Saturday, February 03, 2024

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


Robert Kidd said...

I'd like to ask this apologist why his God did not preempt Human philosophers by giving a detailed account of induction in the Bible. I mean, if this is such a tricky conundrum that is impossible to solve by any other means, why wait and why do it through middlemen? apparently, this god did not think it important to human life.

Miles said...

I wish you'll have more articles in the future.

How about an analysis of modern presup arguments commonly used by Sye Ten, Eli Ayala and etc...


Robert Kidd said...

Hi Miles,

Perhaps my favorite article on this blog:

Miles said...

Eli Ayala just uploaded his video attempting to refute which I think is Objectivism.

Robert Kidd said...

Hi again, Miles. Thanks for bringing this to our attention. I found the video that I think you're referring to:
uploaded one day ago titled: Presup REFUTED?

I'm only 1:37 into it and already there is a fatal flaw: He thinks that existence as such needs to be accounted for. D'oh. And he's going to account for it by something he has no alternative but to imagine. Also since the presuppers define God as the being who created existence then his argument assumes the very thing it seeks to prove.

Will try to finish the rest and I may have some more comments to make.


Robert Kidd said...

Oh boy! Apparently, the statement "existence exists", and "A is A" are ambiguous statements because they don't explain what exists. Oh my, Dawson is going to have a field day with this.


Robert Kidd said...


Do you find this Ayala fellow convincing?


Bahnsen Burner said...

Thanks for surfacing the link to this, Robert. I'll try to find some time this weekend to take a look at it.

Been super busy the past few weeks, and it doesn't look like that's going to change any time soon.


Robert Kidd said...

Hi Dawson,

Thanks. The guy is trying to engage with something that he has no understanding of. A commenter on one of his videos criticized TAG from the perspective of Objectivism, appealing to the axioms and the primacy of existence. He explained that the axioms serve as the ground of knowledge and there is no need for a God to do this. I've left several comments and am engaged with two or three Christians. It's the same old song and dance. "Your axioms are just presuppositions and you can't justify them so you're in the same boat as everyone else. I've explained why this is false. I've answered every criticism. The producer of the video seems to think that the axioms the commenter presented are "ambiguous" since they don't tell us anything about what exists. I explained why this is not a problem, that they are not meant to tell us what exists. I explained that trying to justify existence results in stolen concepts. They are not buying any of it of course. They aren't interested in the truth, only protecting their mystical beliefs.

I only watched about 17 minutes and that was more than enough. He makes so many errors that it would take dozens of pages to correct them all.


Robert Kidd

Robert Kidd said...

Hi Dawson,

A skeptic over in the comments section of the video linked above has taken issue with the fact that I express certainty regarding the axioms being the base of knowledge. He claims that "everything is up for grabs". This is something I run into frequently. I handled it this way this time:

"I'm not saying "everything is subjective", I'm saying "everything is up for grabs". Those are very different things."

Actually, they are not very different. To say that "everything is up for grabs" is to say that man can have no knowledge of reality, that concepts are formed apart from reality and we can't know if they actually have any objective meaning. Therefore ideas are only subjective creations of the mind with no objective meaning. That would make all concepts floating abstractions.

The statement that it is "all up for grabs" is interesting. In all cases "Everything is up for grabs"? That would make it an absolute. But you claim that there are no absolutes.

The statement "everything is up for grabs" would also apply to itself, would it not? That would make it non-absolute.

If this is truly what you believe then I wonder:
Why engage in debate at all? I mean, after all, aren't the laws of logic up for grabs?

I'm just curious what your answer would be.


Bahnsen Burner said...

Thanks Robert. Happy Friday!

From what you describe, it sounds like so much of what we've seen and untangled already right here on IP. The objection that the axiom of existence fails somehow because it doesn't tell us what exists, is not new. If I recall, Paul Manata tried this one years ago.

As for objecting to certainty by insisting that "everything is up for grabs," I'd ask if that individual is certain that "everything is up for grabs." The notion that "everything is up for grabs" is not itself axiomatic in any way, but I'd challenge him to explain what that means and show how it applies to the axiom of existence. After all, it seems to be affirming the axiom of existence by referencing "everything." What is "everything" if not everything that exists? Even if it's intended to denote only a subset of things that exist, that implies a totality of existence on its face. To say that the axiom of existence is "up for grabs" suggests that one should have no confidence in it because it might not after all turn out to be true. But this only exposes the view that truth and reality are completely divorced from one another, suggesting something else must serve as its standard. If that standard is not some expression of subjectivity, then what is it? What is at the base of knowledge?

A big part of the impasse here so far as I can tell is that thinkers generally are unaware of the hierarchical relationship of concepts, even though their own statements confirm this kind of relationship. Just by stringing statements together to lead to a conclusion confirms this. If "everything is up for grabs," ask him why the statement "everything you say is wrong" cannot be one's starting point. Most likely the skeptic is not going to find that very satisfactory, but given his terminally fragmented understanding of knowledge, what problem can he find with it? Any objection he raises against it can simply be met with a re-affirmation of the would-be axiom that "everything you say is wrong," so his objections hit a wall as soon as they roll out of his mouth.

Anyway, I'm really trying to clear my calendar to get some time to look at my blog... I've been neglecting it because other responsibilities are quite pressing these days.


Robert Kidd said...

Good morning, Dawson.

Thank you for taking time out of your busy schedule to answer.

I like your comment that his statement assumes the axioms. I did point out to the author of the video in one of my comments that his starting point assumes mine. They just don't get it. But I try.