Introduction to Health Care Quality: Theory, Methods, and Tools 1st Edition
Introduction to Health Care Quality: Theory, Methods, and Tools 1st Edition
Introduction to Health Care Quality: Theory, Methods, and Tools 1st Edition
Introduction to Health Care Quality: Theory, Methods, and Tools 1st Edition
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7. CONTENTS
List of Figures and Tables xvii
Preface xxi
Acknowledgments xxv
About the Author xxvii
Introduction xxix
PART I: QUALITY MANAGEMENT FUNDAMENTALS 1
1 Foundations of Health Care Quality 3
Defining Quality 4
Contributions of Quality Theorists—Nothing New under the Sun 5
Florence Nightingale • Ernest A. Codman • William Andrew Shewhart
• William Edwards Deming • Avedis Donabedian • Joseph M. Juran
• Philip Crosby
Quality Management Methodologies 14
Total Quality Management • Continuous Quality Improvement
vii
8. viii Contents
Organizations Making an Impact on Quality and Safety Standards 16
Institute of Medicine • The Joint Commission
Centers for Medicare and Medicaid Services 21
Hospital Compare • Patient Education • Pay for Performance • Never Events
Institute for Healthcare Improvement 24
Agency for Health Research and Quality 25
National Quality Forum 27
The Leapfrog Group 27
Data: The Foundation of Quality Management 28
Case Example: Falls • Quality Indicator • Barriers to Using Quality
Data to Assess Care • Case Example: Cardiac Surgery Mortality
Summary 32
Key Terms 33
Quality Concepts in Action 33
References 33
Suggestions for Further Reading 34
Useful Websites 35
2 Understanding the Impact of Health Care Reform 37
The Affordable Care Act 38
Accountable Care Organizations • Health Insurance Exchanges
New Models of Payment 42
Bundled Payment • Pioneer and Advance Payment Accountable Care
Organization • Comprehensive Primary Care Improvement • Value-Based
Purchasing • Pay for Performance • Case Example: Communicating with Clinicians
through P4P Data
New Models of Providing Care 47
Patient-Centered Medical Homes • Community Health Centers • Prevention and
Wellness • Local Prevention Efforts • Case Example: Influenza Vaccination
New Models for Collecting Data 53
Background • Advantages of Electronic Health Records • Challenges to Effective
Use of Electronic Health Records • International Classification of Diseases Codes
Improving Interpersonal Communication 56
Narrative Medicine • Improving Documentation • Looking Ahead
9. Contents ix
Summary 60
Key Terms 60
Quality Concepts in Action 61
References 61
Suggestions for Further Reading 62
Useful Websites 63
3 Making the Case for Change 65
What Is Involved in Change? 66
New Models of Care • Case Example: Advanced Illness Screening
• Improving Quality
Managing and Measuring Quality in the Reform Environment 69
Measuring Quality Performance • Measuring Care in the Community
Who Is Involved in Change? 71
Leaders • Managers • Governance • Case Example: Developing a Quality
Structure for Change • Administrators and Clinicians • Monitoring
Quality • Quality Managers
Changing Communication 77
Breaking Down Silos • Educating Patients • Case Example: Confronting
Choices • Health Literacy • Communicating across Institutions and
Organizations • Organizing Information • Communicating Information
The Role of Data in Promoting Change 86
Tables of Measures • Quality Measures • Performance Improvement
Summary 89
Key Terms 90
Quality Concepts in Action 90
References 91
Suggestion for Further Reading 92
Useful Websites 92
4 New Challenges for Health Care Professionals 93
Meeting Statistical Expectations for Standards of Care 94
The Evolution of Quality • Measures of Quality • Case Example:
Heart Failure Readmission
10. x Contents
Meeting Patient Expectations 97
HCAHPS • Case Example: Cleveland Clinic
Role of Dashboards 100
Leadership Reports
Role of Data Analysis 104
Case Example: Assessing High-Risk Pregnancy • Data for Performance Improvement
Understanding Different Kinds of Data 105
Challenges with Health Information Technology • Different Data Sources and Clinical
Research • Data and Quality
Managing Care for Chronic Illness across the Continuum 109
The Medicare Chronic Conditions Dashboard • Quality Measures
• Case Example: Readmission
Managing Aggregated Patient Care Issues 112
Population-Based Measures • Case Example: Aspirin
Administration • Microsystems/Macrosystems • Microsystems and Lean
• Case Example: Total Joint Replacement
Improving Communication 121
Teamwork • Case Example: Improving Cardiac Mortality
Summary 127
Key Terms 127
Quality Concepts in Action 127
References 128
Suggestions for Further Reading 129
Useful Websites 130
5 Improving Patient Safety 133
Understanding Medical Errors and Adverse Events 134
Reporting Patient Safety Issues • Systems Errors • Institutionalizing
Error Prevention • The Necessity of Culture Change
High-Reliability Organizations 139
Guiding Principles • Becoming a High-Reliability Organization
The Role of Quality Management in Promoting a Safety Culture 142
Using Quality Data to Promote Safety • Case Example: Monitoring Falls
• Monitoring with Measures • Case Example: APACHE
11. Contents xi
Prioritizing Improvements 147
Using Data to Define Priorities • Case Example: Understanding Suicide
• Defining Priorities Locally • Case Example: Implementing Prioritization
Expanding Data Sources: Partnerships to Develop Best Practice 154
Case Example: Collaborations to Promote Patient Safety
Leading Organizational Improvements 155
Supporting Quality Data • Business Intelligence
The Role of Nursing Leaders in Promoting Safety 158
Communication Strategies • Integrating New Responsibilities • Transformational
Leadership • Case Example: Monitoring Patient Safety
The Role of the Medical Staff in Promoting Safety 162
Providing Education to New Physicians • Case Example: Resident Education Program
Promoting Safety through Effective Communication 165
Breaking Down Silos • Case Example: Reducing Length of Stay for Stroke Patients
Summary 169
Key Terms 169
Quality Concepts in Action 169
References 170
Suggestions for Further Reading 170
Useful Websites 171
PART II: APPLYING QUALITY TOOLS AND TECHNIQUES 173
6 Working with Quality Tools and Methods 175
Identifying a Problem 176
Cause-and-Effect Diagram • Flowchart • Checklist • Run Chart • Histogram
Describing Information 183
Mean • Median • Mode
Variability 185
Range • Standard Deviation • Bell Curve
Making Use of Data 188
Significance
12. xii Contents
Using Quality Tools and Techniques to Improve Safety 189
Root Cause Analysis • Case Example: Sepsis Mortality • Failure Mode
and Effects Analysis • Case Example: Blood Transfusion
Clinical Pathways or Care Maps 195
Care Map Characteristics • Variance • Improving Efficiency • Case Example:
Creating Guidelines
Improving Performance: Plan-Do-Study-Act 201
Plan • Do • Study • Act • Case Example: Workplace Violence
Summary 206
Key Terms 206
Quality Concepts in Action 206
Suggestions for Further Reading 207
Useful Websites 207
7 Working with Quality Data 209
Working with Measurements 210
Compliance • Case Example: Using Data to Change Practice • Performance
Improvement • Case Example: Pressure Injury Performance Improvement Initiative
Understanding Issues in Data Collection 214
Case Example: Standardizing Data • Moving from Manual to Electronic
Records • Extracting Accurate Data from Electronic Health Records
Using Data to Understand Appropriateness of Care 218
Case Example: Analyzing Mortality • Analyzing End-of-Life Care • Case Example:
Understanding Mortality
The Value of Aggregated Data in Performance Improvement 222
Case Example: Improving Transplant Mortality
The Role of Data in Managing Chronic Disease 225
Understanding Readmission • Case Example: Heart Failure Readmissions
Using Data to Monitor Variability 230
Control Chart • Variance Analysis
Publicly Reported Data 234
Hospital Compare
Interpreting and Making Use of Data 237
Administrative Concerns • Data Analytics in the Future
Quality Management in the Future 239
13. Contents xiii
Summary 240
Key Terms 241
Quality Concepts in Action 241
References 241
Suggestions for Further Reading 242
Useful Websites 242
8 Working with Quality and Safety Measures 245
Commitment to Quality 246
The Future of Quality
Using Measures to Understand Care 247
For the Consumer • For the Administrator • For the Physician
Defining the Measure 250
Define the Numerator and the Denominator • Measuring for Improvement
Process Measures 253
Case Example: Medication Measures • Complying with Process Measures
• Case Example: Mammography Rate • Understanding Variables • Making
Compliance Meaningful • Case Example: Reducing Central Line Infections
Pay for Performance 263
P4P Measures
Patient Satisfaction Measures 264
Interpreting Patient Satisfaction Scores • Understand the Process
• Refine the Process • Define Expectations
Monitoring Measures 268
Dashboards in the Past • Dashboards Today • Performance Details
Safety and Environment of Care Measures 273
Case Example: Monitoring Safety • Linking Environmental and Clinical Variables
Summary 277
Key Terms 277
Quality Concepts in Action 277
References 278
Suggestions for Further Reading 279
Useful Websites 279
14. xiv Contents
9 Translating Information into Action 281
Maximizing Efficiency 282
Throughput • Bottlenecks • Theory of Constraints • Queueing
Theory • Case Example: Managing Throughput
Determining Appropriate Levels of Care 288
End-of-Life Care/Advanced Illness 289
The Reform Mandate
Understanding Mortality 291
Financial Implications • Mortality Data
Improving ICU Care 295
Case Example: Introducing APACHE
Analyzing Readmission 298
Case Example: Readmission
Using Data for Improvements 299
Case Example: Joint Replacement Surgery • Case Example: Bariatric Surgery
Patient-Centered Care 303
SF-36 • Case Example: Quality of Life
Delivering the Message 305
Data and Nursing Staff • Data and Medical Directors
• Multidisciplinary Teams • Working with Measures
Summary 308
Key Terms 308
Quality Concepts in Action 309
References 309
Suggestions for Further Reading 310
Useful Websites 311
10 Preparing for the Future 313
The New Quality Management 314
The New Role of Administrators
The Business of Health Care 315
Improve the Product • Measures of Success • Transparency • Case Example:
Improving a Hospital in Trouble
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16. Contents xv
Measurements Are the Nuts and Bolts of Quality 319
Know What the Data Mean • Make the Data Useful • Measures Reflect Values
Getting Everyone on Board 322
Case Example: Improving Transplant Services • Changing Behavior
• Case Example: Understanding Complex Processes
Challenges for the Future 324
New Strategies • Break Down the Silos
Summary 326
Key Terms 327
Quality Concepts in Action 327
Suggestions for Further Reading 327
Useful Websites 328
Index 329
18. LIST OF FIGURES AND TABLES
Figures
1.1 Causes of Patient Mortality Pie Chart 6
1.2 Causes of Patient Mortality Histogram 6
1.3 Medication Error Rate Pareto Chart, January 2011–June 2011 12
1.4 Hospital Compare Webpage for Unplanned Readmissions 22
1.5 Hospital Compare for Waiting Times 23
1.6 Quality Indicator 31
2.1 Value-Based Performance at a Community Hospital 46
2.2 Value-Based Performance at a Tertiary Hospital 46
3.1 Screening Tool to Identify Advanced Illness 67
3.2 Dimensions of Care 83
3.3 Lines of Communication 84
3.4 JCPAC Communication 85
4.1 Inpatient Likelihood to Recommend 99
4.2 Quality and Safety Vector of Measures Dashboard 102
4.3 Hospital Comparison Dashboard 103
4.4 Raw Heart Failure Readmission Rate 112
4.5 Tactics and Team Responsibilities 118
4.6 Patient Friendly Care Map for Hip Replacement Surgery 119
4.7 Preoperative Continuum of Care 120
xvii
19. xviii List of Figures and Tables
4.8 Postoperative Continuum of Care 120
5.1 Falls with Injury 144
5.2 Analytics and Interpretation 145
5.3 Monthly Emergency Department Data 149
5.4 Raw Sepsis and Severe Sepsis/Septic Shock Mortality Rate,
January 2008–September 2014 150
5.5 Discharge Follow-Up Information Heart Failure 152
5.6 Prioritization Matrix 153
5.7 Serum Lactate Order to Result within 90 Minutes for Severe
Sepsis/Septic Shock in the Emergency Department 155
5.8 Integrating Data/Generating Reports 158
5.9 Patient Outcome Monitoring Tool 162
5.10 Communication across the Care Continuum 168
6.1 Falls Cause-and-Effect Diagram 178
6.2 Flowchart 179
6.3 Time-Out Checklist 180
6.4 Newborn Deliveries Run Chart 182
6.5 Waiting Time for Emergency Department Triage 182
6.6 Standard Deviation Formula 186
6.7 Blood Pressure Bell Curve 187
6.8 Comparing RCA and FMEA 193
6.9 Transfusion Flowchart 194
6.10 Hip Replacement Care Map 196
6.11 Variance Analysis: CAP Chart 198
6.12 Variance Analysis: CAP Outcome Bar Chart 198
6.13 Quality Improvement through Care Pathways 200
6.14 Improved Efficiency and Throughput 201
6.15 Clinical Guidelines Creation Methodology 202
6.16 PDSA Cycle 203
7.1 Hospital-Acquired Pressure Injury Index 213
7.2 Mortality Surveillance Tool Summary Report 219
7.3 Kidney Transplant Data Input 223
7.4 Wound Infection Rate 224
7.5 30-Day Observed Readmission Rate for Heart Failure Analysis 227
7.6 Heart Failure Readmissions by Age 227
7.7 Heart Failure Readmission Analysis: HF Discharges by Discharge
Disposition 228
7.8 Know Your Heart Failure Zones 229
7.9 Control Chart of Clostridium difficile 233
7.10 Hospital Compare Benchmark Report: Inpatient Clinical
