I.The
Gothic: excerpts from Barbara Fuchs’s Romance
(New York: Routledge, 2004)
a.‘Romancing
the Gothic’
1)Founding
rationale: ‘By the mid-eighteenth century, literary scholars in Germany,
France, and England were reacting to the dictates of neoclassicism, questioning
its privileging of reason, order and proportion. The gradual construction of a
“Gothic” tradition to counter the classical legacy of Greece and Rome involved
a rediscovery of the literary heritage of the Middle Ages and Renaissance,
which had largely been neglected in favour of the classics’ (117-8)
2)Origins:
‘In the narrow sense, “Gothic” referred primarily to the production of ancient
Northern Europeans, the Goths or barbarians who had opposed Rom with their own
traditions of liberty and social or organisation’. More broadly, the Gothic
designated everything that was not classical: both the vernacular works of the
Middle Ages, and those Renaissance texts that eschewed the “rediscovered”
classical heritage in favour of “native” traditions’ (118).
3)Aesthetic
merits: 18th century English critics Richard Hurds said of the
Gothic to be ‘the more sublime and creative poetry … addressing itself solely
or principally to the Imagination’, need not observe the same ‘curious rules of
credibility’ (cited from Fuchs 2004, 118-9). ‘Thus, not only is the Gothic
recuperated, it surpasses the classical in its direct address to the
imagination, becoming the poetic wellspring par excellence’ (119).
b.Gothic
as a genre
1)Genre
characteristics: ‘From its beginnings, the Gothic romance, or novel, is
explicitly presented as a mixture of new and old’ (119).
2)Beginning:
‘The genre is self-consciously inaugurated by Horace Walpole, with The Castle of Otranto (1764), a
fantastically popular tale that has appeared in over 100 editions since ifs
first publication; (119).
3)Conventions:
‘Otranto established some of the most
enduring conventions of the genre: ancient
castles complete with secret vaults and passageways; family secrets; obscure
prophecies; ghosts and apparitions; hidden identities. More importantly, it
exacerbates the narrative tension attendant on what Richetti calls “persecuted
innocence,” a constant among various forms of popular narrative in the
eighteenth century, which in this case involves an innocent princess pursued by
the lascivious and immortal father of the prince she was to wed’ (119).
4)Strange
Place: ‘despite Walpole’s emphasis on nature, and the rationality attributed to
his contemporary and what makes the Gothic so popular is precisely its gallery
of marvelous and otherworldly topoi’ (121).
5)Terror:
‘These “well-wrought scenes of artificial terror which are formed by a sublime
and vigorous imagination,” critics conjured, provided a particular kind of pleasure,
in which the imagination “rejoices in the expansion of its powers,” so that
“the pain of terror is lost in amazement” (121-2).
The
Turn of the Screw (1898),
excerpts from Priscilla Walton’s ‘“He took no notice of her; he looked at me”:
Subjectivities and Sexualities in The Turn of the Screw’ in Peter Beidler’s
edition of The Turn of the Screw
(Boston: Bedford/St Martins’s, 2013) 3rd edition.
1)Critical
heritage: ‘The Turn of the Screw is one of James’s more enigmatic tales.
Although it was written over a century ago, it continues to intrigue readers
and attract critical and creative attention. It has been transformed into an
opera by Benjamin Britten (first performed in 1954), and has inspired a number
of films, such as The Innocents (1961)’
(348).
2)Key
issues: gazing, visibility and invisibility, gender panic at the end of
Victorian age, suffragette’s movements, the fear of governess’s sexuality in
the Victorian era, women as unreliable narrator, ghost stories.
II.Reflections
on ghost stories:
Personal Assignment
Write a short essay on
the treatment of women in Poe’s ‘The Fall of the House of Usher’ and James’s
‘The Turn of the Screw’ in the context of Gothic and ghost stories.
This
chapter deal with the holism of social science. At first, Rosenberg talked
about the definitions of holism and functionalism. Then, he talks about the
theory of Durkheim and why it can connect to the core of holism. Rosenberg then
compare the holism with rather different reductionism, and discusses the differences.
