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
- The Paradigm of Causation
- The Generic Determinations
- The Specific
Determinations
- Immediate Inferences
- Causative Syllogism
- Lists of Positive Moods
- Reduction of Positive
Moods
- Matricial Analyses
- Squeezing Out More
Information
- Wrapping Up Phase One
Appendix. J.S. Mill's Methods
PHASE TWO: MICROANALYSIS
- Piecemeal Microanalysis
- Systematic Microanalysis
- Some More Microanalyses
- Main Three-Item Syllogisms
- Some More Three-Item
Syllogisms
- Outstanding Issues
Appendix. Grand Matrices
PHASE THREE: SOFTWARE ASSISTED ANALYSIS
- Resuming the Research
- Moduses of the Forms
- Defining Causation
- Concerning Complements
- Causative Syllogisms
- Scanning for Conclusions
- Exploring Further Afield
- A Practical Guide to
Causative Logic
Tables and Diagrams
References
Contents in detail
Phase One: Macroanalysis.
1. THE PARADIGM
OF CAUSATION
- Causation.
- The Paradigmic
Determination.
2. THE GENERIC
DETERMINATIONS
- Strong Determinations.
- Parallelism of
Strongs.
- Weak Determinations.
- Parallelism of Weaks.
- The Four Genera of
Causation.
- Negations of Causation.
3. THE SPECIFIC
DETERMINATIONS
- The Species of
Causation.
- The Joint
determinations.
- The Significance of
Certain Findings.
4. IMMEDIATE
INFERENCES
- Oppositions.
- Eductions.
- The Directions of
Causation.
5. CAUSATIVE
SYLLOGISM
- Causal or Effectual
Chains.
- Some Instructive
Examples.
- Figures and Moods.
6. LIST OF
POSITIVE MOODS
- Valid and Invalid
Moods.
- Moods in Figure 1.
- Moods in Figure 2.
- Moods in Figure 3.
7. REDUCTION OF
POSITIVE MOODS
- Reduction.
- Reductions in Figure
1.
- Reductions in Figure
2.
- Reductions in Figure
3.
8. MATRICIAL
ANALYSES
- Matricial Analysis.
- Crucial Matricial Analyses
in Figure 1.
- Crucial Matricial Analyses
in Figure 2.
- Crucial Matricial Analyses
in Figure 3.
9. SQUEEZING
OUT MORE INFORMATION
- The Interactions of
Determinations.
- Negative Moods.
- Negative Conclusions
from Positive Moods.
- Imperfect Moods.
10. WRAPPING UP
PHASE ONE
- Highlights of
Findings.
- Modes of Causation.
- Gaps and Loose
Ends.
Appendix: J. S.
MILL'S METHODS: A Critical Analysis
- Preamble.
- The Joint Method of
Agreement and Difference.
- The Method of
Agreement.
- The Method of
Difference.
- The Method of Residues.
- The Method of
Concomitant Variations.
- Concluding Remarks.
Phase Two: Microanalysis.
11. PIECEMEAL
MICROANALYSIS
- Binary Coding and
Unraveling.
- The Generic
Determinations.
- Contraction and
Expansion.
- Intersection,
Nullification and Merger.
- Negation.
12. SYSTEMATIC
MICROANALYSIS
- Grand Matrices.
- Moduses in a Two-Item
Framework.
- Catalogue of Moduses, for
Three Items.
- Enumeration of Moduses,
for Three Items.
- Comparing Frameworks.
13. SOME MORE
MICROANALYSES
- Relatives Weaks.
- Items of Negative
Polarity in Two-Item Framework.
- Items of Negative
Polarity in Three-Item Framework.
- Categoricals and
Conditionals.
14. MAIN
THREE-ITEM SYLLOGISMS
- Applying Microanalysis to
Syllogism.
- The Moduses of Premises.
- The Moduses of
Conclusions.
- Dealing with Vaguer
Propositions.
15. SOME MORE
THREE-ITEM SYLLOGISMS
- Special Cases of
Three-Item Syllogism.
- Dealing with Negatives.
16. OUTSTANDING
ISSUES
- Four-Item Syllogism.
- On Laws of Causation.
- Interdependence.
- Other Features of
Causation Worthy of Study.
Appendix: GRAND
MATRICES
- Catalogue of moduses for the
four conjunctions of two items (P, R).
- Catalogue of moduses for
the eight conjunctions of three items (P, Q, R).
Phase Three: Software Assisted Analysis.
17. RESUMING THE
RESEARCH.
- History of the Research.
- Matrices of the
Frameworks.
- Comparing Frameworks.
18. MODUSES OF
THE FORMS.
- 2-Item Framework
Moduses.
- 3-Item Framework
Moduses.
- 4-Item Moduses of the
Forms.
- Interpretation of the
Moduses.
19. DEFINING
CAUSATION.
- Back to the Beginning.
- The Puzzle of No
Non-connection.
- The Definition of
Causation.
- Oppositions and Other
Inferences.
20. CONCERNING
COMPLEMENTS.
- Reducing Numerous
Complements to Just Two.
- Dependence Between
Complements.
- Exclusive Weak
Causation.
- The Need for an
Additional Item (or Two).
21. CAUSATIVE SYLLOGISMS.
- Methodology.
- 3-Item Syllogisms.
- 4-Item Syllogisms.
- About 5-item Syllogism.
22. SCANNING FOR
CONCLUSIONS.
- Methodology.
- Forms Studied and their
Oppositions.
- 3-Item Syllogisms.
- 4-Item Syllogisms.
23. EXPLORING
FURTHER AFIELD.
- Possible Forms of
Premises.
- Dealing with Negative
Items.
- Preventive Syllogisms
and their Derivatives.
- Syllogisms with Negative
Premise(s).
- Causal Logic
Perspective.
24. A PRACTICAL
GUIDE TO CAUSATIVE LOGIC.
- What is Causation?
- How is Causation Known?
- A List of the Main
Causative Arguments.
- Closing Remark.
TABLES AND DIAGRAMS
References
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