Responding to Jason Brennan’s Review of Square One

Last year, I put out a challenge to some of my academic friends. I’d written a book called Square One: The Foundations of Knowledge, and shortly after its publication, a small group of professors started attacking it, not for its content, but because I’d circumvented the academic publishing process. I wrote the book and didn’t send it in for official peer review. Instead, I sent it to some peers whom I respect, got their feedback, and published the book myself. This method, according to the professors, was sure to produce poor-quality philosophy.

I disagreed. I knew that Square One was in fact a very tightly-argued book that would be hard to argue against. In fact, I’d restricted the scope of the book so great that it’s almost entirely about ideas that cannot possibly be wrong – i.e. the laws of logic. That’s why it’s titled “Square One.” It’s an investigation into ideas which are universally presupposed before making any intellectual claim whatsoever. Even if we disagree on everything else, we can still agree on square one.

So I challenged them: I’ll supply a copy of the book, you review it, and no matter how critical the review, I’ll publish it on my website for everybody to see. Here’s my original post on social media:

Given the limited scope of the book, I thought it would be interesting to see what kind of criticisms could even be mustered! Jason Brennan, a philosophy professor at Georgetown, ended up reviewing the book. You can see his first pitch in the image above. Originally, I didn’t respond to Brennan, since I just assumed he was trolling. He pitched his services to me a couple more times, which I again ignored, until two of my friends pointed out that accepting his offer could be a great opportunity.

They explained, “If he does a hatchet job, it’ll be obvious to people, and it’ll demonstrate the point you keep making – that the formal academy is filled with petty anti-intellectuals who are not serious about the world of ideas. If he actually reviews it seriously… well great! It’ll show that Square One is actually a tightly-focused, tightly-argued work of philosophy that somehow managed to circumvent the standard peer-review process and remain high quality. And hey – maybe you can crowdfund the $1000 to pay him.” Brilliant. I agreed and accepted.

Make no mistake: I expected a hatchet job from the beginning, as my view of academics is pessimistic indeed. You can listen to my predictions beforehand in this video. However, I didn’t expect what actually happened. Not only was the review a hatchet job, but after I posted it to my website, Brennan started making personal attacks against me, some of which were truly outrageous. During this past year, I’ve seen this phenomenon take place on a much bigger scale with the absurd smears of Jordan Peterson and his ideas. Apparently, this is not unique.

Among other colorful claims, Brennan accused me of being a “liar,” “plagiarist,” “thief,” and claimed that I broke our contract. He even pretended that I might not pay him so perhaps he’d need to sue, despite the fact that I offered to pay him before the review was even written. It was a full-blown smear campaign that exceeded my already low expectations.

In hindsight, this was a smart move by Brennan, and I really should have expected it. The review was transparently bad, but by making a bunch of personal attacks, he successfully diverted attention from the review to his accusations. Instead of engaging and evaluating ideas, people were following the personal drama and trying to evaluate whether or not I was a criminal. Clever!

This must be what it’s like to be involved in politics. I was the naive politician standing on the debate stage talking about political theory, while my opponent was the guy pointing fingers and accusing me of being an evil criminal plagiarist. Suddenly, I’m now forced to explain, “No, no, I’m not really a criminal or a plagiarist. See here’s why…”

So, my hat is off to Brennan for his political savvy. For those unwilling to read Square One or uninterested sorting through the personal attacks, I’m sure his method was effective. However, to the smaller group of people who will investigate for themselves, what transpired couldn’t have been a better example of the problems with the modern academy. It’s filled with people who simply do not place a high enough value on the truth. That’s why so many ideas coming out of the academy are poor quality. It’s why so many professors are willing to engage in personal attacks and smear campaigns in order to preserve their professional egos. Truth isn’t the priority.

In the past couple of years, this phenomenon has been demonstrated even more clearly by the personal and professional attacks on Jordan Peterson. I won’t re-post all the ludicrous and laughable smears and misrepresentations of Peterson by the intelligentsia, as that could fill a book by itself, but they all follow the same template:

“According to the official, accredited thinkers, Peterson/Patterson/Person is a poor thinker who makes a bunch of elementary mistakes and is a really bad person too. So if you find any value in his work, you’re probably a low-quality thinker yourself without sufficient education. And don’t bother investigating his work for yourself, since I’m the expert telling you that it’s really bad.”

Of course, I’ve only experienced a slight taste of the vitriol compared to Peterson, but now I see that it simply doesn’t matter who you are, your credentials, the quality of your ideas, or how carefully you articulate them – if academics feel threatened by you, they will attack without regard for the truth.  I won’t re-hash all the personal attacks against me from Brennan, but if you’re interested, I released a video aptly titled “The Jason Brennan Meltdownas these events were taking place. Brennan’s attacks went so far as accusing me of plagiarism, which is one of the most serious, career-damaging claims you can make. Yet, despite the severity of the allegation, he offered zero evidence. No quotes. No names. Not even a slight mention in the review, despite it being the perfect venue. Instead, he tried to damage my reputation by peddling fabrications on social media.

The purpose of this article isn’t to defend myself against personal smears, but instead to analyze and respond to Brennan’s actual review. I’ve been saying for the past year that the ideas in Square One speak for themselves, and this is also true about Brennan’s review. The ideas speak for themselves, and they are poor. “Lazy” might actually be the best term. While I had low expectations for the review, I did not expect lazy non-engagement with my ideas.

But please don’t take my word for it. Sort the truth out for yourself. For the next five days, you can pick up a free copy of Square One on Amazon and follow along.