Measures—Inpatient Surgical Infection Prevention 235
7.11 Timely Heart Attack Care 236
8.1 Hospital Medication Administration Process 254
20. List of Figures and Tables xix
8.2 Medication Error Measures 255
8.3 Executive Summary Medication Measures 256
8.4 Medication Safety Alert 257
8.5 Mammography Rate 260
8.6 Independent Variables 261
8.7 Non-ICU Central Line–Associated BSI Control Chart 263
8.8 Public Reporting Scores 269
8.9 Executive Summary 270
8.10 Risk-Adjusted Mortality Index 271
8.11 Non-ICU Central Line–Associated BSI Index 272
8.12 Non-ICU Central Line–Associated BSI Index Pivot View 273
8.13 Safety Services Quarterly Report 275
9.1 Throughput 284
9.2 Ambulatory Surgery Log Tracking 288
9.3 Advanced Illness 291
9.4 APACHE Reports 296
9.5 Bariatric Preoperative Checklist 302
9.6 SF-36 Physical and Mental Health Component
Analysis by Time Point 304
10.1 Data Overload 320
Tables
3.1 Inpatient Quality Indicators 87
3.2 Table of Measures for Ambulatory Services 88
7.1 Kidney Transplant Table of Measures 224
9.1 Bariatric Table of Measures 303
22. PREFACE
When I began to think about revising the outdated Quality Handbook
for Health Care Organizations: A Manager’s Guide to Tools and Programs
(Jossey-Bass, 2004), my goal was to introduce and explore the many changes
that have made an impact on health care in the last decade. I quickly real-
ized that I couldn’t simply revise the book for a second edition; too much had
changed. An entirely new book introducing quality management was needed
if I wanted it to be of value to health care professionals and students. This
Introduction to Health Care Quality: Theory, Methods, and Tools seemed necessary.
Even the change in titles is revealing. Quality is no longer the sole purview
of managers. To the contrary, now everyone—clinicians, administrators, exec-
utives, patients—involved in health care services needs to work within a qual-
ity framework and be familiar with quality management processes. Students
who hope to work in health care, whether in the clinical, administrative, or
policy-making roles, need to know the fundamentals of quality management
to succeed. Physicians, nurses, pharmacists, and public health policy makers all
need to involve themselves in performance improvement activities and under-
stand how to transform data into useful information in order to take action.
Administrators and executives have to meet the goals of specific quality mea-
sures set by government agencies in order to be reimbursed for the delivery of
care and medical services.
My books are designed to be of practical use to students and professionals
and are based on my experience working in the field of quality management
xxi
23. xxii Preface
for decades and teaching fundamentals of quality all over the world. I have the
good fortune of being part of a vast health care system that encompasses the
entire spectrum of health care services—21 hospitals, the Feinstein Institute
for Medical Research, the Krasnoff Quality Management Institute, the Cen-
ter for Learning and Innovation, rehabilitation and skilled nursing facilities, a
home care network, a hospice network, and progressive care centers—offering
a range of outpatient services; ambulatory facilities; psychiatric care; long-term
nursing care; and children’s organizations. Thus I have direct and immediate
access to the issues that most concern administrators and executives, floor and
unit managers, clinicians, policy makers, IT professionals, and others. Writing
from personal experience gives me the opportunity to share practical issues
of quality in action and relay the direct application of quality management
theory, methods, and tools.
I have always been a champion of quality and I like to think an advocate
for patients’ rights and patient safety. I have worked diligently to ferret out
gaps in care and potential gaps in safety to improve performance, and further
communication and accountability across the hospital and the continuum of
care. I followed this path because I believe in the tenets of quality management;
I believe in the objectivity of data to make a case for good or poor care. I believe
in numbers, in measurements, in tracking improvements and interventions
over time using reliable and valid data.
But it was not until I myself became a patient that my theoretical exper-
tise quickly became of immediate and practical concern. As a patient, I found
myself vulnerable to issues of safety and communication failures that I had writ-
ten about and spoken about but had never directly experienced. Although I
had always understood the importance of patient identification, for example,
until I was receiving chemotherapy and the nurses made absolutely sure that I
was getting the correct dose of the correct medications in the correct manner,
and asked me multiple times to confirm my name, I didn’t realize how reas-
suring it was to know that the procedures developed to ensure proper patient
identification were in place and being followed. When I needed my MRI results
to be transmitted to my oncologist in a timely fashion, I didn’t want any fail-
ures of communication to take place. Ensuring quality care became deeply
personal.
And although I am probably better educated than most about dealing with
health care data, I found that when I was confronted with three very different
plans of care from three very highly regarded physicians, I needed to under-
stand mortality rates and complications from treatment, numbers, variation,
and evidence in a new way. How many patients with my particular very rare
cancer had each doctor treated and with what outcome? I realized how valu-
able my experience as a quality professional was. I knew what questions to
ask. Quality care is, of course, a goal for organizations to strive for, but it is
also for everyone. I realized that everyone—health care professionals, patients,
24. Preface xxiii
and potential patients—should be quality managers. This book, then, is for
everyone.
New models of health care are so-called patient-centered, making patients
central to the care plan and treatment process. Again, to me, this is no longer
theory. It is in fact critical that patients understand what is happening to them,
why they are having the treatment they are having, what the predicted out-
comes will be, and what complications might occur. All these issues, basic to
quality management, were now basic to me. All patients should indeed be
treated holistically. We are not defined by our disease or our illness; we are
people with psychosocial experiences and needs, some of us more capable
than others or simply luckier than others in being able to take good care of
ourselves.