And he uses the concept of supervinience to support the holism.
The
Social Facts and the Holism
The
social science deals not only psychological personal actions but also some
distinctive social facts. These
facts are is objective and not belong to a singular person. They can be
observed as the behavior of a group of people. In this case, the idea of the
existence of special differences of social facts when we counts large amount of
people are called holism. Some
people will argue that if there really exists group behaviors that cannot be
described by personal causes and actions. Of course, the very complex
collective behavior cannot easy be constructed by the units they consist of.
Sometime it is just like a ‘’collective conscious’’ making decisions.
Holism
relates to another feature of social science—functionalism, which is the method of understand features of
society by their ‘’functions’’. On the other side, the methodological individualists claim that all social facts can be
explained by generalizing individual behavior and the idiom [L] mentioned in
the previous chapters. Traditional aspects from methodological individualists
thinks that all the results should only be translated to observations. The
failure of this point of view is that it abandons too much of explanatory
ability, and the holists do not do so. They imply that the descriptions of
social facts should apply the best explanatory functions.
One
of the important view that holists holds is that the whole is more than just a
group of people. In other words, they may be two kind of social facts, one
about the group, and one about the single person. For them, the social facts
should supply evidences to the beliefs and ideas. However, this argument do not
explain how the small parts influence the whole. To make the viewpoint more
convincing, they need a more powerful argument to stand for their idea.
Autonomy
of Society
Some
sociologists have studied social facts by applying the holism. One example is
Durkheim’s research. He analyzed suicide cases, and found out that the suicide
cases rises up at some period of time. It is not easy to explain by personal
psychology factors. He summed up three different causes of suicide, which are
altruistic suicide (too much of social integration), egoistic suicide (too
little social integration), and anomic suicide (caused by great and rapid
changes of society). He thinks the suicide cases are mainly caused by the
structure of the entire society in the meantime. It seems that Durkheim take
the view that the society is a whole, integrated, organic unity (which can be describe
by the ‘autonomy of society’ or ‘the group mind’). By Durkheim, the
so-called the mental states of a person is also a manifestation of the entire
society.
Reductionism
If
the psychological laws are helpful, they could link the social integrations in
to personal psychology, i.e. the sociology is reducible to psychology. This is
the opposite of holism because the holists claims that there are always
something that cannot be reduced. One of the methods to still apply holism is
to view psychology and the mental changes as appendix phenomena. It not caused
suicide but is a by-product from a causing-suicide society. Also, the problem
with reductionism is that many phenomenon are just too difficult to reduce in
to simple laws. We can only describe nearly right general laws in a much more
huge scale—the macroscopic scale.
Even
in natural science, there are always subjects that cannot reduce to a more
fundamental subject in the near future. Rosenberg claims that maybe we can
never view social facts as psychological facts even if all the psychological
theory is very complete. That is to say,
the social facts can though as a more fundamental and metaphysical laws not
just by methodological meaning.
Supervenience
Rosenberg
also mentions the philosophical concept of supervenience
and multiplerealizablity. This means any being can be observed must obey:
(a) This object will have certain kind of composition.
(b) If another subject have exactly the
same composition, it will have the same function--supervenience.
(c) There are always multiple ways to form an object that is concluded in some kind of concept
(e.g. chair, desk, pencil, person, etc.) – the multiple realizablity.
It
is hard to find a term in social science that is not defined by its functions.
If the function was defined, we will see the supervenience and multiple
realizations it bring. The compositions it supervenes could be actions and
behaviors. Rosenberg strongly suggests that the social facts are not easy
reducible because the object is not just the sum of all its compositions, and
this part stands for the point of view of holists.
Personal
Opinions
After
reading all the articles, I think it is an interesting to discuss about if it
is really impossible to prove all social facts by psychological laws. I think
it is not very realistic. There are three reasons:
(1)
The psychological laws are not absolute; they are not so precise like physics
laws.
