## Search found 319 matches

- Mon Dec 05, 2016 5:19 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**56211**

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

Axiomatic mathematics is fundamentally structured around the concept of absolutes. The First Law of Thought is a statement of the assumption of absolutes: (x = x). This straight up says that x is assumed to have an absolute value. That the value of x does not depend on its relationship with other t...

- Wed Nov 09, 2016 9:53 pm UTC
- Forum: News & Articles
- Topic: 2016 US Presidential Election
- Replies:
**8482** - Views:
**778446**

### Re: 2016 US Presidential Election

I understand Zohar is saying that racism is a continuum, and the less you value fighting racism as a priority, the more racist you are. That's not a very helpful use of the word though. Because it forces you to either claim that protecting minorities must always be the absolute top priority in all ...

- Mon Nov 07, 2016 10:24 pm UTC
- Forum: News & Articles
- Topic: 2016 US Presidential Election
- Replies:
**8482** - Views:
**778446**

### Re: 2016 US Presidential Election

I don't think you know what pragmatic is. Following your belief without considering facts or evidence, or even weighing consequences is not pragmatic - that's exactly what an ideologue does. They would say they have considered the evidence and the consequences No, they *deny* the evidence and the c...

- Mon Nov 07, 2016 10:05 pm UTC
- Forum: News & Articles
- Topic: 2016 US Presidential Election
- Replies:
**8482** - Views:
**778446**

### Re: 2016 US Presidential Election

I don't think you know what pragmatic is. Following your belief without considering facts or evidence, or even weighing consequences is not pragmatic - that's exactly what an ideologue does. They would say they have considered the evidence and the consequences, and have come to difference conclusio...

- Mon Nov 07, 2016 8:55 pm UTC
- Forum: News & Articles
- Topic: 2016 US Presidential Election
- Replies:
**8482** - Views:
**778446**

### Re: 2016 US Presidential Election

If you think pragmatism has anything to do with anything, look at how ridiculous their budgets are - they can't even get right-wing economic organizations to say they won't increase the deficit, but the politicians push for more tax cuts anyway. Why? Because the tax cuts themselves are the goal. Ar...

- Mon Nov 07, 2016 6:51 pm UTC
- Forum: News & Articles
- Topic: 2016 US Presidential Election
- Replies:
**8482** - Views:
**778446**

### Re: 2016 US Presidential Election

Sorry for the confusion, I was responding in the context of why the Republican party seems to be made up of ideologues rather than pragmatists Mostly because you disagree with them. I guarantee you that plenty of conservatives would make a similar observation about Democrats. Not at all, I was rais...

- Mon Nov 07, 2016 5:38 pm UTC
- Forum: News & Articles
- Topic: 2016 US Presidential Election
- Replies:
**8482** - Views:
**778446**

### Re: 2016 US Presidential Election

Thesh wrote:Sorry for the confusion, I was responding in the context of why the Republican party seems to be made up of ideologues rather than pragmatists

Mostly because you disagree with them. I guarantee you that plenty of conservatives would make a similar observation about Democrats.

- Mon Oct 31, 2016 4:36 pm UTC
- Forum: Serious Business
- Topic: Sortition (split from 2016 US Presidential Election)
- Replies:
**70** - Views:
**12395**

### Re: Sortition (split from 2016 US Presidential Election)

How about a hybrid system where you have traditional elections, but the candidates available on the ballot are randomly selected? You'd have to offer significant compensation just for being a candidate, since these people are going to undergo public scrutiny, but it seems to me you get the best of b...

- Wed Oct 26, 2016 8:53 pm UTC
- Forum: Mathematics
- Topic: Three externally tangent circles sharing a single point of tangency
- Replies:
**19** - Views:
**4465**

### Re: Three externally tangent circles sharing a single point of tangency

Unless you define it in such a way that the circle centered at infinity has no interior.

