**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

**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.**

*Future Logic*
(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.**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.**

*Future Logic*
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.

- What is Logic?
- What Logic is Not.
- Modus Operandi.
- Scope.

2. FOUNDATIONS.

- The Law of Identity.
- The Law of Contradiction.
- The Law of the Excluded
Middle.

3. LOGICAL
RELATIONS.

- True or False.
- Branches of Logic.
- Tools of Logic.
- Axioms of Logic.

4. WORDS AND
THINGS.

- Verbalizing.
- Same and Different.
- On Definition

5. PROPOSITIONS.

- Terms and Copula.
- Polarity and Quantity.
- Distribution.
- Permutation.

6. OPPOSITIONS.

- Definitions.
- Applications.
- Validations.

See also, in this context, Appendix 2.

7. EDUCTIONS.

- Definitions.
- Applications.
- Validations.

8. SYLLOGISM:
DEFINITIONS.

- Generalities.
- Valid/Invalid.
- Figures
- Moods.
- Psychology.

9. SYLLOGISM:
APPLICATIONS.

- The Main Moods.
- On the Fourth Figure.
- Subaltern Moods.
- Singular Moods.
- Summary.
- Common Attributes.
- Imperfect Syllogism.

10. SYLLOGISM:
VALIDATIONS.

- Function
- Methods.
- In Practise.
- Derivative Arguments.

PART II. MODAL CATEGORICALS.

11. MODALITY:
CATEGORIES AND TYPES.

- Seeds of Growth.
- Categories of Modality.
- Types of Modality.
- Extensional Modality.
- Temporal Modality.
- Tense and Duration.
- Natural Modality.
- Other Types.

12. SOURCES OF
MODALITY.

- Diversity.
- Time and Change.
- Causality.

13. MODAL
PROPOSITIONS.

- Categories and Types.
- List and Notation.
- Distributions.

14. MODAL
OPPOSITIONS AND EDUCTIONS.

- Quantification of
Oppositions.
- Basic Intramodal
Oppositions.
- Quantified Intramodal
Oppositions.
- Intermodal Oppositions.
- Eductions.

See also, in this context, Appendix 2.

15. MAIN MODAL
SYLLOGISMS.

- Valid Modes.
- Valid Moods.
- Validations.

16. OTHER MODAL
SYLLOGISMS

- Secondary Modes.
- Mixed Modes.
- Summation.
- General Principles.

17. TRANSITIVE
CATEGORICALS.

- Being and Becoming.
- Various Features.
- Various Contrasts.
- Some Syllogisms.

18. PERMUTATION.

- Two Senses of 'Is'.
- Other Permutations.
- Verbs.
- 'As Such' Subjects.
- Commutation.

19. MORE ABOUT
QUANTITY.

Substitution.

Comparatives.

Collectives and Collectionals..

Quantification of the Predicate.

PART III. LOGICAL CONDITIONING.

20. CREDIBILITY.

- Laws of Thought.
- Functions.
- More on Credibility.
- Opinion and Knowledge.

21. LOGICAL
MODALITY.

- The Singular Modalities.
- The Plural Modalities.
- Analogies and Contrasts.
- Apodictic Knowledge.

22. CONTEXTUALITY.

- Statics.
- Dynamics.
- Time-Frames.
- Context Comparisons.
- Personal and Social.

23. CONJUNCTION.

- Factual Forms.
- Oppositions of Factuals.
- Modal Forms.
- Oppositions of Modals.

24. HYPOTHETICAL
PROPOSITIONS.

- Kinds of Conditioning.
- Defining Hypotheticals.
- Strict or Material
Implication.
- Full List of Forms.

25. HYPOTHETICALS:
OPPOSITIONS AND EDUCTIONS.

- Connection and Basis.
- Oppositions.
- Hierarchy.
- Eductions.

26. DISJUNCTION.

- Subjunction.
- Manners of Disjunction.
- Broadening the
Perspective.

27. INTRICATE
LOGIC.

- Organic Knowledge.
- Conjunctives.
- Hypotheticals.
- Disjunctives.

28. LOGICAL
COMPOSITIONS.

- Symbolic Logic.
- Addition.
- Multiplication.
- Expansions.
- Utility.

29. HYPOTHETICAL
SYLLOGISM AND PRODUCTION.

- Syllogism.
- Other Derivatives.
- Production.

30. LOGICAL
APODOSIS AND DILEMMA.

- Apodosis.
- Dilemma.
- Rebuttal.

31. PARADOXES.

- Internal Inconsistency.
- The Stolen Concept
Fallacy.
- Systematization.
- Properties.

32. DOUBLE
PARADOXES.

- Definition.
- The Liar Paradox.
- The Barber Paradox.

PART IV. DE-RE CONDITIONING.

33. CONDITIONAL
PROPOSITIONS.

- De-re Conditioning.
- Types of Causality.
- Laws of Causality.

34. NATURAL
CONDITIONALS: FEATURES.

- Basis and Connection.
- Quantification.
- Other Features.
- Natural Disjunction.

35. NATURAL
CONDITIONALS: OPPOSITIONS, EDUCTIONS.

- Translations.
- Oppositions.
- Eductions.

36. NATURAL
CONDITIONAL SYLLOGISM AND PRODUCTION.

- Syllogism.
- Summary and Quantities.
- Production.

