Yandell’s Presentation and Analysis of the First Way

Keith E. Yandell was a respected philosopher at the University of Wisconsin-Madison, retiring in 2011. He specialized in the philosophy of religion, and wrote the philosophy of religion volume for the Routledge Contemporary Introductions to Philosophy series (which I highly recommend). In that volume, he included a chapter on arguments for monotheism, and spent a considerable space examining some of Aquinas’s famous “five ways.”

The five ways are some of the most well-recognized arguments for the existence of God in the history of philosophy. They are also, at least in modern times, some of the arguments least understood and most mischaracterized. Which is why I so greatly appreciated Yandell’s treatment, which is fair, nuanced, and unique. Here I will examine his account of the first way.

One of the strength’s of Yandell’s presentation is that he spends a good number of pages simply laying terminological and conceptual groundwork before actually looking at the arguments themselves. What makes Yandell’s versions of these arguments unique is that he “updates” them to be more congenial for a contemporary analytic audience. In doing so, he also steelmans them, attempting to formulate them as rigorously as he can.

Yandell begins his conceptual backdrop by distinguishing between reflexive and irreflexive relations. He defines these as follows:

Definition 1: Relation R, holding between X and Y, is reflexive if X has R to Y entails Y has R to X.

Definition 2: Relation R, holding between X and Y, is irreflexive if X has R to Y entails Y does not have R to X [1].

He provides examples of each type of relation. An instance of a reflexive relation would be the relation “being the same height as.” If Jack is the same height as Jill, then, necessarily, Jill is also the same height as Jack. In other words, if two people are the same height as each other, then both have the same height as the other. On the other hand, an instance of an irreflexive relation would be “being the father of.” If Tim is the father of Tom, then, necessarily, Tom is not also the father of Tim.

Next, Yandell presents a terminology of relational direction. He writes: “If X has R to Y then X has R forwardly to Y, and . . . Y has R backwardly to X. Reflexive relations between X and Y are had both forwardly and backwardly by both X and Y. Irreflexive relations between X and Y are had only forwardly by X and only backwardly by y” [2].

Another way to put this might be to say that a reflexive relation can be “reversed” while an irreflexive relation cannot. Take any relational proposition of a general form X : R : Y (where X and Y are the two terms of the relation, and R just is the relation). For any reflexive relation, the terms can be “switched” while the relation stays the same, and the resulting proposition would still retain the same truth-value. If R is a reflexive relation, then X : R : Y has the same truth-value as Y : R : X. For any irreflexive relation, the terms cannot be so switched while the relation stays the same and the resulting proposition retaining the same truth-value. If R is an irreflexive relation, then X : R : Y does not have the same truth-value as Y : R : X.

Yandell then (thankfully) distinguishes between chronological and concurrent causes or causal series. This distinction, as Thomists tirelessly reiterate, is absolutely crucial to understanding the present arguments. Here is how Yandell explains the distinction:

Definition 3: X is a chronological cause of Y if and only if X’s doing something or having some quality at some time before T is necessary for Y at T.

Definition 4: X is a concurrent cause of Y if and only if X doing something or having some quality at T is a necessary condition of Y at T [3].

Cases of chronological causation are relatively obvious: Peter leaving his house is a cause of Peter arriving at the grocery store. Susan eating oatmeal is a cause of her stomach digesting said oatmeal. The assassination of Archduke Ferdinand was a cause of World War I. Cases of concurrent causation are somewhat less obvious and more controversial. Yandell mentions the following examples: “Holding a door to keep it open; holding one’s breath to keep one’s lungs full; pushing the bell to keep the bell ringing” [4]. Each of these examples might be challenged; but for now we will simply note the conceptual distinction between chronological and concurrent causation.

Yandell makes a few further distinctions, but we can skip over these and take a first look at his actual formulation of Aquinas’s first way:

  1. Some things change.
  2. If X changes at time T then there is something Y that changes X at T [understood as that Y is something different from X].
  3. Either (a) there is an infinite series of changed and changing beings (i.e., a series each member of which is both a changed and a changing thing) or (b) there is some being that is a changing being (a cause of motion/change) but is not a changed being (something that changes).
  4. Not-(a).
  5. So (b) [5].