- Tue Oct 25, 2016 10:22 pm UTC
- Forum: Mathematics
- Topic: Three externally tangent circles sharing a single point of tangency
- Replies:
**19** - Views:
**4465**

### Re: Three externally tangent circles sharing a single point of tangency

Some attempts at proof might be tricky, because this conjecture is false in the degenerate case of a circle with radius 0. That is, you have two externally tangent circles, and a third 'circle' of radius 0 centered on the point of tangency. So the point of tangency is the entirety of the third circl...

- Mon Oct 17, 2016 12:51 am UTC
- Forum: News & Articles
- Topic: 2016 US Presidential Election
- Replies:
**8482** - Views:
**778446**

### Re: 2016 US Presidential Election

This is where we disagree on the analogy. You're saying it's hitting the truck vs. hitting the ditch. I'm saying it's hitting the truck at a full 180 degree head-on collision vs. hitting the truck with a 175 degree collision. Sure, you can run the numbers and find that the 175 degree collision is ma...

- Sun Oct 16, 2016 11:29 pm UTC
- Forum: News & Articles
- Topic: 2016 US Presidential Election
- Replies:
**8482** - Views:
**778446**

### Re: 2016 US Presidential Election

Going with the steering analogy, it's more like having a broken steering wheel and trying to balance the short term goal of steering however well you can(voting for someone from a major party) with the long term goal of repairing the wheel(putting pressure on the major parties to nominate better ca...

- Sun Oct 16, 2016 9:12 pm UTC
- Forum: News & Articles
- Topic: 2016 US Presidential Election
- Replies:
**8482** - Views:
**778446**

### Re: 2016 US Presidential Election

...do the major parties need my vote or not? Voting is not about filling the needs of the major parties. It's about affecting the outcome of the race. Theoretically, even I could become president of the United States this year. But no matter how strongly you feel that I'd be a better leader than Hi...

- Sun Oct 16, 2016 5:18 pm UTC
- Forum: News & Articles
- Topic: 2016 US Presidential Election
- Replies:
**8482** - Views:
**778446**

### Re: 2016 US Presidential Election

I haven't decided. But I am neither going to express support for Trump who is unfit for office, nor am I going to contribute to Clinton's mandate to actively work against me on everything I care bout. My vote will indicate failure on the part of the Republicans to earn my vote, not success on the pa...

- Sun Oct 16, 2016 4:58 pm UTC
- Forum: News & Articles
- Topic: 2016 US Presidential Election
- Replies:
**8482** - Views:
**778446**

### Re: 2016 US Presidential Election

First, note that what I'm arguing for only applies to the Presidential election, because of the unique rules of the Electoral college. And yes, the Presidential election truly is both ways. How, exactly? In the presidential election, do the major parties need my vote or not? If they need my vote, t...

- Sun Oct 16, 2016 3:17 pm UTC
- Forum: News & Articles
- Topic: 2016 US Presidential Election
- Replies:
**8482** - Views:
**778446**

### Re: 2016 US Presidential Election

Success looks like having spoilers on a regular basis until it becomes obvious that you have to actually earn those spoiler votes in order to win. Even better if it's clear that supporting electoral reform is the best way to earn those votes. The USA has had regular occurrences of "spoiler vot...

- Sun Oct 16, 2016 6:25 am UTC
- Forum: News & Articles
- Topic: 2016 US Presidential Election
- Replies:
**8482** - Views:
**778446**

### Re: 2016 US Presidential Election

Success looks like having spoilers on a regular basis until it becomes obvious that you have to actually earn those spoiler votes in order to win. Even better if it's clear that supporting electoral reform is the best way to earn those votes.

- Fri Oct 14, 2016 11:00 pm UTC
- Forum: News & Articles
- Topic: 2016 US Presidential Election
- Replies:
**8482** - Views:
**778446**

### Re: 2016 US Presidential Election

And since you ignored this point, let me ask once again: why do you think playing this long-term spoiler game has a more realistic chance of bringing about a better society than the idea of campaigning for electoral reform, campaign finance reform and lower-level third party candidates while pragma...

