We seem to be going through a kind of online Christian revival — as one would expect, from historical patterns of American religiosity, which seems to follow a roughly 80-year cycle. Our current revival has a number of sources, and cannot be attributed exclusively to any singular force. But a large amplifier of the expanding Christian bubble has been the Christian advocates in the world of ‘internet blood sports’ — namely, Jay Dyer and Andrew Wilson.
Dyer and Wilson both specialize in meta-ethics, and deploy a form of a transcendental argument that does not (usually) directly attack the arguments in question, but shifts the focus to the presuppositions which must exist for arguments to take place — what is necessary to make an argument in the first place?
Let’s take a look at this argument.
The transcendental argument for god (T.A.G., for short) goes more or less as follows:
- Any argument — for or against a position — presupposes the knowability of things
- Knowledge is justified true belief
- “Justification” is logical validity
- THEREFORE all arguments and assertions of knowledge presuppose the transcendental existence of logic, as well as the possibility of knowledge
- The preconditions of knowledge are themselves not justified (and therefore not knowable) without some explanatory foundation of their own
- That foundation is GOD
The transcendentalist may also say that without justification, all ad hoc assertions are equivalent: “if you can ‘just say’ something seems unlikely, I can ‘just say’ the opposite.” Further, he might argue that to even participate in a debate is to presuppose the necessity of logical justification (what else could a debate possibly be for?).
On its surface, the transcendental argument is not only powerful, but humiliating — which perhaps might explain a lot of its appeal to its proponents, for whom its adversaries appear to be wrong and also deeply confused about where they are, metaphysically. Every argument appears to be a self-contradiction, because it is an argument (and therefore is an attempt at both logic and demanding logical justification) but it appears unable to justify itself.
The singular problem with the transcendental argument is that it fundamentally misunderstands language (in a couple of different ways). To look at the rough, syllogistic format of the argument presented above, consider the second premise: that “knowledge” is justified, true belief. Since we are making grand proclamations (the transcendentalist is claiming to deduce God from logic itself), let us be precise in our terminology, and examine it closely. Why is knowledge “justified true belief”? Is that how words work? We just hear a definition from Aristotle, and accept it on its face? For that matter, ti estin aletheia — “what is truth?”
Andrew Wilson often cites “words have meaning” as an example of a presupposition underneath arguments, since to state the contrary — that words don’t have meaning — would either be self-contradictory or nonsensical; it is a statement that hinges upon the words comprising the sentence itself having meaning. One might just as easily say “this sentence is not a sentence.”
But suppose we alter the phrase slightly, from the tautology “words have meaning” to “some words have meanings.” Does this change how the presupposition works, for the transcendentalist?
To say a word has a meaning implies a one-to-one mapping of a single word to a single “true” meaning, as in, “the meaning of ‘cat’ is this small furry pet.” But this is not how words actually work. Words acquire their meaning descriptively, by use, and often expand metaphorically (indeed, it can be argued that all words are metaphors), such that words can acquire several meanings — even dozens. The word “set,” for example, has 25 listed definitions as a verb, 24 as a noun, and 7 as an adjective (according to Merriam-Webster). Which of these is the true meaning? After all, ‘words have meaning.’ Which meaning?
Can the meaning of a word be wrong?
This is not some flippant misunderstanding of the transcendentalists’ point, because the purpose of the observation that ‘words have meaning’ is to argue that we can understand each other by means of language through the use of words, and that understanding presupposes meaning in the language. But multiple meanings shows us that meaning in language is insufficient to provide understanding. Moreover, the descriptive, metaphorical nature of language shows us that knowledge precedes language. Language can convey knowledge, but knowledge does not itself come from language.
This will become very important later.
So how does a common understanding of a word come about, of the sort that does make mutual comprehension possible? Put another way: how do words acquire meaning?
It is trivial to point out that the meaning of words are arbitrary, but arbitrariness does not get us to mutual comprehension via language. There must be some method by which we agree to meanings, which we associate with arbitrary sounds.
And the meanings of words can get us into a completely different set of problems.
In my essay Philosophizing with the Body (2025), I argued that the word “murder” — as used in arguments for objective morality — is guilty of a kind of intrinsic circularity:
If a philosopher appeals to the existence of objective moral values by pointing to “murder” as something that is universally and always wrong, we might ask if “murder” is meant in the popular sense or in the strict sense — for a killing on the battlefield might be considered “murder” if the adversary was surrendering, or was an unarmed medical officer, but might not be called “murder” if the killed is an enemy combatant. Similar questions surround circumstances of self-defense. A truly objective moral law, such as a prohibition on murder, must have some objective standard for what constitutes murder. And yet there is no such objective standard. There are certainly commonalities in what human societies tend to agree should and should not be permitted, when it comes to homicide. But descriptively and indeed, definitionally, “murder” is simply killing we have agreed is wrong. Thus, to employ the intuitive wrongness of murder as evidence of objective moral truths presumes what it attempts to demonstrate.