Everyone should be a quality manager. Everyone will have occasion to
interact with a health care delivery system of one kind or another, either for
themselves or for family and loved ones. Everyone needs to be schooled about
quality, how to assess care, what to look for, what is expected, what should not
be tolerated. Everyone should be an advocate for quality care. I hope this book
will be useful to professionals and nonprofessionals alike.
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31. The Project Gutenberg eBook of On the
Philosophy of Discovery, Chapters Historical
and Critical
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Title: On the Philosophy of Discovery, Chapters Historical and
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Author: William Whewell
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*** START OF THE PROJECT GUTENBERG EBOOK ON THE
PHILOSOPHY OF DISCOVERY, CHAPTERS HISTORICAL AND
CRITICAL ***
33. ON THE
PHILOSOPHY
OF
DISCOVERY.
Cambridge:
PRINTED BY C. J. CLAY, M.A.
AT THE UNIVERSITY PRESS.
ON THE
PHILOSOPHY OF DISCOVERY,
CHAPTERS HISTORICAL AND CRITICAL;
BY
WILLIAM WHEWELL, D.D.
MASTER OF TRINITY COLLEGE, CAMBRIDGE, AND
CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE.
34. INCLUDING THE COMPLETION OF THE THIRD EDITION
OF THE PHILOSOPHY OF THE INDUCTIVE SCIENCES.
ΛΑΜΠΑΔΙΑ ΕΧΟΝΤΕΣ ΔΙΑΔΩΣΟΥΣΙΝ ΑΛΛΗΛΟΙΣ
LONDON:
JOHN W. PARKER AND SON, WEST STRAND.
1860.
The following are the latest editions of the series of works which has
been published connected with the present subject:
History of the Inductive Sciences, 3 Vols. 1857.
History of Scientific Ideas, 2 Vols. 1858.
Novum Organon Renovatum, 1 Vol. 1858.
On the Philosophy of Discovery, 1 Vol. 1860.
To the History of the Inductive Sciences are appended two Indexes
(in Vol. 1.), an Index of Proper Names, and an Index of Technical
Terms. These Indexes, and the Tables of Contents of the other
works, will enable the reader to refer to any person or event
included in this series.
35. T
PREFACE
he two works which I entitled The History of the Inductive
Sciences, and The Philosophy of the Inductive Sciences, were
intended to present to the reader a view of the steps by which
those portions of human knowledge which are held to be most
certain and stable have been acquired, and of the philosophical
principles which are involved in those steps. Each of these steps was
a scientific Discovery, in which a new conception was applied in
order to bind together observed facts. And though the conjunction of
the observed facts was in each case an example of logical Induction,
it was not the inductive process merely, but the novelty of the result
in each case which gave its peculiar character to the History; and
the Philosophy at which I aimed was not the Philosophy of
Induction, but the Philosophy of Discovery. In the present edition I
have described this as my object in my Title.
A great part of the present volume consists of chapters which
composed the twelfth Book of the Philosophy in former editions,
which Book was then described as a 'Review of Opinions on the
nature of Knowledge and the Method of seeking it.' I have added to
this part several new chapters, on Plato, Aristotle, the Arabian
Philosophers, Francis Bacon, Mr. Mill, Mr. Mansel, the late Sir William
Hamilton, and the German philosophers Kant, Fichte, Schelling and
Hegel. I might, if time had allowed, have added a new chapter on
Roger Bacon, founded on his Opus Minus and other works, recently
published for the first time under the direction of the Master of the
Rolls; a valuable contribution to the history of philosophy. But the
review of this work would not materially alter the estimate of Roger
Bacon which I had derived from the Opus Majus.
But besides these historical and critical surveys of the philosophy of
others, I have ventured to introduce some new views of my own;
namely, views which bear upon the philosophy of religion. I have
36. done so under the conviction that no philosophy of the universe can
satisfy the minds of thoughtful men which does not deal with such
questions as inevitably force themselves on our notice, respecting
the Author and the Object of the universe; and also under the
conviction that every philosophy of the universe which has any
consistency must suggest answers, at least conjectural, to such
questions. No Cosmos is complete from which the question of Deity
is excluded; and all Cosmology has a side turned towards Theology.
Though I am aware therefore how easy it is, on this subject, to give
offence and to incur obloquy, I have not thought it right to abstain
from following out my philosophical principles to their results in this
department of speculation. The results do not differ materially from
those at which many pious and thoughtful speculators have arrived
in previous ages of the world; though they have here, as seems to
me, something of novelty in their connection with the philosophy of
science. But this point I willingly leave to the calm decision of
competent judges.
I have added in an Appendix various Essays, previously published at
different times, which may serve perhaps to illustrate some points of
the history and philosophy of science.
Trinity Lodge,
February 8, 1856.
ON
THE PHILOSOPHY OF DISCOVERY.
37. CONTENTS.
The chapters marked thus * appear now for the first time.
The chapters marked thus † have appeared in other works.
Chap. I. Introduction.
Chap. II. Plato.
Chap. III. *Additional Remarks on Plato.
1.The Doctrine of Ideas.
2.The Doctrine of the One and Many.
3.The notion of the nature and aim of Science.
4.The Survey of existing Sciences.
5.The Constitution of the human Mind.
Chap. IV. Aristotle.
Chap. V. *Additional Remarks on Aristotle.
1.Induction.
2.Invention.
3.The One in the Many.
4.The "Five Words."
5.Aristotle's contribution to the Physical Sciences.
6.Aristotle's Astronomy.
7.Aristotle on Classification.
8.F. Bacon on Aristotle.
9.Discovery of Causes.
10.Plato and Aristotle.
11.Aristotle against Plato's Ideas.
Chap. VI. The Later Greeks.
Chap. VII. The Romans.
Chap. VIII. *Arabian Philosophers.
Chap. IX. The Schoolmen of the Middle Ages.
38. Chap. X. The Innovators of the Middle Ages.
Raymond Lully.
Chap. XI. The Innovators of the Middle Ages—continued.
Roger Bacon.
Chap. XII. The Revival of Platonism.
1.Causes of Delay in the Advance of Knowledge.
2.Causes of Progress.
3.Hermolaus Barbarus, &c.
4.Nicolaus Cusanus.
5.Manilius Ficinus.
6.Francis Patricius.
7.Picus, Agrippa, &c.
8.Paracelsus, Fludd, &c.
Chap. XIII. The Theoretical Reformers of Science.
1.Bernardinus Telesius.
2.Thomas Campanella.
3.Andrew Cæsalpinus.
4.Giordano Bruno.
5.Peter Ramus.
6.The Reformers in General.
