Inductive Logic

1.    Hume’s Critique

Hume’s denials

David Hume denies the very concept of causality – but in the same breath offers us an explanation of our belief in it, viz. that causal argument proceeds by association of ideas. I have criticized this claim elsewhere[1], but here wish to stress that offering an explanation is claiming to know a cause – therefore, Hume’s thesis is self-contradictory.

Nevertheless, there are some grains of truth in his thesis, which by the way explains why it has seemed credible to so many people since he stated it. To see these undercurrents of truth, it is important to distinguish between the issues of how to define causality in general and of how to get to know particular instances of causality.

Clearly, before we can deny causality, we must have some idea what it is we want to deny. Hume admits a simple definition of causality (or rather causation, to be exact) as “constant conjunction,” This definition has some truth, but is debatable and ultimately inadequate. Thereafter, the issue arises, can we establish contents fitting this definition. Hume denies it, but (as just pointed out) his denial turns out to be self-defeating.

Hume focused on our incapacity to apprehend causes immediately, and suggested that in allegedly ‘reasoning’ from a cause to an effect (or backwards, from effect to cause) we were merely expressing our mental habit of ideating certain things together. Notwithstanding Hume’s errors, I would suggest the following to be the undercurrents of truth he was perhaps (though unsuccessfully) trying to bring out:

Ab initio, nothing has any apparent cause. That is to say: causality is not something one can directly observe. ‘Objectivity’ requires that we do not begin our search for knowledge with a prejudice concerning causality in general and about specific causal propositions. Causality and particular cases of it have to be established gradually over time, because the facts logically point us in this direction. We cannot at first sight make such claims with certainty – but (contra Hume) this does not exclude the possibility that we can eventually arrive at such conclusions through appropriate logical efforts.

Indeed, causes can be found through induction. The method appropriate for finding causes is not deductive – nor for that matter Hume’s ‘association of ideas’ – but inductive. Practical ways to attain such knowledge were first elucidated by Francis Bacon (1605), a century and a half before Hume’s comments. (I have further clarified and developed these methods in my The Logic of Causation.) Hume’s thesis rang true in some ears, because he raised awareness that a process was involved. He identified that process as merely psychological; but in fact, it was logical – using inductive logic.

We should, to be precise in the present discussion, refer to volition by others and our less conscious own volitions, as well as to causation, noting that most of our own volitions are known directly and immediately, in the way of self-experience – i.e. ‘intuition’. It is worth pointing out that Hume tacitly admits this last claim when he tries to explain knowledge of causation through ‘association of ideas’ – since this implies he and the rest of us can look into our mental activities and directly obtain that insight. Thus, Hume’s attempted critique applies specifically to causation and not to volition, note well.

It should be stressed that the present rejection of Hume’s identification of causal reasoning with mere association of ideas does not imply a denial that we do engage in association of ideas. This mental process does occur. Indeed, it sometimes occurs on the basis of assumed causal connection – but it also, and more often, concerns objects known to be without any such connection. The objects of thought may be mentally associated merely because they happened to coexist in our sight once for a moment – even if they have at all other times been visibly separate. Moreover, mental association does not require any coexistence at all ever, but may occur for quite incidental or accidental reasons. Two things may be mentally associated because of some tiny or vague resemblance, or even simply because we happen to have given them names that sound somewhat the same.

Indeed, Hume’s critique depends on these very facts concerning association of ideas for its (illusory) force. If association of ideas was always based on constant conjunction, it would not seem so loose a relation but would indeed suggest underlying causal connection. Thus, Hume on the one hand pretends to equate those two concepts, but on the other hand cunningly exploits their difference, in order to cast doubt on causal reasoning.

Furthermore, he does not explain the distinction we all make between cause and effect, considering that the idea of the effect sometimes (and in some cases, always) mentally precedes that of the cause, even if materially the cause always precedes the effect. Clearly, this opacity is just one aspect of his deliberate confusion between an idea and it object. But such a subjectivist notion is anti-rational, since Hume obviously considers (or wants us to consider) his own skeptical doctrine as objectively true.

Hume’s Mentalism

It should be pointed out that Hume’s position on causation is ‘consistent’ with his position on sensory perception. Given his belief that our apparent perceptions of matter are in fact perceptions of the mental images (“impressions,” or “ideas”) produced by sensations, and not perceptions of the things that triggered the sensations, it is not strange that he should advocate an “association of ideas” view of causation.

Hume is apparently unaware that this position on perception is logically self-contradictory, because it starts with a belief in matter (including a human body with sense organs, receiving sensory signals and passing them on to the mind), and ends with a denial of it (i.e. an affirmation that all we are able to know are mental impressions or ideas). Moreover, Hume leaves unanswered the question as to who has these ‘ideas’; i.e. he ignores the Subject.

Hume’s concept of association of ideas can also be applied to the other type of causality, namely volition, by effectively denying the existence of a willing self. If volition is identified with sequences of mental phenomena like desires, aversions, etc. and perceptible actions of mind and ‘body’, then there is no need for or place for a concept of a ‘self’ engaged in willing. Thus, in this view, attitudes, affections and appetites are ‘ideas’ of sorts, and apparent ‘volition’ is simply causation at the purely mental level between such ideas and certain ‘actions’.

Here, the antinomy consists in leaving unexplained who it is that is associating ideas. If there is no Agent in volition, and no Subject in cognition, no cognitive processes can be depicted as ‘in error’. So, how is it that Hume is wiser than the rest of us, and can spot these errors of thought? And moreover, if we have no choice about our mental behavior, what is the purpose of his indicating our errors?

