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6/Allocating Resources to the Project
6-1
Chapter 6
Allocating Resources to the Project
This chapter extends the previous one on scheduling into the area of allocating resources
among the activities of a project, or among multiple projects competing for the same resources.
The chapter begins with a discussion of expediting project completion times and highlights that
by selectively choosing which activities to crash and by how much, we can determine the
minimum cost for all possible project completion time. The use of Excel’s Solver optimization
routine to facilitate this analysis is also presented. Next, the chapter moves on to the topic of
resource loading and in particular highlights the problems of over scheduling resources. The
topics of resource leveling and resource allocation naturally follow in the subsequent sections.
Finally, the chapter concludes with an overview of several of the concepts Goldratt raises in his
provocative book Critical Chain.
Cases and Readings
A case appropriate to the subject of this chapter is:
Harvard: 9-613-020 Space Constructors, Inc. This 3-page case involves a simple project where
partial crashing has already been planned but more, and less, crashing is also to be considered.
The network has some special characteristics that offer some worthwhile lessons for the
student.

6-2
Answers to Review Questions
1. Given the fact that a project’s resource requirements are clearly spelled out in the
project’s action plan, why are PMs so concerned with resource allocation?
There can be a variety of reasons why resource allocation is of concern to the PM despite
having a properly completed project plan. For example:
• The project plan only lists general categories of resource requirements such as
engineering, purchasing, marketing, and production. In these cases, the project
manager must still arrange to get the specific resources (e.g., personnel, equipment)
needed.
• The project plan may only specify how much of the resource is needed and the
precedence between the activities’ relationships; it may not specify exactly when the
PM will need these resources.
• Although the project plan specifies the amount of a resource needed for a particular
project, there may not be a mechanism in use that balances the load of resources
across multiple projects. This can lead to conflicts and the creation of bottleneck
resources.
2. Explain the difference between a project that has a fixed delivery day and one that has a
fixed limit on resource usage.
A project with a fixed delivery date can vary the level of resources used to meet a firm
project completion date.
A project with a fixed limit on resource usage cannot obtain additional resources but can
possibly delay the project completion date.
Why might a PM be interested in this difference?
The reason this distinction is important is that it specifies which of the fundamental trade-
offs the project manager can exercise. In the case of projects with fixed delivery dates, only
performance and cost (resource usage) can be varied. In projects with fixed resource usage
levels, only schedule and performance can be varied.
3. What does it mean to “fast track” a project?
Fast-tracking is a technique whereby key stages of the project are overlapped.

6-3
In the construction industry, this might entail beginning construction before the design and
planning are finished. In the pharmaceutical industry this may entail developing the
production process as the new drugs are being developed and tested.
4. List as many things as you can think of that should be entered into a specific resource’s
calendar.
Information that should be entered into a resource’s calendar include:
• The resource’s availability (e.g., days in week available, total hours available per
week, hours available each day).
• Times the resource will not be available (e.g., lunch, weekends, holidays, vacations,
scheduled maintenance), and
• Resource cost (e.g., cost per unit of usage, cost for overtime and overuse, known
changes in future resource cost).
5. Explain why project-oriented firms require excess resource capacity.
In project oriented firms there is much more uncertainty about the timing of resource
needs since the resources primarily move between projects rather than moving between
projects and a functional department. Therefore, extra resource capacity is needed as a
buffer given the greater level of uncertainty present.
6. The arrival and departure times of commercial aircraft are carefully scheduled. Why,
then, is it so important to have excess capacity in the airport control tower?
Although the arrival and departure times may be carefully scheduled, we all know that
actual arrivals and departures often deviate significantly from these schedules. Therefore, a
significant amount of uncertainty is present and greatly complicates the ability of the
airport control system to handle arrivals and departures.
Indeed unplanned events (e.g., weather delays, equipment malfunctions, late flight crews,
and so on) often cascade through the system further compounding the problem. Therefore,
excess capacity in control towers is needed as a buffer given this level of uncertainty.
Clearly, the cost of not having this capacity greatly exceeds the cost of some idle capacity.
7. Explain the difference in the problems faced by a PM who is short of secretarial resources
and one who is short of a “Walt.”
The PM that is short of secretarial resources does not face that great of a problem as this
type of resource is relatively abundant and not usually critical to the project’s ultimate
success or failure. The PM that is short of a “Walt” (i.e., an individual with expertise and
knowledge in a critical area) faces a much more daunting problem because a Walt is a

6-4
scarce resource that is important to the project’s successful completion and there are no
readily available substitutes for a Walt.
8. When allocating scarce resources to several different projects at the same time, why is it
important to make sure that all resource calendars are on the same time base (i.e.,
hourly, daily, or weekly …)?
One reason it is important to ensure the resource calendars are on the same time base is
because task duration is not usually dictated by the number of labor hours required to
complete the task, but rather by the calendar time required to complete it. This may involve
waiting for materials (e.g., concrete, glue) to cure, or equipment to warm up, etc.
9. List and describe the three most common criteria by which to evaluate different resource
allocation priority rules.
The three major criteria are:
• Schedule slippage … a measure of the delay suffered by projects as a result of the
application of a resource allocation priority rule.
• Resource utilization … a measure of the total resource cost (including costs such as
the cost of hiring, firing, and maintaining resource inventories) under different
allocation rules.
• In-process inventory … a measure of the cost of unfinished work in the system.
10. Why is the problem of allocating scarce resources to a set of projects similar to the
problem of scheduling a job shop?
In a job shop allocating resources (equipment and workers) to jobs or orders is required. In
projects, a similar allocation is required where specific resources must be allocated to
various projects when they are needed, which represent the jobs.
11. What is meant by the term “student syndrome”?
The “student syndrome” refers to situations in which people wait until the last possible
minute to begin a task. Its name is derived from the belief that students often delay the
start of an assignment until just before it is due. This isn’t necessarily a foolish or lazy
decision since often the task will change at the last minute, thus invalidating much of the
work that was earlier spent on it.

