# Is this “A unified theory of logic”?

(Apologies for the (near) click-baity pun title.) I want to point out that I do have doubts about posting this since it's a very soft question that could just as well fit in at philosophy.stackexchange, but mainly since it's a request for your opinions. However, I am mainly a mathematician, and I want to hear mainly from mathematicians; And I will take this down immediately, if this type of question is prohibited or frowned upon. Also, in no way am I directing any critique or disrespect towards the author and his work.

Setup

I stumbled across this book recently: Unified Logic: How to Divide by Zero, Solve the Liar's Paradox, And Understand The Nature of Truth, by Jesse Bollinger ((allegedly) an amateur mathematician); Published only a couple of months ago. Obviously a very bold title, almost to the point of being silly. I have only read the contents and parts of the text via previews (about 70 pages avaible), but it seems ambitious; It's about 800 pages, in which it claims to define a new unified type of logic that makes sense of dividing by zero (for an interesting and rigorous attempt at this see Wheel theory, by J.Carlström), and resolving the Liar Paradox, amongst other things. One reason for this question is that I can't seem to find much said about this anywhere, by anyone. I did find this, which seems a bit weird considering what the host of that article does. Now, to my question.

Question(s)

Has anyone here read the book in question (whole text or parts thereof), or know anything of Jesse Bollinger and/or his research? If so, would you mind sharing your thoughts about what you have read. Or would someone with a bit more background in logic perhaps feel inclined to give their first impressions based on what you can read in available previews?

My own skepticism

My suspicion is that this has not reached (affected) the mathematical community for understandable reasons. I admit that I do not take this work too seriously at a glance, but then again: I am no logician, and I have not read the whole thing. I can merely state some of my reasons for being skeptic, such as the very informal writing style and language, combined with the extremely bold claims and mostly the fact that I can't seem to find anything published in a mathematical journal about this, or much else about it at all. He also seems to simplify things quite alot more than you would perhaps expect; especially clear in the first sections on truth. There have been bookloads written in philosophy about theories of truth (I personally recommend Kirkham's Theories of Truth). What I did read didn't seem completely dismissible either, but I would rather take a logicians word on it.

It seems perhaps (at a glance) not very likely to be of great significance to logic research, but works of great significance has come from unexpected places before; Also, perhaps I am not used to seeing books of this seemingly profound nature and serious work, being published if they are pure nonsense.

• What would help to make this question better is if you could be explicit regarding your own experience of reading this book, in particular if you could give your own reasons for skepticism that are grounded in your own reading of passages of the book. – Lee Mosher Oct 10 '18 at 0:56
• Apparently a hobby mathematician? There doesn't seem to be any sort of sample online (and I'm not paying for the book), but just the description pings almost every crackpot alarm. – anomaly Oct 10 '18 at 1:10
• @anomaly Well, sorry, 'amateur' was the word they used in the article in the link. That was the only story I found about it. And, about the preview: Sorry, I didn't want to post links to commercial webpages at first, you can find it at amazon amazon.com/Unified-Logic-Divide-Paradox-Understand/dp/… – Christopher.L Oct 10 '18 at 1:58
• @LeeMosher Thank you! ; and you are right of course. I am off to bed now, I will edit tomorrow. However, I was doubtful in writing as much about my skepticism as I did, since that is rather besides the question (so should I perhaps rather remove it instead). Also, I really didn't want it to sound like criticism. I have only read about 50 pages, and I was merely curious about something so supposedly profound, and that I couldn't find more about, but skeptical by the reasons I perhaps unnecessarily gave. Since I got a very mixed feeling, I guess wanted to know if it would be worth a proper read – Christopher.L Oct 10 '18 at 2:11
• Huh, I wonder why that didn't show up before. Maybe you have to be logged into an Amazon account? Anyway, I've skimmed the excerpt, and there's nothing mathematically worthwhile there. Maybe there's something philosophically worthwhile there, but that's some other board's problem. – anomaly Oct 10 '18 at 2:13

Here's an excerpt:

Definition 4. The set of all objects to which a statement refers once properly interpreted will henceforth be referred to as the semantic set of the statement. The semantic set captures as many objects as necessary to capture the full meaning of the statement, including not just physical objects but also any conceptual objects and relationships that are relevant. The semantic set of a statement and the meaning of a statement are synonymous. The semantic set fully expresses a statement's entire meaning. Just like the symbolic set, it is simply an inert object. Once constructed it is no longer open to reinterpretation or parsing.

(The author does not define what a statement is.) So, no: This is not math.

For comparison, here's a similarly early definition from a random introductory book on mathematical logic on my shelf:

Definition 4.1. A deduction of a formula $$P$$ from a set of formulas $${\mathcal E}$$ (in a language $$L$$ in $$\mathfrak{L}_1$$) is a finite sequence of formulas $$P_1, \dots, P_n = P$$ with the property that for each $$i = 1, \dots, n$$, at least one of the following alternatives holds:

(a) $$P_i\in {\mathcal E}$$;

(b) $$\exists j < i$$ such that $$P_i$$ is a direct consequence of $$P_j$$ using Gen;

(c) $$\exists j, k < i$$ such that $$P_i$$ is a direct consequence of $$P_j$$ and $$P_k$$ using MP.

• Yes, my thoughts as well pretty much, but well I guess I didn't want to be too frank my self =). As I said, I didn't feel in a position to criticize, so I was merely looking to see if anyone knew anything about it. Also, there's about 730 more pages. But I'm starting to realize it's just that simple yes, and perhaps this question was unneccessary. I'll leave it for a while, if no objections, I'll delete it in a few days. I'll at least accept your answer, thank you! – Christopher.L Oct 10 '18 at 2:36
• No problem, it's a totally reasonable question to ask. – anomaly Oct 10 '18 at 2:38