The technical terminology introduced before is not mentioned explicitly in this formulation of the argument, but it does highlight the points necessary for an argument of this structure to succeed. Yandell contends that, for the first way to be successful, the following must be true: i) Y changes X (i.e, Y is the cause of X changing) is an irreflexive relation such that Y stands in relation “cause of change for” only forwardly to X and X stands in relation “being changed by” only backwardly to Y; ii) Y changes X is an instance of concurrent causation; iii) any series of items ordered by a relationship of concurrent irreflexive dependence is necessarily a finite domain.

I agree with Yandell that each of i), ii), and iii) being true is necessary for the success of the first way. But Yandell thinks that the first way is ultimately unsuccessful insofar as each of i), ii), and iii), even if true, are not obviously true and are not supported by the first way itself. In other words, if one has no reason to accept i), ii), or iii), then one has no reason to accept the conclusion of the first way.

Let’s examine these points a bit further. Why does the argument require that i) be true? For one thing, if i) is not true, it would be theoretically possible for X and Y to be identical, i.e. for X to be the cause of its own change. This would be an instance of “self-change,” the possibility of which, as Yandell notes, “was hotly disputed in the Medieval period”, and for which Scotus “offered powerful arguments against Aquinas” [6]. So Yandell takes it as plausibly true that there are genuine instances of self-change. But wherever there is self-change, there is not an extended series of changed and changing things; and if there is no such series, there is no ultimate “first member” of the series, arrival at which is the aim of the argument.

Why is it the case that if i) being true rules out the possibility of self-change? The idea is that without a constraint/specification like the one provided by i), it is left ambiguous and open as to whether the relation between X and Y in the proposition “Y changes X” is actually a relation of identity. Consider the proposition “The dog changes itself.” This proposition is the same in form as Y changes X, but here the two terms are actually identical: the dog is identical with itself. But i) rules out the possibility of the relation in propositions of the form “Y changes X” being one of identity. For it is impossible that in any irreflexive relation the terms be simply identical. Or, in other words, every relation of identity is necessarily a reflexive relation. For recall that, for any irreflexive relation, we are not able to “switch” the terms while maintaining the same truth-value of the proposition expressing that relation. But if two terms are actually identical, the truth-value of a proposition should stay the same if the terms in the relation it expresses are switched. So, in summary, since i) stipulates that in a proposition of form Y changes X, the relation expressed is an irreflexive one, necessarily the two terms of the relation are non-identical; and hence if i) is true, self-change is impossible.

Next, what is the function of ii) with respect to the overall argument? The short answer is that, for Aquinas, ii) carries a lot of weight. For one thing, Aquinas thinks that an infinite series of chronological causation is theoretically possible, such that, given a series of chronological causation, it is not absolutely necessary that the series terminate in a first member. On Aquinas’s view, it is series of concurrent causation which necessitate a first member. Thus, in this respect, ii) is necessary for defending the truth of premise 4 in Yandell’s formulation of the argument. There are a number of other significant considerations which a full account of the first way would need to recognize, but the above is sufficient for present purposes.

Finally, what is the function of iii) with respect to the overall argument? Like ii), the truth of iii) is necessary for establishing the truth of premise 4. If iii) is false, then it is theoretically possible for there to be an infinite series of changed and changing things. If this is possible, then it is not justified to conclude that necessarily there is a first member of the series of changed and changing things, a member which changes other members but is not itself changed.