37. NATURAL
APODOSIS AND DILEMMA.

- Apodosis.
- Dilemma.

38. TEMPORAL
CONDITIONALS.

- Structure and Properties.
- Relationships to
Naturals.
- Mixed Modality Arguments.

39. EXTENSIONALS:
FEATURES, OPPOSITIONS, EDUCTIONS.

- Main Features.
- Modal and Other Forms.
- Oppositions.
- Translations and
Eductions.

40. EXTENSIONAL
CONDITIONAL DEDUCTION.

- Syllogism.
- Production.
- Apodoses.
- Dilemma.

41. MODALITIES OF
SUBSUMPTION.

- Formal Review.
- Impact.
- Primitives.
- Transformations.
- Imaginary Terms.

42. CONDENSED
PROPOSITIONS.

- Forms with Complex
Terms.
- Making Possible or
Necessary.

PART Va. CLASS-LOGIC.

43. THE LOGIC OF
CLASSES.

- Subsumptive or Nominal.
- Classes.
- Classes of Classes.

44. HIERARCHIES
AND ORDERS.

- First Order Hierarchies.
- Second Order Hierarchies.
- Extreme Cases.

45. ILLICIT
PROCESSES IN CLASS LOGIC.

- Self-membership.
- The Russell Paradox.
- Impermutability.

PART Vb. ADDUCTION.

46. ADDUCTION.

- Logical Probability.
- Providing Evidence.
- Weighting Evidence.
- Other Types of
Probability.

47. THEORY
FORMATION.

- Theorizing.
- Structure of Theories.
- Criteria.
- Control.

48. THEORY
SELECTION.

- The Scientific Method.
- Compromises.
- Theory Changes.
- Exclusive Relationships.

49. SYNTHETIC
LOGIC.

- Synthesis.
- Self-Criticism.
- Fairness.

PART VI. FACTORIAL INDUCTION.

50. ACTUAL
INDUCTION.

- The Problem.
- Induction of
Particulars.
- Generalization.
- Particularization.
- Validation.

51. ELEMENTS AND
COMPOUNDS.

- Elements and Compounds.
- Gross Formulas.
- Oppositions.
- Double Syllogisms.
- Complements.

52. FRACTIONS AND
INTEGERS.

- Fractions.
- Double Syllogisms.
- Integers.
- Further Developments.

53. FACTORIAL
ANALYSIS.

- Factorization.
- Applications.
- Overlap Issues.
- More Factorial Formulas.
- Open System Analysis.

See also, in this context, Appendix 1.

54. MODAL
INDUCTION.

- Knowability.
- Equality of Status.
- Stages of Induction.
- Generalization vs.
Particularization.
- The Paradigm of
Induction.
- The Pursuit of Integers.

55. FACTOR
SELECTION.

- Prediction.
- The Uniformity
Principle.
- The Law of
Generalization.

56. APPLIED
FACTOR SELECTION.

- Closed Systems Results.
- Some Overall Comments.
- Rules of Generalization.
- Review of Valid Moods.
- Open System Results.

57. FORMULA
REVISION.

- Context Changes.
- Kinds of Revision.
- Particularization.

58. GROSS FORMULA
REVISION.

- Amplification.
- Harmonization.
- Unequal Gross Formulas.
- Equal Gross Formulas.
- Applications.

59. FACTORIAL
FORMULA REVISION.

- Adding Fractions to
Integers.
- Reconciliation of
Integers.
- Indefinite Denial of
Integers.
- Other Formula Revisions.
- Revision of Deficient
Formulas.

PART VII. PERSPECTIVES.

60. PHENOMENA.

- Empirical or
Hypothetical.
- Physical or Mental.
- Concrete and Abstract.
- Presentative or
Representative.

61. CONSCIOUSNESS
AND THE MIND.

- A Relation.
- Kinds of Consciousness.
- The Mind.
- Popular Psychology.

62. PERCEPTION
AND RECOGNITION.

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

63. PAST LOGIC.

- Historical Judgment.
- Aristotle, and Hellenic
Logic.
- Roman, Arab, Medieval European Logic.
- Oriental Logic.
- Modern Tendencies.
- In The 20th Century.

64. CRITIQUE OF
MODERN LOGIC.

- Formalization and
Symbolization.
- Systematization and
Axiomatization.
- Modern Attitudes.
- Improvements and
Innovations.
- The Cutting Edge.

65. DEVELOPMENTS
IN TROPOLOGY.

- Tropology.
- Roots.
- Shifts in Emphasis.
- Setting the Stage.
- Contemporary Currents.
- Philosophical
Discussions.

66. METALOGIC.

- Language and Meaning.
- Definition and Proof.
- Infinity in Logic.
- Conceptual Logic.

67. INDUCTIVE
LOGIC.

- Degrees of Being.
- Induction from Logical
Possibility.
- History of Inductive
Logic.

68. FUTURE LOGIC.

- Summary of Findings.
- Gaps to Fill.
- Concluding Words.

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

APPENDIX 2 - Redefining Majority and Minority in FL.

REFERENCES

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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.

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

*Future Logic*
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.

**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.**

*Future Logic*
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.

**is**

*Future Logic**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).

**is**

*Future Logic**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.

**is**

*Future Logic***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.)

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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.
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