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Fourth post in the ongoing series on important innovations in logic theory to be found in my works.
“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 practice, 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.”
While the categories of modality are well known since antiquity and to a lesser extent so is the notion that there are different types (or modes) of modality, Future Logic breaks new ground in its systematic treatment of this field.
Most modern logicians have often left the categories undefined, arguing between them only as to whether to use necessity or possibility as the starting notion. Some have begun with the Liebniz-like definition of necessity as “true in all possible worlds” – ignoring the circularity of such definition (using the yet-undefined term possible) and its pretentiousness (we have a hard time enough to know this world, let alone “all possible worlds”!) And moreover, most modern logicians have concentrated all their efforts on extensional and logical modality, although the natural and temporal modes have been debated by philosophers since antiquity.
One of the important novelties in Future Logic is the analogous definition of categories of modality in the different modes – for instance, the category of ‘necessity’ is defined as occurrence in all instances in the ‘extensional’ mode, in all circumstances in the ‘natural’ mode, at all times in the ‘temporal’ mode and in all contexts of knowledge in the ‘logical’ mode (similarly, for ‘possibility’, saying ‘some’ instead of all, and for actuality saying ‘this one’). This uniformity of structure of the modalities does not however imply that they can be treated collectively, without regard to their basic differences.
Each mode has a specific utility for us. The extensional mode (concerning instances of a kind) is basic to class logic. The natural mode (circumstances surrounding the existence of something) is basic to causal logic. The temporal mode (times in the existence of something) is somewhere in between those two ‘de re’ (or ontal) modes. The logical mode (contexts) concerns our knowledge as such – it is ‘de dicta’ (or epistemic). The ‘de re’ modes are also ‘de dicta’ in a way, but only indirectly.