For some thousands of years “logic” was viewed as the “theory of inquiry” – “inquiry into inquiry” if you will. This was almost certainly the case with Plato, definitely the case with Aristotle, and by and large true throughout the history of Western thought right up to the revolution in symbolic logic that occurred with Frege, Dedekind and Peano in the late 19th Century. However, with these changes the notion of logic came to be swallowed up by formal and symbolic concerns.

Logic as the theory of inquiry was lost sight of leaving mathematical logic as the sole claimant to the title of “Logic.”

One might argue that this is simply as things ought to be. If there is to be a “theory of inquiry” then surely science and the philosophy of science fulfill this role. But surely such a claim has inverted the relationships involved, as well as narrowed the field of investigation rather gratuitously. For one thing, inquiry is not a mode of science, rather science is a mode of inquiry. Eliminating the theory of inquiry as a general pursuit in favor of the more particular issues of science and its attendant philosophies is to break the specifically logical relations of order and connection between them.

For one thing, science is not the only kind of reasoned inquiry that people engage in. An engineer engages in rational inquiry that only an unmerited abuse of language would call scientific. Similarly with a technician working on a car or a computer network. Each of these persons is inquiring into their respective subject matters, and the techniques that make their inquiries rational are matters that are themselves worthy of inquiry. But they are not scientists and their inquiries deserve to be understood on their own merits, rather than through a forced and unnecessary analogy with a different type of activity.

So collapsing such inquiries under the heading of “science” serves only to conflate the part with the whole and to invite equivocation. But do we really want to fall back on bypassed linguistic usages and refer to such inquiry into inquiry as “logic”? Mightn't we do better to invoke an altogether different term, such as “methodology”?

I would argue against such a move as well, and for many of the same reasons already given regarding the term “science.” Methodology is a part of inquiry, but only a part. There is also that facet of inquiry that involves the precise mapping of relations between relevant aspects of the subject matter, and the ordering and organization of information in appropriate implicative structures. In other words, inquiry into inquiry also necessitates a thorough understanding of those formal aspects of reasoning that have come to exercise exclusive claim to the word “logic.”

It is worth observing that even as formal logic swallowed the topic of logic whole, there were and are a few voices in the wilderness who continue to agitate for the more original meaning of the term. John Dewey was never comfortable with the merely symbolic approach to logic, and one of his most important works in his long and productive career was Logic: The Theory of Inquiry.¹ More recently, Jaakko Hintikka has been a forceful proponent of a return to the original sense of logic.² (One other notable point that Dewey and Hintikka share: they have both been honored with volumes in the Library of Living Philosophers series: http://philosophy.siuc.edu/llp/publications.html)

With these ideas in mind, various specifically logical questions begin to emerge that are neither reducible to mathematical formalisms nor exclusively scientific practices. Comparative questions suggest themselves – for instance, how are the forms of inquiry of a computer technician similar to or different from those of a medical doctor or an astrophysicist? What about logically sound forms of inquiry that evidently are not predicated upon the kinds of empirical bases that are critical to the above – ethical inquiry, for example?

Overlaps between formal and historical questions also emerge: for instance, what is the nature of a good definition? What kinds of logical processes can take a bad definition and improve it (an historical question)? Is a definition really “bad” if such processes can be applied to it, thus polishing it up? Are there examples of “good” definitions that ultimately failed for other types of logical reasons over the temporal course of inquiry?

The topic of ways in which inquiry can fail is certainly a rich area to explore. For example, it is the case that logic is not the same thing as epistemology. Epistemology – which is the theory of knowledge – is ultimately a theory of a final product. Logic as the theory of inquiry is fundamentally a theory about the processes that may or may not terminate in those products. So questions that emerge here include, is it possible for sound inquiry to fail to terminate – even in the long run – in epistemologically sound forms of knowledge?

Also, what sorts of activities might we identify that have long been recognized as of central importance to rational inquiry, but whose character as a specifically logical topic has tended to be overlooked? This question for me is frankly rhetorical, for I would propose an example that has long occupied a central place in my own work: the logic of measurement. The work of Krantz, Luce, Suppes and Tversky³ is in many respects definitive on the formal and mathematical aspects of the theory of measurement. However, there remain logical issues linking the formal aspects of measurement with its practical and methodological ones.

For example, how does any particular inquiry manifest the formal assumptions of measurement in its concrete activities? Are those formal assumptions and practical manifestations logically consistent, or might there be hidden presuppositions that undermine the overall practice? In addition, how might the theory of computable functions contribute to the theory of measurement? Clearly any effective act of measurement must be at least relatively computable.⁴ But this in turn raises the obvious question of how deep the connections go between measurement and computability in general.

Finally, since inquiry is not an exclusively scientific process, inquiry into inquiry evidently cannot be either. Indeed, since the topic is not – and cannot be – reduced to its purely formal, or methodological, or historical dimensions (and let us mention as well the psychological, sociological, biological, and economic aspects) then clearly it cannot be strictly encompassed by those disciplines either. Thus, insofar as a rigorous but synoptic approach is required, inquiry into inquiry – that is to say, Logic – is a peculiarly philosophical topic.

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Notes:

1. Dewey, John: Logic: The Theory of Inquiry, Southern Illinois University Press, Carbondale, 1991. Originally published by Henry Hold and Co., New York, 1938.
   
   
   
2. See for example his "Is Logic the Key to All Good Reasoning?" Argumentation 15: 35–57, 2001. Or, more generally, Hintikka's collection of essays in Inquiry as Inquiry: A Logic of Scientific Discovery, Kluwer Academic Publishers, Dordrecht, 1999.
   
   
   
3. Krantz, David H., Luce, R. Duncan, Suppes, Patrick and Tversky, Amos: Foundations of Measurement, volumes I, II and III, Dover Publications, Mineola,2007. Originally published by Academic Press, 1971 – 1990.
   
   
   
4. See, for example, chapter 16 of Computability, Complexity and Languages, Martin D. Davis and Elaine J. Weyuker, Academic Press, San Diego, 1983.