It’s a short read. Read Square One, then read Brennan’s review and see for yourself if he seriously engaged with the ideas. See if you agree with his remarkable claim that “laypeople would be better off having no exposure to philosophy at all.” Then, if you’re really motivated, re-examine the personal attacks and smears against me, and you might end up seeing why I hold such a bleak view of academia. I do not think Brennan’s dishonesty is unique in academia.

The Review

Brennan’s review is best described as strawmanning the purpose of my book. Instead of engaging with the ideas, he spends most of the review criticizing what isn’t in the book. He pretends as if Square One is supposed to be a philosophical treatise, laying out a complete epistemology and metaphysics. In reality, it’s a short book about logic and truth. This allows Brennan to criticize all the many ways in which Square One doesn’t deliver a new philosophical system. Again, my hat is off to Brennan, since this is a brilliant way to conduct a hatchet job. It doesn’t matter the quality of the ideas in any book – if you strawman its purpose and scope, it becomes trivially easy to attack. If you read Moby Dick as an instruction manual for fishing, it’s one of the worst books ever written.

Despite Brennan’s confusion, the purpose of the book has been clearly understood by readers. The reviewers on Amazon and Goodreads state explicitly that it’s tightly focused, accomplishes its goal, and little more. Nobody else thought it was a treatise on epistemology. Yet, Brennan’s entire review is based on the premise that Square One is supposed to have a broader scope. Keep this in mind as you read through the review. Note just how many words are devoted to discussing other things I could have written about. He spends at least 1,300 words on this. A small fraction of the review engages with the actual material in the book, and it’s mostly packed into the last couple of paragraphs. Brennan simply skips over huge sections of Square One and pretends they don’t exist, hoping that readers will not investigate for themselves.

The last note of preface before: there are actually three different reviews. The first can be read here. The second can be read here. And the third was submitted to The Philosopher’s Magazine. There aren’t substantive differences between them. So for this article, I’ll treat the original review as the primary one, since that’s the one he sent to me to fulfill our agreement. I’ll go through the entire review and give my commentary.

The Review Reviewed

The first four paragraphs are the most accurate, as they are just preface:

Philosophy could use a Tim Harford (The Undercover Economist) or a Steven Landsburg (The Armchair Economist and More Sex is Safer Sex). Both write lucid, engaging books which teach a popular audience the central insights of economics, even if these books do not produce new knowledge.

Steve Patterson wants to do even more. He wants not only to spread philosophical wisdom to the masses, but also to shake philosophy from its dogmatic slumbers. He’s got an audience. As I write this, Square One: The Foundations of Knowledge is among the top 200 epistemology books on Amazon, outselling (older) introductory books by world-class epistemologists like Keith Lehrer, Alvin Goldman, Ernest Sosa, or John Pollock.

In chapter two (and to some degree in later chapters), Patterson presents a range of arguments for radical skepticism. For instance, some skeptics say that claiming to possess knowledge is arrogant. Other skeptics say that to have any knowledge would require us to have far more information than we can possibly acquire. Others claim that knowledge presupposes faith in God. Others claim that natural selection would not evolve truth-tracking brains. Others say we’re stuck inside our subjective perspectives and cannot access objective facts. Still others say that the imprecision or vagueness of language means we lack knowledge, because our language doesn’t carve out nature by its joints. Still others claim that logic and mathematics are Western inventions and cultural artifacts, or that logic and mathematical truths are simply empty tautologies derived from arbitrary definitions and axioms.

Patterson intends to debunk these skeptical arguments. The back cover of Square One declares, “Truth is discoverable. It’s not popular to say. It’s not popular to think. But you can be certain of it.”

A good enough start. It goes downhill from here:

Chapter three—the best chapter in the book—responds to radical skepticism about logic. But his arguments are nothing new. Patterson uses the same argument students learn in week one of PHIL 101: Criticisms of the basic rules of logic are self-refuting. Any argument purporting to invalidate logic presupposes the truth of the rules of logic. Poststructuralist or postmodernist complaints about logic are internally incoherent. Fair enough.

If only students learned the concepts discussed in Square One in PHIL 101! I wouldn’t have had to write the book in the first place.

I assume that Chapter Three was skimmed, unless it’s gone over Brennan’s head. He pretends there’s only one substantial claim that “Any argument purporting to invalidate logic presupposes the truth of the rules of logic.” But this is only one elementary part. There are fourteen parts to Chapter Three.

The whole point of the chapter is to ask, “Why are the laws of logic presupposed?”

Brennan might be content saying, “The laws of logic are presupposed because that’s what we teach you in PHIL 101.” But I’m not content with that explanation. I want to know why and whether or not our presuppositions might be false.

The answer, which you won’t find in a textbook – and indeed, I haven’t found anywhere else – is that logic and existence are inseparable. That’s why logic is presupposed. Everywhere there is something, there are the laws of identity and non-contradiction. Necessarily. It couldn’t be otherwise. It’s a beautiful unification of metaphysics, epistemology, and logic. I spend the entire chapter explaining, in detail, with many examples, this unification of logic and existence. I would be happy to read any other philosopher who has explained this.