- Fri Oct 14, 2016 5:27 pm UTC
- Forum: News & Articles
- Topic: 2016 US Presidential Election
- Replies:
**8482** - Views:
**778446**

### Re: 2016 US Presidential Election

The arguments against voting third party seem to want to have it both ways regarding the importance of a vote. If you don't vote for a major party, you're hurting the outcome of the election. And the long term effect of a protest vote doesn't matter, because nobody cares about that small portion of ...

- Tue Oct 04, 2016 10:10 pm UTC
- Forum: Mathematics
- Topic: Factorization using modular arithmetic
- Replies:
**41** - Views:
**8058**

### Re: Factorization using modular arithmetic

Goahead52, you started by assuming the modulus was prime. LucasBrown was talking about the difficulty of solving the problem with large composite moduli. In my second post I have just copy-paste from my documents a method assuming that c is prime. That`s it. But my method remain available even if c...

- Tue Oct 04, 2016 3:09 pm UTC
- Forum: Mathematics
- Topic: Factorization using modular arithmetic
- Replies:
**41** - Views:
**8058**

### Re: Factorization using modular arithmetic

Goahead52, you started by assuming the modulus was prime. LucasBrown was talking about the difficulty of solving the problem with large composite moduli.

- Wed Aug 24, 2016 11:14 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**56211**

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

Treatid wrote:So which is it? A) Axiomatic mathematics relies on natural language to get started OR B) axiomatic systems are entirely distinct from natural language?

A. No question. The answer is A. We've said this many, many times.

- Mon Aug 15, 2016 9:30 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**56211**

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

I understand the possibility that something can be absolute truth but that we can't be certain of it. Basically something can be true but humans just can't know with certainty that it's true. However, there's yet a further step needed to answer my original question. Let's say things can be absolute...

- Mon Aug 15, 2016 9:07 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**56211**

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

Disagree. You're asking a philosophical question that hinges on the distinction, if there is any, between truth and knowledge. For all the reasons we've explored here, human confidence in mathematical truth can never be absolute. At some point you get back to What the Tortoise Said to Achilles and y...

- Thu Jul 28, 2016 7:03 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**12921**

### Re: Theorem and consequences

Proof by contradiction: Assume x k <y k+1 <(y+1) k+1 <(x+1) k When all numbers involved are positive, taking the (k+1)th root preserves the inequalities: x k/(k+1) <y<y+1<(x+1) k/(k+1) This implies: (x+1) k/(k+1) -x k/(k+1) >1 Since x is restricted to positive integer...

- Thu Jul 28, 2016 4:13 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**56211**

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

{definition of 'know' here is problematic. While I don't think we can have absolute knowledge in a sense that I think axiomatic mathematics implies ; I do think that we can create a complete description of the universe without needing to make any assumptions. At the same time, axiomatic mathematics...

- Wed Jul 27, 2016 7:06 am UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**56211**

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

Some of the responses come very close to saying that my axioms (definitions) are wrong. I'm hoping I'm mis-reading. Specifically, many of the counter-arguments seem to be based on things other than my stated axioms/definitions. There is nothing a-priori 'wrong' with defining things as you have. But...

- Tue Jul 26, 2016 4:51 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**56211**

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

A Socratic Argument The following is a quick summary of essential elements of this thread in terms of the above definitions (with only a smidgen of my bias showing) A: A given system (language, theorem, set of well formed formulae, set of axioms) consists of a set of symbols and a set of rules that...

- Wed Jul 20, 2016 4:15 pm UTC
- Forum: Mathematics
- Topic: The liar paradox as a basis for kantian metaphysics
- Replies:
**11** - Views:
**2855**

### Re: The liar paradox as a basis for kantian metaphysics

It seems to me that P is either empty or is the set of all true sentences, depending on the scope of that negation. That is, if the statement is meant to be: ∀x{x∈P ⇔ (x∈T ∧ ( ~x ) ∈N)} then P is the set of all true sentences. Since sentences aren't sets, every sentence is in N, so (~x)∈N is true wh...

- Wed Jul 13, 2016 5:22 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**56211**

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

i. If Languages are a Logical System and the axioms of a language allow us to write (x & !x) then the axioms of that language are inconsistent with each other. But that would mean that nearly all languages are inconsistent and thus allow us to prove anything within those languages. Here it's im...