As I have explained elsewhere[2], volition is not a causative relation between influences (apprehended conditions) and apparent actions (physical or mental events), but a totally different kind of causal relation, between a soul and its intentions and acts of will. The latter are not phenomenal, but intuited by the Subject. Attitudes, affections and appetites are not substances, but essentially intentions of the self. They influence its acts of will, making them easier or harder; but they are not causatives of them, they are incapable of producing them. The acts of will are caused by the soul, using a causal relation fundamentally different from causation, namely volition.

In both domains, whether through apparent bodily sensations or directly in the mind, Hume seems to consider the arising of ‘ideas’ (which are thereafter mentally associated) as spontaneous: he is effectively denying all causality. His skeptical view of causality is not based on a thoroughgoing psychology, but is filled with inconsistencies.

Hume, like many philosophers before him and since, approached the issue of causality and other topics in the way of a ‘spin doctor’. He was not scientifically minded, but intent on justifying his philosophical slant of skepticism. I submit: he wanted to invalidate our knowledge, and sought pretexts with this goal in mind.

He perhaps only wanted to shock his peers; or maybe he had a perverse wish to destroy human knowledge or to hurt people’s minds.

It is legitimate for logic to admonish: such twisted motives are unworthy of philosophers. Philosophers should not bring their personal problems into the public arena in that way. They should approach the subject in a responsible, mentally healthy way, with benevolent intentions. And perhaps the best way to insure such balanced behavior is to lead a pure life….

2.    Induction of Causatives

Induction of causative propositions, like for most other kinds of proposition, consists largely in the process of trying to ‘fit-in’ the empirical data into this or that morphology (i.e. m, n, p, q, etc.).

The proposition is our (working) hypothesis, while our relevant experiences and memories (the phenomenological facts) are the data used for testing that hypothesis. As usual, we seek for the pattern that will best express and assimilate the data at hand.

The reasoning involved is: ‘try this form – does the data fit in it?’ – ‘no! therefore, this form is not quite appropriate, try another’. This is done repetitively for each set of facts and tentative propositional form.

By trial and error, we repeatedly adapt our estimate of the overall causative relation involved to the available database, which we actively seek to expand.

In formation of a causative proposition, terms (or theses) are variously related according to the conjunctions or non-conjunctions of their presences and/or absences, i.e. through matricial analysis, until the appropriate categorical (or hypothetical) proposition is settled.

Note that this resembles but is not the same as concept formation, where similarity between things is sought and then each new thing is tested for membership.

An example of such ‘construction’ of a fitting hypothesis (propositional form) is to be found in historical judgment[3] (i.e. trying to formulate general propositions about causation in history) – which is mainly extensional in mode.

Note additionally that the disjunction between the specific determinations suggests a possibility of induction by the factorial analysis method described in my Future Logic.

Incidentally, the word ‘conditioning’ (often used there) is an apt adjective for all non-categorical relations, including conditional propositions (that tell us one item is true, if another is so) in the various modes of modality (in the logical mode these are known as ‘hypotheticals’) and their disjunctive forms. The term as such is relatively new, dating I gather from the 15^th Century – but its root (the Latin conditio) is very old, and its underlying meaning is no doubt as old as human reason.

The active form ‘conditioning’ is admittedly originally intended to balance the passive form ‘conditioned’, rather than (as sometimes used, by me and others) a general term covering both directions, i.e. the relations of ‘conditioning and conditioned’ as a whole. But this is a limitation of our language, which in no way renders the term illegitimate. The term is used in this sense not only by logicians, but also by scientists in their theoretical discourse (e.g. by Pavlov) and by common technicians (e.g. ‘air conditioning’), because of its causal connotations.

3.    True of All Opposites

It is true of all opposites (X and nonX) that they invariably must succeed each other, sometime and somewhere, in time (natural modality) and/or space (extensional modality) and/or in thought (logical modality), and therefore such sequences ought not be regarded as causative relations in the strict sense.

For example, we cannot say ‘health causes sickness’ or ‘peace causes war’, just because we observe that the first term (health or peace) invariably precedes the second (sickness or war, respectively)!

Therefore, when we define the causative relation, with reference to conjunctions or non-conjunctions of presences or absences of two or more items, we should, if only parenthetically, except formal relations of mutual exclusion and exhaustiveness between contradictories.

For we normally understand causation as a not-obvious relation, one which we cannot establish a priori. Proposing the sequence of formal opposites as causative provides no new information concerning them, since that is a universal given in a world of multiplicity.

Returning to our first example: it is not health that causes sickness, but some germ or virus (say) that attacks the healthy organism and makes it sick. Again, in our second example: it may well be that peace changes conditions of society in ways that really give rise to eventual war, or vice versa. But in such case, precise analysis of the causatives involved is required. Certainly, it is not peace per se which causes war, but rather (say) the passing of generations and perhaps the rise in wealth and conceit, so that people forget the horror of war and are again willing to engage in it.

4.    Extensional to Natural

On tropology or aetiology: We often reason from extensional to natural modality, i.e. from transverse observations to longitudinal conclusions, or vice-versa.

Such extrapolation occurs notably in astronomy, where the evolution of stars and galaxies is not observed with reference to one and the same star or galaxy, but by observation of different such entities at presumably different stages of their development, and then hypothesizing a common course of development for them all, and the assumption that they are each at a different stage along that standard course.

Conversely, in the field of psychology, from the experience of some people with certain pathologies, we assume that under certain circumstances the same could happen to other people. In other words, we are not satisfied with mere ad hoc observations on individuals, but assume some underlying nature or natural structure in common to individuals of the same kind.

Because of such habits, it is important to identify and clarify the forms these reasoning processes take. There are surely many varieties of it, both categorical and conditional. Such leaping from one mode to another is not formally deductive, but an inductive pattern. We should perhaps give it a name, to ensure we focus on it – say, “modal extrapolation,”

Drawn from Ruminations (2005), Chapter 8:1-5.