I was browsing the Legal Reasoning section at a law library, and stumbled on 2016 Springer book Logic in the Theory and Practice of Lawmaking. I was curious and flipped. OMG! I have J.D. from Canadian law school and LL.M, and I never saw these math-looking symbols before!

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  1. What kind of logic is this? I scanned just the pages with the most logic symbols.

  2. What level and subject in university do you learn this logic?!? Google previews the book, and page xix starts to list contributors' degrees. I don't see any math degree.

  3. If Canada's law schools are so great, why don't they teach this logic? Anybody know if Ivy League/Stanford or Oxbridge law schools teach it? "Canadian law schools have notoriously high admission standards and successful applicants are justifiably proud of their accomplishment." "Canadian law schools are considered difficult to get into since there's on average, higher admissions standards."

    Steven Haddock LL.B. Osgoode

    Canada. luckily, just has “first-tier” law schools where almost all the students pass and go on to get licensed as lawyers.

  4. Most lawyers don't have Ph.D. in math or logic. Thus how does a typical lawyer learn this logic?

  • The book doesn't seem to be meant as a textbook; it's a collection of research articles by different authors. It may be that this article is mainly intended for other researchers in this specific area of law, not for day-to-day working lawyers who might not find it very interesting or useful. Commented Jun 29, 2019 at 16:40
  • "If Canada's law schools are so great, why don't they teach this logic?": That sounds like a logical fallacy right there. Just because there is at least one topic that a law school doesn't teach, it does not follow that that school is not great. It's obviously impossible for any school to teach every possible topic in a curriculum of a few years. Commented Jun 29, 2019 at 16:41

2 Answers 2


You don't need a PhD in math or logic to understand those pages. Just like a nurse does not to be a doctor to read medical charts and a builder does not to be an architect to read architectural documents.

Most of the confusion is simply the notation I expect. Once the notation is explained and understood you will have no problem. I recommend the basic step of finding where in the book the author defines his notation!

Much of the actual content will be set theory. A completely self contained book about set theory is Naive Set Theory by Halmos. No real mathematical understanding required, and the book is super short; I read it in a few hours.

Other than that the only official "logic" symbols seem to be "implies" and "not" (ie negation)

You can start with the traditional logic rules that;

  • A implies B and B implies C therefore also A implies C: if elephants are mammals and mammals live on earth therefore elephants live on earth.
  • A implies B therefore not B implies not A: if elephants are mammals then something that is not a mammal will not be an elephant.

Note that this last rule is often confused with not A implies not B. That is not true since if it is not an elephant it cannot be verified that it is not a mammal, it might be a tiger!

Basically the author is trying to formally (mathematically express) ideas that permit proofs based on axioms. In the section about cross-conflicts suppose you have a set of all actions one could take, A, and then you have one group of illegal actions, B, and a second group of illegal actions, C, then you have a cross conflict if you can't do a single action without it being in either of the sets B or C. In mathematics your would write the "difference between set A and the union of B and C is the empty set":

A / (B U C) = null

A citizens available actions state you can pay tax at either 10% or 12%.
Rule 1: It is illegal for citizens to pay tax above 11%.
Rule 2: It is illegal for citizens to pay tax between 9.5% and 10.5%

I haven't studied law, so don't actually know the answer to your direct question, but I would expect a half lecture primer on the notation and basic mathematical ideas would suffice.


Logic is foundational in philosophy and argumentation, the later of which is essential in practical law. Other disciplines utilize logic, aside from mathematics. It is extensively utilized in physics and similar sciences in formulating theories and analysis of experiments. Logic is of course extensively used in computer science, where it is foundational in the expression of conditions.

Of course a big part of computer science is the codification of process, the same could perhaps be said of law.

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