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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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.

Interview with Rooted In Revelation

A few weeks ago I was interviewed about my book Why Should I Believe Christianity? by Nate and Nick from the Rooted In Revelation podcast. The interview has now been posted on YouTube:

It was a fun conversation, covering a range of topics in Christian apologetics. Check out the other videos on their channel while you’re at it. They include interviews with John Frame, Scott Oliphint, Guy Waters, Benjamin Gladd, Jim Newheiser, Jared Oliphint, Chris Bolt, and other good folk.

A Conversation with Alex Malpass

Last week I had the pleasure of interacting with British philosopher Dr. Alex Malpass on the topic of the argument for God from logic. (Many thanks to podcaster extraordinaire Parker Settecase for hosting and moderating the discussion.) Dr. Malpass recently published an article in the journal Sophia in which he leveled several objections at the Anderson-Welty argument. Here’s the abstract for the article:

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 our 90-minute-or-so live-broadcast discussion, Dr. Malpass summarized his three criticisms and I gave responses to each one. We also fielded a few questions from viewers. In the end, there was a surprising (but gratifying) amount of agreement between us regarding some of the logical and metaphysical issues at stake, even though Alex remains unpersuaded by the argument! Anyway, you can watch the exchange and draw your own conclusions:

Be sure to watch right to the end, where the two Brits are invited to weigh in on the contentious coffee-versus-tea debate.

I’m grateful to Dr. Malpass for his willingness to participate in what proved to be an illuminating and good-humored discussion, and I look forward to further exchanges (including, I hope, a published response to his article). For those interested, Dr. Malpass has his own blog here.