6-5
12. Describe in your own words what is meant by Goldratt’s critical chain.
Traditionally, in project management the concept of the critical path is used. More
specifically, the critical path is defined as the path(s) that if delayed will delay the
completion of the entire project.
One shortcoming of the critical path approach is that it only considers task precedence
information and does not consider issues related to resource usage. The critical chain
addresses this concern and considers both technical precedence relationships as well as the
resources that will be used to complete the tasks. Therefore, the critical chain refers to the
longest chain of consecutively dependent events including both technological as well as
resource dependencies.
How does it work?
The critical chain works by defining two sources that can delay the completion of the
project. One source of delay is uncertainty in the tasks that comprise the critical chain. A
project buffer is added to guard against these uncertainties. The second source of delay is
uncertainty in the tasks external to the critical chain. A feeding buffer is added to these
paths to help ensure they do not delay the tasks on the critical chain.
Suggested Answers to Discussion Questions
1. Describe the fundamental trade-offs when deciding whether or not to crash a project.
The fundamental trade-off in crashing a project is between schedule and budget.
Specifically, crashing entails employing additional resources (cost) in order to reduce the
project’s completion time.
If the decision is made to crash, what additional trade-offs must be made?
If it is decided to crash a project other trade-offs may then be necessary in terms of the
completion time of other projects and perhaps the performance of this and other projects.
2. Discuss the advantages of “labor pools” in a project – oriented company.
The main advantages of “labor pools” versus dedicating workers to specific projects are:
• Less waiting time for key resources.
• The ability to level resource usage, and
• The ability to substitute one worker for another should one become unavailable.
Are there any potential disadvantages with the use of pools?

6-6
Potential drawbacks include:
• Workers who do not identify with a particular project.
• Personnel who may not be well trained in specific tasks required by the assignment.
• Fewer opportunities for job enlargement.
All of these may lead to lower levels of job satisfaction, as well as lower morale and
motivation.
3. What purpose(s) might be served by using each of the following priority rules for
allocating scarce resources?
a. As late as possible.
b. Shortest task duration time first.
c. Minimum slack first.
a. Starting a task as late as possible … preserves resources and delays cash flows as long as
possible.
b. Allocating resources to tasks with the shortest durations first maximizes the number of
tasks that can be completed within a certain time period. This tends to get the little
messy tasks out of the way so workers can give their full attention to the bigger, more
important tasks.
c. The minimum slack priority rule is used to minimize the number of late activities.
4. Linking a group of projects together with pseudoactivities creates a sort of superproject.
What does this mean, and why would anyone want to do it?
Just as a project consists of tasks and activities with precedence relationships, a
superproject can be thought of as consisting of a group of projects with precedence
relationships. In the superproject, pseudoactivities are used to show any precedence
relationships among the projects. These precedence relationships may be actual
technological constraints (e.g., the product development project must be completed before
the process development project) or simply a reflection of management’s priorities.
The reason for creating a superproject is to help identify important relationships and
dependencies across the projects and use this information to better plan the usage of key
resources.
5. Projects A and B are both nearing completion. You are managing a super important
project C that requires an immediate input of resource being used by both projects A and
B, but is otherwise unavailable. Project A has an S-shaped life cycle. Project B’s life cycle
is J-shaped. From which (or both or neither) do you borrow the resource? Why?

6-7
In this case it would be best to borrow from project A. In an S-shaped project, fewer
resources will have little impact on project A’s performance as it nears completion.
Conversely, in a J-shaped project, taking resources away from project B as it nears
completion will dramatically reduce its performance.
6. Goldratt suggested that to avoid the student syndrome,” it is a good idea to set the
activity durations so short that there is a high probability that the task will not be finished
on time. On the other hand, it has long been known that setting up people for failure is
strongly demotivating. What should the PM do?
There is a delicate balance between setting goals that people believe are impossible to
achieve and therefore result in demotivating the team versus stretch goals that serve to
motivate the team.
The project manager should not set goals that have extremely low probabilities of success,
but may find it desirable to set goals that do have a reasonable chance of not being met
(say 40 to 60 percent).
7. Describe as many types of resource allocation problems as you can, based on the
situations described in the chapter.
The chapter identifies three types of resource allocation problems:
• Available resources (resource loading).
• Scarce resources – single projects.
• Scarce resources – multiple projects.
Resource loading recognizes the existence of needed resources and ensures that they are
allocated to the project when needed. An example would be a construction site where the
electrical work is subcontracted to an external supplier. The main task is to determine that
the external firm can have the necessary skilled work force on site at the appropriate time.
Scarce resources are those with limited availability and the key elements of the project have
to be scheduled around that availability of the resource - even if a firm has just a single
project. An example of this situation would be the reliance of a construction site on a
specific piece of equipment such as a crane.
The allocation of scare resources becomes far more complex when the same resources are
need on more than one project. In this case, the utilization of the resource on project A will
also have an impact on project B (and, possibly, other projects). As indicated in the chapter,
the company will need to apply one of the six priority rules to determine which project shall
have the first use of the scarce resource.

6-8
Solutions to Exercises
1. This project involves the landscaping of a building site.
a. The Gantt chart for the project.
b. Assuming a five day week, the critical path is: A-C-D-E-G and the project duration is 14 days.