In the same way, to say “words have meaning” is a tautology, since a “word” is, by definition, a sound with meaning.
The transcendental insertion of a tautological presupposition before an argument, as a precondition of the argument, serves as a sneaky back-door to inject preferable understandings of very important terms which are preferable to the transcendentalist — words such as “knowledge,” “justified,” and “debate.”
Is “knowledge” really “justified, true belief?”
Does “justified” literally just mean “logically valid?”
Is two philosophers exchanging syllogisms the only kind of debate?
All of these are perfectly valid understandings of these words, but they are not the only valid meanings of these words, nor were they even the first meanings. “Knowledge” is an Old English conjugation of knowen, but has been used as a translation for many different Greek words (including those of Plato and Aristotle), such as eidenai, gignōskein, noein, manthanein, and sunienai. These were very often sense perception terms: “I saw” becomes “I know (because I saw).” However, we can know things by other ways. We can “know” something because we heard it from someone else. We can “know” something by divine revelation. We can even know something by instinct. And, of course, we can know things by reason. All of these are perfectly valid ways of using the word “knowledge.” But if we grant that knowledge is only reason, or only “justified true belief,” we actually negate other forms of knowledge.
This becomes a problem when sense experience runs into conflict with our logical reasoning. Consider, for example, the following syllogism:
- The tree is green
- What is green cannot be not-green
- Therefore, the tree is not not-green
The conclusion (3) logically and necessarily follows from the first two premises, and wouldn’t you know it, both premises are true… and yet somehow, the conclusion is false; there are parts of the tree that are, indeed, not-green, but brown or red or grey.
As with Zeno’s famous paradoxes, there are ways of eventually stumbling upon the problem with the syllogism (in this case, it is an equivocal use of the word “the” in (1), treating a part of the tree as if it were the whole). But one could much more simply follow the example of Diogenes and walk away, or look out and simply observe that the tree is not entirely green, thus falsifying the logically sound and valid argument.
(If one says ‘premise (1) is actually not sound, because the tree is not only green,’ then they might be correct, but this introduces the problem of precision into the matter, which plagues all grand, logical assertions about the world.)
Is the observation that the tree is not completely green a “justified, true belief?” Well, it’s ‘justified’ in the sense that it seems reasonable… but it’s not exactly a logical syllogism. And how do we know that what we see is ‘true?’ It seems to be as true as any logical syllogism… but if we’re going by ‘seems,’ then we must suppose that someone else is just as justified to say that it seems completely green (or completely purple) to them… and who are we to judge?
At least we can call it a ‘belief!’
“Justified” can be understood to mean ‘logically valid,’ but it can also mean ‘reasonable,’ not the sense of being ‘guided by reason’ with some couched and preferential, particular definition of ‘reason,’ but in the conventional sense of being sensible, or even common sense. To say “the tree is green, but not entirely green” is reasonable, and therefore justified without any appeal to logic, causality, or the satiation of explaining tautological presuppositions that we inject in front of the claim.
So what are we to do with these presuppositions? These supposed preconditions of knowledge?
It turns out, on the other side of a proper understanding of language, that most of these preconditions are completely unnecessary, or are themselves equivocal. To say that “speaking presupposes that words have meaning” is trivially true, but once this is bootstrapped into some specific idea of making an argument presupposes the possibility of knowledge, we suddenly have a sneaky side-door opening to a very specific notion of knowledge. Arguing, in fact, does not necessarily pre-suppose knowledge; one could defend a position one does not hold (as in, attempting to justify what one does not believe to be true). But more commonly, one can argue in defense of something that one knows, but not through logical justification (i.e., the tree is green).
It is useful here to explore where transcendental arguments came from.
Immanuel Kant famously said that David Hume woke him from his “dogmatic slumber” with his skepticism. Hume argued that our notions of causality and induction are derived from experience, rather than reason. This threatened the entire project of metaphysics, and the possibility of objective knowledge. To a certain kind of person, knowledge is not knowledge unless it is objective. Kant, being of such a kind, set his mind to work, and wrote a defense of pure reason disguised under the most immaculately backwards title, A Critique of Pure Reason.
I wrote a little bit about this in Descending Odin’s Throne (2024):
But Kant was not a skeptic. He believed it was possible to acquire what he called a priori knowledge (“prior to experience”). Such “pure” knowledge does not depend upon the senses, instead deriving true knowledge and the possibility of certainty by means of analysis and synthesis of identities and necessities. In philosophy, this approach is sometimes called transcendentalism, and has given rise to “transcendental arguments” which attempt to show that something is a necessary condition of something else. Kant’s famous categorical imperative – “act only according to that maxim whereby you can at the same time will that it should become a universal law” – is in fact an a priori synthesis of what objective moral law must be, based upon the nature of morality itself. The assumption, of course, is that morality isn’t really morality unless it is universal.
