CHAPTER 33. CONDITIONAL PROPOSITIONS.
Logic has traditionally been focused on two types of proposition, the actual categorical of Aristotle, and the logical hypothetical or disjunctive of later logicians. Categorical propositions (including their factual, positive conjunctions) were seen as essentially ‘de-re‘, telling us about things in themselves. Hypothetical and disjunctive propositions (essentially, modal or negative conjunctions) were seen as essentially ‘de-dicta‘, telling us about connections between thoughts.
However, we will now develop a more accurate, broader theory of conditioning, which acknowledges not only logical conditioning, but also ‘de-re conditioning’, constructed with reference to other types of modality. (The reader is referred to all our previous definitions of the different types of modality.)
This does not mean to imply that logical conditioning is any less ‘real’ than de-re conditioning. But rather, only that the type of modality qualifying the connection and basis is different in each case. As we shall see, each type of conditioning has to do with a distinct type of causality.
The following should serve to illustrate the distinction between types of conditioning:
Logical: ‘if this, then that’, meaning: in such context as this is true, that is also true.
Natural: ‘when this, that’, meaning: in such natural circumstance as this is actual, that is also actual.
Temporal: ‘when this, that’, meaning: at such times as this is actual, that is also actual.
Extensional: ‘where this, that’, meaning: in such cases as this occurs, that also occurs. (By ‘cases’ we here refer to instances of a universal.)
Whereas every de-re conditional implies some kind of de-dicta conditional, the reverse does not always hold. This is because de-re propositions are formally more demanding than logical statements; we need more information to be able to formulate them.
For example, I can formulate an argument like ‘if nothing is knowable, then…’ without thereby suggesting that I acknowledge the antecedent as even logically possible, whereas with other types of conditioning such speculative freedom is lacking. However, note, the rephrasing of de-re into de-dicta will not be studied in detail here.
Natural, temporal and extensional conditionals and disjunctives, are essentially as de-re as two-term, single categoricals, even though they may tell us about connective relationships between three or more terms, or two or more categoricals.
Conditionals have many forms, but we will give most of our attention to those with three terms: the subject and the antecedent and consequent predicate, which best highlight the nature and properties of this family of propositions.
I do not intend to analyze natural, temporal, and extensional conditioning, in as much detail as categorical propositions were and will be treated. I will especially not attempt to develop theories of factorial analysis, and induction by factor selection and formula revision, relating to conditionals. The work done in later chapters on categoricals should be viewed as prototypical, a model for future investigations of the same kind in the field of conditionals.
Each type of modality has its own specific disjunctive propositions, distinguished by their bases and connectives. Relatively little attention will be devoted in this volume to disjunction, although it is in itself valuable, because its logic is derivable from that of conditionals. But some introductory comments will be made in their proper place.
Incidentally, one of the utilities of studying disjunction, is that it clarifies the logic of degrees. The various degrees or measures of any thing X may be viewed as standing in a disjunction ‘X1 or X2 or X3 or…’, of whatever modal type is appropriate. Each degree is a logical, natural, temporal or extensional alternative, and they usually range from some maximum to some minimum.
Disjunctive logic teaches us, for instance, not to confuse the affirmation of X as such (which is indefinite as to degree) with the affirmation of its extreme or most typical manifestation (a specific degree or range, say X1). Likewise, denial of X should mean negation of all its degrees (X1, X2, X3,…), and not mere negation of the more extreme or typical degree or range (as we often intend in practise). The fallaciousness of many an argument is explained with reference to such confusions.
Our expansion of the theory of conditioning is the gateway through which Logic enters into the field of ‘material’ causality.
Hypotheticals are concerned with logical causes; they show us the ‘reasons why’ of items of knowledge, with reference to the contextuality of information. Non-logical conditionals are concerned with more ‘substantive’ causation, occurring in the objective realms of matter or mind, irrespective of the stage of development of our knowledge.
Whereas hypotheticals tell us that ‘In all or this or some knowledge contexts, two theses P and Q both logically arise’, other conditionals tell us that ‘In all or this or some circumstances or times or cases, two events SP and SQ both really happen’.
