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PART III.LOGICAL CONDITIONING.
1.Laws of Thought.
3.More on Credibility.
4.Opinion and Knowledge.
1.The Singular Modalities.
2.The Plural Modalities.
3.Analogies and Contrasts.
5.Personal and Social.
2.Oppositions of Factuals.
4.Oppositions of Modals.
1.Kinds of Conditioning.
3.Strict or Material Implication.
4.Full List of Forms.
25.HYPOTHETICALS: OPPOSITIONS AND EDUCTIONS.
1.Connection and Basis.
2.Manners of Disjunction.
3.Broadening the Perspective.
29.HYPOTHETICAL SYLLOGISM AND PRODUCTION.
30.LOGICAL APODOSIS AND DILEMMA.
2.The Stolen Concept Fallacy.
2.The Liar Paradox.
3.The Barber Paradox.
Summary of findingsin the chapters of this part:
Part III.The Logic of Logical Conditioning.This is a closer inspection of the logical relations used in practise, a field which may also be described as the self-analysis of logic. Its beginnings date from Aristotle and Philo in Ancient Greece, but it has been especially developed formally in modern times. However, our own treatment of the subject is considerably novel, on many counts.
20. We discussed the genesis and role of the three Laws of Thought in logic, and the distinctive functions of each of them. The notion of phenomenal credibility was further highlighted.
21. We made original formal definitions of the categories of logical modality, and justified the knowability of these concepts.
22. We discussed the various aspects of contextuality, which affect logical modality.
23. The formal treatment of logical relations begins with the concepts of conjunction. The factual forms of conjunction were distinguished with reference to polar considerations, and their oppositions to each other were identified. The modal forms followed accordingly, and so did their oppositions, by means of the general theory of opposition earlier presented.
24. Conjunction gives rise to various kinds of conditioning. We began by analyzing logical conditionals, known as hypothetical propositions or ‘strict’ implications. Novel negative forms were also considered, which in the next chapter led us to a hierarchy of forms.
25. We discerned that hypotheticals are defined not only by the connection they signify, but often also with reference to certain logical bases. Thus, we distinguished between hypotheticals with unspecified bases, and those with normal or abnormal specified bases. The oppositions between hypotheticals, and the eductions from hypotheticals, were described and validated.
26. Disjunctive, as distinct from subjunctive, conditioning was considered. Various manners of disjunction were described and interrelated.
27. Then we looked into various intricacies of logic, expanding on what had so far been presented. Conjunctive, hypothetical and disjunctive propositions form a broad continuum of relations, affected by the number of theses involved, their respective polarities, the polarities and modalities of their relations. Nesting and mixed-form relations were looked into, and we evolved the unifying method of matrixual logic.
28. Next, using some modern symbolic techniques, we investigated the principal interactions between logical relations. We did so with reference to matrices, and thus demonstrated the precise intellectual goal of all such manipulations, and the limits of their practical utility.
29. We developed a full list of hypothetical syllogisms, including those with negative forms, showing how they are derived from the most obvious case. We also introduced the novel process of production, drawing conditional conclusions from unconditional premises.
30. Logical apodosis was dealt with, including its modal forms. Dilemmas and their rebuttals were analyzed.
31. Paradoxical propositions were considered. They allowed us to formally define self-contradiction and self-evidence, and some important philosophical applications were pointed out. We also evolved a more thorough theory of hypotheticals, listing all the normal and abnormal forms which may arise, and investigating their distinct properties in opposition, eduction and deduction.
32. We considered apparent double paradoxes, which are not as legitimate as single paradoxes, showing their logical function and how they are to be dissolved. The examples of the Liar Paradox and the Barber Paradox were dealt with.