"When God calculates...
He creates the world."
Phil., VII, 191.
1. Leibniz's
View of Classical Logic
2. Hospinianus's
Theory of the Syllogism
3. The
12 Simple Moods
4. The
24 Figured Moods
5. Reduction
of Moods to the First Figure
6. Subalternation
and Conversion
7. Reduction
by Regression
8. The
Intensional Point of View
9. All
Moods Deduced from the Five Universal Moods
10. Remarks
on the Table of 24 Moods
11. The
Nine Imperfect Moods
12. Principles
of the Universal Moods
13. Discussion
of These Principles
14. Extension
and Intension
15. Implicit
Quantification of the Predicate
16. Schemata
of Propositions in Extension
17. Schemata
of Syllogisms in Extension
18. Schemata
of Propositions in Intension
19. Schemata
of Syllogisms in Intension
1. First
Idea of the Combinatory
2. The
Alphabet of Human Thoughts
3. On
the Art of Combinations
4. Precedents:
Ramon Lull, etc.
5. Criticism
of Lull; Other Precursors
6. Analysis
and Classification of Concepts
7. Finding
All the Predicates of a Given Subject
8. Finding
All the Subjects of a Given Predicate
9. Finding
the Particular Predicates or Subjects of a Given Term
10. Finding
the Negative Subjects or Predicates of a Given Term
11. Finding
All the Middle Terms Capable of Proving a Given Conclusion
12. Leibniz's
Later Opinion of On the Art of Combinations; New Projects
1. Previous
Plans
2. Plan
of On the Art of Combinations
3. Contemporary
Plans
4. Descartes's
Ideas on the Subject
5. Plans
of Wilkins and Dalgarno
6. Leibniz's
Opinion of These Plans
7. Principle
of the Characteristic
8. Plan
for a Rational Grammar
9. Latin
as an Intermediary
10. The
Simplification of Grammar
11. Inflections
and Particles
12. Reduction
of the Parts of Speech
13. Analysis
of Particles
14. Analysis
of Inflections
15. Grammatical
Analysis of Relations
16. Analysis
of Concepts by Definition
17. The
Philosophical Language is Not a Calculus
18. The
Characteristic and the Encyclopedia
1. The
Characteristic Must be Real
2. Algebra
and Infinitesimal Analysis
3. Utility
of a Good Characteristic
4. Conditions
Required of the Characters
5. Analogy
with the Cartesian Method
6. Superiority
over the Cartesian Method
7. Critique
of Descartes's Method of Doubt
8. Logic
Settles Disagreements
9. Utility
of the Logical Calculus
10. The
Calculus Replaces Reasoning
11. Refutation
of Nominalism
12. Application
to Mathematics
13. Importance
of Natural Signs
14. Various
Plans for the Characteristic: Numbers
15. Geometrical
Figures
16. Mechanisms
17. The
Characteristic Was Never Realized
1. First
Works: Juridical Logic
2. Philosophy
of Law: Recasting Legal Codes
3. Application
of Logic to Moral Questions
4. Plan
for the Literary Quarterly (1668-1669)
5. First
Plans for Encyclopedic Compilations
6. Plans
of 1676: the Philadelphic Society
7. Plans
of 1678-1679
8. On
Secret Things
9. Plus
Ultra
10. Preliminaries
of Plus Ultra
11. Foundations
and Illustrations of the General Science
12. Measures
Taken for Oldenburg and Galloys
13. New
Measures for the Royal Society
14. Reports
Addressed to Louis XIV
15. Satire
of the Republic of Letters
16. Plan
of the Demonstrative Encyclopedia
17. Rational
Sciences
18. Experimental
Sciences
19. Arts
and Crafts
20. History
21. The
Elements of Philosophy
22. The
Story of Leibniz's "Vow"
23. Collections
of Definitions
24. Tables
of Definitions (1702-1704)
25. Plan
for an Encyclopedia in the New Essays
26. Plan
Presented to Peter the Great
1, The
Art of Judgment and the Art of Invention
2. Analysis
and Synthesis
3. Development
of the Cartesian Method
4. Analysis
of Truths
5. Demonstration
Rests on Definitions
6. And
on Axioms of Identity
7. Nominal
and Real Definitions
8. Example
of the Geometers
9. Finding
the Most Complete Definition
10. Criterion
of a True Idea
11. Critique
of the Ontological Argument
12. Theory
of Clear, Distinct, and Adequate Ideas
13. Analysis
of Ideas
14. Critique
of the Cartesian Method
15. Demonstration
of Axioms
16. Principle
of the Substitution of Equivalents
17. Every
Truth Is Analytic
18. Truths
of Reason and Truths of Fact
19. Principle
of Reason and Principle of Contradiction
20. Relation
of the Two Principles and of the Two Orders of Truths
21. Necessary
and Contingent Truths
22. Contingency
of the Laws of Nature
23. Theory
of Possibles and Compossibles
24. Principles
of Symmetry and Indiscernibles
25. Principle
of the Simplicity of the Laws of Nature
26. Principle
of Continuity or General Order
27.