6-9
c. Since each resource is assigned 100 per cent to each task, the resource constraints are:
• Resource X is over utilized on the Friday of week 1, Monday of week 2, and Tuesday
of week 3.
• Resource W is over utilized on Tuesday of week 3.
d. After leveling the resources, the project duration is 17 days and the critical path is
A-B-C-D-E-F-G. Because of the scarcity of resources the critical path now includes all
activities.
e. If it is necessary to shorten the project duration without overallocating the resources then
there are several options:
• Since resource X is required by all activities, it makes the most sense to consider
adding this resource first. Adding an additional X resource would shorten the
project by 2 days which would allow tasks B and C to be done simultaneously.
• Adding an additional X and W would shorten the project by 3 days. The extra X
would allow tasks B and C to be done simultaneously and adding an extra W would
further allow tasks E and F to be done simultaneously.
• Adding an additional Y does not help reduce the time with any combination of
additional X and W resources.
• Other possibilities might involve relaxing the predecessor relationships, reducing the
assigned resources to some of the tasks, and so on.

6-10
The project duration is 13 weekdays when the resources work weekends and after leveling.
2. Provided are the predecessors, normal time, normal cost, crash time and crash cost for an
eight activity (a to h) project.
a. The network for this project is as follows:
The critical path is b-c-e-h. The project duration and cost for the all normal level of project
activity is 20 days and $400, respectively.
b. The crash costs per day for all activities are shown in column F.
1
2
3
4
5
6
a
b c
d
e
g
h
f
4
5
6
7
8
9
10
11
12
13
A B C D E F
Normal Normal Crash Crash Crash
Activity Time Cost Time Cost Cost/Day
a 5 $50 3 $150 50
b 4 $40 2 $200 80
c 7 $70 6 $160 90
d 2 $20 1 $50 30
e 3 $30
f 8 $80 5 $290 70
g 5 $50 4 $100 50
h 6 $60 3 $180 40

6-11
c. The spreadsheet below was created to find the optimal way of getting to an 18-day delivery
time. As shown, the total normal cost is $400 (cell C14) and the total crash cost is $80 (cell
I14) for a total project cost of $480 (cell B2). The 18 day duration was achieved by crashing
activity h 2 days (cell H13).
The optimal solution using Solver was found in the following way:
• Cell I14 was specified as the target cell to minimize.
• The ranges H6:H13 and B18:B22 were specified as the changing cells.
The following constraints were added:
• H6:H13 < G6:G13 (maximum amount each activity can be crashed)
• B18 > J7 (node 2)
• B19 > B18 + J8 (node 3)
• B19 > J6 (node 3)
• B20 > B19 + J9 (node 4)
• B21 > B18 + J11 (node 5)
• B21 > B19 + J10 (node 5)
• B22 > B20 + J12 (node 6)
• B22 > B21 + J13 (node 6)
• B22 < B1 (node 6 – project deadline)
• 6:H13 > 0 and B18:B22 > 0 (all decision variables must be > 0)
• The “Assume linear model” check box was also selected.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
A B C D E F G H I J
Deadline: 18
Total Cost: $480
Normal Normal Crash Crash Crash Max Crash Amt Crashing Actual
Activity Time Cost Time Cost Cost/Day Amt to Crash Cost Time
a 5 $50 3 $150 50 2 0.0 0.0 5
b 4 $40 2 $200 80 2 0.0 0.0 4
c 7 $70 6 $160 90 1 0.0 0.0 7
d 2 $20 1 $50 30 1 0.0 0.0 2
e 3 $30 0 0.0 0.0 3
f 8 $80 5 $290 70 3 0.0 0.0 8
g 5 $50 4 $100 50 1 0.0 0.0 5
h 6 $60 3 $180 40 3 2.0 80.0 4
Total $400 $80
Event
Node Time
2 4
3 11
4 13
5 14
6 18

6-12
d. The optimal 16-day project duration can be found by entering 16 in cell B1 and then
resolving using Solver. The optimal solution calls for crashing activity h 3 days, b 1 day, and
d 1 day. The cost of completing the project in 16 days is $400 + $230 = $630.
e. If all activities are crashed as much as possible, the project can be completed in 14 days.
Entering 14 in cell B1 and resolving, it is discovered that the project can be completed in 14
days at a cost of $400 + $ 400 = $800.
3. Given the following AOA network, what is the first activity to be given extra resource?
The following Table shows the activity, duration, successors, critical followers, and slack
associated with each of the four activities:
Activity Duration Successors Critical Followers Slack
a 4 d d 6
b 3 c,d c,d 0
c 7 d d 0
d 5 None None 0
a. Using the shortest task first priority rule for the critical path: Task b has the shortest
duration.
b. Minimum slack first … Tasks b, c, and d all have zero slack.
c. Most critical followers … Task b has the largest number of critical followers.
d. Most successors … Task b has the largest number of successors.

6-13
4. Given the project shown in Figure 5-10 of Chapter 5 and the fact that the facility used by
activities c and d is scarce, which activity would benefit from each of the rules?
The following Table shows the activity, slack, critical followers, duration, and latest start
time for activities c and d:
Activity Slack Followers Critical Followers Duration Latest Start Time
c 3 f,i None 3 8
d 2 g,h,j h,j 4 7
a. Using the minimum slack rule: Activity dD has the least amount of slack and therefore
would get the facility first using this rule.
b. Most followers … d has the most followers and would get the facility first.
c. Most critical followers … d has the most critical followers and would get the facility first.
d. Shortest task first … c has a smaller duration and would get the facility first.
e. With the “as late as possible” priority rule, the latest start times are used. In this case
activity c has a LS of 8 and d has a LS of 7. In using this rule it only makes sense to assign the
facility to the resource with the earliest LS or activity d.