But in all possibilities of a priori knowledge, language is required to reach some conclusion. Language is in fact the mediating mechanism of thought, and the words that comprise language are not a priori knowledge. Even Descartes’ famous ontological argument for a priori knowledge of the triangle requires the language of mathematics in order to conceive of the relationship at all, since thought on abstract subjects like this requires language in order to make inferences or deductions. Identities required for analysis are inherently linguistic. And language – logical, mathematical or conventional – comes from experience.
What is ironic is that Hume’s skepticism still leaves room for empirical knowledge (and other kinds of experiential knowledge); it is only certainty and objectivity that his criticisms undermine. The transcendental argument which holds that arguing itself presupposes the possibility of knowledge engages in a kind of equivocation, where “knowledge” is used in the broad sense when we speak of presupposing (this would include knowledge gained by experience), but in a much narrower sense when they speak of “justified true belief” later on.
The transcendental argument creates what we might call a “transcendental triangle,” a sort of mesh-network of particular definitions which all support each other, comprising a sort of three-part circle of self-justification. These terms are:
- Knowledge
- Justification
- Debate
We have gone on at length about “knowledge,” and explained the distinction between logical justification and justification in the more colloquial sense. But “debate” requires a little bit of unpacking.
On the surface, it does seem like debate is — or ought to be — the adversarial exchange of logical arguments. And indeed, in some cases, this is the case. But in other cases, this is not the case. Indeed, in the vast majority of debates, what we see is not a contest of logical arguments, but a contrast of observations, with each debater making the case to the audience that their particular set of observations is the more relevant and significant. These arguments aspire to be “reasonable” — in the colloquial sense — but do not even attempt to be logical.
Does the absence of formal logic make these debates incomprehensible, or even ‘not really debates’?
Different styles of debate will be appropriate to different contexts; what matters here is not adjudicating which sort of debate is best, but that a debate is not ‘not a debate’ in the absence of formal logical syllogisms. Such an assertion would be a misunderstanding of language, in how we use the term ‘debate.’ One might attempt to argue that a philosopher (at least an analytical philosopher) ought only to engage in formal, logical debates… but one still could not assert that a debate isn’t a debate in the absence of the sacred syllogism.
The transcendental trap is that challenging the meaning of one of these words brings the debaters back to the other two. To challenge the assumed nature of knowledge seems to require “justification”; to challenge the narrow sense of “justification” demanded by the transcendentalist invites the charge of not engaging in debate at all; and to challenge the very notion of debate allows someone to ask how do you know what a debate is?
The circle would be obvious if it were only two items. If someone were to define a “boat” as a “sea-vessel,” and when asked what a “sea-vessel” is, to define it as a “boat”… we would understand that no actual information was being provided (even if the definitions were, technically, correct). But at three items, the bootstrapping logic manages to sneak past most people’s notice.
But what about logic itself? If language has shown us that it isn’t necessarily a precondition of knowledge, or of debate, isn’t it at least a fascinating example of a non-material thing that humans discovered, and did not invent? Does it not remain an example of an ordering principle which seems to point to some orderer?
The problem of language, in fact, reaches here too.
Allow me to reference Descending Odin’s Throne again, here in relation to mathematics, which is just logic for non-philosophy-nerds:
The number “five” does not exist in nature.
It is an abstraction of an idea, a quantity that is relative to another discrete quantity. We identify a single apple as “one,” and only by this assumption do five fruits from an apple tree constitute “five.” The statement “an apple is one” is a premise, but it is not “true” in any objective sense. It is an assertion of identity that is arbitrarily presumed for the sake of convenience. If apples were quantified by weight, rather than by discrete fruits, a completely separate system of quantification could be imagined. Arithmetic done in base-15 is just as valid as arithmetic done in base-10, or base-2. Non-Euclidean geometry is just as valid as Euclidean geometry. They only have different assumptions.
With this in mind, it is clear that mathematics is actually only objective so long as one’s assumptions are objective. The use of mathematics in argumentation today is largely the art of hiding the subjective biases of these assumptions, but this too is being pushed back on, even from within mathematics itself. Gödel’s famous incompleteness theorem demonstrated – mathematically – that a mathematical system cannot prove or justify its own initial assumptions, thus all mathematical systems are “incomplete.”
But we did not need mathematics to know this. We could understand this simply through language, and the recognition that mathematics is just a derivative of language. It is, in fact, language purged of all discrete subject matter; a pure grammar.
It turns out that logic (and mathematics) are actually not discoveries, but inventions. To be precise, they are descriptions. The law of identity (1 = 1) is no more a “discovery” than is the aforementioned “discovery” that murder is always wrong, or that words have meaning. All mathematical equations are tautologies, if they are done correctly; similarly, all logical equations are tautologies. As tautologies, they cannot tell us anything new, outside of their assumed axioms. They simply don’t appear this way to us, intuitively, because we have replaced the semantic content of the “sentences” with abstractions (numbers). The layers of abstractions make it easy for us to forget that mathematical statements are descriptions, and the unreasonable effectiveness of mathematics (or logic) is simply the unreasonable effectiveness of description.