Mathematical Principles and Metaphysical Principles
28. The
Logic of Probabilities
29. Mathematical
Theory of Games
30. Principles
of the Calculus of Probabilities
31. Role of
the Logic of Probabilities
32. Degrees
of Determination of Problems
33. Examples
from Algebra and Geometry
34. Analogy
of Cryptography
35. Role of
Experience in the Sciences
36. Theory
of First Empirical Truths
37. Theory
of Empirical Induction
38. Role of
Deduction in the Experimental Sciences
39. Theory
of Pappus's Analysis
40. Theory
of Hypotheses
41. The
Experimental Method is Deduction
42. The
Characteristic and the Art of Invention
43. The Art
of Invention and the Calculus of Probabilities
44. The Art
of Invention in the Technical and Practical Sciences
45. Logic,
Mathematics, and Metaphysics
1. Formal
Analogy Between Logic and Mathematics
2. Algebra
Subordinated to the Combinatory
3. Conception
of the Combinatory
4. Central
Division of Mathematics
5. Algebra
Is Not the Universal Method
6. The
Combinatory Is the Art of Invention
7. The
New On the Art of Combinations
8. Relations
of Size
9. Relations
of Identity and Inclusion
10. Relations
of Determination
11. Congruence,
Equality, Similarity
12. Axioms
All These Relations Share
13. Axioms
Only These Relations Share
14. Mathematics
Reduced to Logic
15. Logic
Reduced to Mathematics
16. Idea of
Universal Algebra
1. Logical
Multiplication Is Commutative
2. The
System of Characteristic Numbers (1679)
3. Translation
of the Propositions A, E, I, O
4. Translation
of Negation
5. New
Translation of the Propositions A, E, I, O
6. Conversions
and Subalternation
7. Faults
of the System
8. System
Founded on Logical Inclusion
9. An
Illustration of the Universal Calculus: Principles
10. Rules
of Composition and Decomposition
11. Additions
to an Illustration of the Universal Calculus
12. Attempt
at a Calculus of Alternatives
13. General
Investigations of 1686: Principles
14. Theory
of the Syllogism
15. Other
Attempts to Translate the Propositions A, E, I, O
16. Analogy
Between Categorical and Hypothetical Propositions
17. Fragments
of August 1690
18. Logical
Difficulties
19. Addition
from the Extensional Point of View
20. A
Not Inelegant Illustration: Axioms and Definitions
21. Demonstration
of the Principle of the Syllogism
22. Rules
for the Composition of Inclusions
23. Meaning
of Inclusion: Inclusion of Intensions
24. Meaning
of Addition: Addition of Intensions
25. Theory
of Subtraction
26. Properties
of Subtraction
27. Theory
of Compensations
28. Theorems
Relating to Subtraction
29. Summary
and Conclusion
1. The
Essay of 1679
2. Correspondence
with Huygens
3. Correspondence
with L'Hospital
4. Works
Relating to the Geometrical Calculus
5. Defects
of Algebra and Analytic Geometry
6. Defects
of Synthetic Geometry
7. Advantages
of a Properly Geometrical Analysis
8. Analysis
Situs
9. Definitions
of Situation, Point, and Space
10. Description
of Figures by Points and Lines
11. Theory
of Similarity
12. Definitions
of Straight Line and Plane Using the Idea of Similarity
13. Other
Definitions, Using the Ideas of Section and Motion
14. Definitions
Based on the Idea of Congruence
15. Definitions
of Sphere and Circle
16. Definition
of Straight Line
17. Critique
of Euclid's Definition of Straight Line
18. Definition
of Plane, of Intersections
19. Another
Definition of Straight Line
20. Critical
Remarks
1. Universal
Affirmative Judgment
2. Four
Types of Propositions
3. Rules
of Opposition
4. Rules
of Conversion
5. Syllogistic
Rules Relating to Terms
6. Syllogistic
Rules Relating to Propositions
7. Rules
of the Syllogistic Figures
8. Reduction
of Moods
9. Regression
or Reductio ad Absurdum
10. Justification
of the Fourth Figure
1. Citation
of Hobbes in On the Art of Combinations
2. Reasoning
Is Calculation
3. Hobbes's
Conception of Logical Addition
4. Nominalism
and Syllogism
5. Hobbes's
View of the Mathematical Method
6. Relations
Between Leibniz and Hobbes
7. Leibniz
Opposes Hobbes's Materialism
8. Leibniz:
A Cartesian or an Aristotelian?
