THE LOGIC OF CAUSATION - by Avi Sion

THE LOGIC OF CAUSATION:

Definition, Induction and Deduction of Deterministic Causality.

Avi Sion,  Ph. D.

First published, 1999 (Phase I), 2003 (Phases I & II), 2010 (Phases I, II & III).

Abstract

The Logic of Causation is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended as part of a larger work on causal logic, which additionally treats volition and allied cause-effect relations (2004).

The Logic of Causation deals with the main technicalities relating to reasoning about causation. Once all the deductive characteristics of causation in all its forms have been treated, and we have gained an understanding as to how it is induced, we are able to discuss more intelligently its epistemological and ontological status. In this context, past theories of causation are reviewed and evaluated (although some of the issues involved here can only be fully dealt with in a larger perspective, taking volition and other aspects of causality into consideration, as done in Volition and Allied Causal Concepts).

Phase I: Macroanalysis. Starting with the paradigm of causation, its most obvious and strongest form, we can by abstraction of its defining components distinguish four genera of causation, or generic determinations, namely: complete, partial, necessary and contingent causation. When these genera and their negations are combined together in every which way, and tested for consistency, it is found that only four species of causation, or specific determinations, remain conceivable. The concept of causation thus gives rise to a number of positive and negative propositional forms, which can be studied in detail with relative ease because they are compounds of conjunctive and conditional propositions whose properties are already well known to logicians.

The logical relations (oppositions) between the various determinations (and their negations) are investigated, as well as their respective implications (eductions). Thereafter, their interactions (in syllogistic reasoning) are treated in the most rigorous manner. The main question we try to answer here is: is (or when is) the cause of a cause of something itself a cause of that thing, and if so to what degree? The figures and moods of positive causative syllogism are listed exhaustively; and the resulting arguments validated or invalidated, as the case may be. In this context, a general and sure method of evaluation called ‘matricial analysis’ (macroanalysis) is introduced. Because this (initial) method is cumbersome, it is used as little as possible – the remaining cases being evaluated by means of reduction.

Phase II: Microanalysis. Seeing various difficulties encountered in the first phase, and the fact that some issues were left unresolved in it, a more precise method is developed in the second phase, capable of systematically answering most outstanding questions. This improved matricial analysis (microanalysis) is based on tabular prediction of all logically conceivable combinations and permutations of conjunctions between two or more items and their negations (grand matrices). Each such possible combination is called a ‘modus’ and is assigned a permanent number within the framework concerned (for 2, 3, or more items). This allows us to identify each distinct (causative or other, positive or negative) propositional form with a number of alternative moduses.

This technique greatly facilitates all work with causative and related forms, allowing us to systematically consider their eductions, oppositions, and syllogistic combinations. In fact, it constitutes a most radical approach not only to causative propositions and their derivatives, but perhaps more importantly to their constituent conditional propositions. Moreover, it is not limited to logical conditioning and causation, but is equally applicable to other modes of modality, including extensional, natural, temporal and spatial conditioning and causation. From the results obtained, we are able to settle with formal certainty most of the historically controversial issues relating to causation.

Phase III: Software Assisted Analysis. The approach in the second phase was very ‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work involved by means of spreadsheets (to begin with). This increases reliability of calculations (though no errors were found, in fact) – and also allows for a wider scope. Indeed, we are now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of causative and other forms needed to investigate 4-item syllogism. As well, now each modus can be interpreted with greater precision and causation can be more precisely defined and treated.

In this latest phase, the research is brought to a successful finish! Its main ambition, to obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being truly fulfilled. This was made technically feasible, in spite of limitations in computer software and hardware, by cutting up problems into smaller pieces. For every mood of the syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets), testing all forms of causative and preventive conclusions. Until now, this job could only be done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000 pages of spreadsheets to generate the sought for conclusions.

This is a historic breakthrough for causal logic and logic in general. Of course, not all conceivable issues are resolved. There is still some work that needs doing, notably with regard to 5-item causative syllogism. But what has been achieved solves the core problem. The method for the resolution of all outstanding issues has definitely now been found and proven. The only obstacle to solving most of them is the amount of labor needed to produce the remaining (less important) tables. As for 5-item syllogism, bigger computer resources are also needed.

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

PHASE ONE: MACROANALYSIS

1. The Paradigm of Causation
2. The Generic Determinations
3. The Specific Determinations
4. Immediate Inferences
5. Causative Syllogism
6. Lists of Positive Moods
7. Reduction of Positive Moods
8. Matricial Analyses
9. Squeezing Out More Information  
10. Wrapping Up Phase One

Appendix. J.S. Mill's Methods

PHASE TWO: MICROANALYSIS

11. Piecemeal Microanalysis
12. Systematic Microanalysis
13. Some More Microanalyses
14. Main Three-Item Syllogisms
15. Some More Three-Item Syllogisms
16. Outstanding Issues

Appendix. Grand Matrices

PHASE THREE: SOFTWARE ASSISTED ANALYSIS

17. Resuming the Research
18. Moduses of the Forms
19. Defining Causation
20. Concerning Complements
21. Causative Syllogisms
22. Scanning for Conclusions
23. Exploring Further Afield
24. A Practical Guide to Causative Logic

Tables and Diagrams

References

Contents in detail

Phase One: Macroanalysis.

