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boris_mon Human Technology: Text Files

You can have the content in markdown and then go through LaTeX for additional stuff (title page, headers and footers etc.)

boris_mon Human Technology: Text Files

Those are not limitations of plain text, those are limitations of your clients.

boris_mon Category Theory Illustrated – Logic

There is some: https://arxiv.org/abs/quant-ph/0101012

And according to the first sentence of the summary the current formulation is axiomatic as well...

boris_mon Category Theory Illustrated – Logic

It's not "experiment rather than logical inference" it's experiment and logical inference.

boris_mon Category Theory Illustrated – Logic

You can do that, but that's surely not the best way to do it, unless the concepts don't have anything to do with each other aside from being part of that field of study.

boris_mon Category Theory Illustrated – Logic

Not necessarily, you have competing theories based on the same kind of logic - it is just that every theory would be based on different set of postulates and will reside in a different logical space (i.e. a different category). But the fact that that two theories don't agree with each other does not mean that one of them is illogical. Actually, I'd argue that they have to both be logical in order not to agree with each other at all i.e. logic is the common ground which enables you to express the differences.

Also, I do think that physics is pretty axiomatic right from it's roots. Newton's main inspiration for forming his theory is the work of Euclid, i.e. first formal system that was ever created.

boris_mon Category Theory Illustrated – Logic

Read the whole paragraph of the book.

boris_mon Category Theory Illustrated – Logic

Because the definition would be circular.

boris_mon Category Theory Illustrated – Logic

There is no equivalent to "neither true nor false" in classical logic, because in classical logic there are no propositions that are neither true or false.

Actually, there is no "neither true nor false" in intuitionistic logic as well, because there is no True and False in a first place. There is only Proven and not Proven.

Don't think in terms of true and false, think in terms of proofs

boris_mon Category Theory Illustrated – Logic

By higher level, I mean big picture. Not necessarily introductory, but ones that don't employ logical concepts such as "proof", "formal" etc, because you cannot define a field of study using concepts from that field. This example is good, but not sure what are you trying to say by posting it (I didn't say that noone ever wrote anything on what logic is.)

boris_mon Category Theory Illustrated – Logic

Corrected the sentence:

"If we view classical logic as based on set theory, then intuitionistic logic would be based on category theory and its related theories."

And regarding the fact that CT is not "needed" for algebraic logic what I say is "category theory and its related theories." where I consider orders related to categories.

boris_mon Category Theory Illustrated – Logic

Well, it has it's limits, but wouldn't call it "flawed".

Regarding the psyche part, I have actually written an article about that which might change your opinion https://boris-marinov.github.io/logic-thought/

boris_mon Category Theory Illustrated – Logic

For category theory, I like Spivak's books.

For logic, it really depends of what you are searching for, for classical logic you can read the the classics, for example Russell and Tarski.

For constructive logic I cannot think of a good introduction (besides mine ;) ), I personally picked it up from books about category theory and computer science.

boris_mon Category Theory Illustrated – Logic

Thanks for the suggestion

boris_mon Category Theory Illustrated – Logic

Thanks

boris_mon Category Theory Illustrated – Logic

In this book I am focused on category theory, but I may write some more about logic in other places.

boris_mon Category Theory Illustrated – Logic

I meant at a higher lever.

boris_mon Category Theory Illustrated – Logic

Inkscape.

boris_mon Category Theory Illustrated – Logic

The bool category is not involved in this. True and False are the initial and terminal object (related to limit and colimit, but not the same thing) of all logical categories as I call them, of which there are many (one for each set of axioms that you might construct).

1. Ordering is not required for a category to be a category, the necessary requirements are just the ones listed in the beginning of the book. It is just that orders can be seen as categories.

2. You can express "A or not A" in intuitionistic logic it is just that it is not necessarily true. Also, not sure how would you express that or any logical relation in set theory.

boris_mon Category Theory Illustrated – Logic

Author here. Yes. Texts says "If classical logic is based on set theory", that is I am comparing the relations to set theory and category theory to that between classical logic and intuitionistic logic. I will try to fix the ambiguity.

boris_mon Category Theory Illustrated – Logic

Also a good formulation. It's amazing how little has been written on the subject (of what logic is.)

boris_mon Category Theory Illustrated – Logic

Thanks for the hint

boris_mon Category Theory Illustrated – Logic

Author here, let me know what you think.

boris_mon Category Theory: Orders

Thanks for this treatment. The truth is that I wanted to write a full section on this, but I didn't have the time, so I decided to only mark it. I will probably remove the reference, as currently it would not add anything for people who are not already familiar with the result.

boris_mon Category Theory: Orders

Interesting take, but I am not sure I agree - parentheses are used to denote a thought that is not directly related to the one expressed in the rest of the sentence e.g. additional clarifications. Of which (this being an introductory material) there are a lot.

boris_mon Category Theory: Orders

Thanks everyone for pointing that and other problems, just made some corrections.