6-14
5. Consider the following activity information and the constraint that the project must be
completed in 16 weeks.
The above worksheet was used with Excel Solver to find the solution. Solver was set to
minimize N11 by changing cells K4, K7, K9, and K10 subject to the constraints:
• J19 = 16
• K4 ≥ L4
• K7 ≥ L7
• K9 ≥ L9
• K10 ≥ L10

6-15
6. Consider the project network below. Suppose the duration of both activities A and D can be
reduced to 1 day, at a cost of $15 per day of reduction. Also, activities E, G, and H can be
reduced in duration by 1 day, at a cost of $25 per day of reduction. What is the least-cost
approach to crash the project 2 days? What is the shortest “crashed” duration, the new
critical path, and the cost of crashing?
Activity
Normal
Time
Crash
Time
Δ
Time
Slope
$
A 4 1 3 $15
B 3 3 0 $-
C 1 1 0 $-
D 5 1 4 $15
E 4 3 1 $25
F 1 1 0 $-
G 3 2 1 $25
H 5 4 1 $25
I 2 2 0 $-
J 1 1 0 $-

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Greek philosophy in the formulation of the dogma of the church.
This was scientifically stated by the Alexandrian School of Catechists,
of which Clement and Origen were the leaders.
Origen (185–254) and the School of Catechists. Origen,
whose surname was Adamantine, was an early teacher in the School
of Catechists, which had been under the direction of Clement. Like
Plotinus, Origen had been a pupil of Ammonius Saccas. Origen
endured much persecution on account of his teaching, and had to
flee from Alexandria to Cæsarea and Tyre, where he spent his old
age. He was the most influential theologian of the Eastern church,
and he was the father of Christian theological science.
In manner of life Origen was a Christian; in his thought he was a
Greek. He was the Christian Philo, although he was a rival to the
neo-Platonic philosophers. His Christian theology competed with the
philosophical systems of his time. It was founded on both
Testaments, and it also united in a peculiar way toward a practical
end the theology of both the Apologists and the Gnostics. He was
convinced that Christianity could be expressed only as a science, and
that any form of Christianity without scientific expression is not clear
to itself. Although the church was offended at some of his doctrines,
it made his philosophical principle and his theory of development its
own. In trying to state Christianity in terms of intellectual
knowledge, Origen did not make the mistake of burying its principles
under philosophy or mythology, as was the case with the Gnostics.
The Gnostics had created a new Christianity; Origen developed
Christianity from within itself. He was an orthodox traditionalist, a
strong Biblical theologian and idealistic philosopher. He maintained
that there were several ways of interpreting the Scriptures
(allegorical interpretation). The masses see only the somatic or
outward meaning as it has been developed in history. A deeper or
moral interpretation gives a psychical meaning to the Gospel truth.
More profound still is the spiritual interpretation, which gives to the
Gospels a pneumatic or spiritually esoteric meaning. Christianity is
superior to all other religions because it is a religion for all classes,

even for the common man. Christianity is the only religion which,
without being polytheistic, can have its truth in mythical dress.
The aim of Origen was less to show how the world came to be,
than to justify the ways of God to men in the world’s creation and
history. The central principle in his teaching is spiritual monotheism.
God is an unchanging spirit, the author of all things, and He
transcends human knowledge. What distinguishes Him most is the
absolute causality of His will. He is essentially creative, and this
creative activity is co-eternal with Himself. God can have no dealings
with changing individuals directly, since although creative He is
unchanging. He has direct connection only with the eternal
revelation of His own image, the Logos. The Logos is a person, a
special hypostasis, the perfect likeness of God with nothing corporeal
about him. He is not the God, but still God, yet a second God, with
no sharing of divinity.47 The Holy Spirit bears the same relation to
the Logos as the Logos to the Father. In his relation to the world the
Logos is the Idea of Ideas, the norm according to which things are
created.
Origen followed Philo in believing that the original creation
consists of a world of beings that are pure intelligences, and that the
cause of creation is God’s goodness. He further believed that the
Logos or Wisdom of God is God’s Son. Both the creation of the ideal
world of intelligences and the existence of the Son is from eternity.
The origin of the visible world is to be contrasted with this eternal
creation. The visible world had its beginning in time and is only one
of a series of worlds. It will finally return to God, and has in God its
beginning and end. Thus man lives in a visible world of time with
eternities on either side. Creation, viewed as a whole, is everlasting,
and consists of an endless number of beings who are destined to
become a part of the divine holiness and to participate in the divine
blessedness. These beings are endowed with freedom of will, and
they fall away from God. The visible world of matter has been
created to purify the fallen spirits, and in consequence we find

materialized spirits graded into angels, stars, mankind, and evil
dæmons.
In his emphasis on the will as the fundamental mental part of
man, Origen is distinctly Christian and opposed to Greek
intellectualism. The will of God and the will of man form the corner
stone in his system. The will of God is the eternal development of
His being, but the will of spirits is their temporal free choice. The will
of God is reality itself; the will of spirits is phenomenal and changing.
Freedom of the will of the spirits is the ground of their sin, and
consequently of their materiality. Thus it is by the freedom of the
spirits that Origen explains evil and the existence of imperfect matter
without impeaching the eternal purity of God. Origen thus reconciled
the ethical transcendence of God as creator with his immanence in
the material world. God is the creator without being the creator of
sin. Through the conception of free-will Origen reconciled the two
antithetical principles of Christian metaphysics: faith in divine
omnipotence and consciousness of sin.
The function of the church is thus an important one in the divine
plan. For the fallen spirits try to rise by their own wills from the
matter to which they are condemned for purification. They never
lose their divine essence, however low they may fall. They cannot
rise alone, nor are they compelled to, but they always have the help
of divine grace, which is always active within man and has also been
perfectly revealed in Jesus Christ. After the manner of the
Apologists, Origen makes use of the Stoic and Platonic conceptions,
for the eternal Logos takes form in the divine-human unity of Jesus.
Through His physical suffering redemption is made possible to all
believers, and through His essence illumination has been brought to
those especially inspired. There are different grades of redemption:
faith, or a religious understanding of the perceptual world;
knowledge of the Logos; final absorption in God. All shall finally be
saved through the combined forces of freedom and Grace, and then
shall all material existence disappear.

