FUTURE LOGIC - by Avi Sion

FUTURE LOGIC:

Categorical and Conditional Deduction and Induction of the Natural, Temporal, Extensional, and Logical Modalities.

Avi Sion,  Ph. D.

First published, 1990. Revised Edition, 1996.

Abstract

Future Logic is an original and wide-ranging treatise of formal logic. It deals with deduction and induction, of categorical and conditional propositions, involving the natural, temporal, extensional, and logical modalities.

(Simply put, deduction and induction are inferences of more or less certainty; propositions refer to relations between things; modalities are attributes of relations like necessity, actuality or possibility.)

Traditional and Modern logic have covered in detail only formal deduction from actual categoricals, or from logical conditionals (conjunctives, hypotheticals, and disjunctives). Deduction from modal categoricals has also been considered, though very vaguely and roughly; whereas deduction from natural, temporal and extensional forms of conditioning has been all but totally ignored. As for induction, apart from the elucidation of adductive processes (the scientific method), almost no formal work has been done.

This is the first work ever to strictly formalize the inductive processes of generalization and particularization, through the novel methods of factorial analysis, factor selection and formula revision.

This is the first work ever to develop a formal logic of the natural, temporal and extensional types of conditioning (as distinct from logical conditioning), including their production from modal categorical premises.

Future Logic contains a great many other new discoveries, organized into a unified, consistent and empirical system, with precise definitions of the various categories and types of modality (including logical modality), and full awareness of the epistemological and ontological issues involved. Though strictly formal, it uses ordinary language, wherever symbols can be avoided.

Among its other contributions:  a full list of the valid modal syllogisms (which is more restrictive than previous lists); the main formalities of the logic of change (which introduces a dynamic instead of merely static approach to classification); the first formal definitions of the modal types of causality; a new theory of class logic, free of the Russell Paradox; as well as a critical review of modern metalogic.

But it is impossible to list briefly all the innovations in logical science -- and therefore, epistemology and ontology -- this book presents; it has to be read for its scope to be appreciated.

Buy it or read it online

All of Avi Sion’s published books can be purchased at Amazon.com (in paperback or kindle/.mobi form), and at Lulu.com (in hardcover, paperback or e-book/.epub form), as well as other online stores.

They can also be read online free of charge, chapter by chapter, at www.TheLogician.net and, in '3D flipbook' format, at www.AviSionBooks.com, as well as in Google Books and other Internet locations. They are also available in many university and public libraries. 

Contents in brief

Part I. Actual Categoricals.

1. Introduction.

2. Foundations.

3. Logical Relations.

4. Words and Things.

5. Propositions.

6. Oppositions.

7. Eductions.

8. Syllogisms: Definitions.

9. Syllogisms: Applications.

10. Syllogisms: Validations.

Part II. Modal Categoricals.

11. Modality: Categories and Types.

12. Sources of Modality.

13. Modal Propositions. 

14. Modal Oppositions and Eductions.

15. Main Modal Syllogisms.

16. Other Modal Syllogisms.

17. Transitive Categoricals.

18. Permutation.

19. More About Quantity.

Part III. Logical Conditioning.

20. Credibility.

21. Logical Modality.

22. Contextuality.

23. Conjunction.

24. Hypothetical Propositions.

25. Hypotheticals: Oppositions and Eductions.

26. Disjunction.

27. Intricate Logic.

28. Logical Compositions.

29. Hypothetical Syllogism and Production.

30. Logical Apodosis and Dilemma.

31. Paradoxes.

32. Double Paradoxes.

Part IV. De Re Conditioning.

33. Conditional Propositions.

34. Natural Conditionals: Features.

35. Natural Conditionals: Oppositions, Eductions.

36. Natural Conditional Syllogism and Production.

37. Natural Apodosis and Dilemma.

38. Temporal Conditionals.

39. Extensionals: Features, Oppositions, Eductions.

40. Extensional Conditional Deduction.

41. Modalities of Subsumption.

42. Condensed Propositions.

Part V(a). Class-Logic.