Given that this is not Brennan’s area of expertise, I assume he’s simply unaware of the competing theories with regard to logic. I’d recommend listening to some of my interviews on the topic, especially the ones about paraconsistent logic and dialetheism, which tolerate explicit logical contradictions, despite the creators of those theories having attended PHIL 101:

Ep. 9 – Logic, Contradictions, Dialetheism | Dr. Justin Clarke-Doane
Ep. 16 – What is Logic? | Dr. Timothy Williamson
Ep. 42 – Truth and Paraconsistent Logic | Dr. Patrick Girard
Ep. 47 – Problems with Paraconsistent Logic | Interview Breakdown
Ep. 83 – Logic, Contradictions, and the Liar Paradox | Dr. Graham Priest

Another topic to be found in Chapter Three that I must have missed in college is an explanation of the metaphysical status of logic. Here’s an excerpt from Square One:

The most difficult and abstract feature of logic is its metaphysical status. What is logic like? Logic is not some spatially-existent object; you can’t touch it. What is it?

It’s a great question, and I can’t precisely answer it. It’s easier to first state what logic isn’t. Logic is not a “thing.” It isn’t an entity within the universe. It isn’t a “part” of the universe. You can’t say, “Over here is logic, and over there is non-logic.” Logic and existence are universally inseparable. Everywhere you point, there it will be. Logic does not have boundaries. There’s no way to reference “it” as separate from something else.

Logic is the rules of existence. But what is the nature of a rule of existence? Metaphysically speaking, what is a rule?

And it continues. Does this sound like PHIL 101 to you? Brennan is counting on people’s inertia to not pick up and read the book. He simply ignores huge, substantive sections of the book and pretends they don’t exist.

The review continues:

Throughout Square One, Patterson promises to help the reader discover “certain truth” (e.g., pp. 9, 13, 14, 15, passim). It is unclear to me whether Patterson understands the difference between A) the certainty of a proposition itself versus B) the certainty of one’s belief in that proposition. He often seems to conflate logical necessity with epistemic certainty (e.g., p. 54). But these are of course distinct.

A cheap insult designed to imply I’m confused about the basics. In reality, I didn’t write about the difference between logical necessity and epistemic certainty because it’s irrelevant to the focus of my book. The reader doesn’t need to know, so I won’t waste their time. What a wonderful way to criticize somebody by saying, “It’s unclear to me whether the author understands this very basic idea that he doesn’t write about.”

He could have also said, “It’s unclear to me whether Patterson knows how to tie his own shoes,” because after all, I didn’t write about it.

Then, with the highest level of irony, he elaborates:

To illustrate, consider true statement R, a properly constructed formula in sentential logic, which I’ve write below in an abbreviated form:

In unabbreviated form, R is very long. R has 14,000 particles and on the left side of the biconditional and 15,000 particles on the right.

Now, R is not only true, but true in all possible worlds. But since R is so darn long, even the world’s best logician would have less than than perfect epistemic certainty about the truth of R. She would reasonably worry, even if she uses a computer, that she made a mistake when she tried to calculate the truth value for R. This isn’t because she doubts the validity of logic; rather, she doubts herself.

Similar remarks apply to moderately difficult math problems. When I took my last math test in college, I knew my answers were either necessarily true or false. But I also know that I am fallible, so my degree of credence in my answers was less than 100%. I doubt myself, not the universal validity of mathematics. Patterson glosses over or ignores this problem.

Let’s call this a case of “ironic condescension.” Not only does he speculate about whether I know something – due to not writing about it – but he inadvertently demonstrates his own lack of knowledge about the subject. Again, because it’s outside of his area of expertise, Brennan does not understand the competing theories in the philosophy of mathematics.

Take the claim, “I doubt myself, not the universal validity of mathematics.” Sounds like a confident proclamation from somebody who hasn’t studied the subject matter. I guess the idea that mathematics is universally valid sounds intuitively correct to Brennan, so he simply assumes it’s true without a doubt, and continues elaborating on that assumption.

His position, which he incorrectly assumes to be universal, is a version of “mathematical Platonism” – the idea that mathematical truths are “out there,” universally valid, even if humans make mistakes in constructing them. Most mathematicians are mathematical Platonists, but some are not. Take the constructivists, for example. They believe that mathematics is all within the mind, therefore to talk about “universal validity” is nonsense. Or, even more extreme, the intuitionists (founded by mathematicians like L.E.J. Brouwer), who argued that the laws of logic themselves are also human constructions and conventions, and are therefore not universally valid. Intuitionists explicitly deny the law of the excluded middle, and their structure of mathematical knowledge rejects many of the “proofs” and “validities” of orthodox mathematics.

If mathematical constructions are only within the mind – if they do not exist in the Platonic realm – then we cannot coherently talk about many objects in modern mathematics, like “infinite totalities,” since our minds are finite. Thus, what is “universally valid” to some is not “universally valid” to others. See the Banach-Tarski paradox for a vivid example of the perils of assuming valid mathematical constructions cannot be doubted. Hence, the importance of Square One, which does briefly cover the subject of mathematics and logic.

Brennan is entirely ignorant of these ideas and their history. It is a good demonstration of why I’m so critical of peer review. Technically, he’s supposed to be a “peer” reviewing my work, yet he criticizes me for ideas he doesn’t understand.

Even if we grant, as we should, that logical truths are necessary truths, that doesn’t mean we have epistemic certainty about all or even most of them. There are an infinite number of necessary truths in logic and math. But some of these are hard to figure out, so we cannot be certain we got them right, though we know all the true statements are necessarily true and the false statements are necessarily false.

Again he asserts his intuitive notions as certainly true. There are not an “infinite number of necessary truths in logic and math,” unless you assume his one, very particular position on the philosophy of mathematics is the correct one.

