## Search found 191 matches

Sun Jul 09, 2017 11:56 pm UTC
Forum: Mathematics
Topic: Is a meaningful disinction possible?
Replies: 1
Views: 1870

### Is a meaningful disinction possible?

It is perfectly reasonable to think that many small differences can eventually become a distinction such that different rules now apply. Can we quantify this in any way? Do the rules slowly change with the sum of differences? Or is there a sudden phase change at some point? As far as I can tell &quo...
Sun Jul 09, 2017 2:01 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Did I say there would be deflection? Nah - no deflection going on here. @ucim: You are attempting to mock - but, of course we are talking about solipsism. The whole point is to understand what we can 'know' in the face of "Cogito Ergo Sum". We clearly do communicate and understand things (...
Thu Jul 06, 2017 2:49 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

This is both true and seemingly irrelevant. Yay! *Does a little jig of happiness* And, reading between the lines - Cauchy is saying much the same - that he agrees we only have sensory data but doesn't see why I'm making such a fuss about it. In answer to Cauchy's question: "What is the big dea...
Tue Jul 04, 2017 6:14 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

What a glorious Gordian Knot of an argument. What is your argument? I can see that you wholeheartedly believe that there exists a distinction and that this distinction is key. What I don't see is an explanation of what the distinction is, how it arises, what it applies to (in a way that allows me to...
Sun Jul 02, 2017 1:43 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

@LaserGuy: You've drawn an equivalence between mathematics and fiction. I am inclined to agree with this equivalence. And I don't think it helps your argument. (more below - ucim makes a similar kind of argument). @ucim: abstraction isn't unique to mathematics. E.G. While biology has specific strand...
Wed Jun 28, 2017 2:48 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Ah... Magical thinking. Mathematics has different rules to other sciences because... reasons... Let me rephrase what you are trying to convey: "Mathematics isn't constrained by the same rules as apply to everything else in the universe." or "Pure thought is independent of the physics ...
Sun Jun 25, 2017 1:54 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Introduction We agree that there is a pedantic, technical limit that is unreachable. That, in practice, mathematicians don't hold themselves to a standard that is impossible to achieve. This impossibly high bar is specified by the Laws of Thought. The 'practical' solution that mathematicians take i...
Fri Jan 20, 2017 8:09 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Hiding simplicity behind words Last post I posited two sets. One set of symbols and A.N.Other set. I then asserted that there was no way to specify a single known mapping between these sets using only symbols. None so blind as those who will not see In doogly's case, it can be argued that he is re-...
Tue Jan 10, 2017 10:03 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Ho boy! We have Demki insisting that I formally prove that it is impossible to formally prove (or define) anything. We have gmalivuk confidently asserting the existence of definite definitions (without providing any support for his assertions) despite acknowledging the existence of the Foundational...
Sat Jan 07, 2017 6:23 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

d maps to R d(x,y) ≥ 0 d(x,y) = 0 if and only if x = y d(x,y) = d(y,x) d(x,z) ≤ d(x,y) + d(y,z) If it satisfies these properties, it is a distance. x and y are in M, and M is now a metric space. It's not so hard. 1. You are putting the cart before the horse by using an assumption of distance (great...
Wed Jan 04, 2017 4:44 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Happy New Year! Try to define distance A strong subtext of what we are talking about is knowledge; what we can know to what degree of confidence. While there are an unlimited number of things that axiomatic mathematics doesn't define - I think it is illuminating to concentrate on just one element: d...
Mon Dec 12, 2016 2:18 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Treatid: Pretty sure I made this point pages ago, but all the whole of maths says is 'if x is true then y is also true'. There's no 'absolutes' anywhere there. They are a figment of your imagination. I note your use of quotes around 'absolute' to indicate that we haven't formally defined the term (...
Thu Dec 08, 2016 2:37 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

It's unclear what exactly "absolute" and "relative" mean here, and your stance conveniently seems to relieve you of the need to have hard definitions. Let me turn that around on you. Mathematicians cannot define what absolute or relative means; they cannot define dimensions or i...
Mon Dec 05, 2016 4:59 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

