Introduction
In our last lesson, we worked through Michael Dummett's powerful argument for preferring intuitionistic logic over classical logic. We saw that for Dummett, this is not a technical or aesthetic choice but a philosophical imperative. The argument proceeds from the premise that a theory of meaning must account for our public, manifestable understanding of language. This led him to reject semantic realism in favour of an anti-realist, justificationist semantics. The logical consequence of this move was the rejection of the Law of the Excluded Middle, the hallmark of classical logic, and the adoption of intuitionistic logic.
The entire argument is built on the idea that this is a genuine, high-stakes philosophical conflict. Today, we will step back and scrutinize that very idea. Your learning outcome is to assess whether the choice between classical and intuitionistic logic is a substantive philosophical dispute.
We will explore the counter-position that the two sides might not be truly disagreeing but are, in a sense, "talking past each other." By weighing this challenge against the arguments for a substantive conflict, you will be able to form a considered judgment on the nature of this pivotal debate in the philosophy of logic.
1. The Quinean Challenge: Are They Just Changing the Subject?
The most famous argument for the view that disputes over logic are not truly substantive comes from the influential philosopher W.V.O. Quine. His position can be summarized with a simple, provocative question: when a "deviant" logician rejects a fundamental law of classical logic, are they really disagreeing with the classicist, or have they just changed the meaning of the logical words?
According to Quine, the meaning of a logical connective like 'not' () or 'or' () is given by the totality of logical laws it obeys. If you reject the Law of the Excluded Middle (), you have fundamentally altered what you mean by 'or' and 'not'.
[PDF] Logical Pluralism: Where the Conflict Really Lies
The following article explains this Quinean perspective in the context of logical pluralism. It directly addresses the idea that rival logicians might be 'talking past each other'.
Please read the section 'meaning invariance thesis' (this starts on the second page of the PDF, following the introduction). Focus on the long quote from Quine. His claim is that when a deviant logician 'tries to deny the doctrine he only changes the subject'.
On this view, the dispute is merely verbal. The classicist asserts statement , which is an instance of LEM using the classical connectives. The intuitionist denies statement , which looks identical but uses intuitionistic connectives with different meanings. They are not disagreeing about the same proposition. The "choice" between logics becomes a pragmatic decision about which set of concepts, or which "language game," is more useful for a given purpose, not a deep disagreement about the nature of reason itself.
2. The Case for a Substantive Dispute: Metaphysical Stakes
The Quinean challenge is powerful, but it seems to ignore the motivations and self-understanding of the philosophers involved. From the perspective of the intuitionists, the dispute is anything but verbal. They see themselves as correcting a fundamental philosophical error embedded within classical logic.
L.E.J. Brouwer, the founder of intuitionism, did not see himself as designing an alternative logic; he believed he had discovered that classical logic made false assumptions about the nature of mathematical reality. For him, mathematical objects are mental constructions, not inhabitants of a mind-independent Platonic realm. This anti-realist metaphysics is the reason for rejecting LEM.
[PDF] Logical Pluralism: Where the Conflict Really Lies
This same article provides an excellent summary of the metaphysical motivations behind intuitionism, showing that it was born from a deep philosophical conviction.
Please read section 3, 'The real conflict', focusing on the discussion of intuitionism. Note how the choice of logic is rooted in an anti-realist ontology. Pay particular attention to the quotes from Brouwer and Dummett, such as Brouwer's claim that the belief in LEM is a 'phenomenon of history of civilization' and Dummett's view that classical reasoning is 'not valid on any legitimate way of constructing mathematical statements'.
As the text makes clear, intuitionists see classical reasoning as illegitimate because it rests on a mistaken metaphysical realism. They are not proposing a new topic of discussion; they are claiming that the classical logician's account of reasoning is fundamentally flawed. This is the very definition of a substantive dispute.
To see how this deep philosophical commitment plays out, let's revisit a point made by Michael Dummett.
Michael Dummett on Frege, Truth, Meaning & Realism (1997)
In this clip, Dummett explains how metaphysical disputes across philosophy share a common structure. His entire project is to show that these disputes—and by extension, the choice of logic—must be resolved at the fundamental level of the theory of meaning.
