the
properties, the properties from the properties, and beginning to see this intricate structure. So he
says, “The conduct of consciousness which is now up for examination is so composed that it is
no longer merely the act of perceiving, but it’s conscious of its reflective turn into itself, and it
separates this reflective turn into itself from simple apprehension itself.” So this is the point at
which the idea becomes available to it that maybe part of what it’s perceiving is the result of its
activity. Now since the problem was getting unity and diversity, the one and the many, together,
content and negation, now it thinks, well, maybe I’m responsible for one of those and the other
one is out there. So that’s where these two ideas come from. And you can do 119 and 120 which
deal respectively with the Shelleyan and the Kantian scheme. Roughly the idea is just what we
saw at the beginning of the introduction. Either of those make its perception that’s supposed to
be immediate apprehension a falsification. If it’s adding unity or if it’s adding multiplicity, either
it’s synthetic activity or the dome of many colored glass refracting it—either of those things is
falsification. So he devotes most of the space—120 to 127 anyway—to this third alternative.
That’s the one that’s going to give rise to next week’s account. Here’s some passages from that.
So in 123, “the Also, that is the indifferent distinction,…falls just as much into the Thing as it
does into oneness”—So we’ve got these two aspects, the particular as the Also that unifies the
merely different properties and as the excluding One that excludes all the properties that are in
the cloud around each of the instantiated properties.—”...falls just as much into the Thing as it
does into Oneness, but since both are different it does not fall into the same Thing but rather into
different Things.”—That’s the idea now is we’re going to look at these two aspects of the
Oneness of the thing as involving relations to different objects.—”The contradiction which exists
per se in the objective essence”—I mean, objective essence, this is the third time this has come
up. That’s a literal translation of the German, but the essence of the object or the essence of what
it is to be an object would be better—”is distributed into two objects.”—So instead of its being in
that object and the subject we’re now distributing into two objects.
So in 124, “the various Things are therefore posited as each existing on its own...”—So each one
is what it is and not some other thing. They’re at least merely different, these objects.—”...and
the conflict falls into each of them reciprocally such that each is different, not from itself, but
only from the others.” The trouble with conceiving the identity of the object as consisting in its
differences, in the difference of it from its properties and in the two different relations it stands in
to properties, one inclusive and one exclusive, it seems like a difference from itself. That’s not
the form of an identity. “...each is different, not from itself, but only from others.” So Tractarian
conception—we’ve got these merely different objects and any difference that we find in one
object is going to be a matter of relations to different objects. “However, each is thereby itself
determined as something distinct and has the essential distinction from others in it.” If they’re
numerically distinct, as is sometimes that they’re merely different, still there has to be some
content to that difference. But at the same time not in such a way that this would be a contrast in
itself. “Rather it is on its own simple determinateness which constitutes its essential characters,
and distinguishes it from others.” Now in contemporary metaphysics, this would be called
haecceity. Haecceity, I guess that’s Duns Scotus originally, is the this-ness of something. It’s the
property of individuality, of being this thing and not some other thing. That’s an interesting kind
of property to conceive, but you know it’s not a property like being red—that’s clear—but that’s
what’s being tried out here. Well, there is some differences, some this-ness, some particularity
that this thing has and a different one that this thing has that doesn’t dissolve into have different
properties. So the less plausible side of Leibniz’s Law is the identity of indiscernibles, saying
that if two things have the same properties then they’re really one thing. The more plausible side
is the indiscernibility of identicals—if two things are identical then they have the same
properties. Haecceities are a way of denying the identity of indiscernibles. And remember, it was
very important to Kant to see space and time as not properties but as able to distinguish
indiscernibles—his two hands, sitting in space, different, his right hand and left hand, but no
different properties that they had. There’s a huge discussion of this example, but this view—
well, there could be merely different things, even if they shared all the same properties.
Haeccetism is the view that that’s intelligible. I think that’s reading model theory into ontology,
but ok. Yeah, so he considers that.
But he finds in 127 that this is not a coherent conception of determinateness. So he’s going to
have the phenomenal perceiving consciousness reject this notion of haecceitism as unintelligible.
And we hear for that reason in 128 that the object is the opposite (Gegenteil) of itself. Now that’s
the very term that we use when we talk about properties having opposites, having
contradictories, and of course Hegel reminded us in the earlier part that objects don’t have
opposites. So we’ve gotten into a bad place. So in 129, “from out of sensuous being it became a
universal; but…since it emerged from the sensuous, this universal is essentially conditioned by
the sensuous, and thus is not truly in parity with itself.”—Well, it’s not truly identical, selfidentical—”Rather it is a universality affected with an opposition, which for that reason is
separated into the extreme terms of individuality and universality.” So we see that the very
notion of a universal, even if it’s a sense universal, implicitly involves the categorial distinction
between particulars and universals. That is to say, the passage goes on, “of the One
of…properties and the Also of the free-standing matters.”—the One of the properties that are
excluded and the Also of the free-standing matters—”These pure determinatenesses seem to
express essentiality…itself”—what it is to be an object—”however, they are only a ‘being-forself’ which is burdened with…’being-for-another’.”—Now here, the being for self, that’s not a
being for consciousness, but that’s a unity that is burdened by consisting in its relations to some
other things.—”But since…both exist in one unity,…unconditioned absolute universality itself is
now on hand, and for the first time consciousness truly enters into the realm of the
Understanding.” That is, realizing that these things must go together, even though it doesn’t
understand it, it’s now set itself in the level of understanding.
So in a summary in 130, “the sophistry of perceiving seeks to save these moments”—identity
and difference—”from their contradiction,…to hold fast to them by distinguishing various points
of view, by invoking the ‘Also’ and…’insofar’, as well seeking finally to lay hold of what is true
by distinguishing the unessential from an essential that is opposed to the universal. Yet all of
these expedients”—the three experiences—”instead of warding off illusion and apprehension,
prove themselves…to be rather nothing at all; and the true which is supposed to be won through
this logic of perceiving proves to be in one and the same regard the opposite and thereby to have
as its essence that universality completely devoid of distinction and determination.” So none of
those strategies is going to get you determinate universals.
So ok, well, I hope you’re in a position now—this is again, what?, 111-130, we’re talking about
twenty paragraphs. This is a manageable stretch of text. There’s really a lot going on in this and I
keep making reference to contemporary analytic metaphysics. That’s a house with many
mansions. There is nobody running the Hegelian line that he’s running here. Nobody’s trying
that out in contemporary metaphysics. Somebody surely ought to be addressing their problems in
these terms, but when you say Hegelian metaphysics people don’t think of this particular
constellation of ideas.
So “Force and Understanding” next time. Here’s the key thought to keep in mind when you read
it: force is the paradigmatic Newtonian, theoretical concept and Hegel uses force to mean
theoretical objects. Force is just the paradigmatic one, but it’s the whole class of things that are
not observable, properties that are theoretically postulated.
I will post some more detailed discussion. There is some more detailed discussion that I didn’t
get into in the notes and I will post that on the website.