43. The Logic of Classes.

44. Hierarchies and Orders.

45. Illicit Processes in Class Logic.

Part V(b). Adduction.

46. Adduction.

47. Theory Formation.

48. Theory Selection.

49. Synthetic Logic.

Part VI. Factorial Induction.

50. Actual Induction.

51. Elements and Compounds.

52. Fractions and Integers.

53. Factorial Analysis.

54. Modal Induction.

55. Factor Selection.

56. Applied Factor Selection.

57. Formula Revision.

58. Gross Formula Revision.

59. Factorial Formula Revision.

Part VII. Perspectives.

60. Phenomena. 

61. Consciousness and the Mind.

62. Perception and Recognition.

63. Past Logic.

64. Critique of Modern Logic.

65. Developments in Tropology.

66. Metalogic.

67. Inductive Logic.

68. Future Logic.

Appendix 1

Appendix 2

References

Contents in detail:

PART I. ACTUAL CATEGORICALS.

1.         INTRODUCTION.

1. What is Logic?
2. What Logic is Not.
3. Modus Operandi.
4. Scope.

2.         FOUNDATIONS.

1. The Law of Identity.
2. The Law of Contradiction.
3. The Law of the Excluded Middle.

3.         LOGICAL RELATIONS.

1. True or False.
2. Branches of Logic.
3. Tools of Logic.
4. Axioms of Logic.

4.         WORDS AND THINGS.

1. Verbalizing.
2. Same and Different.
3. On Definition

5.         PROPOSITIONS.

1. Terms and Copula.
2. Polarity and Quantity.
3. Distribution.
4. Permutation.

6.         OPPOSITIONS.

1. Definitions.
2. Applications.
3. Validations.

See also, in this context, Appendix 2.

7.         EDUCTIONS.

1. Definitions.
2. Applications.
3. Validations.

8.         SYLLOGISM: DEFINITIONS.

1. Generalities.
2. Valid/Invalid.
3. Figures
4. Moods.
5. Psychology.

9.         SYLLOGISM: APPLICATIONS.

1. The Main Moods.
2. On the Fourth Figure.
3. Subaltern Moods.
4. Singular Moods.
5. Summary.
6. Common Attributes.
7. Imperfect Syllogism.

10.       SYLLOGISM: VALIDATIONS.

1. Function
2. Methods.
3. In Practise.
4. Derivative Arguments.

PART II. MODAL CATEGORICALS.

11.       MODALITY: CATEGORIES AND TYPES.

1. Seeds of Growth.
2. Categories of Modality.
3. Types of Modality.
4. Extensional Modality.
5. Temporal Modality.
6. Tense and Duration.
7. Natural Modality.
8. Other Types.

12.       SOURCES OF MODALITY.

1. Diversity.
2. Time and Change.
3. Causality.

13.       MODAL PROPOSITIONS.

1. Categories and Types.
2. List and Notation.
3. Distributions.

14.       MODAL OPPOSITIONS AND EDUCTIONS.

1. Quantification of Oppositions.
2. Basic Intramodal Oppositions.
3. Quantified Intramodal Oppositions.
4. Intermodal Oppositions.
5. Eductions.

See also, in this context, Appendix 2.

15.       MAIN MODAL SYLLOGISMS.

1. Valid Modes.
2. Valid Moods.
3. Validations.

16.       OTHER MODAL SYLLOGISMS

1. Secondary Modes.
2. Mixed Modes.
3. Summation.
4. General Principles.

17.       TRANSITIVE CATEGORICALS.

1. Being and Becoming.
2. Various Features.
3. Various Contrasts.
4. Some Syllogisms.

18.       PERMUTATION.

1. Two Senses of 'Is'.
2. Other Permutations.
3. Verbs.
4. 'As Such' Subjects.
5. Commutation.

19.       MORE ABOUT QUANTITY.

Substitution.

Comparatives.

