This blog post is geared around establishing two propositions, and deriving two conclusions from them. The two propositions concern the logical ubiquity and necessity of predicate relativization, defined as the act of subdividing a subject term to challenge universal claims. Drawing on the Scholastic tradition of distinguo maiorem (“I distinguish the major premise”), I argue that it is always linguistically possible to distinguish between types or senses of a term—for instance, conceding that “volant birds” fly while denying that “biological birds” (like penguins) do. Furthermore, I contend that such relativization is always permissible in critical inquiry; the alternative, “simpliciter-insistence” (demanding terms be accepted simply as stated), would block the way of inquiry in too many cases, and hence, the right to distinguish is essential for resolving conceptual disagreements and navigating edge cases where definitions break down.
From these premises, I derive two conclusions regarding the indeterminacy of rules and the interpretation of texts. First, I give an analysis of Kripke’s “plus/quus” paradox, which shows that rules cannot be defined tightly enough to prevent future distinctions; this analysis refutes Edward Feser’s argument for the immateriality of the human mind. Second, I argue that interpretive systems relying solely on fixed texts without a living authority—specifically, legal Originalism and theological Protestantism (Sola Scriptura)—are functionally impossible. Because a “dead” or unavailable author cannot settle distinctions regarding ambiguous predicates (e.g., “cruel” punishment or “killing”), these systems cannot yield definitive rules for a community, necessitating a living authority (such as a Supreme Court or Magisterium) to ratify interpretations and halt the infinite regress of relativization.
(1) It is always possible to relativize a predicate. (This is an observation about language.)
It is a fundamental property of language and logic that it is always possible to relativize a predicate. In the course of any argument, when a speaker makes a universal claim—for example, “All Fs are Gs”—an interlocutor can always complicate the matter by subdividing the subject term F.
By “relativizing a predicate,” I mean the act of answering a universal claim by distinguishing between different senses or types of the subject. If the claim is “All Fs are G,” the relativizer counters by separating F into “A-type Fs” (meaning F understood in sense A) and “B-type Fs” (meaning F understood in sense B). The counter-claim then becomes: “All A-type Fs are Gs, but B-type Fs are not G.”
It is possible to relativize a predicate’s definition rather than the predicate. Even if we agree on the surface statement “All Fs are Gs,” we might disagree on what constitutes an F. Suppose we define F as “all-and-only the Hs that are J.” For example, let us define “bachelor” (F) as “an unmarried man” (H that is J). The relativizer might argue, “I grant that bachelors are unmarried men. However, I distinguish the term ‘man’ (H). All-and-only eligible, adult unmarried men (A-type Hs) are bachelors. But Pope Leo is an unmarried man (B-type H), yet we do not call him a bachelor.”
Predicate relativization has a rich history, most notably in the Scholastic tradition of medieval disputation. In these rigorous debates, the “proponent” would advance a syllogism, and the “opponent” was tasked with finding the flaw. If the proponent argued:
- All birds fly. (major premise)
- The penguin is a bird. (minor premise)
- Therefore, the penguin flies. (conclusion)
The opponent could employ the distinguo maiorem (“I distinguish the major premise”). They might argue: “That all volant-type birds (A-type) fly, I concede; but that all biological birds (B-type) fly, I deny.” By relativizing the predicate “bird,” the opponent dismantles the universality of the major premise and blocks the conclusion.
Analysis confirms that this move is always logically available. No matter how precise a term appears, language is sufficiently fluid that a distinction can always be introduced to carve the concept into accepting and rejecting sub-types. Hence, (1) is true.
(2) It is always permissible, in critical discussion, to relativize any predicate. (This is a normative claim about critical inquiry.)