Essentially, his commentary about mathematics is a red herring, a waste of review space, and an opportunity to not engage with the ideas in the book. He’s trying to write about ideas outside the book and failing at it. This is highlighted even more boldly by the next paragraph:

This problem aside, Patterson tries and I think succeeds in refuting skepticism about some of the basic axioms of logic. But what about skepticism about other beliefs? For instance, how do I know I’m not a brain in a vat? May I trust my senses? Is it possible that I am being radically deceived by a demon? If so, how can I be justified in thinking I really do have two kids or that I really am 37 years old? The axioms of logic do little to answer these questions, and Patterson does even less. This means Patterson’s critique of skepticism is rather narrow.

I just can’t help but laugh at this section. So I succeed in doing the very thing I try to do, which is explain why the laws of logic are necessary. But I don’t address the other questions that Brennan thinks should be in the book. Right.

Thus, I say Brennan strawmans the purpose of my book. Because it’s so tightly focused – and he even admits I accomplish what I intended – the only option is to criticize me for what I didn’t write.

My critique of skepticism is indeed narrow – extremely so. That’s the point. I intentionally didn’t cover other skeptical arguments, as ironically illustrated by Brennan:

To illustrate, consider these two forms of skepticism:

Super-duper Radical Skepticism:  We can know nothing, not even the rules of logic or mathematical truths. We don’t even know whether super-duper skepticism is justified!

Radical Skepticism: We have knowledge of some mathematical and logical truths, some analytically true statements, and a small number of metaphysical claims. But we are not justified in most of our beliefs about the outside world, such as the belief that the universe is more than two seconds old, or that we have hands, or that we are not in the Matrix, or that Steve Patterson really did write Square One, etc.

Square One refutes what I call super-duper radical skepticism, but not radical skepticism. So, Patterson is right that truth is discoverable, but he doesn’t show us how to discover most of the interesting truths.

So I refute “super-duper radical skepticism,” but not radical skepticism, and Brennan thinks this is a flaw in the book. The trouble is:

I am a radical skeptic!

I don’t think we can have almost any certain knowledge about the mind-independent world.

It would be odd for a radical skeptic to refute the ideas of radical skepticism, wouldn’t it? Yet, for some unknown reason, Brennan assumes he knows my metaphysical position and decides to criticize me for not refuting my own beliefs.

I particularly love the phrase, “he doesn’t show us how to discover most of the interesting truths.” Oh, the interesting ones? Because to Brennan, questions about the laws of logic are uninteresting. He prefers assuming his intuitions are true with regard to the philosophy of logic and mathematics, and he finds examinations into these issues so boring that they don’t warrant analysis.

It takes a special kind of reviewer – a dishonest academic, to be precise – to explain what a book ought to refute, even if it’s the author’s own position. This is so absurd, it makes the entire review look ridiculous. But he continues:

Square One is meant to present a theory of epistemology, but it is unclear whether Patterson knows what epistemology is. He does not even attempt to answer the basic questions of the field.

No, the book is not meant to “present a theory of epistemology.” That’s a strawman. I briefly cover epistemology, but the book is about logic – as anybody would understand after reading it.

Second, he again chooses the “it’s unclear whether Steve understands something basic” tactic. It’s “unclear” to Brennan, since I didn’t write about the ideas he thinks I should have? Ridiculous.  It’s clear to anybody that reads the book without an agenda that I understand epistemology. Read or listen to my work over the last several years. Again, Brennan is relying on people not reading the book. If they do, his speculation looks completely disingenuous.

In the next section, Brennan doubles down on his strategy of criticism about ideas not found in the book. The following section is nearly 500 words long, and it’s devoted to explaining what epistemology is. I’m not kidding. This is an actual quote from an article that’s supposed to be a book review:

Let’s briefly review. The subfield of epistemology studies the nature of knowledge. Its central questions include A, B, and C:

A) What is knowledge?

For instance, epistemologists generally agree that three necessary (but not sufficient) conditions for a person to know that P are 1) the person must believe P, 2) P must be true, and 3) the person must be justified in believing in P.

This brings us to the most important question in epistemology.

B) What distinguishes justified from unjustified belief?

For instance, if you believe that penicillin kills bacteria because the evidence overwhelmingly shows that, then you are justified; if you believe that Santa is real on the basis of wishful thinking, you are not justified. But there are plenty of interesting questions about what takes to be justified. To be justified in believing P, must it be impossible for you to be wrong? How does evidence in scientific reasoning work? When does the testimony of others confer justification, and when doesn’t it? Am I justified prima facie in trusting my senses?

Patterson makes almost no attempt to answer either question A or B. He discusses some examples of justified or unjustified belief, though, again, it’s unclear whether Patterson understands the difference between 1) the truth of a proposition and 2) the epistemic justification an individual person has in believing that proposition.

Epistemology also asks a third, closely related question:

C) Does knowledge have a structure? How do justified beliefs relate to one another?

There are many competing theories trying to answer this question. All such theories are either internalist or externalist. Internalist theories hold justification is entirely a function of an agent’s mental states, while externalist theories hold that justification also depends on conditions outside the agent’s mind. (For example, process reliabilism, an externalist theory, holds that a belief is justified if and only it comes about through a truth-tracking belief-formation process.)

Internalist theories are either doxastic or non-doxastic. Doxastic theories hold that whether a believing agent is justified is entirely a function of her beliefs. In contrast, non-doxastic internalist theories hold that justification depends not merely on the agents’ beliefs, but also on her other mental states (such as her sensory perceptions rather than her beliefs about her sensory perceptions).

Foundationalist doxastic theories says that all beliefs are justified by being grounded in certain basic beliefs. Coherentist doxastic theories claim that there are no basic beliefs, but instead that the structure of belief is more like a web. All beliefs are justified by reference to other beliefs nearby in the “web”. For foundationalists, justification usually moves in one direction, from basic to non-basic beliefs. For coherentists, justification moves in multiple directions at the same time; beliefs can mutually support each other.