(2)
The social facts are much more complex than a single person’s thinking. There
will be a lot of factors produced by the environment, and it will also be
influenced by the composition of the society.
(3)
It is very hard to set experiments to prove the relationship between personal
laws and the social laws.
However,
we can still try to guess what will happen in the future by the laws we have
known.
Reference
Rosenberg, Alexander (2016).Philosophy of
Social Science (fifth edition), Westview
press,ISBN
978-0813345925
In this chapter the
author discusses the reliabilities of rational
choice theory, which implies that the human take the action of the maximized
utility. The economists use the theory to construct the predictions of human
action. The author introduced the cardinal
utility theory, the marginal utility,
and the instrumentalism view of the theories. These theories may not perfectly
express how human do when they are making choices for a behaviorist because
being too psychological, but they are sometimes useful.
The Theory
of Rational Choice
The Theory of Rational
Choice takes a great part on the economics. It was a way of ordering desires.
From the law [L] mentions in the previous parts of the book, the actions are
related to desires. Thus, the marginalists
transformed it to an assumption that people do things rationally. That is,
between all the choices, people will do the most beneficial one. They call the
additional utilities gained from one unit of commodity the marginal utility. By using the idea, they can construct
relationship between quantity and price, finally predict the market-clearing equilibrium. Farther,
they think the equilibrium will happen naturally, so the government don’t need
to do much planning. The phenomena is called by Adam Smith the invisible hand. The preference of a person was called
‘’cardinal utility’’, which is absolute.
However, is this
theory really true? It seems not so in many cases, but we do not have a way to
test if the utilities are deceptive or not. In order to analyzing the theory of
rational choice mathematically, they assumed the ‘’ordinal preference’’:
1. The utility of
commodities is comparable.
2. The utility of
commodities have transitivity, i.e.
a>b and b>c then a>c.
3. People are
rational and will choose the commodity that maximizes the utility.
This
kind of utility is only relative and only concerns about the behavior (what
people choose).
Behaviorism
and Instrumentalism
The cardinal utility
still have failures. People may change through time, and it is difficult to
know if people really does things rationally. For the behaviorists, it is still
too psychological. If we come to
desire and implicit utilities, it is psychology.
Another kind of view is the instrumentalism. It takes a useful
theory only as a tool to systemize human actions. The terms desire and belief are merely nouns invented to be useful. It comes up with the
view of a ‘’black box’’, that is, we can only deal with the ‘’inputs’’ and
‘’outputs’’ of a person, not going to understand mental reality. And all the
theories applied to economy is just models.
One of the idealized
theory invented to predict general equilibrium assume that:
1. Agents are
rational.
2. Agent can complete
information.
3. Commodity are
infinity divisible.
4. The production
efficient always remains the same.
5. Purchasing and
selling can be done in any time.
These assumptions can
be analyzed with mathematics and prove the existence of equilibrium. Through
the assumptions may be too idealized, they are essential in economics because
they can make predictions in some range of error. The instrumentalists do not
care about is the theory really true or whether they can applied to human mind.
They just care if the theory is practical or not.
Here comes another
point. A practical view still should be tested by experiment. Without testing,
we can never know our predictions really come true in given conditions. It is
also true in natural sciences and all the idealized theories and laws.
The Benefits of
Psychology
Only if we view
economics theories as instruments can we applied idealized assumptions and
psychology to real word. The author claims that some progress in psychology can
also benefit the predictions of economics. New psychological phenomenon are
found and studied every day. These results can someday be used in economics and
other social sciences, even though we can hardly what human mind really is.
Personal Opinions
I think that the
psychological view of [L] seems very easy to accept at first sight. In fact, it
is hard to prove. When using rational choice theory to the complex society, we
often found it too difficult to control all the variations. However, maybe we
can observe the human society and economical behaviors with the statistical
methods to find some new laws.
4.Ifis a family of elements
ofU,
and ifI∈U,
then the unionis an element ofU.