Collectives and Collectionals..

Quantification of the Predicate.

PART III. LOGICAL CONDITIONING.

20.       CREDIBILITY.

1. Laws of Thought.
2. Functions.
3. More on Credibility.
4. Opinion and Knowledge.

21.       LOGICAL MODALITY.

1. The Singular Modalities.
2. The Plural Modalities.
3. Analogies and Contrasts.
4. Apodictic Knowledge.

22.       CONTEXTUALITY.

1. Statics.
2. Dynamics.
3. Time-Frames.
4. Context Comparisons.
5. Personal and Social.

23.       CONJUNCTION.

1. Factual Forms.
2. Oppositions of Factuals.
3. Modal Forms.
4. Oppositions of Modals.

24.       HYPOTHETICAL PROPOSITIONS.

1. Kinds of Conditioning.
2. Defining Hypotheticals.
3. Strict or Material Implication.
4. Full List of Forms.

25.       HYPOTHETICALS: OPPOSITIONS AND EDUCTIONS.

1. Connection and Basis.
2. Oppositions.
3. Hierarchy.
4. Eductions.

26.       DISJUNCTION.

1. Subjunction.
2. Manners of Disjunction.
3. Broadening the Perspective.

27.       INTRICATE LOGIC.

1. Organic Knowledge.
2. Conjunctives.
3. Hypotheticals.
4. Disjunctives.

28.       LOGICAL COMPOSITIONS.

1. Symbolic Logic.
2. Addition.
3. Multiplication.
4. Expansions.
5. Utility.

29.       HYPOTHETICAL SYLLOGISM AND PRODUCTION.

1. Syllogism.
2. Other Derivatives.
3. Production.

30.       LOGICAL APODOSIS AND DILEMMA.

1. Apodosis.
2. Dilemma.
3. Rebuttal.

31.       PARADOXES.

1. Internal Inconsistency.
2. The Stolen Concept Fallacy.
3. Systematization.
4. Properties.

32.       DOUBLE PARADOXES.

1. Definition.
2. The Liar Paradox.
3. The Barber Paradox.

PART IV. DE-RE CONDITIONING.

33.       CONDITIONAL PROPOSITIONS.

1. De-re Conditioning.
2. Types of Causality.
3. Laws of Causality.

34.       NATURAL CONDITIONALS: FEATURES.

1. Basis and Connection.
2. Quantification.
3. Other Features.
4. Natural Disjunction.

35.       NATURAL CONDITIONALS: OPPOSITIONS, EDUCTIONS.

1. Translations.
2. Oppositions.
3. Eductions.

36.       NATURAL CONDITIONAL SYLLOGISM AND PRODUCTION.

1. Syllogism.
2. Summary and Quantities.
3. Production.

37.       NATURAL APODOSIS AND DILEMMA.

1. Apodosis.
2. Dilemma.

38.       TEMPORAL CONDITIONALS.

1. Structure and Properties.
2. Relationships to Naturals.
3. Mixed Modality Arguments.

39.       EXTENSIONALS: FEATURES, OPPOSITIONS, EDUCTIONS.

1. Main Features.
2. Modal and Other Forms.
3. Oppositions.
4. Translations and Eductions.

40.       EXTENSIONAL CONDITIONAL DEDUCTION.

1. Syllogism.
2. Production.
3. Apodoses.
4. Dilemma.

41.       MODALITIES OF SUBSUMPTION.

1. Formal Review.
2. Impact.
3. Primitives.
4. Transformations.
5. Imaginary Terms.

42.       CONDENSED PROPOSITIONS.

1. Forms with Complex Terms.
2. Making Possible or Necessary.

PART Va. CLASS-LOGIC.

43.       THE LOGIC OF CLASSES.

1. Subsumptive or Nominal.
2. Classes.
3. Classes of Classes.

44.       HIERARCHIES AND ORDERS.

1. First Order Hierarchies.
2. Second Order Hierarchies.
3. Extreme Cases.

45.       ILLICIT PROCESSES IN CLASS LOGIC.

1. Self-membership.
2. The Russell Paradox.
3. Impermutability.

PART Vb. ADDUCTION.