“Is it not fascinating that everything we describe as brown is brown?”
The ability for mathematics to “predict” reminds us of the utility of description, and the practical usefulness of logic. As a tradesman, I use mathematics myself, fairly regularly, for measurement in cutting, bending, and calculating ampacity. But it is easy for people to get carried away with the utility of math. Every time someone scratches their head and says “it wasn’t supposed to happen like that…” is an instance of math or logic failing. Usually, this is not a failure of calculation, but the failure to account for a variable. For this reason, most of engineering is an art of approximation.
To put it all together, the transcendental argument — for god, or for anything else — is a language shell game, based upon selective and self-reinforcing definitions of terms, which allow the debater to lose his opponent in a maze of terminology and declare victory. But this brings him no closer to the truth, if “truth” is understood to be “what is.” What is, in the world, is not dependent upon how we describe it, and the coherence model of truth that all transcendentalist arguments depend upon relies upon descriptions for coherence to be achieved. The entire move of pointing to underlying preconditions of knowledge is, itself, a language game.
Is pointing this out a transcendental observation? To observe that a proper understanding of language is presupposed in debate? One could frame it that way. But we actually don’t have to. A discussion which makes use of language does not require us to take a detour down linguistics lane and pay homage to language itself, affirming certain principles of language in order for our sentences to make sense.
Indeed, the sense of our language precedes our understanding of why our sentences sense. And any asserted theory as to how or why language must work is not given a free pass on account of language working. It might be wrong… and language still works.
In the same way, the supposed preconditions of knowledge, debate, and the idea of justification itself asserted by transcendentalists might all be incorrect, and yet here we are, still discussing, and accomplishing tasks more or less effectively — demonstrating knowledge — in the real world. This does not prove their argument, but only makes the language circle they invoke an unfalsifiable wizard’s spell, which can be dismissed simply by insisting upon a clear and consistent concept of “justification.”
It is certainly possible for the transcendentalist to say that actually, logic refers not to structured language, but to principles of identity and stability in the universe itself, prior to language. So long as they don’t use these two senses of the word “logic” interchangeably, that’s all well and good… but our universe also changes. Our body changes. Parts of us stay the same, for a while, while other parts shift. Where does the principle of stability and identity begin? Actually, what is the principle of identity in the material world, where it isn’t just 1 = 1?
Claiming that knowledge presupposes certain logical principles of intelligibility begins to inject language back into the discussion — even where the transcendentalist is ostensibly talking about physical things. How do we know what these “principles” are? How can we derive such principles prior to experience?
To assert Y is a metaphysical precondition of X is to reach beyond what the epistemic hands of experience can touch… and the only tool to artificially extend beyond that reach is language. If the transcendentalist’s criticism of Hume is that his skepticism makes knowledge impossible, then knowledge is, indeed, impossible… and yet somehow, people seem to keep going about knowing things.
Does this disprove Hume? Or does it merely disprove a utopian notion of knowledge that was itself arrived at by language?
In short: debate does not presuppose anything other than disagreement. How, why, and over what that disagreement takes place are in dispute… and indeed, we actually don’t need an account of debate in order to debate, just as we don’t need an account of war in order to go to war. Such an account might be useful, and it might also be the opposite, causing us to look for categories, rather than seeing the reality, and only then searching for the right words to describe what it is we are seeing.
So let’s try to apply it.
Suppose you run into a Jay Dyer in the wild, who says something like this:
What about reasoning about reasoning itself? These are meta-logical questions, meta-ethical questions, meta-physical questions. When I start to ask questions in that domain, and I ask questions about reasoning itself, or words themselves — how do we know that words have meaning? how do we know that logic is logical? — you see, these are questions that you can’t actually be wrong about, because if you’re wrong in that domain, it really destroys the possibility of knowledge.
How do you respond?
Do you simply accept the tautology as tautological?
No!
What is the insertion of meta– doing in these cases, with logic and ethics and physics?
It is turning the subject linguistic, and it is the set-up for equivocation by using the same word to describe different things. Logical consistency pertaining to language is not the same as the “logic” we perceive in the stability of things in the world. The “reasoning” we allude to in language is actually not always the same thing as the “reasonableness” of a conclusion. The reflexive turning back of a concept on itself changes the thing, and it is only by language that we are tricked into seeing the ungroundedness of logical systems as somehow disproving the stability of physical objects (which is already a challengeable interpretation) without some ordering God.
You can simply point out that the sense of knowledge that is being destroyed (coherence) is not the sense of knowledge that most people think of as knowledge (correspondence), and the maneuver to try to point out that the latter is some sort of logical contradiction is just another equivocal word trick to bring you back into the coherence framework. Similarly, if a position is unjustified in a strict, logical manner, it doesn’t mean it is unjustified in all senses of “justified,” and it is not some doorway to say “well, I guess everything is on the table, and I’m just as justified to blindly assert the opposite of your position”.