A Grothendieck universe
is meant to provide a set in which all of mathematics can be performed. (In
fact, it provides amodelfor set theory.) As an
example, we will prove an easy proposition.
Proposition 1.
Ifx∈Uandy⊆x, theny∈U.
Proof.
y∈P(x)becausey⊆x.P(x)∈Ubecausex∈U, soy∈U.
It is similarly easy to
prove that any Grothendieck universeUcontains:
All products of all families of
elements ofUindexed by an element ofU,
All disjoint unions of all
families of elements ofUindexed by an element ofU,
All intersections of all
families of elements ofUindexed by an element ofU,
All functions between any two
elements ofU, and
All subsets ofUwhose cardinal is an element ofU.
In particular, it
follows from the last axiom that ifUis non-empty, it must
contain all of its finite subsets and a subset of each finite cardinality. One
can also prove immediately from the definitions that the intersection of any
class of universes is a universe.
Grothendieck universes
are equivalent tostrongly inaccessible cardinals. More formally, the
following two axioms are equivalent:
(U) For all setsx, there exists a
Grothendieck universeUsuch thatx∈U.
(C) For all cardinals κ, there is a strongly
inaccessible cardinal λ which is strictly larger than κ.
To prove this fact, we
give explicit constructions. Let κ be a strongly inaccessible cardinal. Say
that a setSis
strictly of type κ if for any sequencesn∈ ... ∈s0∈S, |sn|
< κ. (Sitself
corresponds to the empty sequence.) Then the setu(κ)of all sets strictly of
type κ is a Grothendieck universe of cardinality κ. The proof of this fact is
long, so for details, we refer to Bourbaki's article, listed in the references.
To show that the large
cardinal axiom (C) implies the universe axiom (U), choose a setx. Letx0=x, and for alln, letxn= ∪x be the union of the
elements ofx. Lety= ∪nxn. By (C), there is a
strongly inaccessible cardinal κ such that |y| < κ. Letu(κ)be the universe of the
previous paragraph.xis
strictly of type κ, sox∈u(κ). To show that the
universe axiom (U) implies the large cardinal axiom (C), choose a strongly
inaccessible cardinal κ. κ is the cardinality of the Grothendieck universeu(κ). By (U), there is a
Grothendieck universeVsuch thatU∈V. Then κ < 2κ≤ |V|.
In fact, any
Grothendieck universe is of the formu(κ)for some κ. This gives
another form of the equivalence between Grothendieck universes and strongly
inaccessible cardinals:
For any Grothendieck universeU, |U| is a
strongly inaccessible cardinal, and for any strongly inaccessible cardinal κ,
there is a Grothendieck universe u(κ). Furthermore, u(|U|)=U, and
|u(κ)|=κ.
Bourbaki, N.,Univers, appendix to Exposé I
of Artin, M., Grothendieck, A., Verdier, J. L., eds.,Théorie des Topos et
Cohomologie Étale des Schémas (SGA 4), second edition, Springer-Verlag, Heidelberg,
1972.
Inmathematics,
aGrothendieck universeis a setUwith the following properties:
1.Ifxis an element ofUand ifyis an element ofx, thenyis also an element ofU. (Uis atransitive set.)
2.Ifxandyare both elements ofU, then {x,y} is
an element ofU.
3.Ifxis an element ofU, thenP(x), thepower setofx, is also an element ofU.
4.Ifis a family
of elements ofU, and ifIis an element ofU, then the unionis an
element ofU.
Elements of aGrothendieck universeare sometimes calledsmall sets.
A Grothendieck universe is
meant to provide a set in which all of mathematics can be performed. (In fact,
uncountable Grothendieck universes providemodelsof
set theory with the natural ∈-relation, natural powerset operation etc.) As an example, we will
prove an easy proposition.
Proposition.
Ifand,
then.
Proof.because.because, so.
The axioms of Grothendieck
universes imply that every set is an element of some Grothendieck universe.