The controversies within the church during the succeeding
centuries over the theory of Origen are theological rather than
philosophical, and so our account of the relation of Greek philosophy
to Christianity in the Hellenic-Roman period closes here. Origen’s
undertaking was a private one, approved at first in only limited
circles and on the whole disapproved by the church. In his scientific
dogmatics the particular changes which he planned pertain
especially to the conception of salvation and the place of Christ in
the universe. In his teaching about Christ he emphasized more the
cosmological than the soteriological aspect, but neither was fully
developed. The history of the early church shows that Christianity
seized the ideas of ancient philosophy and insisted on revising them
with its own religious principle before it used them. We shall find
that the next period is introduced by a greater than Origen, in whom
again the Christian and the ancient worlds will meet in new and
richer combination,—St. Augustine.
BOOK II
THE MIDDLE AGES (476–
1453)

CHAPTER XV
CHARACTERISTICS AND
CONDITIONS OF THE
MIDDLE AGES
Comparison of the Hellenic-Roman Period and the Middle
Ages. The Middle Ages can be conveniently remembered as
approximately the 1000 years between the fall of old Rome, in 476,
and the fall of new Rome (Constantinople) in 1453. Together these
two periods make a long and a philosophically unproductive stretch
of 1800 years. The intellectual materials which the two periods
possessed, differ but little, although during the first half of the
Middle Ages such materials were very few. There is, however, a
decided difference in the way the two periods look at things. The
ancient had started with Aristotle’s interest in knowledge for its own
sake; the ancient had passed from that to the need of knowledge in
ethical conduct; he had finally made use of knowledge only in
formulating religion. On the other hand, the history of thought in the
Middle Ages was exactly the reverse. The mediæval man starts
satisfied with religion as thus formulated by the preceding period,
and seeks to regain pure knowledge. The perspective in the two

periods is therefore different. Hellenic thought began in freedom and
ended in tradition; mediæval thought begins in tradition and, borne
by the youthful German, who brings with him few original ideas,
pushes forward toward freedom. No doubt one can discover in
mediæval times many fresh transformations of ancient thought and
a new Latin terminology, but, on the whole, all the problems of the
Middle Ages, as well as their solutions, can be found in antiquity.
One may find, too, the germs of modern thought in the Middle Ages,
but they come from mediæval pupils and not from mediæval
masters. In the Middle Ages humanity is again at school; its
problems appear in succession, but they always are expressed in the
conceptions of the ancients.
The Mediæval Man. Antiquity had brought together three
civilizations,—those of Greece, of Rome, and of Christianity. Greek
civilization in the form of an intellectual culture, called Hellenism,
had been superimposed upon Roman political society. The result was
a society with a twofold stratum, and in such a society the Christian
church had grown as an organization of controlling cultural and
political influence. It was into this society that the German
barbarians, by a series of invasions, entered during the first three
centuries of the Middle Ages.
The Middle Ages began and antiquity ended when these German
tribes finally broke down the barriers of the Roman empire. It was a
new period; for a new race had taken upon itself the responsibility of
bearing the burden of the future of western Europe. The German
was of course unconscious of the magnitude of his self-imposed
burden, for the German was young, vigorous, and moved by
primitive instincts. He had leaped into the world’s fields as a
conqueror; he remained as a laborer.
At the beginning the German seemed likely to destroy the entire
product which antiquity had bequeathed. He was quite unprepared
to assimilate the rich fruits of that ancient civilization. He had,
indeed, less mind for the elaborate forms of Greek philosophy than

for the lighter forms of Greek art. In his first contact he could
understand neither. Moreover ancient society was so weak that it
could not educate him, who was its conqueror, into its culture.
Nevertheless, there was one element in that ancient society that did
appeal to the German. That was the spiritual power of the Christian
church. Alone amid the ruins of antiquity the power of the church
had grown so strong that the men of the north bowed before it, and
religion accomplished through the emotions of the Germans what
art, philosophy, and statecraft failed to achieve. The preaching of the
Gospel laid hold of the feelings of these primitive people, for the
church in its pretensions, and sometimes in fact, represented the old
Roman political unity. Moreover the church was also the repository of
what was left of Greek science. The church expressed for the
German his own ideal of the personal inner life. The Germans
became the supporters of the church, and in this way the protectors
of ancient culture. Mediæval history in western Europe is therefore
the record of the development of the Germans under the influence
of the Christian church. In contrast with the development of the
Eastern church, which was the development of a state church, the
Western church was the development of an ecclesiastical state. The
Western church, and not the later empire, was the true successor of
the Roman empire. Thus the early beginnings of the Middle Ages
rested with the church, but the later development of the Middle Ages
rested with the German people.
How the Universe appeared to the Mediæval Man. The
mediæval man had very indistinct ideas about the world around him,
since his interest did not lie in the earthly realm, but in the spirit that
controlled it. He was content in his sciences with conclusions without
their demonstrations. Although it is said that relations of space and
number are never indistinct in the mind of the civilized man, the
man of the Middle Ages certainly did not possess such conceptions
in so vigorous a manner as to enable him to discover new truths. We
must, furthermore, make a sharper distinction between mediæval
popular opinion and mediæval scientific opinion than we should
about popular and scientific opinion of modern times; for the results

