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February 18, 2010

1:11 AM

Introduction to the theory of induction: about adduction

Seventh post in the ongoing series on important innovations in logic theory to be found in my works. First, let me apologize to readers for not posting new blogs more often, but I am at this time very busy with new research and writing. As of the present posting, I will begin presenting to you the major advance in induction theory published in my book Future Logic 20 years ago. I skip (at least for now) other matters covered in that work, so as to maintain the continuity of the narrative here.

Before presenting (hopefully in my next posting) “factorial induction”, however, I must for the sake of some readers explain certain traditional notions and processes underlying induction. We all at any given time have a mass of experiences and ideas, which are constantly in flux. At each moment, we regard this sum of concrete and abstract information as our “world”. Most of us are aware that this punctual information may not all be reliable, since we remember that parts of it were different at earlier times. That is, though we trust our faculties of knowledge for the most part, we are also well aware that we are neither omniscient nor infallible.

Although the human way of acquiring and verifying knowledge has no doubt not changed very much in its essentials since mankind arose on earth, it is only in relatively modern times that the theoretical understanding of the crucial mental/logical process of induction has crystallized. The equally important process of deduction (inferring particulars or narrower universals from larger universals) has been an object of study since antiquity, but it was not then very clear that or how universals emerged out of particulars (inductive inference). We only began to realize the nature of induction by observing modern scientists like Galileo or Newton at work.

It then became evident that the “scientific method” for acquiring knowledge is “hypothetico-deductive”. That is, modern thinkers realized that their ideas were hypotheses related to their experiences in the way that an antecedent is related to a consequent in a hypothetical proposition. The bond between the two aspects of knowledge, i.e. between the abstract/universal aspect and the concrete/particular one, was to be established through deductive reasoning. But the essentially inductive nature of knowledge was that theories were imaginary constructs deeply dependent on empirical evidence for their credibility.

Our ideas are attempts to explain experiences, and thus our theories have to logically imply the evidence at hand. But even so, it is the empirical data that justifies the theory, not the other way round. The way this occurs is through adduction. The term adduction refers to the adducing of empirical evidence in support of an idea or theory. An adductive argument is a deductively invalid apodosis. In deductive reasoning, given that a proposition P implies another proposition Q, we can when we find P to be true infer Q to be also true, but we cannot proceed in reverse fashion and infer P from Q (unless, of course, we have established that ‘if Q then P’ is also true, as occasionally happens).

However, in inductive reasoning, we do consider the reverse argument as having some value (i.e. even though Q does not imply P). Given that ‘if P then Q’ is true, we regard the empirical occurrence of Q as slightly strengthening the probability that the theory P is also true. Probability is not proof in the strict sense of the term, but it adds credibility, and many such small additions of credibility proportionally increase our trust in the theory. But this is not the only basis for induction. Early on, Francis Bacon realized the crucial importance of the negative instance in the rejection of theories. A theory may be supported by a mass of positive indices like that, but all it takes is one erroneous prediction from it for it to lose all credibility (at least as it stands, without modifications). This is simple deduction, the argument being: “given ‘if P then Q’ and finding that Q is false, it follows that P is false”. This means that the credibility of a theory depends not only on the positive evidence going for it, but also on the absence of any damning negative evidence, note well.

There are many other issues in inductive logic that we won’t go into here. But one more issue must be mentioned here: induction rarely occurs with reference to one hypothesis – it is usually, implicitly or explicitly, a contest between two or more alternative theories, so that we cannot evaluate a theory in isolation, merely with reference to the positive and negative evidence, but must compare the success or failure of competing theories at explaining or predicting the same data.

Anyway, as the above described inductive understanding of scientific knowledge developed, it became obvious to scientists, philosophers, logicians and psychologists that these patterns of thinking did not merely concern science – but were descriptive of all human thought. Everyone functions in this trial and error manner: acknowledging empirical data; formulating some imaginary proposition concerning it; testing that proposition as time goes on and new related evidence makes its appearance; and eventually, if contrary information happens to be found, realistically abandoning it. This is valid for any kind of information – not just information about the external material world seemingly perceived by the senses, but also information about our inner life manifested in our intuitions, feelings and mental projections.

Of course, we do not all always proceed so rationally and carefully in practice, so our thought is not always so ‘scientific’, so rigorous. We may, for instances, fail to show a strong logical connection between our idea and the empirical data it is conventionally attached to, or we may fail to consider competing ideas, or again we may simply disregard counter-evidence for emotional reasons. Nevertheless, what has become clear is that the methodology of human acquisition of knowledge is essentially inductive (deduction being, in the last analysis, just a tool of induction, albeit a crucial one).

One of the most important processes of induction is generalization and particularization. It is necessary to realize that this two-sided process fits into the pattern of induction above described. A general proposition is related to particular data in the way that a hypothesis is related to empirical evidence supporting it. So long as a generalization continues to be supported by the particular facts that gave rise to it in our minds, it is to that extent trustworthy; but the moment some contrary evidence comes to our attention, we must obviously particularize, i.e. retreat from our attempted generalization. This will be dealt with in more detail in the next posting, where factorial analysis will be introduced.

For more details on induction in general, see FUTURE LOGIC, PART V (only CHAPTERS 46-49), on adduction.

http://www.thelogician.net/2_future_logic/2_fl_part_5.htm

See also: PHENOMENOLOGY, chapter 7.1, on the principles of adduction; and RUMINATIONS, chapter 2 sections 1-13, for more details on induction.

2 Comment(s).

Posted by Rachel:

As an amateur scientist I find all this fascinating. Looking forward to the next post!
March 27, 2010 @ 7:19 AM

Posted by Rachel:

Fascinating. I'm looking forward to your next post.
March 27, 2010 @ 12:44 PM