It is similarly easy to prove
that any Grothendieck universeUcontains:
·All products of all families of
elements ofUindexed by an element ofU,
·All disjoint unions of all families
of elements ofUindexed by an element ofU,
·All intersections of all families
of elements ofUindexed by an element ofU,
·All functions between any two
elements ofU, and
·All subsets ofUwhose cardinal is an element ofU.
In particular, it follows
from the last axiom that ifUis non-empty, it must contain all of
its finite subsets and a subset of each finite cardinality. One can also prove
immediately from the definitions that the intersection of any class of
universes is a universe.
Other examples are more
difficult to construct. Loosely speaking, this is because Grothendieck
universes are equivalent tostrongly inaccessible cardinals.
More formally, the following two axioms are equivalent:
(U) For each
setx, there exists a
Grothendieck universeUsuch thatx∈U.
(C) For each
cardinal κ, there is a strongly inaccessible cardinal λ that is strictly larger
than κ.
To prove this fact, we
introduce the functionc(U).
Define:
where by |x| we mean
the cardinality ofx. Then
for any universeU,c(U) is either zero or
strongly inaccessible. Assuming it is non-zero, it is a strong limit cardinal
because the power set of any element ofUis an element ofUand every element ofUis a subset ofU. To see that it is regular,
suppose thatcλis a collection of cardinals indexed
byI, where the
cardinality ofIand of eachcλis less thanc(U). Then, by the
definition ofc(U),Iand eachcλcan be replaced by an element ofU. The union of elements ofUindexed by an element ofUis an element ofU, so the sum of thecλhas the cardinality of an element ofU, hence is less thanc(U).
By invoking the axiom of foundation, that no set is contained in itself, it can
be shown thatc(U)
equals |U|; when the axiom of foundation is not assumed, there are
counterexamples (we may take for example U to be the set of all finite sets of
finite sets etc. of the sets xαwhere
the index α is any real number, and xα= {xα} for each α. ThenUhas the cardinality of the continuum,
but all of its members have finite cardinality and so ;
see Bourbaki's article for more details).
Let κ be a strongly
inaccessible cardinal. Say that a setSis strictly of type κ if for any
sequencesn∈ ... ∈s0∈S,
|sn| < κ. (Sitself corresponds to the empty
sequence.) Then the setu(κ)of all sets strictly of type κ is a
Grothendieck universe of cardinality κ. The proof of this fact is long, so for
details, we again refer to Bourbaki's article, listed in the references.
To show that the large
cardinal axiom (C) implies the universe axiom (U), choose a setx. Letx0=x,
and for eachn, letxn+1=xnbe the union
of the elements ofxn.
Lety=xn.
By (C), there is a strongly inaccessible cardinal κ such that |y| < κ. Letu(κ)be the universe of the
previous paragraph.xis strictly of type κ, sox∈u(κ).
To show that the universe axiom (U) implies the large cardinal axiom (C),
choose a cardinal κ. κ is a set, so it is an element of a Grothendieck universeU. The cardinality ofUis strongly inaccessible and strictly
larger than that of κ.
In fact, any Grothendieck
universe is of the formu(κ)for some κ. This gives another form of
the equivalence between Grothendieck universes and strongly inaccessible
cardinals:
For any
Grothendieck universeU, |U|
is either zero,,
or a strongly inaccessible cardinal. And if κ is zero,,
or a strongly inaccessible cardinal, then there is a Grothendieck universe
u(κ). Furthermore, u(|U|)=U, and |u(κ)| = κ.
Since the existence of
strongly inaccessible cardinals cannot be proved from the axioms ofZermelo-Fraenkel
set theory(ZFC), the
existence of universes other than the empty set andcannot be
proved from ZFC either. However, strongly inaccessible cardinals are on the
lower end of thelist of large cardinals;
thus, most set theories that use large cardinals (such as "ZFC plus there is
ameasurable cardinal",
"ZFC plus there are infinitely manyWoodin cardinals") will prove that
Grothendieck universes exist.