46.       ADDUCTION.

1. Logical Probability.
2. Providing Evidence.
3. Weighting Evidence.
4. Other Types of Probability.

47.       THEORY FORMATION.

1. Theorizing.
2. Structure of Theories.
3. Criteria.
4. Control.

48.       THEORY SELECTION.

1. The Scientific Method.
2. Compromises.
3. Theory Changes.
4. Exclusive Relationships.

49.       SYNTHETIC LOGIC.

1. Synthesis.
2. Self-Criticism.
3. Fairness.

PART VI. FACTORIAL INDUCTION.

50.       ACTUAL INDUCTION.

1. The Problem.
2. Induction of Particulars.
3. Generalization.
4. Particularization.
5. Validation.

51.       ELEMENTS AND COMPOUNDS.

1. Elements and Compounds.
2. Gross Formulas.
3. Oppositions.
4. Double Syllogisms.
5. Complements.

52.       FRACTIONS AND INTEGERS.

1. Fractions.
2. Double Syllogisms.
3. Integers.
4. Further Developments.

53.       FACTORIAL ANALYSIS.

1. Factorization.
2. Applications.
3. Overlap Issues.
4. More Factorial Formulas.
5. Open System Analysis.

See also, in this context, Appendix 1.

54.       MODAL INDUCTION.

1. Knowability.
2. Equality of Status.
3. Stages of Induction.
4. Generalization vs. Particularization.
5. The Paradigm of Induction.
6. The Pursuit of Integers.

55.       FACTOR SELECTION.

1. Prediction.
2. The Uniformity Principle.
3. The Law of Generalization.

56.       APPLIED FACTOR SELECTION.

1. Closed Systems Results.
2. Some Overall Comments.
3. Rules of Generalization.
4. Review of Valid Moods.
5. Open System Results.

57.       FORMULA REVISION.

1. Context Changes.
2. Kinds of Revision.
3. Particularization.

58.       GROSS FORMULA REVISION.

1. Amplification.
2. Harmonization.
3. Unequal Gross Formulas.
4. Equal Gross Formulas.
5. Applications.

59.       FACTORIAL FORMULA REVISION.

1. Adding Fractions to Integers.
2. Reconciliation of Integers.
3. Indefinite Denial of Integers.
4. Other Formula Revisions.
5. Revision of Deficient Formulas.

PART VII. PERSPECTIVES.

60.       PHENOMENA.

1. Empirical or Hypothetical.
2. Physical or Mental.
3. Concrete and Abstract.
4. Presentative or Representative.

61.       CONSCIOUSNESS AND THE MIND.

1. A Relation.
2. Kinds of Consciousness.
3. The Mind.
4. Popular Psychology.

62.       PERCEPTION AND RECOGNITION.

1. The Immediacy of Sense-Perception.
2. Logical Conditions of Recognition.
3. Other Applications.

63.       PAST LOGIC.

1. Historical Judgment.
2. Aristotle, and Hellenic Logic.
3. Roman, Arab, Medieval European Logic.
4. Oriental Logic.
5. Modern Tendencies.
6. In The 20th Century.

64.       CRITIQUE OF MODERN LOGIC.

1. Formalization and Symbolization.
2. Systematization and Axiomatization.
3. Modern Attitudes.
4. Improvements and Innovations.
5. The Cutting Edge.

65.       DEVELOPMENTS IN TROPOLOGY.

1. Tropology.
2. Roots.
3. Shifts in Emphasis.
4. Setting the Stage.
5. Contemporary Currents.
6. Philosophical Discussions.