At the end of the day, I don’t think the transcendental argument is actually persuading many people. It allows the apologist to abuse and defeat adversaries with clever word games, like Socrates destroying Thrasymachus in Book 1 of Republic, but leaving sincere and intelligent onlookers on the side watching unpersuaded, saying “do you want to seem to have persuaded us, or truly to persuade us?” It rallies and energizes people already convinced with the feeling that they’re on the ‘winning side,’ but this too is an illusion… and I don’t think it even demoralizes the opponents, who generally walk away, not feeling stumped by a serious problem, but as someone feeling tricked, in a manner they can’t quite untangle.
Their feelings are correct, and the sooner we — in the collective world of online debate — can untangle this word game, the sooner we can get back to more serious arguments.
Language Games and the Ground of Being: A Response to Robertson’s Dismantling of the Transcendental Argument
Introduction
Robertson’s critique of the transcendental argument is clever, readable, and ultimately self-defeating in ways that are both precise and ironic. It is clever because it correctly identifies real weaknesses in certain formulations of the transcendental argument — particularly the Kantian and presuppositionalist versions deployed by internet apologists. It is readable because Robertson writes well and has a genuine talent for making philosophical maneuvers feel like common sense. It is self-defeating because the very moves he makes to dissolve transcendental reasoning presuppose exactly the kind of stable, intelligible, mind-independent structure of reality that his argument is designed to deny.
Before proceeding it is necessary to distinguish what Robertson is actually arguing against from what the Aristotelian-Thomistic tradition actually holds. Robertson targets a specific formulation — the TAG as deployed by Jay Dyer and Andrew Wilson — which is broadly presuppositionalist and Kantian in character. This is a legitimate target and some of his criticisms land against that specific formulation. But Robertson consistently treats this as a refutation of transcendental reasoning as such, and of the metaphysical realism underlying the classical theistic tradition. It is not. The Aristotelian-Thomistic tradition does not ground logic in language. It does not derive the PSR from a linguistic tautology. It does not need the word knowledge to mean justified true belief in order for its arguments to work. Robertson has identified real problems with a particular apologetic style and then performed a sleight of hand — concluding that because this formulation fails, the entire tradition of classical metaphysical reasoning fails with it. That conclusion does not follow, and demonstrating why it does not follow is the purpose of this response.
I. The Language Argument and Its Limits
Robertson’s central claim is that transcendental arguments are fundamentally language games — that they achieve their apparent force by exploiting semantic ambiguity, injecting preferred definitions of terms like knowledge, justification, and debate, and then declaring victory when opponents are lost in the resulting terminological maze. He supports this with observations about the multiple meanings of words, the descriptive and metaphorical nature of language, and the way that logical and mathematical systems are themselves dependent on linguistic conventions.
There is genuine philosophical content here. It is true that words have multiple meanings. It is true that presuppositionalist formulations of TAG sometimes rely on stipulative definitions that do considerable hidden work. It is true that Gödel’s incompleteness theorems demonstrate that formal systems cannot justify their own axioms from within. These are real observations that any serious defender of classical theism should acknowledge rather than dismiss.
But Robertson draws conclusions from these observations that they cannot support.
The first and most immediate problem is that Robertson’s own argument is saturated with the very commitments he is trying to dissolve. He claims that logic and mathematics are not discoveries but inventions — descriptions rather than disclosures of mind-independent reality. He claims that all logical equations are tautologies that cannot tell us anything new beyond their assumed axioms. He claims that the transcendental argument is a language shell game that brings us no closer to truth understood as what is.
Notice what has happened. Robertson has made a series of robust claims about what logic actually is, what mathematics actually is, what truth actually consists in, and how language actually works. These are not merely reports of his subjective experience. They are presented as true — as corresponding to the actual structure of reality, as being the case whether or not anyone’s linguistic preferences align with them. When Robertson says logic is a description rather than a discovery he means this to be correct — not merely coherent within his preferred linguistic framework, not merely a useful fiction, but actually right about what logic is.
But this is precisely the kind of claim Robertson’s argument is supposed to make impossible. If all grand assertions about the structure of reality are language games dependent on preferred definitions, then Robertson’s assertion that logic is a description rather than a discovery is a language game dependent on his preferred definition of discovery. If pointing to necessary preconditions of knowledge is merely a linguistic maneuver with no genuine metaphysical purchase, then Robertson’s claim that what is in the world is not dependent on how we describe it is itself a metaphysical claim with no genuine purchase beyond his own linguistic preferences. He cannot stand outside language to make claims about language’s inability to reach reality while simultaneously expecting those claims to reach reality.
