Rationalism and empiricism are not at odds; but, on the contrary, deeply mutually dependent. True rationalism is firmly grounded in experience; and true empiricism is made possible by application of reason. Induction is the methodological bridge between experience and reason.
Most of my logic and philosophy work through the years has been directly or indirectly about induction. For that reason, and in view of the large volume of my work, it would be impossible for me to collect my writings on induction in one volume. This is why I have long hesitated to produce a ‘thematic compilation’ on inductive logic.
However, having remained painfully aware of readers’ need for a relatively short book on the subject, I have decided to collect a number of essays in the present volume. Obviously, this book cannot reproduce the very detailed work to be found in my books, especially in Future Logic and The Logic of Causation; but it provides readers with some introductory and conclusive material to chew on. Those interested enough will then hopefully push their research further, and read those larger studies.
Even so, I must stress that the technical details given in my major studies are essential to full understanding and conviction of inductive logic. It is the formal details that really make up and teach inductive logic; the surrounding informal introductions and conclusions cannot replace them. So, the present volume, while not a mere ‘teaser’, should certainly not be viewed as constituting my entire work on induction. Very important material had to be left out here, just to save space.[1]
One cannot sufficiently stress the importance of formal inductive logic to the elaboration of a realistic theory of knowledge. People, still nowadays, think of ‘formal logic’ as essentially a deductive enterprise. This is due in part to the historic fact that the science of logic was kicked off by Aristotle’s marvelous work on the syllogism. But it is also largely due to the almost exclusive focus on deductive logic by most modern logicians.
Modern deductive ‘logicians’ seem to have been, and to still be, inane wankers (excuse the graphic expression) trying to get a name for themselves in academe and in history by reshuffling simplistic symbols ad nauseum, without being able to step back and view the actual ways and means of human knowledge acquisition with a fresh look and an open mind. In truth, deduction is only a fraction of man’s intellectual work; his main instrument of knowledge is induction. Deduction is only one of the tools of induction, the easiest tool to master (nonetheless, it is essential, of course). Man’s mind is essentially inductive in its functioning, and could not be anything else.
Induction implies knowledge that is, for the most part, if not entirely, approximate and temporary. This is the first and basic lesson of inductive logic, that we must accept our cognitive limitations. It is no use looking for means to an absolute and definitive body of knowledge; and it is absurd (self-contradictory) to reject human knowledge due to its relativity and non-finality. We are not gods – just human beings, just sophisticated animals, doing our best to survive on our little planet, which is a mere speck of dust in an enormous universe. Many logicians and philosophers seem unable to accept this simple, primary fact.
The good news is that inductive logic, if properly practiced, can, at all times, provide us with the very best ‘approximate and temporary’ knowledge. We can never honestly claim to possess the final truth on any subject; but we can certainly claim to have chosen the best hypothesis among the currently imagined ones, thanks to inductive logic. This is the great gift of inductive logic, its power.
But note that induction is not an invention of logicians; it is man’s instinctive cognitive heritage. Logicians only uncover what mankind has naturally, always, from cradle to grave, from the cave to space travel, practiced to varying degrees, and been aware of more or less clearly. The science of inductive logic is itself a product of inductive practice, and not some externally-imposed, artificial system. Its value lies in theoretically justifying and improving practice.
Inductive logic can be summarized in one sentence that I refer to as the principle of induction, and identify as the fourth law of thought. This has many formulations, depending on the context to which it is applied; listed below are some of its guises. What is common to all of them, notice, is the conjunction of a positive clause and a negative one. The phrase ‘until and unless’ (or ‘until if ever’) is essential to all of them, stressing that induction is never definitive but always open to revision.
The basic principle of generalization is to assume observed, particular uniformities to be applicable generally, until and unless we have reason to think otherwise.
…
The experiences of similarity or difference are phenomenal, and are taken at face value, until and unless otherwise proven, like all other experiences.
Future Logic (1990).
This is a generalization, an inductive act which upgrades an indefinite particular (I) to a universal of the same polarity (A), until if ever evidence is found to the contrary.
Judaic Logic (1995).
Inductively, appearance implies reality, until and unless it is judged to be illusion (by virtue of some inconsistency being discovered).
Buddhist Illogic (2002).
We consider concepts or propositions compatible, until and unless we find some incompatibility between them. (We do not ‘prove consistency’ but rather ‘find inconsistencies’.)
…
We do not need an epistemological ‘axiom’ to defend sensation and memory as universally reliable. It suffices to consider the products of these faculties as true, until and unless found false.
Phenomenology (2003).
The proposition “If X is followed by Y, then X causes Y” may logically be assumed to be true, especially if the X+Y combination is repeatedly found to occur, until and unless it is found that X is sometimes not followed by Y.
…
Thus, the right-wrong or good-bad experiences at the ground of ethics are technically akin to the true-false or correct-incorrect experiences at the ground of non-ethical knowledge. The procedure for judging them is the same: we grant them some ab initio credibility, but reserve our final judgment till further research has confirmed them in all respects (until and unless new evidence or arguments emerge to the contrary).
Volition and Allied Causal Concepts (2003).
One may credibly assume something that appears to be real is indeed real, until and unless it is proved illusory or at least put in doubt for some specific reason.
Ruminations (2005).
In accord with general rules of induction, we presume any two items P and Q to be without causative relation, until if ever we can establish inductively or deductively that a causative relation obtains between them.
…
We must obviously usually resort to generalization: having searched for and never found such conjunction, we may reasonably – until and unless later discoveries suggest the contrary – assume that such conjunction is in fact impossible.
The Logic of Causation (2010).
The principle of induction: given any appearance, we may take it to be real, until and unless it is found to be illusory.
Logical and Spiritual Reflections (2008).
In accord with the principle of induction, we treat a hypothetical term as a realistic term, until and unless we have reason to believe otherwise.
A Fortiori Logic (2013).
[1] Among the significant segments I had to leave out are the following. From Future Logic, I left out: most of the deductive logic work (which is, of course, essential to, and arguably a part of, the inductive logic work); all of the more detailed work on factorial analysis, factor selection and formula revision (although this is, of course, the heart of formal inductive logic); and my comments on the history of inductive logic. From The Logic of Causation, I left out most of the formal work, and could only include the initial definitions of the determinations of causation (which are of course formal and essential) and the concluding ‘insights’ of the three phases of my research. I was also forced to leave out my critical essays, published in Logical and Spiritual Reflections, on Hempel's ‘paradox of confirmation’ and Goodman’s ‘paradox of prediction’, both of course directly relevant to inductive logic. I also wanted to leave out the essay, first published in A Fortiori Logic, on the ‘existential import’ doctrine, because most of it relates to deductive logic; but decided that its conclusions are so relevant to inductive logic that I had to keep it in.