What is the Problem of Induction, and Why are Christians Uniquely Situated to Answer It?

[From a short article written for the ILIAD Forum.]

The problem of induction is a notorious philosophical problem concerning inductive inferences; more specifically, whether that form of reasoning is generally reliable or rationally justified. An inductive inference aims to draw a general conclusion from a series of particular observations. For example, if I observe one thousand swans, and every one of those swans is white, I can infer inductively that probably all swans are white, and on that basis predict that any future swans I observe will (probably) be white. Unlike deductive inferences, in which the conclusion follows necessarily from the premises, inductive inferences cannot deliver absolute certainty—for example, the possibility of observing a non-white swan in the future cannot be decisively ruled out—but all else being equal, the greater the number of past observations confirming a general law or pattern, the stronger the inductive conclusion becomes.

Inductive inferences have been widely used in scientific research to discover laws of nature. To take one example, Newton’s universal law of gravitation was inferred inductively from empirical observations of the attractive forces between two masses. We haven’t observed the forces between every pair of masses in the universe at every point in time, of course, so we don’t have direct and infallible knowledge of a universal law. Nevertheless, we have made enough observations to be confident that they are instances of a universal law, and we can make reliable predictions about future events by positing that the universal law holds.

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To Err is Humorous (2022 Edition)

I’ve finally finished all the grading for my Spring semester classes, so it seems fitting to celebrate by cracking open a bottle of Irn-Bru and posting a new collection of amusing typos drawn from various student assignments over the last five years. (For previous editions, see here and here.)

Once again, it’s only fair to repeat the qualification I included with the earlier postings:

I should emphasize that most of these are innocent mistakes and no reflection on the abilities of the students who wrote them. Some of them appeared in otherwise excellent papers. They’re the sort of errors any of us could make, and many of us have made, especially when under the pressure of a deadline or ambushed by the AutoCorrect feature of our word processors. So enjoy them, but don’t forget that these are human errors — and we’re all human.

In case anyone has doubts, let me assure you that all the following are 100% genuine. I hope you enjoy them as much as I did.

Molinism and Other Determinisms

In which it is argued that Molinists are determinists, but this is not to their shame.

Robert Kane is one of the world’s leading experts on the philosophy of free will. He’s the editor of The Oxford Handbook of Free Will and one of the contributors to Four Views on Free Will (Blackwell, 2007). He’s written dozens of articles on the subject of free will. So it’s safe to say he knows whereof he speaks when it comes to debates over free will.

Kane is an incompatibilist, which is to say, he believes that determinism is incompatible with free will (at least, the kind of free will needed for moral agency). But what is determinism? Here’s how Kane explains the term in his book A Contemporary Introduction to Free Will:1

An event (such as a choice or action) is determined when there are conditions obtaining earlier (such as the decrees of fate or the foreordaining acts of God or antecedent causes plus laws of nature) whose occurrence is a sufficient condition for the occurrence of the event. In other words, it must be the case that, if these earlier determining conditions obtain, then the determined event will occur. (pp. 5-6)

In more familiar terms, we say that a determined event is inevitable or necessary (it cannot but occur), given the determining conditions. If fate decreed or God foreordained (or the laws of nature and antecedent causes determined) that John would choose at a certain time to go to Samarra, then John will choose at that time to go to Samarra. Determinism is thus a kind of necessity, but it is a conditional necessity. A determined event does not have to occur, no matter what else happens (it need not be absolutely necessary). But it must occur when the determining conditions have occurred. If the decrees of fate had been different or the past had been different in some way, John may have been determined to go to Damascus rather than to Samarra. Historical doctrines of determinism refer to different determining conditions. But all doctrines of determinism imply that every event, or at least every human choice and action, is determined by some determining conditions in this sense. (p. 6)

Now here’s an interesting (to me) and perhaps surprising (to you) observation: According to Kane’s understanding of determinism, Molinism is clearly a species of determinism. (To use Kane’s phrase, it is a “doctrine of determinism.”) For according to Molinism, God has an infallible decree; God foreordains all things, including human free choices. As the Molinist will be quick to insist, God foreordains on the basis of his middle knowledge, that is, his knowledge of the counterfactuals of creaturely (libertarian) freedom. God “weakly actualizes” a possible world by creating agents with libertarian freedom and arranging their circumstances such that they freely choose what he has planned (on the basis of his middle knowledge) for them to choose. But the fact remains that on the Molinist scheme, despite its commitment to libertarian free will, God has an infallible decree and foreordains whatsoever comes to pass. As one prominent Molinist explains:

Not only does this view make room for human freedom, but it affords God a means of choosing which world of free creatures to create. For by knowing how persons would freely choose in whatever circumstances they might be, God can, by decreeing to place just those persons in just those circumstances, bring about his ultimate purposes through free creaturely actions. Thus, by employing his hypothetical knowledge, God can plan a world down to the last detail and yet do so without annihilating creaturely freedom, since God has already factored into the equation what people would do freely under various circumstances.2

Thus, according to Molinism, if God has foreordained that Sam mows the lawn next Saturday, then Sam will mow the lawn next Saturday. God’s act of foreordination is a sufficient condition for Sam’s action (P is a sufficient condition for Q if Q necessarily follows from P) and therefore, according to Kane, Sam’s action is determined by prior conditions, namely, God’s act of foreordination. (Notice that Kane explicitly includes “the foreordaining acts of God” among his examples of determining conditions.)

  1. Robert Kane, A Contemporary Introduction to Free Will (Oxford: Oxford University Press, 2005).
  2. William Lane Craig, “God Directs All Things,” in Four Views on Divine Providence, ed. Dennis W. Jowers (Grand Rapids, MI: Zondervan, 2011), 82, bold added.

What are Worldviews, and Why Should University Students be Mindful of Them?

[From a short article written for the ILIAD Forum.]

As the word itself suggests, a worldview is an overall view of the world. It isn’t a physical view of the world (like the sight of planet Earth you might get from an orbiting space station) but rather a philosophical view of the world—and not just of our planet, but of all of reality. A worldview is an all-encompassing perspective on everything that exists and matters to us. A worldview represents a person’s most fundamental beliefs and assumptions about the universe they inhabit. It reflects how they would answer all the “big questions” of human existence, the fundamental questions we ask about life, the universe, and everything.

Worldviews matter, in the first place, because everyone has one, although not everyone is aware that they have one. A worldview is as indispensable for thinking as an atmosphere is for breathing. You can’t think in an intellectual vacuum any more than you can breathe without a physical atmosphere. Most of the time, you take the atmosphere around you for granted; you look through it rather than at it, even though you know it’s always there. The same goes for your worldview: normally you look through it rather than directly at it. It’s essential, but it usually sits in the background of your thought.

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In What Ways is God the Foundation for all Knowledge?

[From a short article written for the ILIAD Forum.]

According to a Christian worldview, God is the foundation of all knowledge simply because God is the ultimate foundation for everything in the most general sense. God is a maximally perfect being and therefore is perfect in knowledge: God knows infallibly and comprehensively every truth that there is to know (Ps. 139:1–16; Isa. 44:6–7; Isa: 46:8–11; Heb. 4:13). Furthermore, God is the creator and sustainer of everything else, including human beings and any other creatures (e.g., angels) who have the capacity for knowledge (Gen. 1:1, 27; Heb. 1:1–3; Heb. 11:3; Rev. 4:11). In other words, our knowledge—like everything else we possess—is a gift from God, and all human knowledge is derivative of divine knowledge. As it has often been said, we have been created by God “to think God’s thoughts after him.” Although from our perspective we regularly discover “new truths” and extend our collective knowledge, human knowledge is never truly original in any absolute sense, but only reflective and reconstructive of God’s knowledge (and even then, in a very limited fashion).

Thus, we might say, the Christian worldview affirms a “revelational epistemology”: all human knowledge is ultimately dependent upon divine revelation. Put simply, we can know truth only because God has revealed truth to us—about himself, about ourselves, and about the world around us (scientific truths, historical truths, and so forth). Christian theologians have often distinguished between two basic forms of divine revelation:

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Does Predestination Make the Problem of Evil More Pressing?

[From a short article written for the ILIAD Forum.]

This is a tough question to answer in a short space, not least because it ties together two complex and controversial topics! Let’s begin with some basic definitions. The problem of evil refers to the challenge of reconciling the reality of evil with the existence of an all-good, all-powerful God. If God is all-good, presumably he would want to prevent all evil. If God is all-powerful, presumably he would be able to prevent all evil. How then can God and evil co-exist?

As many Christian philosophers have pointed out, the apparent logical conflict can be resolved once we recognize that God could have morally sufficient reasons for permitting an evil; for example, if permitting that evil were necessary to accomplish some greater good. Thus, there is no inherent conflict between the existence of an all-good, all-powerful God and the existence of evil. This insight points us in the direction of a greater-good theodicy: a more detailed explanation of why God permits various evils within the world, whether natural evils (such as diseases and earthquakes) or moral evils (such as murders and rapes). Christian thinkers have developed and defended a variety of greater-good theodicies, but it’s enough for our purposes here to recognize that such theodicies exist and many of them are complementary (i.e., they can be combined to address a wide range of different evils).