[Story] A man is punching himself in the face {punch}. Otherman: Hey! You are punching yourself in the face. Man: {punch} no I'm not {punch} that would be silly {punch} therefore I'm not punching myself {punch} in the face {punch}. [/Story] We are at the point where you agree that it is futile to c...
Fri Dec 02, 2016 4:14 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

You have a point: I said in my own words that since mathematics hasn't had an absolute then everything that mathematics has done is already relative. If mathematics is already relative then what is all the fuss about not being absolute? Theory vs practice The practice of mathematics is necessarily r...
Tue Nov 29, 2016 11:00 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Relative vs Absolute A short while ago in this thread we agreed that no one has been able to define anything in an absolute, epistemically certain, way. While there was some discussion, the overall impression was that this was a pedantic technicality. A bothersome formal result, but without signifi...
Wed Sep 07, 2016 3:07 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

I'm pretty sure there is an intended difference between mathematics and physics. A physical model/description/map has value according to how well it describes an actual physical phenomena. Mathematical descriptions (axiomatic mathematics) are valued according to whether they are internally consisten...
Mon Sep 05, 2016 5:05 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Okay. I'm wrong about statements. A statement is only a true or false sentence within an axiomatic system. It is incorrect to refer to anything outside the scope of an axiomatic system as a mathematical statement. Axiomatic systems themselves are neither true nor false and cannot be considered as ma...
Mon Sep 05, 2016 9:48 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Yeah... I've calmed down a bit. I'm sorry Cauchy. I now understand the argument you were making. I disagree with it - but I now see you weren't being as arbitrarily stubborn as I perceived. I am still convinced that it is a fundamental principle of axiomatic mathematics that anything can be proposed...
Mon Sep 05, 2016 7:14 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

The fact that all the math people are telling you you're misusing a term doesn't give you any cause for concern? A 'statement' is an incredibly generic object right up there with 'symbol'. gmalivuk made a mistake and you are doubling down on that mistake. Don't try to bully me into believing you be...
Fri Sep 02, 2016 10:50 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

The first law of thought is the law of identity. x = x. A thing is itself. I want to try and illustrate two extremes - I don't want to convince anyone of anything about these extremes (yet). Just show... i. A closed system: everything about the system is within the system. We are ignoring the issue ...
Wed Aug 31, 2016 9:45 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Hmm - it looks to me as though showing reason to question the validity of the 3 laws of thought; and how we can work constructively after explicitly rejecting the assumption of the laws of thought will accomplish much of what I want to show. I think this will take a few posts to get through. Cauchy ...
Sat Aug 27, 2016 1:08 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

I agree with what you are saying, rmsgrey. You seem to be understanding my argument and then... well... I'm not sure what. My whole point was that if !x does not equal everything except x then there is a problem. You are definitely seeing that. So you are understanding that portion of my argument - ...
Sat Aug 27, 2016 12:16 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Cauchy: I hope you are also a teacher outside these forums. Even when you think people are wrong - you don't tell them they are wrong, you give them a carefully measured piece of rope exquisitely judged to let them hang themselves (realise where they have made a mistake). Your consistent constructiv...
Thu Aug 25, 2016 11:53 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

I want to take my time about responding to Cauchy and rmsgrey. What they are saying is accurate - but is missing (very reasonably) the point I'm (trying to) make. I think that they, and axiomatic mathematics, are missing how important the difference between "absolutely distinct in every conceiv...
Thu Aug 25, 2016 3:34 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Furiously Agree with each other It looks like it was a mistake to try and move things forward without explicitly acknowledging the points that I agree or disagree with: edit: Oh and another important point. We identified four types of mathematical questions: 1) Questions about the truthhood of cert...
Wed Aug 24, 2016 11:04 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