7.Melancthon.
Chap. XIV. The Practical Reformers of Science.
1.Character of the Practical Reformers.
2.Leonardo da Vinci.
3.Copernicus.
4.Fabricius.
5.Maurolycus.
6.Benedetti.
7.Gilbert.
8.Galileo.
9.Kepler.
10.Tycho.
Chap. XV. Francis Bacon.
39. 1.(I.) General Remarks.
2.Common estimate of him.
3.We consider only Physical Science.
4.He is placed at the head of the change:
5.(II.) He proclaims a New Era;
6.(III.) By a Change of Method;
7.Including successive Steps;
8.Gradually ascending.
9.(IV.) He contrasts the Old and the New Method.
10.(V.) Has he neglected Ideas?
11.No.
12.Examples of Ideas treated by him.
13.He has failed in applying his Method;
14.(VI.) To the Cause of Heat.
15.He seeks Causes before Laws.
16.(VII.) His Technical Form worthless.
17.He is confused by words.
18.His "Instances."
19.Contain some good Suggestions.
20.(VIII.) His "Idols."
21.(IX.) His view of Utility.
22.(X.) His Hopefulness.
23.(XI.) His Piety.
Chap. XVI. *Additional Remarks on Francis Bacon.
1.Mr. Ellis's views.
2.Mr. Spedding's views.
Chap. XVII. From Bacon to Newton.
1.Harvey.
2.Descartes.
3.Gassendi.
4.Actual Progress in Science.
5.Otto Guericke, &c.
6.Hooke.
40. 7.Royal Society.
8.Bacon's New Atalantis.
9.Cowley.
10.Barrow.
Chap. XVIII. Newton.
1.Animating effect of his Discoveries.
2.They confirm Bacon's views.
3.Newton shuns Hypotheses.
4.His views of Inductive Philosophy.
5.His "Rules of Philosophizing."
6.The First Rule.
7.What is a "True Cause"?
8.Such as are real?
9.Or those which are proved?
10.Use of the Rule.
11.Rule otherwise expressed.
12.The Second Rule.
13.What are Events "of the same kind"?
14.The Third Rule:
15.Not safe.
16.The Fourth Rule.
17.Occult Qualities.
18.Ridiculed.
19.Distinction of Laws and Causes.
Chap. XIX. Locke and his French Followers.
1.Cause of Locke's popularity.
2.Sensational School.
3.His inconsistencies.
4.Condillac, &c.
5.Importance of Language.
6.Ground of this.
7.The Encyclopedists.
8.Helvetius.
41. 9.Value of Arts.
10.Tendency to Reaction.
Chap. XX. The Reaction against the Sensational School.
1."Nisi intellectus ipse."
2.Price's "Review."
3.Stewart defends Price.
4.Archbishop Whately.
5.Laromiguière.
6.M. Cousin.
7.M. Ampère.
8.His Classification of Sciences.
9.Kant's Reform of Philosophy.
10.Its Effect in Germany.
Chap. XXI. Further Advance of the Sensational School.
M. Auguste Comte.
1.M. Comte on three States of Science.
2.M. Comte rejects the Search of Causes.
3.Causes in Physics.
4.Causes in other Sciences.
5.M. Comte's Practical Philosophy.
6.M. Comte on Hypotheses.
7.M. Comte's Classification of Sciences.
Chap. XXII. †Mr. Mill's Logic.
(I.)What is Induction? §§ 1-14.
(II.)Induction or Description, §§ 15-23.
(III.)In Discovery a new Conception is introduced, §§ 24-37.
(IV.)Mr. Mill's Four Methods of Inquiry, §§ 38-40.
(V.)His Examples, §§ 41-48.
(VI.)Mr. Mill against Hypotheses, §§ 49, 50.
(VII.)Against prediction of Facts, §§ 51-53.
(VIII.)Newton's Vera Causa, §§ 54, 55.
(IX.)Successive Generalizations, §§ 56-62.
(X.)Mr. Mill's Hope from Deductions, §§ 63-67.
42. (XI.)Fundamental opposition of our Doctrines, §§ 68-71.
(XII.)Absurdities in Mr. Mill's Logic, §§ 72-74.
Chap. XXIII. *Political Economy as an Inductive Science.
1.Moral Sciences.
2.Political Economy.
3.Wages, Profits, and Rents.
4.Premature Generalizations.
5.Correction of these by Induction—Rent.
6. " Wages.
7. " Population.
Chap. XXIV. †Modern German Philosophy.
(I.)Science is the Idealization of Facts, §§ 1-8.
(II.)Successive German Philosophies.
Kant, Fichte, Schelling, Hegel, §§ 9-16.
Chap. XXV. †The Fundamental Antithesis as it exists in the Moral World.
Moral Progress is the Realization of Ideas.
Chap. XXVI. *Of the "Philosophy of the Infinite."
God is Eternal.
Chap. XXVII. *Sir William Hamilton on Inertia and Weight.
1.Primary and Secondary Qualities.
2.Meaning of the Distinction.
3.Sir W. Hamilton adds "Secundo-Primary."
4.Inertia.
5.Sir W. Hamilton's arguments and reply.
6.Gravity.
Sir W. Hamilton's arguments and reply.
Chap. XXVIII. †Influence of German Systems of Philosophy in Britain.
1.Stewart on Kant.
2.Mr. G. H. Lewes on Kant.
4—6.Mr. Mansel on Kant.
His objection to our Fundamental Ideas, and Reply.
7—10.New Axioms are possible.
11—13.Mr. Mansel's Kantianism.
43. 14—16.Axioms are not from experience.
Chap. XXIX. *Necessary Truth is Progressive.
Objections considered.
Chap. XXX. *The Theological Bearing of the Philosophy of Discovery.
1—4.How can necessary truths be actual?
5, 6.Small extent of necessary truth.
7.How did things come to be as they are?
8.View of the Theist.
9—12.Is this Platonism?
13.Idea of Time.
14, 15.Ideas of Force and Matter.
16.Creation of Matter.
17.Platonic Ideas.
18—21.Idea of Kind.
22.Idea of Substance.
23.Idea of Final Cause.
24, 25.Human immeasurably inferior to Divine.
26.Science advances towards the Divine Ideas.
27.Recapitulation.
Chap. XXXI. *Man's Knowledge of God.
1, 2.Opinions.
3.From Nature we learn something of God.
4—6.Though but little.
7, 8.From ourselves we learn something concerning God.
9—11.Objections answered.
12.Creation.
13.End of the World.
14.Moral and Theological views enter.
