A: How much is 2 + 2 x 0?
B: Uhm... I'm not sure. I guess 0?
A: It's 2! Ha-ha, you don't know math!
B: I can infer by what you say, that there is a mathematical convention that I didn't know of, which defines a preset order of operations in the absence of parentheses. However, although it is important to master such details, I believe the essence of mathematics is not convention, but proof. To understand mathematics one must master precise definitions of the concepts which make up mathematical propositions, and engage in demonstrative reasoning to obtain new and interesting propositions. Moreover, in a deeper and more personal sense, mathematics is about using those propositions to understand the objects that make up an abstract realm, full of chaos and complexity, full of breathtaking beauty and the horror of being in presence of something eternal, infinitely greater than oneself. So, yeah, 2 + 2 x 0= 2. Sorry about that.
A:
Pieces of knowledge do not follow upon one another as a matter of mere succession. Rather, they enter into logical relations with each other, they follow from each other, they agree with each other, they confirm each other, thereby strengthening their logical power.
 — Edmund Husserl
You see, there is a branch of human knowledge known as symbolic logic, which can be used to prune away all sorts of clogging deadwood that clutters up human language.
 — Salvor Hardin in Foundation (Isaac Asimov).
Faith: is the possible world framework a variation on quantum mechanics?

Thanks:

Thanks for this interesting question, Faith!  I’m going to give an explanation of the question in simple terms, folks that already know the basics of the many-worlds interpretation and possible world semantics may skip to the two sections at the end of this post.

First I’m going to talk about the many-world interpretation of quantum mechanics. Sorry if I’m sloppy or plain wrong, I don’t know very much about this, I just want to give a general idea!

The paradox of knowability is a logical result suggesting that, necessarily, if all truths are knowable in principle then all truths are in fact known. The contrapositive of the result says, necessarily, if in fact there is an unknown truth, then there is a truth that couldn’t possibly be known. More specifically, if p is a truth that is never known then it is unknowable that p is a truth that is never known. The proof has been used to argue against versions of anti-realism committed to the thesis that all truths are knowable. For clearly there are unknown truths; individually and collectively we are non-omniscient. So, by the main result, it is false that all truths are knowable. The result has also been used to draw more general lessons about the limits of human knowledge. Still others have taken the proof to be fallacious, since it collapses an apparently moderate brand of anti-realism into an obviously implausible and naive idealism.

10 Logic Questions for Hegelians

1- What is the Hegelian conception of logic?

2- What is the role of formal logic, if any, within the Hegelian conception of logic?

3- Is there something like a fixed logic canon (for a given time in history)?

4- If there is something like a fixed logic canon for a given time in history, does that change over time?

5- Are inductive inferences valid?

6- Is there a logic foundation for inference to the best explanation?

7- Is the principle of identity valid? Why?

8- Is the principle of non-contradiction valid? Why?

9- Is existential quantification more primitive than universal quantification or viceversa?

10- Is there unrestricted quantification?

When a Hegelian classmate speaks against the principle of non-contradiction during logic class.