500 words of Brennan talking to himself. You can’t make it up. I cannot imagine anybody reading Square One, then reading this review and thinking there’s any connection. It’s just pompous bluster, designed to waste space.

I assume he thought, “I’ll show Steve what epistemology should be about!” Or something. I’m sure his philosophy friends thought it was a really strong refutation.

None of this monologue has anything to do with my book. I’ll leave it to the reader to speculate how it’s possible for somebody to think it was actually a good idea to publish this in a paid book review. Given that the majority of the review is about ideas not found in the book, I suppose it would be appropriate to counter:

Book reviews are supposed to be about the book in question.

He continues:

Patterson seems to want to defend a doxastic foundationalist theory of knowledge in Square One. He laments:

Modern philosophy is dominated by schools of thought that deny the existence of foundations. They argue that worldviews aren’t like trees; they are more like spider webs. Each part is connected together with no clear hierarchy of importance. Each thread is fallible and can be removed without destroying the whole structure. (2)

But there are two big problems with this claim.

First, that’s not a fair description of what coherentists actually think. In fact, most coherentists agree that the web of beliefs is structured. Some beliefs carrying more weight than others. Removing some beliefs (e.g., “There is an external world”) would severely damage the web; removing others (e.g., “There is hot sauce in the fridge”) would not. Further, coherentists can agree that beliefs are certain or express logically necessary claims, though they deny this makes such beliefs foundational.

No, I am not “defending a doxastic foundationalist theory of knowledge,” because I’m not working within the confines of academic taxonomy. Square One has very clear goals:

  1. Discover certain truth.
  2. Figure out how we know it’s certain.
  3. Analyze the relationship between logic and existence.

That’s just about it. I’m uninterested in how academics might label it, but it’s another solid tactic from Brennan to mislead and critique. “Oh, well I think he’s really trying to make the case for X, even though he doesn’t say so. Since he doesn’t make the case for X very well, it’s not a good book.”

However, I will give Brennan some credit here. He did find an ambiguous sentence that, if isolated out of context, is poorly written. When I say, “Each part is connected to another part with no clear hierarchy of importance,” if you stop reading immediately, then it would appear incorrect. The next sentence, however, clarifies its meaning, “Each thread is fallible and can be removed without destroying the whole structure.”

The point is that it’s not a layer-by-layer building of one belief on top of another. It’s not to say that each thread is completely isolated from one another. Again, with the spider web analogy, some threads are clearly more important than others for maintaining the structure. There’s still some kind of hierarchy, but not a linear one built upon clear foundations.

So, I can see where an uncharitable reader might find that sentence incorrect. Finally, criticism that could pass as substantive. Unfortunately, he then takes this point too far:

Second, Patterson is right that foundationalism is now unpopular, but, pace Patterson, so is coherentism. The PhilPapers survey finds that only 26.2% of philosophy faculty accept any form of internalism, while 43.7% accept some form of externalism. The numbers are roughly the same for specialists in epistemology.[1]

Patterson advises his readers to doubt themselves and vigorously check their premises (5). He should take his own advice: If he bothered to research what philosophers think and why, he wouldn’t strawman the field.

The perils of thinking like an academic. Again, I am not writing about “Foundationalism” or “Coherentism” proper. I’m uninterested in labels. They’re a poor shortcut for getting around critical thinking. You cannot understand somebody’s ideas by their self-label. I know lots of people who label themselves as “conservative,” “liberal,” or “libertarian,” while believing ideas that are inconsistent with their labels. Thus, I focus on the ideas, not the labels.

My book is about the foundations of knowledge, not Foundationalism-the-formal-theory. The ideas I cover are those found in the book – what can we know with certainty, how can we know it, and are the laws of logic universal and necessary? That’s an examination into the foundations of knowledge, not Foundationalism Proper.

To demonstrate my point, take the interview I had with Timothy Williamson, the most prominent logician on the planet. Williamson is known for being a Classical Logician. But that doesn’t tell you anything about his ideas. That’s simply his label.

Williamson has spent his career defending classical logic, yet when I asked him whether the laws of identity and non-contradiction are certain, he said no! Timothy Williamson, of all people, was not comfortable claiming certainty about the laws of logic. That’s not something you’d discover simply by polling him about his label. You have to sit down and talk with people, in detail, about these topics in order to get at their ideas.

From my experiences talking with philosophers in depth about this question, I’d say that the majority would reject the idea of 100% certain knowledge – even the self-labeled “Foundationalists.” That’s what I’m interested in, and that’s what my book addresses.

Next, Brennan wastes more space criticizing what I didn’t write:

All this aside, Square One never actually gets around to defending foundationalism. He gives us lots of unoriginal metaphors about trees and roots, houses and foundations, and the like. He declares in chapter three that logical axioms are among the foundations (32). But he never tries to show us 1) which beliefs (aside from logical axioms) are basic, 2) how these basic beliefs justify our non-basic beliefs, or 3) which mental states justify the majority of our non-mathematical beliefs. He therefore provides no evidence that our beliefs form a foundationalist structure. He responds to none of the common objections to foundationalism; he may be unaware of them.

Yet again, to say “Patterson never gets around to defending a set of ideas he doesn’t espouse” is not a good criticism. This excerpt is especially revealing, so I want to break it down even further.