of science did not reach the people then as now. To the ordinary
mediæval man the world in which he lived was what it appeared to
be to his eye. The earth was flat; the sky was a material dome,
which sustained the waters of the world above it. Through this sky-
floor the water sometimes breaks and the earth receives showers of
rain. These popular notions sometimes appeared in the verse of the
time.
The mediæval scientific opinion was based on the theory of
Ptolemy and his school of Alexandrian astronomers, who lived in the
second century A. D., some details to the theory having been added
by the Arabians. Ptolemy says, “The world is divided into two vast
regions; the one ethereal, the other elementary. The ethereal region
begins with the first mover, which accomplishes its journey from east
to west in twenty-four hours; ten skies participate in this motion,
and their totality comprises the double crystalline heaven, the
firmament and the seven planets.” (See diagram.) The mediæval
man of science thought that, inasmuch as he was upon the earth, he
was therefore standing at the centre of things. Directly above him
was the cavity of the sky, ruled by the moon; and below the moon
were the four elements,—fire, air, water, and earth. This region was
the realm of imperfection. But above the moon the scientist saw a
series of nine other heavens, each with an orderly revolution of its
own; and beyond all is God. The universe was therefore to Ptolemy
a great but a limited sphere, consisting of ten spheres one inside
another (like the rings of an onion). Each planet moved with the
motion of its own heaven (or sphere), which was sometimes called
“crystalline” because it was transparent. The movements of the
heavenly bodies, each in its own revolving heaven, were contained
in the whole sphere, which revolved with a motion of its own. By
ascribing other movements to the planets within their respective
heavens, the mediæval astronomers were able to predict every
conjunction and eclipse to the minute. These separate movements of
the planets were called epicycles, the form of which is shown in the
diagram on the opposite page.

PTOLEMAIC COSMOGRAPHY
A diagram showing the division of the universe into the ten spheres or heavens
(From the private library of Professor R. W. Willson of Harvard University)
Such a scientific astronomy would easily lend itself to the
theological conceptions of the time. The realm of perfection above
the moon was supposed to be under the direct supervision of God
and to be inhabited by spirits. Thus the conjunction and relation of
the heavenly bodies were thought to have influence upon human
life, and they furnished the basis of the astrology, necromancy, and
spiritism so common in the Middle Ages. The ninth heaven embraced
all the others. It swept around them all, without interfering with
their own special motions, and completed its revolution in twenty-
four hours. The ninth heaven was both the source and the limit of all
motion and all change. Beyond it lies the eternal peace of God,
which the Christian astronomer regarded as “the abode of the
blessed.” This was called the tenth heaven or the Empyrean. This, in
Dante’s words, is “the heaven that is pure light; light intellectual full
of love, love of the good full of joy, joy that transcends all
sweetness.” The tenth heaven is Paradise and is within the life of
God. It is important to note that the Ptolemaic conception of the
universe is the background upon which Dante constructs his Divine
Comedy (see diagram, p. 376),48 and appears in part at least as the

cosmological basis of the Paradise Lost of Milton. For thirteen
centuries—from 200 to 1500—conviction remained unshaken in the
Ptolemaic system of astronomy as an adequate explanation of the
universe.
PTOLEMAIC COSMOGRAPHY
(Showing the Epicyclic Movements of Saturn, Jupiter, and Mars in respect to the
Earth)
The Mediæval Man at School. In the eleventh and twelfth
centuries there was a revival in intellectual interests that was deep
and broad, and the characteristics of this revival will be discussed
subsequently (see Transitional Period, p. 329). Our curiosity,
however, is aroused upon our entrance into the Middle Ages, as to
what the man of the early Middle Ages studied and how much he
learned. We must remind ourselves at the outset of the oft-repeated
fact that, on the whole, in western Europe, for the first five hundred
years of the Middle Ages, the only people who had any book-
learning were the churchmen. Furthermore, with them the learning
was very meagre. Their purpose in study will show this, for it was to
enable them “to understand and expound the Canonical Scriptures,
the Fathers, and other ecclesiastical writings.” The training was as
follows:—

1. Theological. Elementary instruction in the Psalms and church
music, but no systematic training in theology,—just enough training
to enable the priest to understand the Bible and the Church Fathers.
2. Secular training. Knowledge in the “Seven Liberal Arts,” i. e.
the trivium—grammar, rhetoric, and dialectic; and the more
advanced quadrivium,—music, arithmetic, geometry, and astronomy.
These names are suggestive of a vast amount of knowledge, while,
in truth, very little was known or taught in these subjects.
Astronomy and arithmetic were employed to find the time of Easter.
Geometry included some propositions of Euclid without
demonstrations. Music included plain song and a mystic doctrine of
number. More was made of grammar, the study of rhetoric from
Latin classics, and dialectics. Dialectics was logic in the Middle Ages,
and its mysteries fascinated the mediæval man. But even in logic
there were only some remnants of the Aristotelian logic known.
A Mediæval Library. Here again is an interesting question:
What did this mediæval churchman read? But we must make a
distinction between books most commonly read, books that the
scholars might use, and books most influential upon thought.
1. Books most commonly read. These would be the text-
books used in instruction. They are as follows:—
The Psalms.
The Grammar of Donatus.
The Christian poets: Prudentius, Psychomachia; Juvencus, Gospels in
Verse; Sedulius, Easter Hymn.
Dionysius Cato, Disticha de Moribus, a collection of proverbs (moral
maxims) in rhyming couplets.
Virgil, Ovid, and the rhetorical works of Cicero.

Æsop’s Fables (in Latin).
2. Books that the scholars might use. It is difficult to say
what any particular scholar actually did read, for the libraries of
monasteries differed enormously in the character and number of
their books; some monasteries had several hundred books, some
none at all. Some libraries were composed almost entirely of works
of the Fathers; some possessed a good many works of ancient
classical writers. One might expect to find any one or more of the
following works in a scholar’s library:—
Aristotle, De Interpretatione and the Categories in Boëthius’
translation.
This explains why the logical problems occupied the almost
exclusive attention of the first schoolmen.
Plato, the Timæus.
This was known to the Irish monks perhaps in Greek, but on the
continent in a translation by Chalcidius. The only other sources of
knowledge of Plato were in the works of Augustine and the neo-
Platonists.
Commentaries on Aristotle,—The Isagoge by Porphyry, in a
translation into Latin by Boëthius, and some commentaries by
Boëthius himself on Aristotle’s De Interpretatione and Categories.
Cicero, the rhetorical and dialectical treatises, such as the Topica, De
Officiis.
Seneca, De Beneficiis.
Lucretius, De Rerum Natura.
Augustine’s works and some pseudo-Augustinian writings.

