Jason Brennan’s Original Review of Square One

Update: read my full response to Brennan’s review here. The ideas speak for themselves.

Here is the review Jason sent me and submitted to NDPR. He apparently updated it afterwards. Below you’ll find the original version, which is what my video responds to. Not too much gets changed – except now he tries to give even less credit than before, by changing lines like:

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.

And turning it into:

Square One repeats the arguments which refute super-duper radical skepticism, but it does not respond to 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 now, it’s no refutation – it’s repeating somebody else’s argument! You can’t make this stuff up. The original review is  below:

Steve Patterson, Square One: The Foundations of Knowledge. CreateSpace Independent Publishing, 2016. 125 pages (ppk), $9.99. ISBN: 978-1540402783

Review by Jason Brennan, Georgetown University

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 that we can possibly acquire. Others claim that knowledge presupposes faith in God. Others claim that natural selection would not evolve truth-tracking brains. Others says 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.”

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.

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.

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. 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.

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. 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 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.

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

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.

Patterson seems to want to defend a doxastic foundationalist theory of knowledge 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.

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.

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 foundationalism; he may be unaware of them.[2]

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.

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 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 car; if you want us to buy the 3-series you need to show us it’s better than the C Class.

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. Still, his book beautifully written, takes only an hour to read, and at least defeats super-duper radical skepticism. 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. 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. Laypeople would be better off having no exposure to philosophy at all.

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. 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. 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. 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.

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.

[1] https://philpapers.org/surveys/results.pl?affil=Philosophy+faculty+or+PhD&areas0=11&areas_max=1&grain=coarse

[2] See, e.g., John Pollock and Joseph Cruz, Contemporary Theories of Knowledge (Boulder: Rowman and Littlefield, 1999), pp. 60-65; Keith Lehrer, Theory of Knowledge (Boulder: Westview Press, 2000), pp. 50-95); Ali Hasan and Richard Fumerton, “Foundationalist Theories of Epistemic Justification,” The Stanford Encyclopedia of Philosophy (Winter 2016 edition), ed. Edward N. Zalta, URL = <https://plato.stanford.edu/archives/win2016/entries/justep-foundational/>