9. Leibniz
and Hobbes's Physics
10. Leibniz
and Hobbes's Nominalism
11. Leibniz's
Critique of Nominalism
12. Leibniz's
Apparent Nominalism
13. Leibniz's
Real Nominalism
1. Binary
Arithmetic
2. Metaphysical
Symbol: Interpretation of Fohi's Characters
3. Periodicity
of Columns in the Number Series
4. Alleged
Periodicity of Prime Numbers
5. Algebraic
Tables or Canons
6. The
Difference Between Arithmetic and Algebra
7. Notation
for Coefficients Using Imaginary Numbers
8. Elimination
in First-Degree Equations
9. Rule
of Determinants. Casting Out Nines
10. Resolution
of First-Degree Equations (Cramer's Rule)
11. Elimination
in Higher-Order Equations
12. Multiplication
of Polynomials; Symbolic Homogeneity
13. Division
of Polynomials
14. Method
of Undetermined Coefficients (De Moivre's Theorem)
15. Notation
of Algebraic Forms
16. Tables
for the Calculus of Forms and the Resolution of Equations
17. The
Binomial Formula: Powers of a Polynomial
18. Analogy
Between the Binomial and Differentials
19. Theorems
of Divisibility Derived From the Combinatory
20. Demonstration
of Fermat's Theorem
1. Literary
Quarterly (1668)
2. Trusteeship
of Books
3. First
Plan for an Encyclopedic Society
4. Plan
for a German Society
5. Plan
for a Philadelphic Society
6. Plans
of 1676-1679
7. Plans
Submitted to the Dukes of Hanover
8. Imperial
Historical College (1688)
9. Idea
of a Religious Order (1693)
10. Approaches
to the Jesuits
11. Plan
for a Teutophilic Society
12. Founding
of the Academy of Sciences in Berlin (1700)
13. Scientific
Functions of the Academy
14. Financial
Resources of the Academy
15. Project
for Sericulture
16. Plan
for an Academy of Sciences in Dresden (1704)
17. Plan
for an Imperial Academy in Vienna (1712)
18. Failure:
Opposition of the Jesuits
19. Plans
Submitted to Tsar Peter the Great
20. Leibniz's
Patriotism and Cosmopolitanism
1. Principles
of Ausdehnungslehre
2. Fundamental
Definitions
3. Equality
and Congruence
4. Regressive
Multiplication
5. Geometrical
and Mechanical Applications
6. Comparison
with Leibniz's Geometrical Calculus
I. Thomas
Barton
II. The
Ars Magna of Ramon Lull and Athanasius Kircher
III. Dalgarno's
Ars Signorum
IV. Wilkins's
Philosophical Language
V. On
Conditions
VI. Extract
from On the Art of Combinations
VII. New
Method of Learning and Teaching Jurisprudence (1667)
VIII. Specimen of
Demonstrations in Politics (1669)
IX. Definition
of Universal Justice
X. Definition
of Love
XI. The
Usefulness of Albert von Hotten's Cylindrical Grammar
XII. The
Reason for Completing and Emending Alsted's Encyclopedia
XIII. Judgment on
the Writings of Comenius
XIV. Leibniz as a Librarian
XV. Leibniz's
"Distractions"
XVI. The Principle of Least
Action
XVII. Mathematical Theory of Games
XVIII. Letter to Eler (10 May 1716)
XIX. Letter to Lange (5 June
1716)
XX. Letter to
Kestner (1 July 1716)