The works of the Church Fathers, Clement of Alexandria and Origen.
The Pseudo-Dionysius, translated from the Greek by Erigena.
The encyclopedic collections of some of the last of the scholars of
antiquity, like Cassiodorus, Capella, Boëthius, and the
Etymologies of Isidore of Seville.
3. The Books most influential philosophically upon the
time. These were not necessarily the books most widely read, but
the epoch-making books, so to speak. They were as follows:—
Augustine, City of God.
Boëthius, Consolation of Philosophy.
Aristotle, De Interpretatione and the Categories in translation by
Boëthius.
Pseudo-Dionysius, translated by Erigena.
Porphyry, Isagoge translated by Boëthius, an introduction to
Aristotle’s Categories.
The Three Periods of the Middle Ages.
1. Early Period, 476–1000.
2. Transitional Period, 1000–1200.
3. Period of Classic Scholasticism, 1200–1453.
There is one great natural division line of the Middle Ages, the
year 1200. At this time the surging of the western peoples eastward
in the Crusades was at its height, and the works of Aristotle were
coming into western Europe from the East. These events mark a
change in the political and intellectual situation in Europe. But this
change did not take place suddenly. There are intervening two

centuries that are indeed transitional, but at the same time are
animated by a distinct and independent philosophical motive. These
two centuries may be set apart as a period, different from the earlier
and the later periods. We shall call these three periods the Early
Period, the Transitional Period, and the Period of Classic
Scholasticism.
The Early Period takes us from the fall of old Rome (476) to the
birth of modern political Europe (1000). It is a period of religious
faith governed by the theology of Augustine. Mysticism has no
independent following, but on the contrary rules within the church.
The Christian principle of individual personality and the Greek
Platonic conception of universal realities are not fused, but they are
held without arousing controversy. This is because the human
reason has no standard code, nor does it yet feel the need of one.
The only two philosophers, Augustine and Erigena, of the period are
animated by neo-Platonism.
The Transitional Period extends from the birth of political Europe
(1000) to the arrival of the works of Aristotle (about 1200). This
epoch is one of logical controversy, in which the Christian and the
Greek motives conflict. This controversy gives rise to the first group
of great schoolmen, who discuss the reality of general ideas in their
application to dogma. Mysticism still rules the churchman, but now
in a modified form. Plato has become the standard of the reason in
orthodox circles and Aristotle in those inclined to heresy, but as yet
only fragments of the works of either are known.
The Period of Classic Scholasticism extends from 1200 to the end
of the Middle Ages (1453). It is a period when a theological
metaphysics arises by the side of the logical controversy and
predominates over that controversy. The problem now concerns the
respective scopes of the reason and faith. The period is Aristotelian,
and Aristotle’s philosophy is made the standard code for the
churchman for all time. Mysticism has now no place of authority in

the church, but has an independence. The period contains the
greatest schoolmen of the Middle Ages.
Summary of the Political and Educational
Worlds of the Mediæval Man.
I. Early Period, 476–1000.
395 The Roman empire divided
into Eastern and Western
empires.
(Augustine, 354–430)
476 Fall of the Western empire,
the Eastern empire lasting
about 1000 years longer.
375–600 Northern barbarians
overrun the Western empire in
series of invasions.
476–800 Disappearance of
municipal and imperial
schools and rise of
episcopal and monastic
schools.
525 Boëthius died, the last
notable Roman scholar
who knew Greek.
529 Closing of philosophical
Schools at Athens;
founding of monastic
school by St. Benedict.
600 Roman power almost entirely
in hands of barbarians.
476–800 Dark Ages.
622–732 Mohammedans conquer
Arabia, Northern Africa, and
Spain.
732 Mohammedans repulsed at
the battle of Tours.
600–800 Fusion took place among
German and Roman peoples.

800 Empire of Charlemagne
founded. Civilization higher
than the German, lower than
the Roman.
800–1000 Benedictine Age:
only period in Western
Europe when education is
entirely in hands of monks.
The Palace school;
episcopal, cathedral, and
monastery schools.
(Erigena, 810–880, the
forerunner of
Scholasticism.)
900–1000 Empire of Charlemagne
broken up. Demoralization.
Invasions by Danes and
Northmen from the north;
Saracens from south by sea;
Slavs, Hungarians, Russians,
and Poles by land. The church
demoralized, Papacy
temporarily disappears,
feudalism replaces empire.
900–1000 Dark century with
decline of learning.
IN THE EARLY PERIOD AND
THE TRANSITIONAL
PERIOD LITTLE OF PLATO
WAS KNOWN EXCEPT IN
THE FORM OF NEO-
PLATONISM AND LITTLE
OF ARISTOTLE EXCEPT OF
FRAGMENTS OF HIS
LOGIC.
II. Transitional Period, 1000–1200.
1000 France and Germany get
their first form as nations just
before this year; England just
after. Beginning of new birth of
Europe, caused by conversions
of northern nations, by
enlightened rule of the Ottos,
by regeneration of Papacy, by
development of civic life.
Beginning of political order,
ecclesiastical discipline, and
social tranquillity.
First Scholasticism.
(Anselm, 1033–1109)
(Roscellinus, d. 1110)
(Abelard, 1079–1142)
1000 Passion for inquiry takes
the place of the old
routine.
1160–1200 Traces of the
origination of the earliest
universities.

