## Search found 921 matches

Thu Jul 21, 2016 8:25 am
Forum: Logic and Philosophy of Mathematics
Topic: To understand maths
Replies: 41
Views: 5156

### Re: To understand maths

I wonder if the OP got anything out of this discussion.

Automated theorem proving is interesting. Some mathematicians speculate that eventually computers will be capable of creative math. I don't believe that personally.
Tue Jul 19, 2016 4:42 pm
Forum: Logic and Philosophy of Mathematics
Topic: To understand maths
Replies: 41
Views: 5156

### Re: To understand maths

I am talking about a machine that is constructed according to a finite set of axioms which is then set in motion (and perhaps, but not necessarily, guided by human intervention) and which then generates strings of symbols, called theorems. That is all. I see no reason why such a machine cannot be c...
Tue Jul 19, 2016 4:56 am
Forum: Logic and Philosophy of Mathematics
Topic: To understand maths
Replies: 41
Views: 5156

### Re: To understand maths

The theorems that are generated are then necessarily true within that system, for they have been generated following the axioms and inferential logic of the system. And only those theorems that it generates can be considered to be statements of mathematics. It is the role of mathematicians to desig...
Thu Jul 14, 2016 3:58 am
Forum: Logic and Philosophy of Mathematics
Topic: To understand maths
Replies: 41
Views: 5156

### Re: To understand maths

Not sure how it works in maths but how does infinity affect 'completeness'? You get incompleteness in any axiomatic theory strong enough to express number theory. By number theory is typically meant a Peano-like structure with induction. Like the natural numbers. Once you believe in the set of natu...
Thu Jul 14, 2016 3:44 am
Forum: Logic and Philosophy of Mathematics
Topic: To understand maths
Replies: 41
Views: 5156

### Re: To understand maths

Perhaps the symbols don't 'mean' anything. They are just symbols. If you (or I ) choose to associate those symbols with, say, sheep in a field, then we may do so. But otherwise the symbols are entirely abstract. All the more reason to get incredibly precise about what the rules are for manipulating...
Wed Jul 13, 2016 6:44 am
Forum: Logic and Philosophy of Mathematics
Topic: To understand maths
Replies: 41
Views: 5156

### Re: To understand maths

[Note: I wrote this long and ungainly post but Arising_uk said the exact same things only in way fewer words]. OK, perhaps there do exist formal and explicit axioms that can generate all the theorems of mathematics, but they are not ones that I use or want to use. Perfectly ok by me. If you've gone ...
Tue Jul 12, 2016 10:15 pm
Forum: Logic and Philosophy of Mathematics
Topic: To understand maths
Replies: 41
Views: 5156

### Re: To understand maths

Ok I challenge you then! (I presume you are a "mathematician or competent undergrad math major".) Using the axioms in either of your links, show how "2+2=4" can be proven or generated as a theorem. I think you are going to struggle to do so as in a cursory read of the links I could find no referenc...
Tue Jul 12, 2016 9:06 pm
Forum: Logic and Philosophy of Mathematics
Topic: To understand maths
Replies: 41
Views: 5156

### Re: To understand maths

The problem is that the axioms and processes are not explicitly stated The axioms of math are explicitly stated. The standard set of axioms is Zermelo-Fraenkel set theory, or ZF. https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory The underlying system of logic is first-order predicat...
Tue Dec 29, 2015 7:08 pm
Forum: Philosophy of Science
Topic: What is a quantum computer?
Replies: 121
Views: 14745

### Re: What is a quantum computer?

Arising_uk wrote: I'll leave it here as I've reached my limit of comprehension and maybe your reply will help clarify my thoughts.
I have some things to do this morning but I will post a more clear explanation later today.
Tue Dec 29, 2015 7:04 am
Forum: Philosophy of Science
Topic: What is a quantum computer?
Replies: 121
Views: 14745

### Re: What is a quantum computer?

You've completely missed the point of my argument. I'm certain that's the case. My comments are objections, yes; but more than that, they're pitons . Pitons are the spikes mountain climbers pound into the rock face to get a hand or foot hold. I am not so much picking away at tiny little points. I'm...
Tue Dec 29, 2015 3:22 am
Forum: Philosophy of Science
Topic: What is a quantum computer?
Replies: 121
Views: 14745

### Re: What is a quantum computer?

... Mathematically, if you conceptually threw a dart at the real line -- in other words picked a real randomly -- the probability that you picked a computable real is zero. The probability is 1 that you picked an uncomputable real. All this can be formalized. ... Is this true? As whilst vanishingly...
Tue Dec 29, 2015 2:34 am
Forum: Philosophy of Science
Topic: What is a quantum computer?
Replies: 121
Views: 14745

### Re: What is a quantum computer?

I accept your point about the "I frame no hypothesis" angle but countless hypotheses have been framed in his name. We're in agreement on this point. The fact that SOME scientists think they're possessed of ultimate truth does not indict science. You have a lot of similar strawman arguments in your ...
Tue Dec 29, 2015 1:22 am
Forum: Philosophy of Science
Topic: What is a quantum computer?
Replies: 121
Views: 14745

### Re: What is a quantum computer?

@Obvious Leo, I just had a glance at the article on your website. I admit that I found it hard going but also that I did not read word for word, so perhaps I'll have another go. I do happen to be a bit of a Newton fan so I wanted to mention that Newton most definitely DID understand the difference b...
Tue Dec 29, 2015 12:05 am
Forum: Philosophy of Science
Topic: What is a quantum computer?
Replies: 121
Views: 14745

### Re: What is a quantum computer?

My blood runs cold when I see the word "random" find its way into a scientific conversation. As far as I'm concerned random means uncaused and an uncaused event is a metaphysical absurdity. I only mean incompressible to a finite-length description or algorithm. Nothing more. Does that help you to u...
Mon Dec 28, 2015 9:50 pm
Forum: Philosophy of Science
Topic: What is a quantum computer?
Replies: 121
Views: 14745

### Re: What is a quantum computer?

Have you read David Deutsch's work on this subject? A little Googling reveals that Deutch's idea is a quantum UTM . This idea is also (as far as I understand) the same as a nondeterministic TM. It is presently unknown, repeat it is presently unknown, whether NTMs are capable of any computations bey...