iii) introduces terminology that we have not yet explicitly defined. Briefly, a series S is “ordered by an irreflexive relationship” just in case that for every member M of S, M stands in an irreflexive relation R to some other member (either forwardly or backwardly); and R is the same for every M. Yandell provides the following example: suppose that Al is the father of Bob, and Bob is the father of Carl. “Being a father” is an irreflexive relation. So in the series Al, Bob, and Carl, each member has a standing with respect to the irreflexive relation “being a father”, although one member (Al) has this relation only forwardly (Al is the father of Bob, but with respect to this domain, Al has no father), one member has the relation both forwardly and backwardly (Bob’s father is Al, and Bob is the father of Carl), and one member has the relation only backwardly (Carl’s father is Bob, but Carl is not the father of anyone). Furthermore, it is the same irreflexive relation (fatherhood) that each member has (either forwardly or backwardly). As such, we can say that the series whose members are Al, Bob, and Carl is, with respect to the relation “being a father”, ordered by an irreflexive relationship.

Second, “irreflexive dependence” refers to an irreflexive relation where one term is in some sense dependent on the other. Let propositions of the form A : R : B express irreflexive dependence just in case R stands for some dependence relation and R is irreflexive.

Finally, a finite domain is simply “a collection having a finite number of members” [7].

Consider, then, a series of changed and changing things as picked out in Yandell’s formulation of the first way. Say A is being changed, and B is changing A (i.e. B is the cause of A’s changing, or B is causing A to change). But, C is changing B. Let this series S be a series ordered by a relationship of concurrent, irreflexive dependence. A, in order to be changed, depends on B; and B, in order to be changed, depends on C. So A stands in a dependence relation to B, and B stands in a dependence relation to C. Call this relation R. Given i), R is an irreflexive relation. On supposition, it is a concurrent relation. If S is exhausted by members A, B, and C, then, like the series with Al, Bob, and Carl, one member has relation R only forwardly (A), one member has R both forwardly and backwardly (B), and one member has R only backwardly (B). A is changed by B but does not change anything, B changes A and is changed by C, C changes B but is not changed by anything.

But now suppose that S is not exhausted by A, B, and C. Suppose C is further changed by D, and D by E. Now the question becomes: can S be infinite, either forwardly or backwardly? Is it possible for there to be a series of item, ordered by a relationship of irreflexive dependence R, where each item has R both forwardly and backwardly? Consider the following options:

Option 1: S is simply finite just in case S contains one member which has R only forwardly, and S contains one member which has R only backwardly.

Option 2: S is infinite forwardly (finite backwardly) just in case S contains one member which has R only forwardly, and S contains no members which have R only backwardly. (Alternatively: S is infinite forwardly just in case every member of S has R forwardly, one member of S does not have R backwardly, and no member of S has R only backwardly).

Option 3: S is infinite backwardly (finite forwardly) just in case S contains one member which has R only backwardly, and S contains no members which have R only forwardly. (Alternatively: S is infinite backwardly just in case ever member of S has R backwardly, one member of S does not have R forwardly, and no member of S has R only forwardly).

Option 4: S is simply infinite just in case every member of S has R both forwardly and backwardly.

The overall aim of the first way is to conclude that there is some being which has R backwardly but not forwardly (here, have R backwardly means causing another member of the series to change; while having R forwardly means being caused to change by another member of the series). So, to be successful, the first way needs Option 4 and Option 2 to be ruled, since both of these deny that there is any member of S which has R backwardly but not forwardly. So we actually need to modify iii) to something like iii*): Any series of items ordered by a relationship of concurrent irreflexive dependence is necessarily a finite domain, either by being simply finite or by being at least finite forwardly (where “being finite forwardly” for irreflexive dependence relation R orients the terms of the relation such that A has R forwardly with respect to B just in case A is relatively dependent on B, but not B on A).

To reiterate: if there is a series S ordered by a relationship of concurrent irreflexive dependence R that is simply finite, such a series will necessarily have a member that has R only backwardly and not forwardly. If S is finite forwardly, S will likewise necessarily have a member that has R only backwardly. The first way requires that be a member of S that has R only backwardly, so the first way requires that S be either simply finite or at least finite forwardly.