1.         THE PARADIGM OF CAUSATION

1. Causation.
2. The Paradigmic Determination.

 

2.         THE GENERIC DETERMINATIONS

1. Strong Determinations.
2. Parallelism of Strongs. 
3. Weak Determinations.
4. Parallelism of Weaks.           
5. The Four Genera of Causation.         
6. Negations of Causation.        

 

3.         THE SPECIFIC DETERMINATIONS

1. The Species of Causation. 
2. The Joint determinations. 
3. The Significance of Certain Findings.

 

4.         IMMEDIATE INFERENCES

1. Oppositions. 
2. Eductions. 
3. The Directions of Causation. 

 

5.         CAUSATIVE SYLLOGISM

1. Causal or Effectual Chains.
2. Some Instructive Examples. 
3. Figures and Moods. 

 

6.         LIST OF POSITIVE MOODS

1. Valid and Invalid Moods. 
2. Moods in Figure 1.
3. Moods in Figure 2.    
4. Moods in Figure 3.

 

7.         REDUCTION OF POSITIVE MOODS

1. Reduction.     
2. Reductions in Figure 1. 
3. Reductions in Figure 2. 
4. Reductions in Figure 3. 

8.         MATRICIAL ANALYSES 

1. Matricial Analysis. 
2. Crucial Matricial Analyses in Figure 1.       
3. Crucial Matricial Analyses in Figure 2.       
4. Crucial Matricial Analyses in Figure 3. 

 

9.         SQUEEZING OUT MORE INFORMATION

1. The Interactions of Determinations.
2. Negative Moods.       
3. Negative Conclusions from Positive Moods.
4. Imperfect Moods.

 

10.       WRAPPING UP PHASE ONE

1. Highlights of Findings. 
2. Modes of Causation.   
3. Gaps and Loose Ends. 

Appendix:       J. S. MILL'S METHODS: A Critical Analysis

1. Preamble.
2. The Joint Method of Agreement and Difference. 
3. The Method of Agreement. 
4. The Method of Difference. 
5. The Method of Residues.
6. The Method of Concomitant Variations.
7. Concluding Remarks. 

 

 Phase Two: Microanalysis.

 

11.       PIECEMEAL MICROANALYSIS

1. Binary Coding and Unraveling.
2. The Generic Determinations.
3. Contraction and Expansion.
4. Intersection, Nullification and Merger.
5. Negation.

 

12.       SYSTEMATIC MICROANALYSIS

1. Grand Matrices.
2. Moduses in a Two-Item Framework.
3. Catalogue of Moduses, for Three Items.
4. Enumeration of Moduses, for Three Items.
5. Comparing Frameworks.

 

13.       SOME MORE MICROANALYSES

1. Relatives Weaks.
2. Items of Negative Polarity in Two-Item Framework.
3. Items of Negative Polarity in Three-Item Framework.
4. Categoricals and Conditionals.

 

14.       MAIN THREE-ITEM SYLLOGISMS

1. Applying Microanalysis to Syllogism.
2. The Moduses of Premises.
3. The Moduses of Conclusions.
4. Dealing with Vaguer Propositions.

 

15.       SOME MORE THREE-ITEM SYLLOGISMS

1. Special Cases of Three-Item Syllogism.
2. Dealing with Negatives.

 

16.       OUTSTANDING ISSUES

1. Four-Item Syllogism.
2. On Laws of Causation.
3. Interdependence.
4. Other Features of Causation Worthy of Study.

Appendix:       GRAND MATRICES

1. Catalogue of moduses for the four conjunctions of two items (P, R).
2. Catalogue of moduses for the eight conjunctions of three items (P, Q, R).

 Phase Three: Software Assisted Analysis.

17.       RESUMING THE RESEARCH.

1. History of the Research.
2. Matrices of the Frameworks.
3. Comparing Frameworks.

18.       MODUSES OF THE FORMS.

1. 2-Item Framework Moduses.
2. 3-Item Framework Moduses.
3. 4-Item Moduses of the Forms.
4. Interpretation of the Moduses.

19.       DEFINING CAUSATION.

1. Back to the Beginning.
2. The Puzzle of No Non-connection.
3. The Definition of Causation.
4. Oppositions and Other Inferences.

20.       CONCERNING COMPLEMENTS.

1. Reducing Numerous Complements to Just Two.
2. Dependence Between Complements.
3. Exclusive Weak Causation.
4. The Need for an Additional Item (or Two).

21.       CAUSATIVE SYLLOGISMS.

1. Methodology.
2. 3-Item Syllogisms.
3. 4-Item Syllogisms.
4. About 5-item Syllogism.

22.       SCANNING FOR CONCLUSIONS.

1. Methodology.
2. Forms Studied and their Oppositions.
3. 3-Item Syllogisms.
4. 4-Item Syllogisms.

23.       EXPLORING FURTHER AFIELD.

1. Possible Forms of Premises.
2. Dealing with Negative Items.
3. Preventive Syllogisms and their Derivatives.
4. Syllogisms with Negative Premise(s).
5. Causal Logic Perspective.

24.       A PRACTICAL GUIDE TO CAUSATIVE LOGIC.

1. What is Causation?
2. How is Causation Known?
3. A List of the Main Causative Arguments.
4. Closing Remark.

TABLES AND DIAGRAMS

References