... if their first digits are the same in base n .The
theoryof quadratic residues is concerned with the first digits ofthe squares. Of
particular interest is the case where the base is a prime, and ... composition a number called the weight,which
is the product ofthe summands. We shall determine the sum w(n)ofthe
weights ofthe compositions of n. The generating function of w(n)is
∞
n=1
w(n)x
n
=
∞
m=1
(x ... 2 exactly to the
second power. If we assume the second of these possibilities then (11) can be
put in the form
m +1
2p
+1≡ 0 (mod p). (12)
We multiply together all the congruences ofthe type...
... Contentsviii
4Mentalcontent69
Propositions70
Thecausalrelevanceofcontent74
Theindividuationofcontent79
Externalisminthephilosophyofmind82
Broadversusnarrowcontent84
Content,representationandcausality89
Misrepresentationandnormality92
Theteleologicalapproachtorepresentation95
Objectionstoateleologicalaccountofmentalcontent99
Conclusions100
5Sensationandappearance102
Appearanceandreality103
Sense-datumtheoriesandtheargumentfromillusion107
Otherargumentsforsense-data110
Objectionstosense-datumtheories112
Theadverbialtheoryofsensation114
Theadverbialtheoryandsense-data116
Primaryandsecondaryqualities119
Sense-datumtheoriesandtheprimary/secondarydistinction121
Anadverbialversionoftheprimary/secondarydistinction125
Docolour-propertiesreallyexist?126
Conclusions128
6Perception130
Perceptualexperienceandperceptualcontent131
Perceptualcontent,appearanceandqualia135
Perceptionandcausation137
Objectionstocausaltheoriesofperception143
Thedisjunctive
theoryofperception
145
Thecomputationalandecologicalapproachestoperception149
Consciousness,experienceand‘blindsight’155
Conclusions158
7Thoughtandlanguage160
Modesofmentalrepresentation162
The languageofthought’hypothesis164
Analogueversusdigitalrepresentation167
Imaginationandmentalimagery169
Thoughtandcommunication175
Doanimalsthink?178
Naturallanguageandconceptualschemes183
... concep-
tion ofthe whole of reality, we cannot hope to render compat-
ible the theories and observations ofthe various different
sciences: and providing that conception is not the task of any
one of ... partisan, in the sense of espousing an
exclusive approach to questions about the mind in general –
Anintroductiontothe philosophy of mind34
is debatable whether, whenever one event causes another,
there...
... the whole of reality, we cannot hope to render compat-
ible the theories and observations ofthe various different
sciences: and providing that conception is not the task of any
one of those sciences, ... point of these remarks is to emphasise there cannot
be progress either in the philosophy of mind or in empirical
psychology if metaphysics is ignored or abandoned. The
methods and findings of empirical ... broad
sense to embrace any kind of sensation, perception or
thought. This agreed, we can say that the philosophy of mind
is the philosophical study of subjects of experience – what
they are, how they can...
... causes
the monkey to make the call: and yet we want to say that
what the call represents is only one of these causes – the
presence ofan eagle. A teleological theoryof representation
can explain ... whether
Anintroductiontothe philosophy of mind82
content of John’s belief that snow is white. It would be wrong
for us – and wrong for John – to say that the inhabitants of
the distant planet ... teleological theoryof representation
over the causal theory may encourage us to try to extend it
to the case of mental representation, that is, tothe attitudinal
states of subjects of experience....
... machinery. But
rejection of any type–type theoryof mental and physical
states is consistent with acceptance of a token–token theory,
that is, a theory according to which any token mental state,
such ... experience the tang of lemon, the whiff
of woodsmoke, the colour of ripe tomatoes, or the sting of a
nettle. And the issue raised here by the absent qualia argu-
ment is whether the existence of such ... friends of functionalism
may want to respond to this argument, other than by
resorting toan outright denial ofthe existence of ‘qualia’
altogether.
8
Some may contend that the hypothesis of spec-
trum...
