An Introduction to Logic and Scientific Method

by Cohen, Morris R.; Nagel, Ernest

• ISBN13: 9781931541916
• ISBN10: 1931541914
• Format: Paperback
• Copyright: 2003-11-01
• Publisher: Lightning Source Inc

Table of Contents

Preface	iii
The Subject Matter of Logic
Logic and the Weight of Evidence	3	(2)
Conclusive Evidence or Proof	5	(3)
The Nature of Logical Implication	8	(5)
Partial Evidence or Probable Inference	13	(3)
Is Logic about Words, Thoughts, or Objects?	16	(5)
The Use and Application of Logic	21	(6)
BOOK I: FORMAL LOGIC
The Analysis of Propositions
What Is a Proposition?	27	(3)
The Traditional Analysis of Propositions	30	(14)
Compound, Simple, and General Propositions	44	(8)
The Relations Between Propositions
The Possible Logical Relations between Propositions	52	(4)
Independent Propositions	56	(1)
Equivalent Propositions	57	(8)
The Traditional Square of Opposition	65	(3)
The Opposition of Propositions in General	68	(8)
The Categorical Syllogism
The Definition of Categorical Syllogisms	76	(2)
The Enthymeme	78	(1)
The Rules or Axioms of Validity	78	(2)
The General Theorems of the Syllogism	80	(1)
The Figures and Moods of the Syllogism	81	(3)
The Special Theorems and Valid Moods of the First Figure	84	(1)
The Special Theorems and Valid Moods of the Second Figure	85	(1)
The Special Theorems and Valid Moods of the Third Figure	85	(1)
The Special Theorems and Valid Moods of the Fourth Figure	86	(1)
The Reduction of Syllogisms	87	(4)
The Antilogism or Inconsistent Triad	91	(3)
The Sorites	94	(2)
Hypothetical, Alternative, and Disjunctive Syllogisms
The Hypothetical Syllogism	96	(4)
The Alternative Syllogism	100	(1)
The Disjunctive Syllogism	101	(2)
The Reduction of Mixed Syllogisms	103	(1)
Pure Hypothetical and Alternative Syllogisms	103	(2)
The Dilemma	105	(5)
Generalized or Mathematical Logic
Logic as the Science of Types of Order	110	(3)
The Formal Properties of Relations	113	(2)
The Logical Properties of Relations in Some Familiar Inferences	115	(2)
Symbols: Their Function and Value	117	(4)
The Calculus of Classes	121	(5)
The Calculus of Propositions	126	(3)
The Nature of a Logical or Mathematical System
The Function of Axioms	129	(4)
Pure Mathematics---an Illustration	133	(4)
Structural Identity or Isomorphism	137	(4)
The Equivalence of Axiom Sets	141	(2)
The Independence and Consistency of Axioms	143	(4)
Mathematical Induction	147	(1)
What Generalization Means in Mathematics	148	(3)
Probable Inference
The Nature of Probable Inference	151	(7)
The Mathematics or Calculus of Probability	158	(6)
Interpretations of Probability	164	(9)
Some Problems of Logic
The Paradox of Inference	173	(4)
Is the Syllogism a Petitio Principii?	177	(4)
The Laws of Thought	181	(4)
The Basis of Logical Principles in the Nature of Things	185	(6)
BOOK II: APPLIED LOGIC AND SCIENTIFIC METHOD
Logic and the Method of Science	191	(227)
Hypotheses and Scientific Method
The Occasion and the Function of Inquiry	197	(3)
The Formulation of Relevant Hypotheses	200	(2)
The Deductive Development of Hypotheses	202	(5)
The Formal Conditions for Hypotheses	207	(8)
Facts, Hypotheses, and Crucial Experiments	215	(6)
The Role of Analogy in the Formation of Hypotheses	221	(2)
Classification and Definition
The Significance of Classification	223	(1)
The Purpose and the Nature of Definition	224	(10)
The Predicables	234	(4)
Rules for Definition	238	(3)
Division and Classification	241	(4)
The Methods of Experimental Inquiry
Types of Invariant Relations	245	(4)
The Experimental Methods in General	249	(2)
The Method of Agreement	251	(5)
The Method of Difference	256	(4)
The Joint Method of Agreement and Difference	260	(1)
The Method of Concomitant Variation	261	(3)
The Method of Residues	264	(1)
Summary Statement of the Value of the Experimental Methods	265	(2)
The Doctrine of the Uniformity of Nature	267	(2)
The Plurality of Causes	269	(4)
Probability and Induction
What Is Inductive Reasoning?	273	(6)
The Role of Fair Samples in Induction	279	(5)
The Mechanism of Sampling	284	(2)
Reasoning from Analogy	286	(3)
Measurement
The Purpose of Measurement	289	(2)
The Nature of Counting	291	(2)
The Measurement of Intensive Qualities	293	(3)
The Measurement of Extensive Qualities	296	(1)
The Formal Conditions for Measurement	297	(1)
Numerical Laws and Derived Measurement	298	(4)
Statistical Methods
The Need for Statistical Methods	302	(1)
Statistical Averages	303	(7)
Measures of Dispersion	310	(2)
Measures of Correlation	312	(4)
Dangers and Fallacies in the Use of Statistics	316	(7)
Probable Inference in History and Allied Inquiries
Does History Employ Scientific Method?	323	(3)
The Authenticity of Historical Data	326	(3)
Establishing the Meaning of Historical Data	329	(5)
Determining the Evidential Value of Historical Testimony	334	(6)
Systematic Theories in History	340	(4)
The Comparative Method	344	(3)
The Weighing of Evidence in Court	347	(5)
Logic and Critical Evaluation
Are Evaluations Beyond Logic?	352	(1)
Moral Judgments in History	353	(4)
The Logic of Critical Judgments on Art	357	(5)
The Logic of Moral and Practical Judgments	362	(5)
The Logic of Fictions	367	(9)
Fallacies
Logical Fallacies	376	(5)
Sophistical Refutations	381	(1)
The Abuse of Scientific Method	382	(9)
Conclusion
What Is Scientific Method?	391	(8)
The Limits and the Value of Scientific Method	399	(8)
Appendix--Examples of Demonstration
1. What Does a Demonstration Establish?	407	(6)
2. Some Fallacious Demonstrations	413	(5)
Exercises	418	(43)
Index	461