A Book Smarter Than You: Gottlob Frege’s The Foundations of Arithmetic

I’ve recommended a lot of books on this blog, but I’m certain that none of them will be a harder sell than Gottlob Frege’s The Foundations of Arithmetic. Despite being a pretty slim book, it’s an extremely dense read, it has a title that would bore most people, and it’s about analytic philosophy, which there’s a good change you either haven’t heard of or would be equally bored by. Plus, it’s so hard to understand that even I, who voluntarily read it wanting to comprehend it all, only feel like I grasped about 60-70% of the content.

So why am I writing about it? Because I think reading this book makes you a better reader, a stronger reader. And so even if you aren’t exactly thrilled by the title, I hope you’ll read on and allow me explain just how valuable this book – and books like it – can be.

And by books like it, I’m referring to books smarter than you.

Let me explain what I mean by that. One of the things that concerns me most when I talk to students about books is that too many of them are frequently intimidated by certain texts or authors. They have been conditioned somehow to imagine Shakespeare is simply beyond their grasp, or that they could never read, let alone understand, authors like Simone de Beauvoir or Hegel. So they tend to gravitate toward more accessible books. There’s nothing inherently wrong with that, of course, but reading such books doesn’t make you a stronger reader. Also, I flatly refuse to believe them when they say – and a few have literally told me this – that particular subjects, books, or authors are permanently beyond their cognitive reach. No – the fact is that anyone can read anything, and I frankly think that if a text is so obscure and dense that not even someone who wants to get it can get through a single sentence, well, that’s the fault of the author. Texts should be written to be understood, and anything that just wants to “sound smart” isn’t worth reading.

Which brings me to Frege’s The Foundations of Arithmetic and what is has to offer you:

  1. Analytic philosophy is a subject worth familiarizing yourself with on its own and is extremely new, in the history of all philosophy. It also epitomizes the massive impact science had on philosophy. In essence, certain philosophers (especially members of the Vienna Circle) felt that earlier philosophers were too vague, their works little more than fiction or baseless theories without any evidence to back them up. For instance, consider Thomas Hobbes – his Leviathan still influences the way people talk about the “state of nature” before civilization, but his notions of what the earliest humans were like and how they interacted had no basis in any facts whatsoever. Modern anthropology has actually disproved pretty much all of his primary arguments, especially the idea that human sociability is something that only arose by being forced upon them by “civilization.” In contrast, these new analytic philosophers were concerned about what we can know and how we know what we think we know. That’s where logic comes in. This new philosophy attracted more mathematically-inclined men and women who saw the effort to precisely define words and the way we reason as critically important if we were ever going to try and discuss anything “big” or…clearly I could write a whole post on analytic philosophy so I’ll stop there.
  2. Frege’s book is reminiscent of a Platonic dialogue, except here the question is “what is a number?” (this point was helpfully made by an Amazon reviewer). It’s one of those questions that seems obvious until you start to really think about how you would define it and how we even come to know of the concept’s existence. Similarly, what if I asked you to explain, as if to a child or alien, the difference between a sign and a symbol? Could you do it? What about the concept of space or time? Again, this effort to rigorously define things reflects the unease certain philosophers felt when they saw how loose the foundation was upon which so many ideas rested. To take another similar case, consider language – you undoubtedly learned to speak before learning the rules of your language, and perhaps don’t know all of them even now. But if you wanted to talk about the language, teach it to someone else, or explore it on a conceptual level, don’t you think it would help to know those rules? And what would you think if you realized those rules didn’t exist? Would you make them up? How would that affect your understanding of language?
  3. Finally, pushing through this book and trying your best to understand all the twists and turns of Frege’s arguments will indeed make you a stronger reader because it will sharpen your thinking itself. Personally, I decided to tackle this book after reading a series of history books because the subjects were getting increasingly complex and I wanted to make sure that, when I thought about them, my mind was as sharp as possible. And I’m certain I’ll continue to punctuate my historical or political reading with similar texts in the future.

In short, if you’re someone at all interested in philosophy, this is a must-read, as it’s among the first texts that truly kicked off analytic philosophy. I’m not saying Frege is 100% right (in fact, Bertrand Russell was among those who pointed out a fatal flaw in Frege’s larger philosophical system), and there’s plenty that could be said about how Wittgenstein’s later work can be seen as a rebuttal of some of Frege’s points, etc. but engaging with the ideas can only help you better understand why you believe what you believe. And if you’re not someone who isn’t that interested in the subject, you’ll still find immense value in this book for all the aforementioned reasons.

Plus it’s a hell of a challenge, and who doesn’t like a challenge?

So go read it. Now.





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