Page 2 of 3
Re: An Axiomatic Proof
Posted: Tue Jan 27, 2015 5:44 pm
by Arising_uk
HexHammer wrote:What you areally are saying is that this is a premise for religion.
Nope, what I was really saying is that what you said about courts, companies and science were all examples of the contingent propositions being addressed by empiricism and that the machine you type upon is in effect a great big logic-chopper, i.e. NAND and NOR gates, so theoretical babble has a place in reality.
No idea why you've associated what I've said with a premise for religion?
Re: An Axiomatic Proof
Posted: Wed Jan 28, 2015 1:20 am
by Blaggard
lol nice come back UK.
NAND. Hilarious.
When in doubt make an anaology, only the cleverest will get it, but only a white elephant will dissappeer entirely. Which triteness just means just STFU and do better at it even if it's "grammar".
Re: An Axiomatic Proof
Posted: Wed Jan 28, 2015 7:18 am
by HexHammer
Arising_uk wrote:HexHammer wrote:What you areally are saying is that this is a premise for religion.
Nope, what I was really saying is that what you said about courts, companies and science were all examples of the contingent propositions being addressed by empiricism and that the machine you type upon is in effect a great big logic-chopper, i.e. NAND and NOR gates, so theoretical babble has a place in reality.
No idea why you've associated what I've said with a premise for religion?
No, who says the succeeding report is better than the former? We have a very huge train (choo choo train) scandal in Denmark, there has been loads of reports and analysis that contradict each other, and each with their perspective, it's only about which sounds more plausible.
It's not only for this huge scandal, but loads of other minor to huge scandals and problems etc, everybody wants to earn money on consulting and analysis, but only so few are very qualified and high expertise is a very rare thing.
So you mistakenly think that something is definitive when it's subjective and very relative.
Re: An Axiomatic Proof
Posted: Wed Jan 28, 2015 7:26 am
by Blaggard
After you typed that Hex did you actually think there was any reason to be here at all. Or did you just think as usual you deserve special attention for being Hex, because you are important, and big and everyone needed to know just how majestic you are?
Lead by making decent arguments, don't make crap ones and then swan around like you are the cock of the walk.
The big train crashed is an analogy to reality via nothing to do with what anyone said, wtf are you banging on about this year? You are an expert on what, and what in my humble opinion does that have to do with anything? You say a lot with that post, but little of it has to do with the thread itself. You have no idea what you are talking about and in that respect neither do I, but at least I am honest enough to admit it.
https://www.youtube.com/watch?v=YIP6EwqMEoE
"You keep using that word, I do not think it means what you think it means"
Re: An Axiomatic Proof
Posted: Wed Jan 28, 2015 12:27 pm
by egg3000
So I posted the same problem elsewhere and a user named Melanie Turner responded with a solution. Here's the proof, I've edited it slightly, but only in order to make the notation more consistent with the previous posts in this thread—everything else is untouched.
