Concepts and Induction

Years ago I was in correspondence with a Christian apologist who presupposed that Christianity and only Christianity could solve the problem of induction. There were many Christians at one time who actually believed this. Perhaps some still do.

This apologist carefully demonstrated how a number of prominent academic treatments of the matter missed the mark, sometimes by wide margin, when it came to providing a justification for inductive presuppositions. The apologist of course claimed that the existence of a universe-creating deity which actively “ordains and sustains” the “created order” provides the rational justification which secular scholars could only miss due to their chronic “unbelief.”

It was never made clear what exactly the supernatural being’s alleged existence has to do with inferences which human thinkers perform on the basis of limited samples to wider generalizations, but I suspect that at the end of the day, this really doesn’t matter to the apologist: once he has asserted the existence of his god, even if doing so moves us no closer to understanding the problem it supposedly solves, he believes his task is complete.

After reviewing what the apologist presented, I stated that I'm always surprised, when reading apologetic treatments of induction, that there is no discussion of concepts, the nature of their forming, or their relationship to inductive generalization, as if these issues did not matter.

To this, the apologist confessed by way of reply:

It's not immediately obvious to me how the nature of concept formation bears either on the description of the problem of induction or on the development of cogent solutions. Perhaps you can elaborate.

Here’s a handy way to look at this: concepts are in essence mini-generalizations; that is, a concept is a single dynamic unit of mental integration which contains all instances of an entire category of things, qualities, attributes, even actions, including those instances which we have not perceived directly, even those which we will never perceive. Concepts expand an individual’s awareness beyond what he perceives, either in the moment or across his lifetime. A concept is dynamic in the sense that we can continually add more data to it, packing it further and further with more information that we learn about the nature of the existents which the concept subsumes.

The concept ‘table’, for example, includes all tables – not only those tables which exist now, but all tables which have ever existed in the past, and all tables which will exist in the future. It includes all tables in my neighborhood, in my county, in my nation, in the world, regardless of where they might exist. The scope of reference of a concept in its rawest state is not bound by temporal or locational constraints. Nor is a concept restricted to some quantity of instances – it is potentially infinite in this sense: there is no limit to how many tables can be included in the concept ‘table’.

To confirm this understanding of concepts, notice how we must qualify our use of concepts in order to narrow the scope of our intended reference. If I say “tables are brown,” one might immediately recall from memory seeing tables that are white, grey, light blue, tan, black, etc. As an unqualified pronouncement, the statement “tables are brown” is unreservedly general in nature, implying an affirmation about all tables, because the concept ‘table’, constituting a mini-generalization, is unqualified. But if I say “This table is brown,” hearers will understand immediately that I am speaking about a specific table rather than all tables, because I have used the qualifier “this” to enhance the meaning of the concept ‘table’ in my utterance. If concepts were not a kind of generalization already, without qualification, such qualification would not be necessary.

With this rudimentary understanding of the nature of concepts in mind, now it really should be “immediately obvious” that at the very least concepts have something to do with induction. If we recognize that concepts are in fact essentially mini-generalizations, then any expressly inductive inference which makes use of concepts is already drawing on a well of previously generalized data, arguably even taking the generalizing dynamics of concept-formation as an implicit model.

One might suppose, then, that a conceptual analysis of induction simply moves the problem of induction back a step. Indeed, if one is hard-pressed to provide a justification for the generalization “all multi-storied buildings require structural engineering,” especially when no thinker has had occasion to examine every multi-storied building which has ever been built (or will be built in the future), how much more difficult would it be to justify our formation of the concept ‘building’ in the first place?

That’s a great question!

To which we put the question back on the apologist: how does Christianity account for concepts? Since induction depends on concepts, and concepts already expand our awareness from immediately perceptible samples to broad generalities, Christianity would need to provide an account for concepts if we’re to take the claim that Christianity and only Christianity can justify induction seriously. But herein is the problem: Christianity has no theory of concepts to begin with. So how can Christianity at all factor in any kind of answer to the problem of induction?

It cannot.

Meanwhile, I refer readers to Ayn Rand’s Introduction to Objectivist Epistemology for the best theory of concepts I’ve ever examined. And I’m happy to report it’s not all that mysterious after all. There’s certainly no justification for asserting the existence of a supernatural mind for which there is no objective evidence whatsoever. Of course, if readers know of something better, please share your discovery in the comments section.

The Christian view seems to be that the problem of induction is best answered by asserting the existence of an omniscient mind which has comprehensive a priori knowledge of the universe since it wished the universe into being and is said to have “revealed” itself through human artefacts, such as fantastical writings handed down through the ages. As the creator of the universe, it would know everything about the universe, right? Again, it is unclear how this moves us any closer to understanding the cognitive process which the human mind performs to take us from “this egg broke when I dropped it onto the floor” to “all eggs will likely break when dropped on a hard surface.” If I imagine the Christian god (what alternative do I have other than to imagine it?), how does that in any way enlighten me as to how I draw general conclusions from isolated samples? It doesn’t. Even if I believe there’s a supernatural being which has all possible knowledge of the universe, that would not explain how I draw even the most rudimentary generalization. It does not even explain how I can form the simplest concepts. I can only suspect that theists making this kind of claim (to wit: “only Christianity can account for induction”) are taking so much for granted with respect to the operations of human cognition that they fail to grasp just how hollow their apologetic gambit is.

Back in 2007 I posted an entry here on Incinerating Presuppositionalism addressing the provocative question: Would an Omniscient Mind Have Knowledge in Conceptual Form? The Christian god is said to be all-knowing and all-seeing (cf. Job 34:21, Prov. 15:3, Heb. 4:13, et al.).

A. W. Tozer, in The Pursuit of God, describes it as follows:

He is omniscient. He knows in one free and effortless act all matter, all spirit, all relationships, all events. He has no past and He has no future. He is, and none of the limiting and qualifying terms used of creatures can apply to Him. (p. 45)

My answer to the question in the title of that entry is that an omniscient mind, being one which has immediate and direct awareness of everything that exists, that has existed, that will exist, etc., would have no need for concepts. Concepts would be useless to such a mind for it would have the capacity to have direct awareness of each and every particular in existence at all times, something the human mind cannot do. It is because human beings lack such a capacity that we need to economize our mental activity by forming concepts. This has implications for induction: where a human mind would need to infer that “all multi-storied buildings require structural engineering” – an inference which takes man’s awareness far beyond the range of what he has personally observed, an omniscient mind would have direct awareness of all buildings and their physical requirements without any need to make any inferences, for it would not need to perform any kind of mental action to expand its awareness beyond the range of what it can observe – it would already be observing everything. Concepts and induction, then, are human capacities, and problems pertaining to these capacities require human solutions. Pointing to an omniscient mind, then, misses the fundamental natures of concepts and induction as well as why they are essential to human cognition.

So, to address the apologist’s confession I quoted above: One thing we can know with certainty is that thinkers will not be sufficiently equipped to explain and justify induction without a good understanding of the nature of concepts and how they factor in inductive thinking. Since we find no information about the nature of concepts or their formation in any of the books of the Christian bible, where would Christians go to get a <i>distinctly Christian understanding</i> of the nature of concepts?

by Dawson Bethrick