I'm really not trying to be obtuse here. That one axiomatic system is distinct from another axiomatic system seems to me to be a really important part of axiomatic mathematics. I can see that the distinction is essential. I understand that the distinction is an assumed part of what axiomatic mathema...
Wed Aug 24, 2016 7:55 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Oh dear - it seems I have mis-communicated again. I was not trying to re-write set theory or say anything new about The Empty Set. I was trying to point to an existing precedent that says that things that are indistinguishable are one thing. ... Referencing this universe is no different to referenci...
Tue Aug 23, 2016 9:44 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Fluffy Intro I really want to reply to so many of the points raised - lots of agreement, some disagreement, quite a bit of adding my own slant and a few misapprehensions about what I think (my fault for poorly expressing myself). Unfortunately, a point by point addressing of the issues would make t...
Sat Aug 20, 2016 10:14 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Here, and paying very close attention to the conversation. Lots of really good points being made - many of which I've got really strong opinions on. But right now it seems to me that I'm more likely to derail the conversation than contribute - and between you all, you are doing a brilliant job of co...
Sat Aug 13, 2016 12:21 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

I'm an idiot. Regarding the End post bit: (A != B) != !(A = B) I should not have referred to !A. I should have referred to the complement of A: A'. That was a stupid mistake on my part. gmalivuk's point regarding exactly how one goes about constructing a complement of an axiomatic system A such that...
Fri Aug 12, 2016 6:08 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

I did not intend to claim that I had proven axiomatic mathematics to be 'wrong'. I had intended to convey that the subsequent clause was a hypothetical by my use of "even if". Having said that, various comments including those be Demki, rmsgrey and the nearby thread on the Liar's Paradox p...
Tue Aug 02, 2016 3:44 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Intro When I first stumbled into these forums I had no subtly and it wasn't clear I'd even heard of 'nuance'. The responses I got were the ones I deserved. Now Cauchy throws in the distinction between entirely prescriptive axiomatic systems and permissive ones in the full expectation that I'll appr...
Thu Jul 28, 2016 7:44 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Introduction (waffle - can skip) gmaliveuk's warning that I'm close to another locked thread flustered me and I sort of skipped over the fact that rmsgrey, Cauchy and arbiteroftruth provided really good responses. Rmsgrey provides a good high level overview. What he lays out is a good first pass ap...
Wed Jul 27, 2016 5:03 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

@gmaliveuk: thank you for your forebearance. 1. I posted a lot and I understand the reluctance to read all of it, especially when you vehemently disagree with me. However, some of the points you are making I directly addressed. I may have been wrong - but you aren't responding to the argument I've a...
Tue Jul 26, 2016 6:13 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Definition of terms Twistar's six definitions: They are all sets of symbols with a set of rules that apply to those symbols (or the result of having applied a set of rules to a set of symbols). Set of symbols: Anything that isn't a set of rules. Also known as: any possible domain (and/or range) of ...
Wed Jul 13, 2016 3:00 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Sorry for taking so long to respond - trying to make whatever point(s) I might have as clear and unambiguous as I can. This post is mainly me trying to get to the same page as everyone else with regard assumptions/premises. The arguments I put forward are sincere - but not proof. Falsifiability. I'v...
Sun Jun 19, 2016 12:06 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

My deepest thanks to everyone in this thread and previous ones. Proof: The premises for this proof are the axioms/rules of propositional logic. That is, we assume that all the rules of propositional logic are true. The proof is intended to show that the axioms/rules of propositional logic are incons...
Sat Jun 04, 2016 11:45 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

Absolutely, I want to explain myself clearly. Cauchy is doing a brilliant job of looking at what I'm actually saying and pointing out where I'm failing to be concise - or perhaps just wrong. What Cauchy is doing feels constructive for me and for the progress of the thread. I neglected to check for a...
Tue May 31, 2016 4:39 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 75215

### Re: Misunderstanding basic math concepts, help please?

@Cauchy: Thank you very, very, much for your recent responses. They are well reasoned, coherent and to-the-point. I hugely respect the amount of effort you are putting into trying to understand me, despite myself. Much of what you are saying I agree with. For example, Your careful analysis of my att...