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The ILIAD Forum

Readers of this blog may be interested to know about a new online resource, the ILIAD Forum. (‘ILIAD’ stands for Ivy League Informational Apologetics Database.) According to the website:

The Iliad Forum was founded in 2021 by undergraduate students from all across the Ivy League, who wanted to provide an online, accessible, and rigorous database of answers to common questions about the nature and commitments of orthodox Christianity. The Iliad Forum site is intended to be a resource for both Christians and non-Christians, where answers to deep and complex questions and objections can be found almost immediately. Many of the questions that we deal with are tailored to the specific interests of undergraduate students at Ivy League universities. However, we also deal with broader topics, such as Christianity in the job market, philosophical apologetics, and Biblical history.

The website already contains dozens of short articles in answer to a wide range of questions. The articles are written by scholars with expertise in the relevant area, including Vern Poythress, William Edgar, and Scott Oliphint.

I was invited to submit answers to five questions in the area of philosophical theology and apologetics. I gather the articles will be posted on the website at intervals, so I’ll post the links here as they become available.

On Malpass’s Dilemma

Alex Malpass has offered one of the most thoughtful critiques of the argument for God from logic in his 2020 Sophia article, “Problems for the Argument from Logic: a Response to the Lord of Non-Contradiction.” Here’s the abstract:

James Anderson and Greg Welty have resurrected an argument for God’s existence (Anderson and Welty 2011), which we will call the argument from logic. We present three lines of response against the argument, involving the notion of necessity involved, the notion of intentionality involved, and then we pose a dilemma for divine conceptualism. We conclude that the argument faces substantial problems.

In this post I will share some thoughts on the third of these “three lines of response,” which I take to be the most interesting point of criticism.1 (Note: I’m speaking only for myself in this post; Greg can speak for himself!)

The argument for God from logic involves defending a version of divine conceptualism (or better, “theistic conceptual realism,” to use Welty’s terminology) according to which the laws of logic, as necessarily true propositions, are ultimately just divine thoughts. Strictly speaking, the argument can be run from any necessary truths, not just the laws of logic, but the laws of logic serve as familiar and convenient examples of necessary truths.2

Horns of a DilemmaIn the last major section of his article, Malpass presents a “dilemma for divine conceptualism.” Rather than quote him at length, I will try to summarize the thrust of his challenge. He begins by observing that parts of our argument appeal to a distinction between “thoughts and the content of those thoughts” (see, e.g., footnote 31 of our 2011 article). But then he points out that this seems to raise a problem for the claim that propositions are divine thoughts. In the first place, he argues, “a thought cannot be the content of itself” (p. 251). The idea that a thought can be its own content is either flat-out incoherent or leads to a “vicious infinite regress” (p. 252). To avoid this, the divine conceptualist has only two options:

  1. A divine thought has no content.
  2. A divine thought has content distinct from the thought itself.

Option 1 looks like a non-starter. If divine thoughts have no content, they can’t be about anything. Isn’t it obvious that God’s thought that 2+2=4 is contentful? Doesn’t it have some content that distinguishes it from other thoughts (e.g., God’s thought that Socrates is mortal)?

Option 2, however, doesn’t look any more promising. Recall our contention that the laws of logic, as necessarily true propositions, are a special category of divine thoughts. Let LL be some proposition that expresses a law of logic (e.g., the law of non-contradiction). LL is ultimately just a divine thought, so we argue. But according to option 2, the content of LL is something other than LL itself. So what could it be? Presumably that content would have to be propositional or intentional in nature. But it couldn’t be a proposition other than LL, for two reasons. First, that would mean LL has the wrong content; the divine thought would be about something other than what it’s supposed to be about. To use Malpass’s example, LL couldn’t have the Pythagorean theorem as its content; it’s supposed to be about the law of non-contradiction, not a geometrical theorem. The second reason is that if the content of LL is a proposition, but not LL itself, then it must be some other proposition, and therefore (given divine conceptualism) some other divine thought. Call that other divine thought LL*. But then the same considerations will apply to the content of LL*, in which case we’re on the road to a never-ending regress of divine thoughts containing divine thoughts, their content being endlessly deferred.

  1. This criticism also came up in our conversation last September hosted by Parker Settecase.
  2. As we note in our paper, someone might take the laws of logic to be something other than propositions (e.g., relations), but in that case we can simply restate the argument in terms of necessarily true propositions about the laws of logic.