This is not a rhetorical reversal. It is the precise self-refutation that runs through everything Robertson writes on this topic. He needs his own argument to be true in a correspondence sense — to actually describe how language and logic work — while his argument’s conclusion would make correspondence truth unavailable. He has sawed off the branch he is sitting on and is surprised to find himself falling.
II. The Mathematics Argument and What It Actually Shows
Robertson’s treatment of mathematics deserves specific attention because it is the most developed part of his case and contains a genuine error that is philosophically important.
He argues that mathematics is a description rather than a discovery, that the number five does not exist in nature, that arithmetic in base fifteen is as valid as arithmetic in base ten, and that Gödel’s incompleteness theorems demonstrate that mathematical systems cannot justify their own axioms. He concludes that mathematics is simply logic for non-philosophy-nerds — a sophisticated language game whose apparent objectivity is an illusion created by layers of abstraction.
The Gödel point is particularly worth addressing because Robertson deploys it as if it supports his position when it actually undermines it. Gödel’s incompleteness theorems demonstrate that any sufficiently powerful formal system contains true statements that cannot be proven within that system. This is not the same as saying that mathematical truth is merely conventional or that logic is a description without objective purchase. It is the precise opposite. Gödel’s theorems demonstrate that mathematical truth outruns any formal system we construct to capture it — that there are truths that are true independently of whether our axioms can derive them. This is an argument for the mind-independence of mathematical truth, not against it. Robertson has cited as evidence for his position one of the strongest arguments against it.
Furthermore the claim that arithmetic in base fifteen is as valid as arithmetic in base ten, while technically correct as a claim about notational systems, does not establish what Robertson needs it to establish. Different notational systems for representing the same mathematical relationships are equally valid in the sense that they are equally effective at tracking those relationships. But this shows that the relationships themselves are independent of any particular notation — not that the relationships are merely conventional. The fact that you can describe the same truth in multiple languages does not show that the truth being described is merely linguistic. It shows the opposite — that truth is robust enough to survive translation between notational systems precisely because it does not depend on any of them.
The deeper problem with Robertson’s mathematics argument is that it proves far too much. If mathematics is merely a sophisticated description with no genuine correspondence to mind-independent reality, then the extraordinary predictive success of mathematical physics — the fact that equations developed in purely abstract contexts turn out to describe physical phenomena with extraordinary precision — is an inexplicable coincidence. Robertson addresses this briefly by appealing to the utility of description and noting that every time something does not go as expected represents a failure of math or logic. But this response is inadequate. The question is not whether mathematics sometimes fails to predict correctly. The question is why it succeeds as often and as precisely as it does. Useful fictions that consistently track real patterns are not fictions. They are discoveries expressed in a particular notational vocabulary. Robertson has not explained the unreasonable effectiveness of mathematics. He has renamed it and moved on.
III. The Real Problem with the Presuppositionalist Formulation
Robertson is correct that the specific TAG formulation he targets has genuine problems, and it is worth acknowledging this clearly rather than defending a position the Aristotelian-Thomistic tradition does not hold.
The presuppositionalist formulation — as Robertson accurately reconstructs it — moves from the claim that argument presupposes knowledge to the claim that knowledge requires logical justification to the claim that logical justification requires God as its transcendental ground. Robertson correctly identifies that this argument relies on stipulative definitions of knowledge and justification that do hidden work, that it exploits semantic ambiguity between different senses of these terms, and that it constructs what he calls a transcendental triangle of mutually reinforcing definitions that creates the appearance of an inescapable trap without providing genuine illumination.
These are fair criticisms of this specific formulation. The Kantian inheritance in presuppositionalist apologetics does produce exactly the kind of linguistic circularity Robertson identifies. When the argument depends on getting the opponent to accept specific definitions of knowledge, justification, and debate — and then showing that those definitions imply God — it is vulnerable to the response that the definitions are not compulsory. Robertson is right about this.
But here is where his argument overreaches decisively. The failure of a Kantian-presuppositionalist formulation of the transcendental argument does not touch the Aristotelian-Thomistic tradition. The classical theistic tradition does not ground logic in language. It does not need the word knowledge to mean justified true belief. It does not derive the necessity of God from the preconditions of linguistic debate. It grounds logic in being — in the actual structure of reality — and argues that the mind’s ability to apprehend that structure is itself evidence of the kind of world we inhabit and the kind of mind we possess.
Robertson conflates these two very different projects throughout his essay. He refutes the presuppositionalist and then acts as if classical metaphysical realism has been defeated. It has not been touched.
IV. Logic as Discovery: What Robertson Gets Wrong About the Law of Non-Contradiction
Robertson’s claim that logic is a description rather than a discovery — that the law of identity is no more a discovery than the observation that murder is wrong — is the philosophical heart of his essay and the place where it fails most completely.