The various types of conditioning are differentiated by the type of modality intended, in the connection (which qualifies the whole relation of antecedent and consequent), and in the basis (the underlying possibilities), which they respectively imply.
In typical hypotheticals, of the form ‘if P, then Q’, the connection is a logical incontingency and the basis is a problemacy or logical possibility of truth.
In contrast, typically, for natural conditionals like ‘when P is, Q must be’, the connection is a natural necessity and the basis is a potentiality of actualization in some circumstances.
For temporal conditionals like ‘when X is, Y always is’, the connection is a temporal constancy and the basis is the sometime occurrence of the events concerned.
For extensional conditionals ‘where X applies, Y applies’, the connection is a generality and the basis is applicability to part of the subject’s instances.
Through such formal analysis of conditioning, using the tools of modal logic, we can begin to understand and seriously examine the concept of causality.
Causality is of various types, in parallel to the types of modality. We can talk of logical causality, natural causality, temporal causality, and extensional causality. These are distinct, yet not unrelated, types of determinism. Making this distinction allows for more accurate and efficient reasoning processes.
Each type of causality orders reality in a special way. Logic determines reality in accordance with the order of development of knowledge; nature and time order individual external events as such; extension refers to the classification of universals. These represent distinct methods of explanation.
When we say that X causes Y, or Y is caused by X, we must first establish the type of causality intended Expressions like ‘because of’ or ‘as a result of’ or ‘depends on’, and such, are in everyday discourse used indiscriminately, without awareness of the modality type involved. Yet, epistemologically and ontologically the difference is important.
The various types of causality display both some similarities and some differences in structure and in logical behavior patterns. The common properties of all types of causality may be seen as the general laws of causality. The distinctive uniformities within each type give rise to a special logic for that specific modality. Thus, both the similarities and differences are significant.
The field of aetiology, the study of causality, is not intended to be within the scope of this dissertation. I have personally already done the needed logical work, so I know how vast and interesting it is. But these results belong in a separate volume. My purpose here is to give one more justification for my theory of modality, to highlight how useful to logic and all areas of knowledge this tool is. My policy here will therefore be to focus on information most relevant to this purpose, the bare essentials.
The differentiation of modality into types and categories allows for hitherto unmatched clarity and precision in the development of conceptual knowledge. Not that modality is something new to human thinking, but its systematic study greatly improves our understanding of it and our reasoning processes.
For the concept of modality, as indeed that of causality, transcends any specific content of knowledge, and is equally valuable in physical sciences, psychology, politics, religious discourse, or personal deliberations. It is not attached to any particular theory of the universe, or of any domain within it. It is grounded in common overall experience and logical consistency.
I should perhaps, however, say a word or two about the so-called ‘Laws of Causality’ which some philosophers have advanced.
a. Some claim that ’cause and effect must be substantially the same’. Thus, they deny that G-d could have created the world, ‘because’ a purely spiritual entity (G-d) cannot generate a material and mental one (the world we commonly experience). But there is no formal justification for such an argument, for spirit and matter still have in common one thing, namely existence, so that the conclusion is not inferable from the premise. In any case, we commonly regard material and mental phenomena, though substantially different, as having mutual causal relations, whether in acts of will or in more reactive psychological situations, so that even within the empirical world such a ‘law of causality’ is untenable.
b. Some claim that ‘something static cannot cause a motion’, in order to prove that G-d, who is unchanging, cannot have created a world of change, or to deny that human volition is initiation of motion by an unmoved soul. But this is contrary to common-sense intuition, so that aetiology may not ab-initio reject this from formal possibility. One may seek to prove it eventually, but not posit it as a logical principle from the start.
c. Some claim that ‘everything must have a cause, ad infinitum‘. They say that there are no prime movers, that everything is mechanistically determined, and from thence argue that G-d, and likewise human action, must also have a cause. Here again, there is no formal basis for such a claim. As we proceed, it will become clear that causality is quite definable without reference to such ‘laws’. We might posit such infinite regression as a generalization, an inductive principle, but there is no conceptual necessity in it.