Chap. XXXII. *Analogies of Physical and Religious Philosophy.
1, 2.Idealization of Facts and Realization of Ideas;
3, 4.Both imperfect.
5, 6.Divine Ideas perfect.
7—9.Realization of Divine Love.
44. 10—13.Realization of Divine Justice.
14.Analogy of Physical and Moral Philosophy.
15, 16.Supernatural Beginning, Middle, and End indicated.
17.Suggestion of a Future State.
18—20.Confirmation from the Intellect of Man.
21.From the Moral Nature of Man.
APPENDIX.
PAGE
Append. A.Of the Platonic Theory of Ideas 403
B.On Plato's Survey of the Sciences 417
BB.On Plato's Notion of Dialectic 429
C.Of the Intellectual Powers according to Plato 440
D.Criticism of Aristotle's Account of Induction 449
E.On the Fundamental Antithesis of Philosophy 462
F.Remarks on a Review of the Philosophy of the Inductive
Sciences 482
G.On the Transformation of Hypotheses in the History of
Science 492
H.On Hegel's Criticism of Newton's Principia 504
Appendix to the Memoir on Hegel's Criticism of
Newton's Principia 513
K.Demonstration that all Matter is Heavy 522
ON THE
PHILOSOPHY
OF
DISCOVERY.
45. Wär' nicht das Auge sonnenhaft
Wie könnten wir das Licht erblicken?
Lebt' nicht in uns des Gottes eigne Kraft
Wie könnte uns das Göttliche entzücken?
Goethe.
Were nothing sunlike in the Eye
How could we Light itself descry?
Were nothing godlike in the Mind
How could we God in Nature find?
46. B
CHAPTER I.
INTRODUCTION.
y the examination of the elements of human thought in which I
have been engaged, and by a consideration of the history of the
most clear and certain parts of our knowledge, I have been led
to doctrines respecting the progress of that exact and systematic
knowledge which we call Science; and these doctrines I have
endeavoured to lay before the reader in the History of the Sciences
and of Scientific Ideas. The questions on which I have thus ventured
to pronounce have had a strong interest for man from the earliest
period of his intellectual progress, and have been the subjects of
lively discussion and bold speculation in every age. I conceive that in
the doctrines to which these researches have conducted us, we have
a far better hope that we possess a body of permanent truths than
the earlier essays on the same subjects could furnish. For we have
not taken our examples of knowledge at hazard, as earlier
speculators did, and were almost compelled to do; but have drawn
our materials from the vast store of unquestioned truths which
modern science offers to us: and we have formed our judgment
concerning the nature and progress of knowledge by considering
what such science is, and how it has reached its present condition.
But though we have thus pursued our speculations concerning
knowledge with advantages which earlier writers did not possess, it
is still both interesting and instructive for us to regard the opinions
upon this subject which have been delivered by the philosophers of
past times. It is especially interesting to see some of the truths
which we have endeavoured to expound, gradually dawning in men's
minds, and assuming the clear and permanent form in which we can
now contemplate them. I shall therefore, in the ensuing chapters,
pass in review many of the opinions of the writers of various ages
concerning the mode by which man best acquires the truest
knowledge; and I shall endeavour, as we proceed, to appreciate the
47. real value of such judgments, and their place in the progress of
sound philosophy.
In this estimate of the opinions of others, I shall be guided by those
general doctrines which I have, as I trust, established in the histories
already published. And without attempting here to give any
summary of these doctrines, I may remark that there are two main
principles by which speculations on such subjects in all ages are
connected and related to each other; namely, the opposition of
Ideas and Sensations, and the distinction of practical and speculative
knowledge. The opposition of Ideas and Sensations is exhibited to
us in the antithesis of Theory and Fact, which are necessarily
considered as distinct and of opposite natures, and yet necessarily
identical, and constituting Science by their identity. In like manner,
although practical knowledge is in substance identical with
speculative, (for all knowledge is speculation,) there is a distinction
between the two in their history, and in the subjects by which they
are exemplified, which distinction is quite essential in judging of the
philosophical views of the ancients. The alternatives of identity and
diversity, in these two antitheses,—the successive separation,
opposition, and reunion of principles which thus arise,—have
produced, (as they may easily be imagined capable of doing,) a long
and varied series of systems concerning the nature of knowledge;
among which we shall have to guide our course by the aid of the
views already presented.
I am far from undertaking, or wishing, to review the whole series of
opinions which thus come under our notice; and I do not even
attempt to examine all the principal authors who have written on
such subjects. I merely wish to select some of the most considerable
forms which, such opinions have assumed, and to point out in some
measure the progress of truth from age to age. In doing this, I can
only endeavour to seize some of the most prominent features of
each time and of each step, and I must pass rapidly from classical
antiquity to those which we have called the dark ages, and from
them to modern times. At each of these periods the modifications of
48. opinion, and the speculations with which they were connected,
formed a vast and tangled maze, the byways of which our plan does
not allow us to enter. We shall esteem ourselves but too fortunate, if
we can discover the single track by which ancient led to modern
philosophy.
I must also repeat that my survey of philosophical writers is here
confined to this one point,—their opinions on the nature of
knowledge and the method of science. I with some effort avoid
entering upon other parts of the philosophy of those authors of
whom I speak; I knowingly pass by those portions of their
speculations which are in many cases the most interesting and
celebrated;—their opinions concerning the human soul, the Divine
Governor of the world, the foundations or leading doctrines of
politics, religion, and general philosophy. I am desirous that my
reader should bear this in mind, since he must otherwise be
offended with the scanty and partial view which I give in this place
of the philosophers whom I enumerate.
51. T
CHAPTER II.
Plato.
here would be small advantage in beginning our examination
earlier than the period of the Socratic School at Athens; for
although the spirit of inquiry on such subjects had awakened in
Greece at an earlier period, and although the peculiar aptitude of the
Grecian mind for such researches had shown itself repeatedly in
subtle distinctions and acute reasonings, all the positive results of
these early efforts were contained in a more definite form in the
reasonings of the Platonic age. Before that time, the Greeks did not
possess plain and familiar examples of exact knowledge, such as the
truths of Arithmetic, Geometry, Astronomy and Optics became in the
school of Plato; nor were the antitheses of which we spoke above,
so distinctly and fully unfolded as we find them in Plato's works.