He declares in chapter three that logical axioms are among the foundations (32). But he never tries to show us 1) which beliefs (aside from logical axioms) are basic…

I can’t help but laugh at the words inside the parentheses, “aside from logical axioms.” To be clear, the entire purpose of my book is to show that logical axioms are square one – or more specifically, the unification of the laws of logic with existence. That’s it. Brennan is admitting that the book accomplishes its purpose. Yet, because he’s interested in other beliefs, the book fails to deliver.

2) how these basic beliefs justify our non-basic beliefs…

I have exactly zero words dedicated to “justification” in my book. Irrelevant and inappropriate for Square One.

3) which mental states justify the majority of our non-mathematical beliefs.


He therefore provides no evidence that our beliefs form a foundationalist structure. He responds to none of the common objections to foundationalism; he may be unaware of them.[2]

I don’t engage with literature that’s irrelevant to the focus of my book. That’s correct. I also don’t address trolley problems. I may be unaware of them.

I do want to focus again on one quote:

He declares in chapter three that logical axioms are among the foundations (32)…

I recommend Brennan reread my book, since he’s not understood its central point. (That’s why hyper-focusing on the foundations is so important – even professors being paid to review something can miss the whole point.)

Logical axioms are not among the foundations. They are the foundations. Logic and existence are universally inseparable. To imply that there are other foundations is to imply that some beliefs are non-logical – that they do not presuppose the laws of identity and non-contradiction.

It seems that Brennan’s expectation of reading a complete theory of epistemology has stunted his thinking about logic. Square One is about logical axioms. Logical axioms are square one. They are the foundations of knowledge. Hence the name of the book. Every other reviewer of Square One understood this. For some reason, Brennan did not.  Next:

Patterson asserts that the axioms of logic are the foundations of our beliefs. He’s right, of course, that our beliefs should be compatible with logic. But it doesn’t follow that these axioms somehow justify most of my beliefs or that my beliefs are “grounded” in logic in any interesting way. I believe I own more than two guitars, that I have brown hair, that I have thirty-two teeth, that Australia is bigger than Rhode Island, and so on. If any of these beliefs violated the axioms of logic, they would necessarily be false. But other than that, there’s no obvious way in logic provides the roots from which these beliefs grow.

At risk of repeating myself, I’ll again break this paragraph into parts:

Patterson asserts that the axioms of logic are the foundations of our beliefs.

We begin with a tension from the previous claim. Are the axioms of logic “among” the foundations, or are they the foundations?

He’s right, of course, that our beliefs should be compatible with logic. But it doesn’t follow that these axioms somehow justify most of my beliefs or that my beliefs are “grounded” in logic in any interesting way.

Again, Brennan doesn’t want to read about logic. He wants to read about “justification” – a rabbit hole that academic philosophers have wasted goodness-knows-how-much time going down. I do my readers a favor and don’t cover it. Brennan uses the absence of commentary about justification as another opportunity to strawman.

More importantly, it’s bizarre to see a philosopher claim that the axioms of logic are uninteresting. We’re talking about a set of truths that are presupposed by 100% of our other beliefs, that we can be certain about because they couldn’t possibly be wrong, and that form the foundation for our entire worldview. This is uninteresting to a philosopher? Preposterous! Nothing could be more interesting or important.

I suspect Brennan is simply unaware of the many different opinions regarding the laws of logic. There are philosophers who’ve been arguing for a long time that the laws of logic are a human convention, that they’re optional, or that downright logical contradictions are tolerable. Brennan should know this, but I suspect he does not.

He continues:

I believe I own more than two guitars, that I have brown hair, that I have thirty-two teeth, that Australia is bigger than Rhode Island, and so on. If any of these beliefs violated the axioms of logic, they would necessarily be false. But other than that, there’s no obvious way in logic provides the roots from which these beliefs grow.

Truly, you can’t make it up. “If any of these beliefs violated the axioms of logic, they would necessarily be false. But other than that…”

That’s quite the hand wave. Allow me to rephrase:

Square One explains a set of truths which are so fundamental that any refutation of them would necessarily be false. But other than that…”

Well, given that’s the whole purpose of the book and a personal obsession for the last decade, I’d say it’s an accomplishment.

Instead, the justification of these beliefs depends on various perceptual states I’ve had, on the reliability of the testimony I’ve received from others, and whole host of other interesting issues which epistemologists routinely discuss and which Patterson mostly ignores. If Patterson intends to defend foundationalism, his project is radically incomplete. He’s not even 1% of the way there.


Patterson does not discuss or attempt to refute rival epistemology theories. That’s not some minor oversight. To defend foundationalism, he needs to show the theory does a better job explaining the phenomena than the rival theories. Defending an epistemological theory is like selling a car; if you want us to buy the 3-series you need to show us it’s better than the C Class.

Again, irrelevant.

I did not set out to “refute rival epistemological theories” or “defend Foundationalism.” Square One is not about academic philosophy. It’s about philosophy.

Brennan somehow didn’t understand the scope of my book. Perhaps he skipped the introduction. I’ll post it here for reference:

Truth is discoverable. I’m certain of it. It’s not popular to say. It’s not popular to think. But I know it’s true. Anybody can discover truth if they know where to look. It only requires skepticism and an open mind. Don’t take my word for it. Scrutinize every claim in this book, and if you discover no truth, then you may confidently discard it in the trash.

The reader can rest assured: this book is not a work of academic philosophy. It’s not incomprehensible or irrelevant. It doesn’t try to sound profound by hiding behind opaque language. It is meant to be read and understood.