Revival of architecture followed
by renewal of art. The
Romanesque appeared about
1000, the Gothic about 1150.
Poetry of Trouvères in north
and of Troubadours in south.
1150–1250 Translation into
Latin directly from Greek
of the works of Aristotle,
previously unknown in
Western Europe.
III. Period of Classic Scholasticism, 1200–1453.
1200 Crusades at their height. 1200 The Mendicant Friars.
1200–1453 Commerce of Europe
with Asia begins to grow to
large proportions in countries
on the Mediterranean. The
Third Estate grows in strength,
national governments prevail
over the feudal system.
Classic Scholasticism.
(Thomas Aquinas, 1224–
1274.)
(Duns Scotus, 1270–1308.)
(William of Ockam, 1280–
1349.)
1300–1453 The period is well
supplied with schools.
1350–1453 Deterioration of
Scholasticism.

CHAPTER XVI
THE EARLY PERIOD OF THE
MIDDLE AGES (476–1000)
The General Character of the Early Period. It is no accident
that these five hundred years of the Middle Ages were spiritualistic.
Both the political disturbances and the intellectual inheritance from
the Hellenic-Roman period made the period such. The troubles
during the long death agony of the Roman empire had deprived the
people of their interest in this world. The world of kingdoms and
material things presented no ideals; and the age would have been
pessimistic had not the Church through Augustine presented a
heavenly ideal and the means to win that ideal. Both what the
material world had taken away from man and what the spiritual
seemed to offer him, made the age an age of faith. The principle of
inner spirituality was moved to a central position. All things pointed
to the supernatural and the transcendent. Men dwelt upon the
nature of God, the number and rank of the angels, the salvation of
the soul. In this, as in the Transitional Period following, little was
known of Aristotle except some fragments of his logic; and little was
known of Plato except in the form of neo-Platonism. But in this

period (before the year 1000) the pupil was instructed in both
Aristotle and Plato, and held them both together without
controversy. Mysticism had little independence of church doctrine, as
appears in the case of Erigena, the consequences of whose doctrine
were not at first seen. The monastery became the fundamental
social organization and the central social force. Organized ascetic life
permitted an absorbing contemplation of heaven. Prayer superseded
thought; faith prescribed knowledge. The intellectual world was
dominated by neo-Platonic idealism, and the all-important topic in
men’s minds was that of God’s grace. Augustine stood at the
beginning of the period and organized its conception of grace for it.
Erigena stood near the end and stated the neo-Platonism of the
period in extreme form, presenting the issue for the scholasticism of
the many years to come. The presentation of the doctrine of these
two men will therefore be the philosophical exemplification of the
attitude of the time.

MEDIÆVAL GEOGRAPHY. THE COSMAS MAP, A. D. 547
From J. Keane’s Evolution of Geography
(Cosmas was an Egyptian monk who had once been a merchant and traveler. He did not
use the records of his own travels to supplement the Greek and Roman plans, but he laid
down as a fact that the earth is flat. Then he piously adduced evidence from the Scriptures
to support his view. The maps drawn by Cosmas are the earliest Christian maps that have
survived. Their crudeness, compared with the maps of the Romans and Arabs, reveals the
low state of knowledge among the Christians.)
The Historical Position of Augustine. The Middle Ages were
inaugurated by a mind of the highest order,—Augustine.49 If one
were to select the most influential figures in the history of
philosophy, Augustine might be chosen to stand with Plato, Aristotle,
Spinoza, and Kant. “In some respects Augustine stands nearer to us
than Hegel and Schopenhauer.”50 For the church, but no less for the
period, it was a fortunate circumstance that Augustine should have
lived just as antiquity was closing and the mediæval period
beginning. Through him the various influences of the past were
gathered up and presented in a scientific statement for the Middle
Ages. “The history of piety and of dogma in the West was so
thoroughly dominated by Augustine from the beginning of the fifth

century to the era of the Reformation, that we must take this whole
time as forming one period.”51
In his relation to antiquity Augustine drew especially upon the
fundamental teachings of St. Paul, the neo-Platonists, and the
Patristics for the presentation of his own doctrine. He was familiar
with a great number of the doctrines of antiquity, and was the
medium of their transmission to the Middle Ages. He does not seem
to have known the system of Aristotle, but the importance which he
attached to the dialectic in the explanation of the Scriptures
contributed a good deal to the use of the logic of Aristotle by the
scholastics of the Middle Ages. He had some knowledge of the
Pythagoreans, the Stoics, and the Epicureans through the writings of
Cicero. But the most important philosophical influence upon
Augustine was the neo-Platonic teaching of Plotinus and Porphyry.
Neo-Platonism, the Pauline theology, and the Patristic are the large
factors in the doctrine of Augustine.
In his relation to the Middle Ages, what in brief was the position
of Augustine? By means of neo-Platonism and a discriminating
psychological analysis he transformed the previous belief in God as a
judge into a belief in the personal relations between God and man.
That is to say, he carried out monotheism spiritually, and in doing
this the influence of neo-Platonism is very strong in him. Augustine
made one of the centres of his teaching the living relation of the soul
to God. He took religion out of the sphere of cosmological science,
where it had been placed by Origen and the Gnostics, and made it
personal. Furthermore, he offered with this new ideal a plan of
salvation; for Augustine made it his task to show (1) what God is,
and (2) what the salvation of the soul requires. Whereas before
Augustine the only dogmatic scheme had presented the place and
function of Christ in salvation, Augustine was interested in the place
of man in salvation. Thus he elaborated monotheism into spiritual
monotheism and delineated the inward processes of the Christian
life, i. e. of sin and grace. This important advance made by

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