The question which hinges upon one of these antitheses, occupies a
prominent place in several of the Platonic dialogues; namely,
whether our knowledge be obtained by means of Sensation or of
Ideas. One of the doctrines which Plato most earnestly inculcated
upon his countrymen was, that we do not know concerning sensible
objects, but concerning ideas. The first attempts of the Greeks at
metaphysical analysis had given rise to a school which maintained
that material objects are the only realities. In opposition to this,
arose another school, which taught that material objects have no
permanent reality, but are ever waxing and waning, constantly
changing their substance. "And hence," as Aristotle says1, "arose the
doctrine of ideas which the Platonists held. For they assented to the
opinion of Heraclitus, that all sensible objects are in a constant state
of flux. So that if there is to be any knowledge and science, it must
be concerning some permanent natures, different from the sensible
natures of objects; for there can be no permanent science
respecting that which is perpetually changing. It happened that
52. Socrates turned his speculations to the moral virtues, and was the
first philosopher who endeavoured to give universal definitions of
such matters. He wished to reason systematically, and therefore he
tried to establish definitions, for definitions are the basis of
systematic reasoning. There are two things which may justly be
looked upon as steps in philosophy due to Socrates; inductive
reasonings, and universal definitions;—both of them steps which
belong to the foundations of science. Socrates, however, did not
make universals, or definitions separable from the objects; but his
followers separated them, and these essences they termed Ideas."
And the same account is given by other writers[2]. "Some existences
are sensible, some intelligible: and according to Plato, if we wish to
understand the principles of things, we must first separate the ideas
from the things, such as the ideas of Similarity, Unity, Number,
Magnitude, Position, Motion: second, that we must assume an
absolute Fair, Good, Just, and the like: third, that we must consider
the ideas of relation, as Knowledge, Power: recollecting that the
Things which we perceive have this or that appellation applied to
them because they partake of this or that Idea; those things being
just which participate in the idea of The Just, those being beautiful,
which contain the idea of The Beautiful." And many of the
arguments by which this doctrine was maintained are to be found in
the Platonic dialogues. Thus the opinion that true knowledge
consists in sensation, which had been asserted by Protagoras and
others, is refuted in the Theætetus: and, we may add, so
victoriously refuted, that the arguments there put forth have ever
since exercised a strong influence upon the speculative world. It may
be remarked that in the minds of Plato and of those who have since
pursued the same paths of speculation, the interest of such
discussions as those we are now referring to, was by no means
limited to their bearing upon mere theory; but was closely connected
with those great questions of morals which have always a practical
import. Those who asserted that the only foundation of knowledge
was sensation, asserted also that the only foundation of virtue was
the desire of pleasure. And in Plato, the metaphysical part of the
53. disquisitions concerning knowledge in general, though independent
in its principles, always seems to be subordinate in its purpose to the
questions concerning the knowledge of our duty.
Since Plato thus looked upon the Ideas which were involved in each
department of knowledge as forming its only essential part, it was
natural that he should look upon the study of Ideas as the true
mode of pursuing knowledge. This he himself describes in the
Philebus[3]. "The best way of arriving at truth is not very difficult to
point out, but most hard to pursue. All the arts which have ever
been discovered, were revealed in this manner. It is a gift of the
gods to man, which, as I conceive, they sent down by some
Prometheus, as by Prometheus they gave us the light of fire; and
the ancients, more clear-sighted than we, and less removed from the
gods, handed down this traditionary doctrine: that whatever is said
to be, comes of One and of Many, and comprehends in itself the
Finite and the Infinite in coalition (being One Kind, and consisting of
Infinite Individuals). And this being the state of things, we must, in
each case, endeavour to seize the One Idea (the idea of the Kind) as
the chief point; for we shall find that it is there. And when we have
seized this one thing, we may then consider how it comprehends in
itself two, or three, or any other number; and, again, examine each
of these ramifications separately; till at last we perceive, not only
that One is at the same time One and Many, but also how many.
And when we have thus filled up the interval between the Infinite
and the One, we may consider that we have done with each one.
The gods then, as I have said, taught us by tradition thus to
contemplate, and to learn, and to teach one another. But the
philosophers of the present day seize upon the One, at hazard, too
soon or too late, and then immediately snatch at the Infinite; but the
intermediate steps escape them, in which resides the distinction
between a truly logical and a mere disputatious discussion."
It would seem that what the author here describes as the most
perfect form of exposition, is that which refers each object to its
place in a classification containing a complete series of
54. subordinations, and which gives a definition of each class. We have
repeatedly remarked that, in sciences of classification, each new
definition which gives a tenable and distinct separation of classes is
an important advance in our knowledge; but that such definitions
are rather the last than the first step in each advance. In the
progress of real knowledge, these definitions are always the results
of a laborious study of individual cases, and are never arrived at by a
pure effort of thought, which is what Plato appears to have imagined
as the true mode of philosophizing. And still less do the advances of
other sciences consist in seizing at once upon the highest generality,
and filling in afterwards all the intermediate steps between that and
the special instances. On the contrary, as we have seen, the ascents
from particular to general are all successive; and each step of this
ascent requires time, and labour, and a patient examination of actual
facts and objects.
It would, of course, be absurd to blame Plato for having inadequate
views of the nature of progressive knowledge, at the time when
knowledge could hardly be said to have begun its progress. But we
already find in his speculations, as appears in the passages just
quoted from his writings, several points brought into view which will
require our continued attention as we proceed. In overlooking the
necessity of a gradual and successive advance from the less general
to the more general truths, Plato shared in a dimness of vision[4]
which prevailed among philosophers to the time of Francis Bacon. In
thinking too slightly of the study of actual nature, he manifested a
bias from which the human intellect freed itself in the vigorous
struggles which terminated the dark ages. In pointing out that all
knowledge implies a unity of what we observe as manifold, which
unity is given by the mind, Plato taught a lesson which has of late
been too obscurely acknowledged, the recoil by which men repaired
their long neglect of facts having carried them for a while so far as
to think that facts were the whole of our knowledge. And in
analysing this principle of Unity, by which we thus connect sensible
things, into various Ideas, such as Number, Magnitude, Position,
Motion, he made a highly important step, which it has been the
55. business of philosophers in succeeding times to complete and to
follow out.
But the efficacy of Plato's speculations in their bearing upon physical
science, and upon theory in general, was much weakened by the
confusion of practical with theoretical knowledge, which arose from
the ethical propensities of the Socratic school. In the Platonic
Dialogues, Art and Science are constantly spoken of indiscriminately.