Not only is predicate relativization always possible, it is always allowed in critical discussion, or inquiry. By critical discussion, I mean a truth-seeking discussion along the lines of what Frans van Eemeren and Rob Grootendorst meant by it when they defined their normative pragma-dialectical model of critical discussion. Eemeren and Grootendorst correctly point out that certain norms are required by the practice of a dispute-resolution process designed to ensure rationality; a core tenet, the Freedom Rule, is that parties must be free to advance any standpoint or cast doubt on any standpoint. I am arguing, then, that blocking the ability to make distinctions stifles this process and prevents the resolution of the underlying conceptual disagreement.
To see the necessity of relativization, consider the alternative, which we might call “simpliciter-insistence.” This is the stance of a debater who refuses to accept distinctions, demanding that terms be taken simply (simpliciter) as stated. Such an opponent of relativization would argue something like the following:
I am not talking about A-type Fs and B-type Fs. I reject the relevance of your distinction. The question was about whether Fs, taken simpliciter and without any extra predicates, are Gs. You may grant that the object of our discussion is a B-type F, and deny that it is an A-type F; but in doing this, you change the subject. You must commit to an answer on whether the object of our discussion is an F, simply speaking, just an F, without any extra predicates.
For instance, in a normative discussion about freedom: “I reject your distinction between positive and negative freedom. I am talking about freedom, period. By distinguishing, you are changing the subject. You must answer whether the object of our discussion is in accordance with freedom, simply speaking.”
The fatal flaw of simpliciter-insistence is that it collapses when faced with “odd cases out-of-domain.” These are edge cases where a predicate is applied to a subject outside its usual context. For instance, suppose we know what “addition”, or summing, means for numbers. We may also have an intuition that “addition”, or summing, is possible with concepts, not only with numbers. But then there are conflicting, equally plausible answers as to what adding concepts means. For instance, what is the sum of the concepts “rational” and “animal”? If we demand that adding the concepts means adding their intensions, we know that the sum of the concepts is “rational and animal”, i.e., a human. But if we demand that adding the concepts means adding their extensions, we know then that the sum of the concepts is “rational or animal”, a concept that applies to humans, dogs, and, if there are any, rational non-animals such as angels. These result in opposite logical operators (AND vs. OR). If one insists on “addition simpliciter” in the domain of concepts, the question is unanswerable.
The defender of simpliciter-insistence might reply by saying that we can solve this by restricting a concept’s domain of application. As the philosopher Alvin Plantinga said, after all, “No prime minister is a prime number.” The opponent of relativization can argue, then, that we can simply restrict the domain to clear cases, e.g., addition is only defined for numbers, not for concepts. Very well. But here we have a regress, since the domain itself can be relativized: do only natural numbers count as numbers, or possibly complex numbers, and even more foreign algebraic systems? If we restrict the domain to algebraic systems with a well-defined addition, this is the same as leaving it to a disputant’s linguistic intuition whether some particular case is addition or not, which was the original problem. And in any purported particular application of addition, we may deny that this particular application constitutes a number in the sense required by arithmetic, and hence that 2+2=4 is relevant to an issue. This is always doable fully in good faith, in a truth-seeking way.
If the simpliciter-insistence defender restricts the domain, the relativizer can always relativize the domain restriction. Because critical discussants must be able to navigate these boundary cases to reach truth, the right to distinguish (distinguo maiorem) must be preserved, and hence, (2) is true.
(3) Conclusions and implications.
If we accept that predicates can always be relativized (1) and that we must allow this in discourse (2), two profound implications follow regarding rule-following and textual interpretation.
(3.1) An analysis of the plus/quus problem.
The inevitability of relativization sheds light on the famous “plus/quus” paradox presented by Saul Kripke in his reading of Wittgenstein.
Kripke challenges us to prove that when we used the “plus” function in the past, we didn’t actually mean “quus,” where x quus y equals x + y if x, y < 57, but equals 5 otherwise. If we have never performed a calculation with numbers larger than 57, all our past behavior is consistent with both “plus” and “quus.”