- Tue Jun 07, 2016 6:27 pm UTC
- Forum: Mathematics
- Topic: λ-calculus + modal logic = unrestrained self-reference
- Replies:
**2** - Views:
**2353**

### Re: λ-calculus + modal logic = unrestrained self-reference

It occurs to me that a better method of avoiding explosion might be to leave all the classical deduction rules alone, and instead put limitations on the use of β-equivalence. Specifically, P⊢(β-equivalent form of P) is not a valid deduction, but □P⊢□(β-equivalent form of P) is a valid deduction, as ...

- Mon Jun 06, 2016 6:44 pm UTC
- Forum: Mathematics
- Topic: λ-calculus + modal logic = unrestrained self-reference
- Replies:
**2** - Views:
**2353**

### λ-calculus + modal logic = unrestrained self-reference

I've spent a lot of time thinking about ways to formally capture the way informal language handles things like the liar paradox. Using a formal logic that's simply unable to state a paradox is disappointing. You can use three-valued logic to deal with it, but then you have to limit your ability to d...

- Tue May 31, 2016 5:47 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**56211**

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

I'll take #12 from the worksheet. 1. (A V B) ⊃ K [Prem] 2. C ⊃ (A V B) [Prem] 3. D ≡ C [Prem] 4. D ⊃ C [3, Bicond.] 5. D ⊃ (A V B) [2, 4, Hyp. Syll.] 6. D ⊃ K [1, 5, Hyp. Syll.] 7. ~K ⊃ ~D [6, Contrap.] QED In English, a 'partial description' is a completely mundane idea. The...

- Sun May 29, 2016 4:44 am UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**56211**

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

Treatid, the first half of your post is, frankly, incoherent. So I'm going to skip it. The whole point and purpose of The Law of Excluded Middle is that the middle is explicitly excluded. There is no middle ground between 'specified' and 'not-specified'. "specified imperfectly" has been de...

- Wed May 25, 2016 9:44 pm UTC
- Forum: Mathematics
- Topic: V=L → ω_1=ω_1^CK ?
- Replies:
**2** - Views:
**1809**

### V=L → ω_1=ω_1^CK ?

Does the axiom of constructibility imply that ω 1 is the Church-Kleene ordinal? Intuitively, it seems so. If I understand correctly, ω 1 CK is the first ordinal without a *constructible* bijection to the natural numbers, and the axiom of constructibility implies that if there is no constructible bij...

- Wed May 25, 2016 9:28 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**56211**

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

In axiomatic mathematics 'provable' and 'true' are the same thing. No they aren't. The fact that they aren't is essentially the point of Godel's theorems. It looks to me like a lot of effort is being expended on anything but the point at hand. The point at hand, as per the thread title, is that you...

- Mon May 23, 2016 4:45 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**56211**

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

@Arbiteroftruth: You are wholly right. I do equate "100% unambiguous" with the law of the excluded middle. I think of "100% unambiguous" as being a definite thing. Either a thing is completely (100% unambiguous) or it is not(100% unambiguous). The first half of this quote isn't ...

- Wed May 11, 2016 6:29 pm UTC
- Forum: Mathematics
- Topic: Seating problem
- Replies:
**6** - Views:
**2299**

### Re: Seating problem

Asking how many courses can be seated with n people is equivalent to asking how many non-isomorphic, non-compound stars can be made with n vertices. For n=1, there's only one 'star' of a single vertex. For n=2, there's only the 'star' that is the line segment connecting the two vertices. For n=3, th...

- Wed May 11, 2016 3:07 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**56211**

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

The problem is that you're taking the law of the excluded middle, which says essentially that every sentence is either true or false with no 'middle' option, and you're trying to equate that law to something completely different. You're trying to equate it to some law about things being 100% unambig...

- Sun May 08, 2016 10:10 pm UTC
- Forum: Mathematics
- Topic: Misunderstanding basic math concepts, help please?
- Replies:
**338** - Views:
**56211**

### 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 seem...