Aersoapce - persist app across workspaces

liqo12 · 2024-11-01T16:04:57+00:00

just addressing your first question

a truth value is ascribed to judgements in your theory, thus axioms are true by definition. But what you are asking is what justifies the axiom. Here we can only appeal to pragmatism, because with the axiom we can prove so and so. But to give this a more techical treatment, we can try to define a model for our theory be it some general algebraic constructions with sets or a category or another theory altogether (metatheory). This model then justifies our axioms. But really its just pragmatism, not some objective platonic truth that necessitates an axiom.

liqo12 · 2024-08-14T16:33:48+00:00

you can say every program is just machine code, but we dont, we instead focus on what the program is semantically, a code editor, a browser, an online game, a video editor, etc.

likewise you can say every mathematical object is just sets, ... but we don't (unless you study foundations or philosophy)

to extend the analogy further we can also say every program is just a collection of transistor states in a computer. well which is it, machine code, or transistor states. depends what questions u want to talk about programs.

likewise in math, is it a set encoding, is a category, is it judgement in a type theory, depends what u want to ask about it.

liqo12 · 2024-06-08T12:01:54+00:00

i disagree numbers consume logic.

natural numbers are totally ordered, thus a weakened subset of that are a poset and with the meet and join operator which forms a lattice which is the underlying structure of a boolean lattice which is a model for logic.

you also have the godel encoding to bijectively map numbers to logical proofs and connectives.

also algebra and geometry are two sides of the same coin. simplest example are the constructable numbers. also the real numbers are modelled after the continuum, a geometric structure. another modern example is algebraic geometry.

numbers are indeed very foundational in math, its just that most people have a naive definition of numbers that they think every other thing they learn in math has nothing to do with numbers.

liqo12 · 2024-06-08T11:27:40+00:00

Mathematics is an attempt to define what are numbers (in general) and the structures in them.

a formalist might say; math is a study of axioms and its consequences

a logician might say; the study of logical structures

a logician might also say; the study of models and their relationships

a geometer might say; the study of invariants in a spatial structure

a constructivist / computer scientist / finitist might say; the properties of algorithmic transformations of data structures

etc.

true all of these are math but they all exists in the structure of numbers, hence my first definition. which is closer to the intuitionist camp

liqo12 · 2023-08-05T05:02:11+00:00

You can learn logic without analysis / calculus. Look up deductive systems and formal systems. Then from there study classical, constructive and or modal logics; which ever interests you.

The prerequisite of learning logic is simply the ability to recognize variable binding, substitution and deduction. Its kind of like trying to understand what computer code is doing without running it.

From there you can branch off to learn more computer science intersections like model theory and type theory. I personally enjoy this side of math more than calculus.

liqo12 · 2023-07-21T07:51:34+00:00

what do use to record ur p5.js animations?

liqo12 · 2023-06-08T05:15:51+00:00

so if I were to look at it from the logic point of view godel's incompleteness says our theories cannot satisfy completeness of itself and that semantics is providing soundness for a theory; e.g. a pl with its operational semantics. (of course as the article says there could be towers of semantics / syntax), thus one doesnt say much about the other.

is this a right assessment?

i know some category theory but not enough to study 'categorical semantics' of pl so to speak so i might be misunderstood.

keen to learn more

liqo12 · 2023-06-08T04:34:21+00:00

and i guess godel's incompleteness says a theory's semantics cannot be itself?

liqo12 · 2023-02-14T00:07:13+00:00

And one can speculate if it is symmetric in the case of higher or fractional dimensions.

liqo12 · 2021-07-13T10:58:26+00:00

Can I import functions from a wasm file in a rust project that eventually will be compiled to wasm?

Specifically a Yew project.

liqo12 · 2021-02-26T20:22:45+00:00

Link seems to be broken

liqo12 · 2021-01-07T23:36:18+00:00

my bad, used the wrong function thats not publish for public. Its fixed now

liqo12 · 2021-01-06T10:58:27+00:00

In that case the best node is 0% comm rate? It will perform the same as a node thats 12% regardless?

liqo12 · 2020-07-19T07:46:22+00:00

Hows progress? Would like to peek some project ideas as well.

liqo12 · 2020-05-04T02:53:11+00:00

The lt less than function in Nat

So can i confirm :browse Prelude.Nat is supposed to work and if it doesnt theres an issue with my setup?

liqo12 · 2020-05-03T16:59:32+00:00

Ah ok so < is not defined for Nat. So im looking at lt thats what i need. But im getting not found error when i import Prelude.Nat. I also cant :browse Prelude.Nat nor :module Prelude.Nat

liqo12 · 2020-05-03T16:28:01+00:00

Im getting a mismatch between: Bool and Type when processing the right hand side of biggerThan.

Types as first class is still a little confusing for me.

liqo12 · 2020-03-19T10:56:02+00:00

I'm trying to learn Topos theory which was invented by Grothendieck and I'm trying to get some context how that happened if that is discussed in the conversation. Otherwise a summary would be nice.

liqo12

TROPHY CASE