The law of non-contradiction — that something cannot both be and not be in the same respect at the same time — is not a linguistic convention that we have found useful to adopt. It is not a tautology that tells us nothing beyond its own assumed axioms. It is the condition under which any assertion, any denial, any argument, any description is possible at all. Robertson’s essay presupposes it on every page. When he says that transcendental arguments are language games he is asserting that they are language games and not genuine metaphysical arguments — that these two descriptions cannot both be correct simultaneously, in the same respect. He is using the law of non-contradiction as the ground of his own claim while arguing that it is a merely conventional description.
This is not a subtle point. It is a direct performative contradiction of the most obvious kind. The law of non-contradiction cannot be a merely conventional description because it is presupposed by the very act of making a description. You cannot describe something as merely conventional without presupposing that it is not also non-conventional in the same respect. The law is operative before any linguistic convention is in place precisely because it is the condition of coherent thought and speech, not a product of them.
Robertson anticipates something like this objection and attempts to deflect it by noting that our universe changes, that things are not simply identical to themselves across time, and that the principle of identity in the material world is more complex than 1 = 1. This is a red herring. The law of non-contradiction does not assert that things do not change. It asserts that in any given respect at any given time a thing cannot both have and lack a property. The tree can be green now and not green later without violating the law of non-contradiction, because the temporal qualifications distinguish the respects in which the predications are made. Robertson’s counterexample with the partially green tree actually demonstrates the law’s operativeness rather than challenging it — we recognize that the tree is not entirely green precisely because we apply the law of non-contradiction to distinguish the green parts from the non-green parts.
The Aristotelian tradition is explicit about what the law of non-contradiction actually is. It is a first principle — not derived from experience, not justified by argument, not dependent on linguistic convention — but grasped by the intellect directly as the most fundamental feature of being. Aristotle’s defense of the law in the Metaphysics is precisely a demonstration that it cannot be coherently denied, because any attempted denial presupposes it. Robertson has produced a contemporary version of the kind of argument Aristotle was already refuting in the fourth century before Christ. The response has not changed because the error has not changed.
V. The PSR, Intelligibility, and What Remains After Robertson’s Dissolution
Robertson ends his essay with what he apparently regards as a decisive observation: debate does not presuppose anything other than disagreement, knowledge still seems to work despite Hume’s skepticism, and the supposed preconditions of knowledge asserted by transcendentalists might all be wrong and yet here we are still discussing things and accomplishing tasks effectively.
This is the most philosophically casual move in the essay and it deserves a direct response.
Robertson is essentially arguing that because we seem to manage knowing things and having debates without being able to justify the ultimate preconditions of knowledge, those preconditions are either unnecessary or unknowable. This is equivalent to arguing that because planes fly without pilots understanding the complete physics of aerodynamics, the physics is either unnecessary or unknowable. The practical success of an activity does not show that its theoretical foundations are optional. It may simply show that we are operating in accordance with those foundations without having articulated them.
The Aristotelian position is precisely this. The PSR — that everything that exists has a sufficient reason for being the way it is rather than otherwise — is not a conclusion that needs to be derived from premises. It is a first principle that the intellect grasps in grasping being at all. When Robertson successfully makes an argument — when he moves from premises to a conclusion and expects that conclusion to follow necessarily — he is presupposing that there is a sufficient reason why those premises entail that conclusion rather than some other conclusion or no conclusion at all. He is presupposing that the world has a rational structure that his reasoning can track. He is presupposing intelligibility. Not as a linguistic convention. Not as a useful fiction. As a real feature of the world his mind is engaged with.
Robertson’s response to this would presumably be that we cannot know whether these presuppositions are true — that they might all be wrong and yet we stumble along anyway. But this response misses the point entirely. The question is not whether we can live without articulating these principles. The question is whether their denial is coherent. And here the answer is no — not because of a linguistic tautology, not because of a stipulative definition of knowledge, but because the denial of the PSR, the denial of intelligibility, and the denial of the law of non-contradiction all presuppose exactly what they deny in the very act of denial. This is not a language game. It is the recognition that certain truths are more fundamental than the arguments that might be constructed for or against them — that they are the conditions under which argument is possible at all.
VI. What the Aristotelian-Thomistic Tradition Actually Claims
Robertson’s essay would be strengthened considerably if he engaged with the Aristotelian-Thomistic tradition on its own terms rather than treating it as a more sophisticated version of internet presuppositionalism. The differences are significant and Robertson’s criticisms largely miss the actual position.
The Aristotelian-Thomistic tradition does not ground logic in language. It grounds logic in being. The law of non-contradiction is not a linguistic convention for Aristotle — it is the most fundamental feature of reality, grasped by the intellect in its direct contact with being. The PSR is not derived from the definition of knowledge — it is a first principle apprehended in the act of inquiry itself. The immateriality of the intellect is not asserted on the basis of semantic preferences — it is demonstrated through a rigorous analysis of what it means to grasp universals, follow rules in their full generality, and apprehend meaning that is not in physical particulars.