The skill possessed by the Painter, the Architect, the Shoemaker, is
considered as a just example of human science, no less than the
knowledge which the geometer or the astronomer possesses of the
theoretical truths with which he is conversant. Not only so; but
traditionary and mythological tales, mystical imaginations and
fantastical etymologies, are mixed up, as no less choice ingredients,
with the most acute logical analyses, and the most exact conduct of
metaphysical controversies. There is no distinction made between
the knowledge possessed by the theoretical psychologist and the
physician, the philosophical teacher of morals and the legislator or
the administrator of law. This, indeed, is the less to be wondered at,
since even in our own time the same confusion is very commonly
made by persons not otherwise ignorant or uncultured.
On the other hand, we may remark finally, that Plato's admiration of
Ideas was not a barren imagination, even so far as regarded physical
science. For, as we have seen[5], he had a very important share in
the introduction of the theory of epicycles, having been the first to
propose to astronomers in a distinct form, the problem of which that
theory was the solution; namely, "to explain the celestial phenomena
by the combination of equable circular motions." This demand of an
ideal hypothesis which should exactly express the phenomena (as
well as they could then be observed), and from which, by the
interposition of suitable steps, all special cases might be deduced,
falls in well with those views respecting the proper mode of seeking
knowledge which we have quoted from the Philebus. And the Idea
which could thus represent and replace all the particular Facts, being
not only sought but found, we may readily suppose that the
56. philosopher was, by this event, strongly confirmed in his persuasion
that such an Idea was indeed what the inquirer ought to seek. In
this conviction all his genuine followers up to modern times have
participated; and thus, though they have avoided the error of those
who hold that facts alone are valuable as the elements of our
knowledge, they have frequently run into the opposite error of too
much despising and neglecting facts, and of thinking that the
business of the inquirer after truth was only a profound and constant
contemplation of the conceptions of his own mind. But of this
hereafter.
57. T
CHAPTER III.
Additional Remarks on Plato.
he leading points in Plato's writings which bear upon the
philosophy of discovery are these:
1. The Doctrine of Ideas.
2. The Doctrine of the One and the Many.
3. The notion of the nature and aim of Science.
4. The survey of existing Sciences.
1. The Doctrine of Ideas is an attempt to solve a problem which in
all ages forces itself upon the notice of thoughtful men; namely, How
can certain and permanent knowledge be possible for man, since all
his knowledge must be derived from transient and fluctuating
sensations? And the answer given by this doctrine is, that certain
and permanent knowledge is not derived from Sensations, but from
Ideas. There are in the mind certain elements of knowledge which
are not derived from sensation, and are only imperfectly exemplified
in sensible objects; and when we reason concerning sensible things
so as to obtain real knowledge, we do so by considering such things
as partaking of the qualities of the Ideas concerning which there can
be truth. The sciences of Geometry and Arithmetic show that there
are truths which man can know; and the Doctrine of Ideas explains
how this is possible.
So far the Doctrine of Ideas answers its primary purpose, and is a
reply (by no means the least intelligible and satisfactory reply) to a
question still agitated among philosophers: What is the ground of
geometrical (and other necessary) truth?
But Plato seems, in many of his writings, to extend this doctrine
much further; and to assume, not only Ideas of Space and its
properties, from which geometrical truths are derived; but of
58. Relations, as the Relations of Like and Unlike, Greater and Less; and
of mere material objects, as Tables and Chairs. Now to assume Ideas
of such things as these solves no difficulty and is supported by no
argument. In this respect the Ideal theory is of no value in Science.
It is curious that we have a very acute refutation of the Ideal theory
in this sense, not only in Aristotle, the open opponent of Plato on
this subject, but in the Platonic writings themselves: namely, in the
Dialogue entitled Parmenides; which, on this and on other accounts,
I consider to be the work not of Plato, but of an opponent of
Plato[6].
2. I have spoken, in the preceding chapter, of Plato's doctrine that
truth is to be obtained by discerning the One in the Many. This
expression is used, it would seem, in a somewhat large and
fluctuating way, to mean several things; as for instance, finding the
one kind in many individuals (for instance, the one idea of dog in
many dogs); or the one law in many phenomena (for instance, the
eccentrics and epicycles in many planets). In any interpretation, it is
too loose and indefinite a rule to be of much value in the formation
of sciences, though it has been recently again propounded as
important in modern times.
3. I have said, in the preceding chapter, that Plato, though he saw
that scientific truths of great generality might be obtained and were
to be arrived at by philosophers, overlooked the necessity of a
gradual and successive advance from the less general to the more
general; and I have described this as a 'dimness of vision.' I must
now acknowledge that this is not a very appropriate phrase; for not
only no acuteness of vision could have enabled Plato to see that
gradual generalization in science of which, as yet, no example had
appeared; but it was very fortunate for the progress of truth, at that
time, that Plato had imagined to himself the object of science to be
general and sublime truths which prove themselves to be true by the
light of their own generality and symmetry. It is worth while to
illustrate this notice of Plato by some references to his writings.
59. In the Sixth Book of the Republic, Plato treats of the then existing
sciences as the instruments of a philosophical education. Among the
most conspicuous of these is astronomy. He there ridicules the
notion that astronomy is a sublime science because it makes men
look upward. He asserts that the really sublime science is that which
makes men look at the realities, which are suggested by the
appearances seen in the heavens: namely, the spheres which revolve
and carry the luminaries in their revolutions. Now it was no doubt
the determined search for such "realities" as these which gave birth
to the Greek Astronomy, that first and critical step in the progress of
science. Plato, by his exhortations, if not by his suggestions,
contributed effectually, as I conceive, to this step in science. In the
same manner he requires a science of Harmonics which shall be free
from the defects and inaccuracies which occur in actual instruments.
This belief that the universe was full of mathematical relations, and
that these were the true objects of scientific research, gave a vigour,
largeness of mind, and confidence to the Greek speculators which no
more cautious view of the problem of scientific discovery could have
supplied. It was well that this advanced guard in the army of
discoverers was filled with indomitable courage, boundless hopes,
and creative minds.
But we must not forget that this disposition to what Bacon calls
anticipation was full of danger as well as of hope. It led Plato into
error, as it led Kepler afterwards, and many others in all ages of
scientific activity. It led Plato into error, for instance, when it led him
to assert (in the Timæus) that the four elements, Earth, Air, Fire and
Water, have, for the forms of their particles respectively, the Cube,
the Icosahedron, the Pyramid, and the Octahedron; and again, when
it led him to despise the practical controversies of the musicians of
his time; which controversies were, in fact, the proof of the truth of
the mathematical theory of Harmonics. And in like manner it led
Kepler into error when it led him to believe that he had found the
reason of the number, size and motion of the planetary orbits in the
application of the five regular solids to the frame of the universe[7].
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