... relative to one another – things such as the colour
and shape ofthe tree and ofthe house, the intervening
ground between them, the sky behind them, and other
objects in their vicinity (together ... causal theory – the disjunctive
theory – but concluded that it does not have any significant
advantages over the causal theory and has, besides, certain
disadvantages. Then we went on to discuss the ... properly belongs to a philosophical analysis of the
concept of perception and what properly belongs toan empir-
ical theoryof perception ofthe sort that is more appropri-
ately advanced and evaluated...
... of difference Hypothesis of cause
Introduction
At the turn ofthe twentieth century, the best known of all
dream investigators would be Sigmund Freud, who set out to
base his theoryofthe ... developed and strengthened over the past
SO years. In the process, the book offers the reader a unique
opportunity to reconsider his or her own dream theory and, into
the bargain, to learn about the ... that
changes the whole mode of operation ofthe brain and the mind.
As we see in Chapters 4 and 5, this change in mode is affected
11
Why did the analysis of dream content fail to become...
...
THE GERMAN INVASIONS AND THE BREAK-UP OFTHE ROMAN
EMPIRE
The Huns force the Goths into the Empire. Battle of Adrianople, 378.
9. Previous tothe year 375 the attempts ofthe Germans to penetrate ... Europe than any ofthe other German races.
Besides the kingdoms ofthe East Goths and the Franks, the West Goths had their
kingdom in Spain, the Burgundians had established themselves on the Rhone, ... volume of
the chief changes in western Europe since the German barbarians overcame the armies
of the Roman Empire and set up states of their own, out of which the present countries
of France,...
... of such effects to be sure the results of
analysis are useful. On the other hand, in some cases, analysis ofan algo-
rithm can help identify ways for it to take full advantage ofthe programming
environment.
Occasionally, ... probability theory tells us that other facts
about the distribution
Nk
of costs are also relevant to our understanding
of performance characteristics ofan algorithm. Fortunately, for virtually all
of the ... accurate to within O N
−3
or indeed to within O N
−k
for
any constant k. Such approximations, called asymptotic expansions, are at the
heart ofthe analysis of algorithms, and are the subject of Chapter...
... their hope of enjoying some ofthe advantages of their civilized neighbors, or the
need of new lands for their increasing numbers. And the Romans, by means of their armies, their walls, and
their ... than any ofthe other German
races. Besides the kingdoms ofthe East Goths and the Franks, the West Goths had their kingdom in Spain, the
Burgundians had established themselves on the Rhone, and ... volume ofthe chief changes in western Europe since the
German barbarians overcame the armies ofthe Roman Empire and set up states of their own, out of which the
present countries of France, Germany,...
... Earth,
the velocity ofthe Earth round the Sun and the Solar System around the centre
of the Galaxy, in addition to any velocity ofthe star. The rotational velocity of
the Galaxy makes the largest ... systematically tothe red or tothe blue by an
amount that depends on the velocity ofthe observed star relative tothe Earth.
The overall relative velocity is the sum ofthe rotational velocity ofthe ... programme
of cosmology is the same as that of any other branch of physics: to explore the
known laws of physics to their limits.
2.8 The evolving Universe
The most surprising aspect ofthe night...
... con-
sists of guesses, of hypotheses, rather than of final
and certain truths; and that criticism and critical
discussion are our only means of getting nearer to
the truth. It thus leads tothe tradition ... tends to separate them. When the mixture of
elements and forces is just right, parts of animals and
humans form and combine into almost all possible
arrangements. Only a limited number ofthe random
arrangements ... that the gods are born, and have
clothes and speech and shape like their own. . . .
But if cows and horses or lions had hands [and]
could draw with their hands and make the things
men can make, then...
... into an alliance, momentous for the history of Europe. In order to
understand this we must glance at the motives which led the popes to throw off their allegiance to their
ancient sovereigns, the ... interest ofthe treaty of Verdun lies in the tolerably definite appearance of a western and an
eastern Frankish kingdom, one of which was to become France and the other Germany. In the kingdom of
Charles ... Germans to penetrate into the Empire appear to have been due
to their love of adventure, their hope of enjoying some ofthe advantages of their civilized neighbors, or the
need of new lands for their...