Please watch the segment from 34:09 to 37:27. Dummett connects disputes about the external world, science, and mathematics. His key idea is that we cannot settle the metaphysical questions directly. Instead, we must first decide on the correct 'account of the meanings of such statements', and the metaphysical (and logical) consequences will follow. This demonstrates why, for Dummett, this is a core philosophical battle, not a terminological choice.
Dummett's argument reinforces the idea that the debate over logic is a proxy war for a much larger battle between realism and anti-realism—a central and enduring conflict in philosophy.
3. A Direct Rebuttal: Disagreement vs. Equivocation
Philosopher Timothy Williamson offers a more direct refutation of the Quinean "talking past each other" thesis. He argues that it relies on a flawed view of meaning.
Williamson points out that deviant logicians, like Dummett, explicitly state they are not stipulating new meanings for words like 'or' and 'not'. Instead, they are proposing a new, and better, theory about the logical powers of the existing, public meanings of those words.
[PDF] Logic and Philosophy in the Twenty-First Century
In this excerpt, Timothy Williamson argues forcefully that logical disputes are genuine disagreements, not cases of equivocation (using the same word with different meanings).
Please read the first three paragraphs of Section 4 (starting with 'To deny the reality...'). Williamson argues that a logician can have a false theory about a connective's powers without thereby changing its meaning. He contends that all parties are 'employing the connectives with those publicly available meanings in order to engage in unequivocal public debate'.
Williamson's point is subtle but crucial. He distinguishes between:
- The meaning of a word (which is public and shared).
- A person's theory about that word's properties (which can be right or wrong).
An intuitionist is not simply using 'or' differently. They are arguing that the classical logician's theory about what 'or' entails (namely, that is always true) is incorrect. The disagreement is about which theory is true, which makes it a substantive, not a verbal, dispute. The fact that the debate can even happen in a shared natural language is evidence that they are not simply talking past one another.
Conclusion
So, is the choice between classical and intuitionistic logic a substantive philosophical dispute? Having weighed the arguments, the evidence points overwhelmingly in one direction.
The Quinean view that the two sides are "talking past each other" offers a clean way to dissolve the conflict, but it does so at the cost of ignoring the stated intentions of the participants and relying on a questionable theory of meaning.
In contrast, the view espoused by Brouwer, Dummett, and Williamson takes the philosophical arguments at face value. It shows that the choice of logic is deeply entangled with fundamental questions about metaphysics, truth, and meaning. The intuitionist is not offering a polite alternative; they are mounting a radical critique of the philosophical foundations of classical thought. The dispute is not about which words to use, but about what it is for our statements to be true and how we are justified in reasoning about them. This is as substantive as philosophical disputes get.
Key Takeaways:
- The 'Verbal Dispute' Thesis: Attributed to Quine, this view suggests that by rejecting classical laws, intuitionists change the meaning of the logical connectives. Therefore, they are not genuinely disagreeing with classicists but are "changing the subject."
- The 'Substantive Dispute' Thesis: Proponents like Brouwer, Dummett, and Williamson argue that the conflict is a genuine disagreement about the correct logical principles.
- Metaphysical Roots: The disagreement is not purely formal but is grounded in a deep metaphysical conflict between realism (the classical view) and anti-realism (the intuitionist view).
- Disagreement, Not Equivocation: The participants see themselves as having a genuine debate over the properties of shared, public concepts, not as stipulating different private meanings.
Preview of the Next Module:
Having concluded our first module, you have now built a foundational "Philosopher's Toolkit" and applied it to a major debate in contemporary logic. We have seen how questions about truth, meaning, and justification directly impact which logical laws we ought to accept.
In the next module, we will journey back to the birth of modern logic. We will start by examining the Kantian philosophical landscape against which these new ideas rebelled, setting the stage for the revolutionary work of Gottlob Frege. Our first lesson will be to explain Kant's view of logic as formal and his conception of analytic and synthetic judgments. This will provide the essential background for understanding the philosophical earthquake that Frege initiated.