Are Logical Disputes Genuine or Merely Verbal?

1. Quine's Meaning-Variance Thesis: "Change of Logic, Change of Subject"

The starting point for this debate is a powerful and influential argument from W.V.O. Quine, which has come to be known as the meaning-variance thesis. At its core, the thesis claims that when logicians appear to disagree about a fundamental logical law, they are actually failing to talk about the same thing.

To understand this challenge, let's turn to a paper that lays out the problem very clearly.

As Hjortland explains, Quine's position can be summarised as follows: The meaning of a logical expression (like 'not' or 'or') is not some abstract entity but is constituted by the laws that govern its use. If you reject a law that is central to the classical understanding of 'not' (e.g., the law of non-contradiction), you are no longer talking about negation. You have changed the meaning and, therefore, changed the subject.

The implication is that the apparent disagreement is a verbal dispute. It's a misunderstanding based on equivocation, not a substantive clash of ideas about a common topic. If the parties could just clarify their terms, the "dispute" would dissolve.

Another helpful way to frame this is by distinguishing between two kinds of conflict.

In this framing, Quine's argument is that what looks like a genuine conflict (Gc) is always, in fact, a partial conflict (Pc). According to Quine, there is no "residual essence" of conjunction or negation apart from the laws governing its use. Therefore, a true Gc is impossible. The deviant logician doesn't refine classical logic; they reject it by changing the subject.

2. The Case for Genuine Disagreement

While Quine's argument is elegant, most philosophers of logic today find it unconvincing. It seems to mischaracterize the rich, rational debates that actually take place between proponents of different logics. Let's explore two powerful ways to argue that these disagreements are indeed genuine.

Argument 1: The Dispute is About Facts, Not Just Words

One way to push back against Quine is to show that logical disagreements are often grounded in disagreements about how the world is, or how our language relates to it. The dispute isn't just about the meaning of symbols, but about substantive, often metaphysical, issues.

A classic example is the debate over the Law of Excluded Middle, particularly concerning future contingent statements.

As the video explains, the classical logician might claim that "I will eat eggs for breakfast tomorrow" is either true or false right now, even if we don't know which. A many-valued logician might argue that since the future is not yet determined, the proposition is currently neither true nor false.

Here, the disagreement is not merely verbal. It is a genuine philosophical dispute about:

• Metaphysics of time: Is the future open or fixed?
• Philosophy of language: Do statements about the future have truth-values before the event occurs?

The choice of logic becomes a consequence of these deeper, substantive disagreements. They are not just "changing the subject"; they are proposing rival theories about the relationship between language, truth, and reality, and arguing that a different logic is required by the superior theory.

Argument 2: The Dispute is Normative (Conceptual Engineering)

A more sophisticated response accepts Quine's premise that meanings change but denies his conclusion that the dispute is merely verbal. On this view, logical debates are normative. They are not about what logical terms do mean, but about what they ought to mean. This activity is a form of conceptual engineering.

Hjortland, drawing on philosophers like Michael Dummett and Graham Priest, argues that even if classical and intuitionistic negation are different concepts, the debate between them is a genuine, rational disagreement about which concept is better. The intuitionist, for example, argues that the classical concept of negation is defective because its meaning cannot be fully manifested in its use, and they propose intuitionistic negation as a superior replacement.

This is not a merely verbal dispute any more than the debate between a Newtonian and an Einsteinian physicist over the concept of 'mass' is merely verbal. In both cases, the parties are engaged in theory-choice. They are weighing the theoretical virtues of rival conceptual frameworks (simplicity, explanatory power, fruitfulness) and arguing that one is superior. The disagreement is substantive, rational, and central to the progress of the discipline.

3. A Lived Example: A Classical Logician Debates a Dialetheist

To see how these abstract ideas play out in practice, let's watch a real-time example of a logical dispute. In the following video, Robert Koons (who defends a version of classical logic) and Graham Priest (a leading proponent of dialetheism, the view that some contradictions are true) discuss their disagreements. According to a simplistic Quinean view, they should be talking past each other. Let's see if they are.

The conversation between Priest and Koons is a powerful exhibition of a genuine logical disagreement.

• They are not confused about what the other means by "negation" or "contradiction."
• They locate their disagreement in deeper philosophical commitments about the nature of reality and in methodological questions about how to weigh evidence for a logical theory.
• Their debate aligns perfectly with the anti-exceptionalist view of logic (which Priest explicitly espouses), where logic is a theory like any other, subject to revision based on abductive reasoning (inference to the best explanation).

The debate is not about the definition of 'not', but about the substantive question of whether a theory that allows $p \land \neg p$ to be true can ever be a better overall theory of truth, validity, and reality than one that does not. This is a profound and genuine philosophical dispute.

Conclusion and Course Retrospective

Today we confronted Quine's influential claim that disagreements between classical and non-classical logicians are merely verbal disputes arising from a "change of subject." While this meaning-variance thesis is an important philosophical challenge, the evidence from the actual practice of logic suggests it is mistaken.

Key Takeaways:

• The Quinean Challenge: Rejecting a basic logical law changes the meaning of the logical constants, resulting in a verbal dispute, not a genuine disagreement.
• The "Genuine Dispute" Response 1 (Factual): Logical disagreements are often proxies for substantive disagreements about metaphysics or the philosophy of language (e.g., the nature of future contingents).
• The "Genuine Dispute" Response 2 (Normative): Logical disagreements can be seen as a form of conceptual engineering—a rational, normative debate about which logical concepts we ought to use, judged by criteria of theoretical virtue.
• The Verdict: While meaning-variance is a real phenomenon, it does not reduce logical debate to a merely verbal squabble. The disputes are substantive, rational, and essential to the philosophical project of understanding and refining the tools of reason.

Course Retrospective:

This final lesson encapsulates the entire journey of our course. We began by building a philosopher's toolkit, distinguishing epistemology from metaphysics and exploring theories of truth and justification. We traced the history of logic from Kant through Frege's revolution, the crisis of logicism, and Gödel's landmark theorems, seeing how philosophical motivations drove formal innovations. We then dove into the core philosophical debates surrounding the nature of logical consequence, the challenges from intuitionism and modality, and the very status of logic itself.

The question of whether logical disputes are genuine is, in many ways, the ultimate question for the philosophy of logic. Your answer determines whether you see logic as a monolithic, a priori structure or as a dynamic, evolving field of inquiry, continuous with science and metaphysics. The evidence, as we have seen, points strongly toward the latter. The ongoing, rational debates between classicists, intuitionists, dialetheists, and pluralists are not a sign of confusion, but a testament to the vitality and depth of a field dedicated to understanding the very foundations of thought.