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Fifth post in the ongoing series on important innovations in logic theory to be found in my works.
One of the most striking demonstrations of the importance of distinguishing between the different types (or modes) of modality is the way this makes possible more accurate reasoning using conditional propositions. For each type of modality gives rise to a different type of conditioning; and though these various types are analogous in many respects, if we treat them in an undifferentiated manner in our reasoning processes we are bound to make very serious errors.
We must first distinguish between ‘de dicta’, i.e. logical, conditioning – and various forms of ‘de re’ conditioning, notably the natural, the temporal and the extensional. The ‘de dicta’ versus ‘de re’ distinction between modalities, signifying a difference between epistemological and ontological modes of thought, was (as the Latin names we use suggest) known since antiquity, and to a lesser extent so were the varieties of ‘de re’ modality.
However, while logical conditioning has been extensively studied (especially in modern times), the natural, temporal and extensional forms of conditioning have received little attention. Logicians have tended to look upon the logical ‘if--then—’ form as one applicable to all conditioning. But this is far from true or wise, though in practice we often do use this as an undifferentiated form. Logical conditioning in truth relates primarily to states of knowledge.
In Future Logic, I develop a detailed analysis of ‘de re’ types of conditioning, how they are produced and the arguments we can form with them. It soon becomes obvious that, despite the analogies or parallelisms between them, their distinction cannot be ignored. Natural or temporal conditioning concerns states of being of individual things, whereas extensional conditioning concerns instances of a kind of thing. This is evident to us in everyday discourse, and we are quite able to express the differences in meaning linguistically when we feel the need to be precise.
Thus, when we mean natural or temporal conditioning we tend to say “When any X is Y, it is Z”, whereas we mean extensional conditioning we tend to say “In such cases as an X is Y, it is Z”. What do we mean here? In the former statement, we mean that all X are potentially or sometimes Y, and for each X the Y predicate is by natural necessity or always accompanied by the Z predicate. In the latter statement, we mean that some X are Y, and all those instances of X that are Y are also Z. These are just two examples, of course; there are many other forms of each type.
We notice that ‘de re’ conditioning involves a ‘base’ and a ‘connection’. In natural or temporal conditioning, the base is the implied modal statement that “All X can be or sometimes are Y” and the connection is the necessity that ties the actualization of this potentiality or temporal possibility with the consequent predicate Z. In extensional conditioning, the base is the particular proposition that “Some X are Y” and the connection is the universality that ties the instantiation of this particularity with the consequent Z.
In logical conditioning, too, we have a base as well as a connection, but we avoid the restriction implied by a base because it would straitjacket our discourse excessively, because it would make dealing with logical paradoxes a very complicated matter. More precisely put, a peculiarity of logical modality is that logical possibility may always be assumed to be true until and unless it is found, through some implied breach of the laws of thought, to be false. For this reason, logical conditioning may always be assumed to have an appropriate base, except when it is proven to lack one.
Such assumption of possibility until impossibility is proved is not applicable to the 'de re' types of modality, which are subject to more stringent inductive rules. This implies, for instance, that 'de re' necessary conditional propositions cannot automatically be contraposed. This is all said in passing – what I want to stress here is the importance of distinguishing the various ‘de re’ forms of conditioning, of understanding their implicit base and connection. For, once we do this, we realize how different reasoning in each of these modes really is.
One important effect of the study of conditioning in its various ‘de re’ modes is the realization of the logical continuity between categorical and conditional propositions; they are not two opposed forms of expression but greater or lesser degrees of relation. This insight becomes essential when we get into the formal logic of induction. Another important result of the study of the modes of conditioning is the deeper understanding of causation that it makes possible.
For more details on this topic, see FUTURE LOGIC, PART IV (CHAPTERS 33-40).