The first two chapters are preface. The core ideas are in Chapters Three and Four, and the last chapter is my response to anticipated objections. My conclusions are based on a decade of radical doubt and introspection. I was not sure if truth could be discovered, but now my extreme skepticism has been overcome, and I want to share the reasons why.

Note how many times I use the terms “foundationalism”, “epistemology,” and “justification” in the introduction. Every other reader of Square One grasped the book’s purpose, except Brennan.

To summarize: Patterson does a decent job defeating what I call “super-duper radical skepticism.” He does almost nothing to defeat what I call “radical skepticism.” He does not actually bother to defend a foundationalist theory of knowledge.

Again, you really can’t make it up. I successfully refute the ideas I intended to refute, but I did not refute ideas that I believe to be true. What an oversight.

Still, his book beautifully written, takes only an hour to read, and at least defeats super-duper radical skepticism.

Well thanks. So Square One is a short, well-written book that accomplishes its goals. Could have just said that at the beginning.

We might ask: Is this at least a good book for a lay audience? Unfortunately, the answer is no, for two big reasons. First, there are far better books, such as Thomas Nagel’s The View from Nowhere or Michael Huemer’s Skepticism and the Veil of Perception.

An ironic choice of books, given that neither explains the laws of logic, nor their unification with existence. Huemer’s book is about skepticism of the external world, which Brennan apparently thinks is the only skepticism worth writing about. It’s especially ironic, since Huemer’s book is a defense of direct realism, which is the exact opposite of my own position. Brennan spent no time investigating whether I’m actually a skeptic and erroneously assumed he knew my metaphysics.

Second, Patterson’s book is chock full of elementary errors. Nearly every page contains some major mistake or conflates two or more distinct ideas together.

Ah, now we’re talking! Brennan waits until the very end of the review to make any concrete claims about inaccuracies in my book. Let’s see how he does.

For instance, on p. 61, he says that “The study was unbiased” and “The study was conducted properly” are “concepts”. But these are propositions, not concepts.

And, pray tell, what are propositions?

In Brennan’s defense, I don’t think metaphysics is his area of expertise. So perhaps that’s why he thought his first intuitions might pass as a proper argument.

Propositions are, in fact, concepts.

What unifies a bunch of words into a proposition? What makes a proposition different from random sounds and words on paper? A mind. Propositions are ideas inside the mind.


On p. 83, he says, “Mathematical truths, if carefully constructed, can also be immune from the possibility of error.” But this once again conflates metaphysical/logical necessity with epistemic certainty/justification or with a person’s math skills. Mathematical truths cannot be in error, but I could be in error when I try to do a math problem or when I form beliefs about mathematics.

Brennan again blunders outside his area of expertise. He apparently doesn’t understand the philosophy of mathematics, either, yet feels his intuitions are good enough to attempt criticism. To explain:

There are many mathematical “truths” that in fact presuppose a particular metaphysics. If you doubt the metaphysics, you can actually doubt the mathematical “truths.” Take, for example, the Banach-Tarski paradox. From the online article:

“The “paradox” – in fact an impeccable mathematical theorem – says that a small sphere, for example a pea, can be cut into as few as five pieces which can then be reassembled so as to make a far bigger sphere, for example the sun.“

A remarkable claim. How is this possible?

In fact, the secret lies in the strange dissection used – the “pea” is cut into five pieces according to a method that could never in real life be implemented. The pieces are so-called “non-measurable” sets, which means just what it sounds like: sets that cannot be assigned any size (or “measure”) at all without causing contradiction. By their nature, non-measurable sets cannot be constructed via explicit geometric steps, and, as the author says: “Some might find it disagreeable that such sets exist, but that is mathematics!”

Ah, the secret is revealed: metaphysics! The Banach-Tarski paradox explicitly presupposes mathematical Platonism in order to be valid – the real existence of so-called “non-measurable sets,” that reside outside of space, time, and the mathematicians’ own minds.

If you doubt mathematical Platonism or the existence of actual infinities – say you’re an intuitionist – then the Banach-Tarski paradox does not hold.

Thus, Brennan’s naive claim that “mathematical truths cannot be in error” is simply a matter of ignorance. What one mathematician considers “impeccable” or “certain” is dogmatic nonsense to another. Mathematics is not immune from metaphysics.

There are many more examples of this in the philosophy of mathematics. I assume Brennan is unaware of them.


On p. 36, he discusses the phrase “The elephant outside my window”. He says that since there isn’t actually an elephant outside his window, then the referent of “elephant” is an idea or a concept in someone’s head. But that’s not right. To see why, let’s use Russell’s example. Suppose we say, “The present king of France is bald.” If, as Patterson claims, the definite description “the present king of France” refers to an idea, then the sentence “The present king of France is bald” is true; after all, ideas are hairless and so therefore bald. But that’s absurd.

More strong opinions based on what I assume are Brennan’s simple intuitions. It would be tempting not to blame him for errors in metaphysics, since that’s not his area of training. However, since he felt confident enough in his grasp of metaphysics to include them in a book review of Square One, sloppy thinking on this topic has little excuse.

Brennan has again assumed his own position in the philosophy of language and metaphysics is self-evidently correct, while other positions are “absurd.”

It’s entirely debatable what exactly I’m referring to when I say, “the elephant outside my window.”

Though it’s beyond the scope of Square One, I think it must be the case I’m referring to an idea. Again, I start from a position of radical skepticism – meaning, I don’t presuppose the existence of an external world – when examining the fundamentals of language.

We know words refer. But since we don’t know there’s anything outside our minds, words must refer to ideas in our heads. Whether they also refer to objects outside of our mind is a separate question.

