Search found 183 matches

by Treatid
Tue Jan 10, 2017 10:03 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Sat Jan 07, 2017 6:23 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Wed Jan 04, 2017 4:44 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Mon Dec 12, 2016 2:18 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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 (...
by Treatid
Thu Dec 08, 2016 2:37 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Mon Dec 05, 2016 4:59 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Fri Dec 02, 2016 4:14 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Tue Nov 29, 2016 11:00 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Wed Sep 07, 2016 3:07 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Mon Sep 05, 2016 5:05 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Mon Sep 05, 2016 9:48 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Mon Sep 05, 2016 7:14 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Fri Sep 02, 2016 10:50 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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 ...
by Treatid
Wed Aug 31, 2016 9:45 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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 ...
by Treatid
Sat Aug 27, 2016 1:08 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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 - ...
by Treatid
Sat Aug 27, 2016 12:16 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Thu Aug 25, 2016 11:53 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Thu Aug 25, 2016 3:34 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Wed Aug 24, 2016 11:04 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Wed Aug 24, 2016 7:55 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Tue Aug 23, 2016 9:44 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Sat Aug 20, 2016 10:14 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Sat Aug 13, 2016 12:21 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Fri Aug 12, 2016 6:08 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Tue Aug 02, 2016 3:44 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Thu Jul 28, 2016 7:44 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Wed Jul 27, 2016 5:03 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Tue Jul 26, 2016 6:13 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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 ...
by Treatid
Wed Jul 13, 2016 3:00 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Sun Jun 19, 2016 12:06 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Sat Jun 04, 2016 11:45 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Tue May 31, 2016 4:39 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

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...
by Treatid
Sun May 29, 2016 4:10 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

Re: Misunderstanding basic math concepts, help please?

If your arguments have logical flaws, why should we accept them? Umm... Personally, if a deduction has logical flaws, I might consider pointing out those logical flaws so that the deducer can learn from their errors. I can't imagine why any one would continue to consider an argument to be valid aft...
by Treatid
Sun May 29, 2016 4:08 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

Re: Misunderstanding basic math concepts, help please?

Cauchy is correct. My last post went a little crackpotty. I jumped from "all mathematical propositions regarding axiomatic mathematics are excluded middle" through "axiomatic mathematics demands perfection, anything less than perfection is nothing" to "so axiomatic mathemati...
by Treatid
Wed May 25, 2016 8:36 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

Re: Misunderstanding basic math concepts, help please?

You know that feeling when you aren't sure whether a comment is serious or sarcastic (poe's law)? In axiomatic mathematics 'provable' and 'true' are the same thing. If it can be proven (with respect to the axioms) then it is true (with respect to the axioms). It looks to me like a lot of effort is b...
by Treatid
Sun May 22, 2016 11:55 am UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

Re: Misunderstanding basic math concepts, help please?

Much as I imagine it is tempting to just assume that everything I say is wrong, the classic laws of thought are explicitly the foundation of mathematical logic and all of mathematics that does not explicitly disavow the specified law. This information can be readily found through links on the Law of...
by Treatid
Wed May 11, 2016 1:33 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

Re: Misunderstanding basic math concepts, help please?

In logic, the law of excluded middle (or the principle of excluded middle) is the third of the three classic laws of thought. It states that for any proposition, either that proposition is true, or its negation is true.- Before we get on to more complicated logic... it appears I can't read this sim...
by Treatid
Sun May 08, 2016 9:56 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

Re: Misunderstanding basic math concepts, help please?

While I was working on your responses I was struck by the following: In logic, the law of excluded middle (or the principle of excluded middle) is the third of the three classic laws of thought. It states that for any proposition, either that proposition is true, or its negation is true.- This seems...
by Treatid
Fri May 06, 2016 1:08 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

Re: Misunderstanding basic math concepts, help please?

You tell me to forget about the excluded middle and then discuss the distinction between binary and continuous systems? Invoking the excluded middle is explicitly specifying a binary system versus a continuous system. But you are absolutely right that the distinction between a binary system and a co...
by Treatid
Wed May 04, 2016 3:12 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 311
Views: 24780

Re: Misunderstanding basic math concepts, help please?

Twistar, I think you have a good grasp of what I'm getting at. You are right that the bar for 'description' is too high for axiomatic mathematics to reach (I think arbiteroftruth also agrees with this). However, that bar is set by Axiomatic Mathematics itself. Axiomatic Mathematics specifies exactly...

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