Axioms:
P1. a → (b → a)
P2. (a → (b → c)) → ((a → b) → (a → c))
P3. (~a → ~b) → ((~a → b) → a)
Lemma 1: P → P
1. P → ((P → P) → P) [P1]
2. (P → ((P → P) → P)) → ((P → (P → P)) → (P → P)) [P2]
3. (P → (P → P)) → (P → P) [1, 2, MP]
4. P → (P → P) [P1]
5. P → P [3, 4, MP]
Lemma 2: (P → Q) → ((R → P) → (R → Q))
1. (R → (P → Q)) → ((R → P) → (R → Q)) [P2]
2. ((R → (P → Q)) → ((R → P) → (R → Q))) → ((P → Q) → ((R → (P → Q)) → ((R → P) → (R → Q)))) [P1]
3. (P → Q) → ((R → (P → Q)) → ((R → P) → (R → Q))) [1, 2, MP]
4. ((P → Q) → ((R → (P → Q)) → ((R → P) → (R → Q)))) → (((P → Q) → (R → (P → Q))) → ((P → Q) → ((R → P) → (R → Q)))) [P2]
5. ((P → Q) → (R → (P → Q))) → ((P → Q) → ((R → P) → (R → Q))) [3, 4, MP]
6. (P → Q) → (R → (P → Q)) [P1]
7. (P → Q) → ((R → P) → (R → Q)) [5, 6, MP]
Lemma 3: P → ((P → Q) → Q)
1. (P → Q) → (P → Q) [Lemma 1]
2. ((P → Q) → (P → Q)) → (((P → Q) → P) → ((P → Q) → Q)) [P2]
3. ((P → Q) → P) → ((P → Q) → Q) [1, 2, MP]
4. (((P → Q) → P) → ((P → Q) → Q)) → ((P → ((P → Q) → P)) → (P → ((P → Q) → Q))) [Lemma 2]
5. (P → ((P → Q) → P)) → (P → ((P → Q) → Q)) [3, 4, MP]
6. P → ((P → Q) → P) [P1]
7. P → ((P → Q) → Q) [5, 6, MP]
Lemma 4: (~P → Q) → (~Q → P)
1. (~P → ~Q) → ((~P → Q) → P) [P3]
2. ((~P → ~Q) → ((~P → Q) → P)) → ((~Q → (~P → ~Q)) → (~Q → ((~P → Q) → P))) [Lemma 2]
3. (~Q → (~P → ~Q)) → (~Q → ((~P → Q) → P)) [1, 2, MP]
4. ~Q → (~P → ~Q) [P1]
5. ~Q → ((~P → Q) → P) [3, 4, MP]
6. (~Q → ((~P → Q) → P)) → ((~Q → (~P → Q)) → (~Q → P)) [P2]
7. (~Q → (~P → Q)) → (~Q → P) [5, 6, MP]
8. ((~Q → (~P → Q)) → (~Q → P)) → (((~P → Q) → (~Q → (~P → Q))) → ((~P → Q) → (~Q → P))) [Lemma 2]
9. ((~P → Q) → (~Q → (~P → Q))) → ((~P → Q) → (~Q → P)) [7, 8, MP]
10. (~P → Q) → (~Q → (~P → Q)) [P1]
11. (~P → Q) → (~Q → P) [9, 10, MP]
⊢ ~((~P → Q) → Q) → P
1. ~P → ((~P → Q) → Q) [Lemma 3]
2. (~P → ((~P → Q) → Q)) → (~((~P → Q) → Q) → P) [Lemma 4]
3. ~((~P → Q) → Q) → P [1, 2, MP]
As for Hex, I stopped paying much attention after the first post (the one with the rhetorical question about using logical tautologies as a means to determine whether or not a criminal is lying). However, from what I did pick up after lightly skimming over the other posts, Hex seems to be attempting to give an
a priori argument for some variety of radical empiricism. The argument is so incoherent that to engage oneself in any attempt to refute it is to waste one's time—and time is a precious thing.
Otherwise, thanks to Arising_uk for going to the effort to try to solve my problem.
—egg3000
Re: An Axiomatic Proof
Posted: Wed Jan 28, 2015 8:22 pm
by HexHammer
egg3000 wrote:As for Hex, I stopped paying much attention after the first post (the one with the rhetorical question about using logical tautologies as a means to determine whether or not a criminal is lying). However, from what I did pick up after lightly skimming over the other posts, Hex seems to be attempting to give an a priori argument for some variety of radical empiricism. The argument is so incoherent that to engage oneself in any attempt to refute it is to waste one's time—and time is a precious thing.
Otherwise, thanks to Arising_uk for going to the effort to try to solve my problem.
—egg3000
Well ofc you did, you lack rationallity and are most likely a "rain man" lacking basic rationallity, likst most others here. Why you in the first place posted this nonsense in OP.
Re: An Axiomatic Proof
Posted: Thu Jan 29, 2015 1:03 am
by Blaggard
We can all learn from hex, ignore anyone who hit's the nail on the head, is not one "LESSON" I want to learn though.
To sum up he is nail and not a hammer.
Now Arizing UK is a rising star in a bad world. That was deliberate the bad spelling, don't worry- I fell off my horse.
Re: An Axiomatic Proof
Posted: Fri Jan 30, 2015 4:25 am
by Arising_uk
HexHammer wrote:Well ofc you did, you lack rationallity and are most likely a "rain man" lacking basic rationallity, likst most others here. ...