Reference can be either direct or indirect. When I’m talking about “the laptop in front of me,” I pretend that I’m directly referring to a physical object in the world. However, I cannot know such an object exists. I do know I’m referring to something directly (an idea), and I assume it correlates indirectly to an object in the world.

All of our direct referents are mental. Indirect referents can be anything.

So, when we’re talking about “the elephant outside my window,” we’re directly referring to an idea in my mind. It has no indirect referent (or so I assume).

When we’re talking about “the tree outside my window,” we’re directly referring to an idea in my mind. It has an indirect referent (or so I assume).

The same is true with “the present King of France.” I’m directly referring to a set of ideas in my head. It does not have an indirect referent (or so I assume).

Thus, Brennan is conflating direct and indirect referents. When referring directly to “the present King of France,” we’re referring to an idea. However, unless we’re explicitly in a philosophical conversation, most people don’t use language this way, and we walk around pretending that we’re talking about the indirect referents of our language. Since there is no indirect referent of “the King of France,” Brennan’s criticism falls flat.

Now, it’s entirely reasonable to have a different metaphysics and philosophy of language. However, it’s not reasonable to assert that ideas contrary to your own are “absurd,” then waste space in a book review criticizing somebody for not sharing your own assumptions.

0-for-3. Brennan’s last attempt:

His treatments of the theory-ladenness of observation (63-66) or the problem of vagueness (pp. 100-104) are superficial, though a lay audience won’t know better.

… And that’s it! He finishes his list of concrete criticisms with a hand wave. No examples of superficiality. No quotes. Just his own expert conclusion, backed up with literally nothing. How does one respond to such a vacuous claim? Read the section on theory-ladenness for yourself. It’s quite short.

My favorite line from Brennan’s review:

Laypeople would be better off having no exposure to philosophy at all.

Ah, now we get to the heart of the matter. This cheap insult is most accurately read as a plea not to read literature unapproved by the intelligentsia. They like to think of themselves as the gatekeepers of good and bad ideas, and they need you to think so as well. Academics in general, like those who lambast Jordan Peterson, are desperate to maintain relevance and prestige. Fortunately, technology is rendering them obsolete.

Brennan knows that every person who reads Square One with an open mind, then reads his review, will see a hatchet job. It’s blatant. Arrogant. Reflective of something toxic within the academic mind.

He’s making a request that people won’t read heretics like me, because if they do, they’ll be left with some perplexing questions. They might end up losing faith in the expertise, trustworthiness, and credibility of experts. After all, how could a review be so critical, when the actual book is tightly argued, well-reasoned, and well-written? How could a professor of philosophy confidently dismiss ideas he’s utterly clueless about?  Is this an isolated case, or might it be a systemic problem? What were the real motives involved?

I admit a large part my motivation for accepting Brennan’s request to review my book is because I thought he would butcher it, thus demonstrating my point and perpetual criticism of academia. These people cannot resist an opportunity to preen themselves to try and cope with their personal and professional insecurities. By my metric, the review was a spectacular success.

But really, don’t take my word for it. Read Square One and decide for yourself. It’s currently free. According to Brennan, it’ll only take you an hour. Then you’ll understand why either of the following must be true:

  1. Philosophy shouldn’t be done by amateurs, and people would truly be better off having no exposure to philosophy than reading my book.
  2. Philosophy must be done by amateurs, because the profession has been overtaken by disingenuous anti-intellectuals who place their petty insecurities above serious engagement with ideas.

Brennan concludes his review:

In the end, Square One is a beautifully written text, with lucid prose and delightful metaphors. But nearly every page contains a major mistake. What’s new isn’t good and what’s good isn’t new. Five stars for style; one star for substance.

I do appreciate the compliment of my writing style, but the claim that “nearly every page contains a major mistake” is a lazy lie that anybody with a spare hour can refute. It’s even inconsistent with his own previous claims. Instead of mistakes on every page – which he gives zero evidence of – I’ve seen him identify one single sentence in the entire book that was poorly written.

The flippant remark “what’s new isn’t good” is another easily-refuted dismissal. Square One does cover a few other subjects including a novel resolution to the Liar’s Paradox. Brennan addressed exactly zero points from Chapter Five, which cover concepts like vagueness, universal flux, “nothingness.” Eastern mysticism, quantum physics, and tautologies. He simply pretends these sections don’t exist.

A Dull Hatchet

In all, it’s clear that Brennan’s review was a hatchet job. A hit-and-run review. His primary tactic was to strawman the purpose of the book and pretend it was a treatise on epistemology. The majority of the review is spent elaborating about ideas not found in Square One. It also skips over important sections and glosses over the central claim that logic and existence are inseparable.

The few concrete engagements with the material are failures. Brennan chose to engage in areas related to the philosophy of mathematics, language, and metaphysics. Yet, he demonstrates a poor grasp of the relevant concepts – a completely insufficient level of understanding to justify criticizing somebody else’s ideas on the topic. When taken together with the personal attacks and attempted character assassination of me, it paints a bleak picture indeed.

Unfortunately, I do not think Brennan is an isolated case. I think the academy is filled with people like him – not because academics are inherently unethical, but because the structure of the academy enables this kind of behavior. If academics are the only ones allowed to criticize academics, it shouldn’t be surprising that the industry is corrupt. The incentives do not reward truth-seeking. They reward pettiness, politics, and insularity from the outside world.  I hope his review serves as a good demonstration of the bad apples currently rotting inside the ivory tower while professionally flourishing. For anybody else working independently in the world of ideas, now you know what caliber of engagement to expect.