When asked in 1962 on what he was working Kazimierz Ajdukiewicz replied: Several years ago Polish Scientific Publishers suggested that I pre­ pare a new edition of The Logical Foundations of Teaching, which I wrote 1 before 1939 as a contribution to The Encyclopaedia of Education. It was a small booklet covering elementary information about logical semantics and scientific methodology, information which in my opinion was necessary as a foundation of teaching and as an element of the education of any teacher. When I recently set to preparing the new edition, I rewrote practically everything, and a booklet of some 100 pages swelled into a bulky volume almost five times bigger. The issues have remained practically the same, but they are now analysed much more thoroughly and the threshold of difficulty is much higher now. The main stress has been laid on the methods used in the empirical sciences, and within that field, on the theory of measurement and the methods of statistical inference. I am now working on the last chapter of the book, concerned with explanation procedures and theory construction in the empirical sciences. When that book, which I intend to entitle Pragmatic Logic, is com­ pleted I intend to prepare for the press Vol. 2 of my minor writings, 2 Language and Cognition, which will cover some of my post-war pa­ pers.

Inhalt

1. Logic as a Foundation of Teaching.- I Words, Thoughts and Objects.- I Expressions and Their Meanings.- 2. Understanding of Expressions.- 3. Meaning of Expressions.- 4. Language and Meaning.- 5. Speech as a Way of Communicating Thoughts.- II Statements and Their Parts.- 6. Proposition and Sentence.- 7. Parts of Statements Syntactical Categories.- 8. Complex Statements.- 9. Simple Statements.- 10. Statement Schemata and Statements Derived from Them.- III Objective Counterparts of Expressions.- A. Extension of Terms.- 11. Designating and Designata.- 12. Denotation and Extension.- 13. Relations between Extensions.- 14. Unions and Intersections of Sets.- 15. Logical Partition.- B. Intension of Terms.- 16. Complete and Characteristic Intension.- 17. Linguistic Intension.- IV Ambiguity of Expressions and Defects of Meanings.- 18. Ambiguity.- 19. Vagueness.- 20. Incomplete Formulations.- V Definitions.- 21. Two Ways of Understanding the Term "Definition".- 22. The Concept of Nominal Definition.- 23. Definitions by Abstraction and Inductive Definitions.- 24. Errors in Defining.- 25. Stipulating and Reporting Definitions.- 26. Definitions by Postulates and Pseudo-definitions by Postulates.- 27. The Concept of Real Definition.- VI Questions and Interrogative Sentences.- 28. The Structure of Interrogative Sentences.- 29. Decision Questions and Complementation Questions.- 30. Assumptions of Questions Suggestive Questions.- 31. Improper Answers.- 32. Thoughts Expressed by an Interrogative Sentence.- 33. Didactic Questions.- II Inference.- I Formal Logic and the Consequence Relation.- 34. Formal Logic.- 35. Logical Consequence.- 36. The Relationship between the Truth of the Reason and the Truth of the Consequence.- 37. Enthymematic Consequence.- II Inference and the Conditions of Its Correctness.- 38. The Concept of Inference.- 39. Conditions of Correctness of Inference.- III Subjectively Certain Inference.- 40. The Conclusiveness of Subjectively Certain Inference.- 41. The Conclusiveness of Subjectively Certain Inference in the Light of the Knowledge of the Person Involved.- 42. Deductive Inference.- 43. Deducing.- IV Subjectively Uncertain Inference.- 44. The Conclusiveness of Subjectively Uncertain Inference.- 45. Logical Probability versus Mathematical Probability.- 46. Statistical Probability.- 47. Reductive Inference.- 48. Induction by Enumeration.- 49. Inference by Analogy.- 50. Induction by Elimination.- III Methodological Types of Sciences.- I The Division of Sciences into Deductive and Inductive.- 51. The Methodology of Sciences.- 52. Deductive and Inductive Sciences.- II Deductive Sciences.- 53. Deductive Sciences at the Pre-axiomatic Intuitive Stage.- 54. Deductive Sciences at the Axiomatic Intuitive Stage.- 55. The Philosophical Controversy over the Substantiation of Primitive Theorems in Intuitively Approached Deductive Sciences.- 56. Deductive Sciences at the Abstract Axiomatic Stage.- 57. Formalized Deductive Theories.- (a) Rules of Defining.- (b) Rules of Inference.- (c) Construction of Formalized Theories.- 58. Deductive Theories from the Apragmatic Point of View.- (a) Consistency of Theories.- (b) Independence of Axioms.- (c) Deductive Completeness of Theories.- (d) Completeness of Deductive Systems.- III The Inductive Sciences.- A. the Empirical Foundations.- 59. Irrevocable Assumptions and Theorems in the Inductive Sciences.- 60. Protocol Statements.- 61. The Method of Direct Experience as Subjective and Unrepeatable.- 62. Observation and Experiment.- B. Counting and Measurement.- 63. Selected Concepts in the Theory of Relations Numbers and Counting.- (a) Preliminary Remarks.- (b) The Concept of Relation.- (c) Properties of Equivalence Relations. Types of Equivalence Properties.- (d) Many-one, One-many Relations. The Concept of Equipotence of Sets.- (e) Numbers.- (f) Counting.- 64. Selected Concepts in the Relations Theory (ctd.). Ordering Relations. Isomorphism and Homomorphism of Relations.- (a) Preliminary Remarks.- (b) Ordering Relations.- (c) Isomorphism of Relations.- (d) Homomorphism of Relations.- (e) Abstraction Relations.- 65. Magnitudes and Scaling.- (a) Primary and Secondary Properties of Abstraction.- (b) Ordered Families of Abstraction Properties Magnitudes.- 66. Additive Magnitudes.- 67. Examples of Definitions of a Physical Sum of Magnitudes.- 68. The Measurement Function.- 69. Measurement Proper.- 70. Measurement without a Unit of Measurement and Measurement without a Zero Point.- IV Inductive Sciences and Scientific Laws.- A. General Laws.- 71. General Laws which State Relationships between Constant and Variable Properties.- 72. General Laws which State Relationships between Variable Properties Functional Laws and Parametric Laws.- B. Statistical Laws.- 73. Statistical Laws which State the Degree of Association of Constant Properties.- 74. Laws of Statistical Distributions.- (a) Laws of Distribution of Probabilities of Discrete Variables.- (b) Laws of Probability Density Distribution for Continuous Variables.- (c) Binomial Distribution.- (d) Normal Distribution.- 75. Laws on Correlation of Variable Properties.- V Statistical Reasoning.- 76. Introductory Remarks.- 77. Estimation of Parameters.- 78. Levelling of Errors of Measurement as Example of Estimation of Parameters.- 79. Verification of Hypotheses and Statistical Tests.- Supplement: Proving and Explaining.