Since we ordinarily talk about very universal and general laws of arithmetic, such as the axiom of induction, it is not possible that, when we used “plus” in the past, we meant “quus” as specifically defined by Kripke. Nevertheless, although “plus” is indeed defined well outside the range of 57, it is not well-defined for every arbitrary argument. There are always borderline cases (e.g., adding transfinite numbers, or adding symbols) where the definition breaks down. The Kripkean “quus” proponent is essentially exploiting the infinite potential for predicate relativization. We cannot define a rule so tightly that it pre-empts every possible future distinction or out-of-domain application.
Edward Feser’s case for the immateriality of the human mind rested largely on the plus/quus problem: Feser says neural and behavioral features of humans are consistent with multiple interpretations of our words, which suggests our words should be indeterminate, but in fact when we use words, we actually mean an absolutely definite concept which is not indeterminate between all concepts that are consistent with our past behavioral and neural features, and hence, our minds must be immaterial, wholly independent from our behavioral and neural features. I argue that human concepts are not, after all, all that determinate, since in fact infinitely many questions can be raised about them which the concepts themselves do not determine, and hence, Feser has not shown that the human mind is immaterial.
(3.2) The impossibility of Protestantism and Originalism.
Finally, the universal possibility and permissibility of predicate relativization poses a devastating challenge to systems of interpretation that rely solely on a fixed written text without a living authority that can answer questions about it, such as, specifically, legal Originalism about the U.S. Constitution, and theological Protestantism, resting on the Sola Scriptura principle. The challenge is that it is impossible to use these systems consistently to determine rules of belief or practice for a collectivity, such as the community of believers or the community of U.S. citizens.
This is because, if we have a written text by an author who is dead or otherwise unavailable to answer questions (either in person or through a representative), then it is not always possible to apply the text to issues of theory or practice and get a definite result, which is acceptable to all reasonable parties to a discussion about the text. In particular, we cannot always apply the Bible to get definite answers on theology and on moral law; and we cannot always apply the U.S. Constitution to get definite answers on how to judge a federal issue. Some examples of relativization:
Constitutional law: If the Constitution forbids “cruel and unusual punishment,” and we ask, “Is the death penalty cruel?”, we are asking for a judgment on a predicate. An opponent can always distinguish: “It is cruel in the modern sense (A-type), but not in the 18th-century sense (B-type).”
Theology: If the Bible says “Thou shalt not kill,” does this apply to war? One can distinguish: “It forbids murder (A-type killing) but allows martial combat (B-type killing).”
Originalism and Protestantism both rely on a “dead author” in our current, Barthes-inspired sense, i.e., the Founding Fathers or the author(s) of the biblical texts, respectively. Protestants may argue that the true author of the Bible is God, who is indeed living rather than dead, but this does affect my point here, which is that the author is unavailable to answer clarifying questions. Some Protestants may here press onward, by arguing that God is available to the individual believer via the “inner witness of the Holy Ghost”; but this does not change the case I was arguing, which is that it is impossible for Sola Scriptura to get a definite result, which is acceptable to all reasonable parties to a discussion about the text, and hence to determine rules for the community of Christian believers; this is, of course, obvious now, in light of the manifold splinters of the Protestant community since Luther’s time.
If the author is available to answer questions, either in person or through a representative, then he can settle the matter: “I meant A-type, not B-type.” But if the author is unavailable to discussants, and we do not agree that anyone on earth is his representative, then we are left with the text “simpliciter.” Because the text cannot distinguish its own predicates when faced with new contexts or edge cases, and because the author cannot respond to a distinguo maiorem, the reader is forced to supply the distinction, leading to a fork in how the predicate is understood.
Thus, without a living authority (such as a Supreme Court or a Magisterium) to ratify which distinction is authoritative, the text alone cannot yield definite answers to theoretical or practical problems. It remains forever open to the infinite regress of relativization.
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| Illustration for this blog post, drawn by Nano Banana. |
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