Given you repeat phrases continuously I think it's becoming clear where the rationality is lacking.
Why you in the first place posted this nonsense in OP.
HELLO! EARTH TO HEXHAMMER!! EARTH CALLING HEXHAMMER!!!
Take a look at the title of this forum section and then look at what the OP contained then look at what you posted in reply.
Re: An Axiomatic Proof
Posted: Fri Jan 30, 2015 4:32 am
by Arising_uk
egg3000 wrote:...
Otherwise, thanks to Arising_uk for going to the effort to try to solve my problem.
—egg3000
Faint praise I think as I got no-where but will have a dent at this from the ND approach once my books come out of storage and I can refresh my memory.
One thing egg3000, could you point me towards or name this type of axiomatic proof as I've never encountered this kind before and would like to read-up. From what I see its using what I presume are tautologies(haven't checked yet) and one of the ND rules plus substitution to make deductive proofs?
Re: An Axiomatic Proof
Posted: Fri Jan 30, 2015 4:55 am
by Blaggard
No one's going to praise an idiot: mea culpa.
Egg the only thing I hope is that anything helped more than pain killers.
Re: An Axiomatic Proof
Posted: Fri Jan 30, 2015 1:16 pm
by HexHammer
Arising_uk wrote:HexHammer wrote:Well ofc you did, you lack rationallity and are most likely a "rain man" lacking basic rationallity, likst most others here. ...
Given you repeat phrases continuously I think it's becoming clear where the rationality is lacking.
Why you in the first place posted this nonsense in OP.
HELLO! EARTH TO HEXHAMMER!! EARTH CALLING HEXHAMMER!!!
Take a look at the title of this forum section and then look at what the OP contained then look at what you posted in reply.
This is little different that metaphysics, irrelevant!
Re: An Axiomatic Proof
Posted: Fri Jan 30, 2015 2:57 pm
by HexHammer
So, now that you guys insist that I'm utterly wrong, then it should be easy to tell me where excatly this axiomatic proofe are used.
Re: An Axiomatic Proof
Posted: Sat Jan 31, 2015 3:47 am
by Arising_uk
HexHammer wrote:So, now that you guys insist that I'm utterly wrong, then it should be easy to tell me where excatly this axiomatic proofe are used.
Sure, go to the Imperial College website and check out the advanced computing department or any of the technology institutes for that matter and you will find Logic and Logicians at work developing numerous things alongside the purely theoretical, e.g. deductive databases, natural language parsers, new programming paradigms, program and algorithm provers, expert systems, etc. Are they using the axiomatic deductive method posted here? No, as such stuff is analogous to the mathematician having to learn the mathematical operations before they can get to the complex stuff, i.e. learning such methods is the base for the budding logician to build upon and allows them to later understand the more complex Logics that are been used in Computing Science.
Re: An Axiomatic Proof
Posted: Sat Jan 31, 2015 4:00 am
by HexHammer
Arising_uk wrote:HexHammer wrote:So, now that you guys insist that I'm utterly wrong, then it should be easy to tell me where excatly this axiomatic proofe are used.
Sure, go to the Imperial College website and check out the advanced computing department or any of the technology institutes for that matter and you will find Logic and Logicians at work developing numerous things alongside the purely theoretical, e.g. deductive databases, natural language parsers, new programming paradigms, program and algorithm provers, expert systems, etc. Are they using the axiomatic deductive method posted here? No, as such stuff is analogous to the mathematician having to learn the mathematical operations before they can get to the complex stuff, i.e. learning such methods is the base for the budding logician to build upon and allows them to later understand the more complex Logics that are been used in Computing Science.
I suspected so, only area where such feeble logic can exist. No wonder it sometimes end catastrophic.
Thanks for clarification tho!
Re: An Axiomatic Proof
Posted: Sat Jan 31, 2015 4:04 am
by Arising_uk
HexHammer wrote:I suspected so, only area where such feeble logic can exist. No wonder it sometimes end catastrophic.
The area you talk about is changing the world of work and communication. You are barking mad and a luddite to boot.