Most importantly the esse/essence distinction — Aquinas’ most powerful and original contribution — has nothing to do with linguistic convention. It is the conclusion of a rigorous metaphysical analysis of why contingent beings exist at all. In every contingent being what a thing is and that it exists are really distinct — you can fully define the essence of a thing without that definition containing its existence. This real distinction demands explanation. It terminates in a being in whom essence and existence are identical — who does not have existence as a property added to an essence but simply is existence itself. This is not a language game. It is not a tautology. It is a metaphysical demonstration that Robertson has never engaged because his essay is directed at a different target.
Robertson claims that to assert Y is a metaphysical precondition of X is to reach beyond what the epistemic hands of experience can touch and that the only tool to artificially extend beyond that reach is language. But this claim is itself a metaphysical assertion — a claim about the limits of knowledge that reaches beyond what experience alone can establish. Robertson is doing exactly what he says cannot be done, in the act of saying it cannot be done. The self-refutation is total and it is the same self-refutation that runs through his ontological argument, his treatment of internally grounded concepts, and now his critique of transcendental reasoning. In every case Robertson makes robust metaphysical claims about the structure of reality — about what logic is, about what language does, about what experience can and cannot reach — while simultaneously arguing that such claims cannot correspond to the actual structure of reality.
VII. A Note on Intellectual Charity and the Limits of Cleverness
Robertson ends his essay by suggesting that the transcendental argument is not actually persuading many people — that it allows apologists to abuse opponents with clever word games while leaving sincere and intelligent onlookers unpersuaded. He compares it to Socrates destroying Thrasymachus in Book One of the Republic — technically victorious but not genuinely persuasive.
The comparison is more revealing than Robertson intends. Thrasymachus was destroyed because he was wrong. Socrates did not win by a word game. He won because Thrasymachus could not maintain a coherent position under examination. The fact that Thrasymachus felt tricked rather than genuinely refuted is not evidence that Socrates was playing games. It is evidence that being genuinely refuted often feels like being tricked to the person being refuted.
Robertson’s essay throughout exhibits a pattern that is worth naming directly. He is genuinely intelligent and writes with real philosophical sophistication. But he consistently mistakes cleverness for rigor. Showing that a word has multiple meanings is not the same as showing that a philosophical argument relying on that word is a language game. Noting that Gödel proved formal systems incomplete is not the same as showing that mathematical truth is merely conventional. Pointing out that presuppositionalist apologists sometimes exploit semantic ambiguity is not the same as showing that classical metaphysical realism is a series of word tricks.
The Aristotelian-Thomistic tradition has been engaging with precisely the kinds of objections Robertson raises for over two thousand years. It has done so not by retreating into linguistic circularity but by following the intellect’s own telos — its constitutive orientation toward truth — wherever it leads. Robertson’s essay represents a sophisticated contemporary attempt to dissolve that tradition by reducing its foundations to language. But the dissolution fails because language itself — as Robertson uses it, as everyone uses it — presupposes exactly the kind of stable, intelligible, mind-independent structure of reality that the tradition affirms.
The sense of our language, as Robertson himself notes, precedes our understanding of why our sentences make sense. He intends this as a point against transcendental reasoning. It is in fact a precise expression of what the Aristotelian tradition has always held — that the intellect is in contact with being before it theorizes about that contact, that first principles are operative before they are articulated, that reality is intelligible prior to and independently of any particular linguistic convention we construct to describe it.
Robertson’s essay, carefully read, is not a refutation of classical metaphysical realism. It is an inadvertent demonstration of it.
Conclusion
Robertson’s critique of the transcendental argument succeeds as a critique of a specific presuppositionalist formulation and fails as a critique of classical metaphysical reasoning. It succeeds in showing that certain internet apologists exploit semantic ambiguity and construct terminological mazes rather than genuine arguments. It fails because it draws from this limited success the sweeping conclusion that transcendental reasoning as such is a language game — a conclusion that its own argument cannot support without self-destruction.
The Aristotelian-Thomistic tradition does not need words to mean specific things in order for its arguments to work. It does not derive God from the preconditions of linguistic debate. It follows the intellect’s own telos — its constitutive directedness toward truth and being — through a rigorous analysis of contingency, teleology, the immateriality of the intellect, the PSR, and the intelligibility of being, arriving at conclusions that are forced on any honest inquiry rather than constructed from preferred definitions.
Robertson’s attempt to reduce this tradition to a language shell game reveals more about the limits of a purely linguistic approach to philosophy than it does about the tradition it targets. When you have only a hammer every problem looks like a nail. When you have only language every problem looks like a word game. The classical tradition has always insisted that the mind reaches further than language — that the intellect grasps being directly, that first principles are not linguistic conventions but disclosures of reality, that the demand for sufficient reason is not a semantic preference but the intellect’s most fundamental operation.
Robertson’s essay ends by suggesting we get back to more serious arguments. That is an excellent suggestion. The Aristotelian-Thomistic tradition has been waiting.