66.       METALOGIC.

1. Language and Meaning.
2. Definition and Proof.
3. Infinity in Logic.
4. Conceptual Logic.

67.       INDUCTIVE LOGIC.

1. Degrees of Being.
2. Induction from Logical Possibility.
3. History of Inductive Logic.

68.       FUTURE LOGIC.

1. Summary of Findings.
2. Gaps to Fill.
3. Concluding Words.

APPENDIX 1 - Factorial Analysis of Elements and Gross Formulas (Open System).

APPENDIX 2 - Redefining Majority and Minority in FL.

REFERENCES

Further Description

The science of Logic stands at the interface between the two main branches of Philosophy, namely Epistemology (the study of knowing) and Ontology (the study of being). Its task is to determine precisely the way people can and do get to know the world around them. Its role is both descriptive and prescriptive. Its means include: observation of common thought-processes and everyday language, analysis of recurring patterns and components, and evaluation with reference to rational and empirical criteria. Logic is thus a study of form, irrespective of content.

Future Logic is an original, wide-ranging, profound and timeless treatise of formal logic, intended for both the uninitiated and the specialist.

What do we mean when we say that something is 'necessarily', 'actually' or 'possibly' so and so? These so-called 'modalities' are attributes of relations, and they vary in meaning. For each category of modality (like necessity or possibility), there are several types of modality (the natural, the temporal, the extensional, the logical, and others), and each of these modalities serves a distinct purpose, expressing some aspect of reality or the state of our knowledge about it. Each category and type of modality has its own peculiar logical properties, and a host of relations to the various others.

Future Logic demonstrates the centrality of modal concepts in human knowledge and in the processes leading to it. Starting with precise definitions of the various categories and types of modality, it develops a systematic study of reasoning processes involving them, which not only retraces past achievements in the field but also enables a great many new discoveries.

Modality is significant not only in the study of categorical propositions, but also in that of conditional propositions. There are as many forms of conditioning as there are categories and types of modality; and while some of their logical properties are similar, many are quite different. What this means in practise, is that we cannot reason properly without awareness of these differences. The study of conditioning is of fundamental importance to an understanding of causal relations.

Future Logic is the first work ever to develop a thorough formal study of the natural, temporal and extensional types of conditioning (as well as logical conditioning), including their production from modal categorical premises.

Our knowledge of things is of very variable certainty: some of it seems solidly established almost immediately and forever, some of it requires a lot of work to acquire and seems tentative and open to revision. This observation suggests a distinction between 'deductive' and 'inductive' logic. Each of these fields comprises a multitude of specific processes, which require detailed investigation. While deductive processes have traditionally received much attention, logicians have done little formal work in relation to inductive processes, apart from the crucial and relatively recent elucidation of adduction (the processes of confirmation or elimination of hypotheses).

Future Logic is the first work ever to strictly formalize the inductive processes of generalization and particularization, through the novel methods of factorial analysis, factor selection and formula revision.

Science (i.e. the special sciences) and logical philosophy have throughout history fed off each other. The practises of scientists have often caused theoretical reflections by logicians; indeed, many scientists were themselves logicians. Likewise, the methodological principles clarified by logicians have often facilitated and improved the work of scientists.

Future Logic is a revision of the 'scientific method', challenging scientists with new, more rigorous methodological standards, but also providing them with finer cognitive tools likely to greatly enrich science. (Hence, the book's title.)

Reading Suggestions

The most important discovery in Future Logic is the formalization of induction by generalization and particularization (Part VI, chapters 50-59 and the appendix).

This work is crucial because it frees formal logic, and therefore epistemology, from the oversimplification of purely deductive approaches.

But to well understand this research, one ought to get acquainted with the sections concerning categorical modal propositions (Part II, chapters 11-17) and conditional modal propositions (Part IV, chapters 33-40).

It would be useful, to conclude this topic, to also read chapter 67.

The listed chapters would in themselves suffice, but it must be stated that Future Logic addresses the epistemological context, for I understand the term "logic" in its broader sense.

In this regard, I would like to also recommend reading of chapters 2, 4, 20, 31, 60, 61, 62, 64 and 66.

You will find a summary of the book in chapter 68.