Now that we have explained why the success of the first way necessitates the truth of i), ii), and iii*), we can turn to Yandell’s evaluation of the argument as a whole. Yandell concludes that the first way is unsuccessful as a proof because each of i), ii), and iii*) are unsubstantiated. With respect to iii*) he writes: “It is not obvious that the world of physical things and non-divine minds is a finitely large domain of things ordered by the relationship of non-reflexive dependence” [8]. With respect to i) he suggests that it is plausible that there be instances of self-change. And with respect to ii) he writes that “It is not obvious why there cannot be an infinite series of changed and changing things, whether we have chronological or concurrent cases of causation in mind”, and, after evaluating Aquinas’s own argument against such an infinite series, concludes that “Thus the First Way seems not to be a proof of its conclusion” [9].

What should we make of this evaluation? For the most part, I think that Yandell is largely correct. He is correct that the success of the first way depends upon the truth of i), ii), and iii); he is correct that i), ii), and iii) are not “obviously true” (in the sense that any person who considers them will be immediately compelled by them); and he is also correct that at least ii) is not explicitly defended in the text of the first way itself. Though the first way does offer defenses of i) and iii), these defenses presuppose a deep metaphysical backdrop which the average reader today (even among professional philosophers) does not understand.

And this brings me to a crucial point, a point which has been driven home for me more and more recently: there is a certain disconnect between the scholastic and the analytic approaches to arguments of natural theology which creates something of a disadvantage for the scholastic. As I have said elsewhere, the scholastics, perhaps more than any other era of philosophers, were thoroughly systematic thinkers. Their systems have been likened to both grand gothic cathedrals and complex living organisms, in which every part can only be understood in reference to the whole. Every principle, every conclusion, is interconnected and interwoven with every other. This is, in my view, a triumph and a strength; but it also creates undeniable difficulties for the modern mind. Learning and engaging the scholastics is particularly challenging for contemporary analytics, insofar as the latter wants to analyze a single argument on its own. You can analyze an individual part of a gothic cathedral on its own, but necessarily there will be a certain incompleteness to it; for the part was made for and in the whole. Similarly, a single argument from Aquinas can be outlined and evaluated, but there will again be an incompleteness to it.

Let me be more specific. The scholastics inherited and developed a particular understanding of scientific/philosophical method and procedure from Aristotle (passed through the Neoplatonists). For them, a “science” is to be constructed as a wholistic edifice from the ground up, starting from first principles as the necessary foundation. Without the foundation, the structure cannot stand; it collapses. So it is no wonder that an analytic examining one of the five ways on its own judges that it does not prove its conclusion, anymore than it would be a wonder that the branches of a tree fall to the ground unsupported by a trunk with deep roots. For the scholastics in general and Saint Thomas in particular, the question of God’s existence belongs to the science of metaphysics, and so depends on prior metaphysical principles and conclusions. This is something many analytics struggle with, for whom it is a virtue that an argument be as free from “metaphysical baggage” as possible.

Where does this leave us? My own position is that there are strengths to both traditions, and that both can benefit from dialogue and engagement. But in order to actually engage with a tradition, one must, to an extent, enter into that tradition and seek to understand it on its own terms. On the other hand, it can also be useful for one tradition to “translate” its concepts to the language/framework of the other, even while admitting that necessarily some elements will be lost in translation.

For instance, Yandell provides the scholastic with a fantastic outline for how one might translate the five ways into an analytic context. And yet this translation is still imperfect and incomplete. Earlier I praised Yandell for his making the distinction between chronological and concurrent causation; but this distinction still does not capture the nuance of the scholastic understanding of per se and per accidens causation. In the end, the only complete way to understand the scholastic arguments is to understand the scholastic systems.


[1]. Keith E. Yandell. Philosophy of Religion: A Contemporary Introduction. Second edition. New York: Routledge, 2016. Page 131.

[2]. Ibid.

[3]. Ibid., 132.

[4]. Ibid.

[5]. Ibid., 134.

[6]. Ibid., 134-135.

[7]. Ibid., 132.

[8]. Ibid., 133.

[9]. Ibid., 136.

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