What is a proof?
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22-08-2014, 05:57 AM
What is a proof?
(22-08-2014 04:13 AM)Muslim Wrote:  
(20-08-2014 10:24 PM)alegzac54 Wrote:  I think logic is acting accordingly to what one observes . Not only that but acting on what makes sense to avoid becoming insane.
Yes, but this is very general

Quote:Logic is what triggers our brain.
Absolutely, need to formalize that

Quote:I also believe logic is what drives good and bad actions.
Not really!
I am in no way saying saying this may be right. But thats the best that i could come up with. Thanks for your input
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22-08-2014, 06:16 AM (This post was last modified: 22-08-2014 06:21 AM by Mathilda.)
RE: What is a proof?
(22-08-2014 04:13 AM)Muslim Wrote:  
(20-08-2014 10:24 PM)alegzac54 Wrote:  Logic is what triggers our brain.
Absolutely, need to formalize that

Wrong.

There is some suggestion that binary logic can be performed using dendritic trees, but if so then it is just one small aspect of how the brain works.

For example, logic certainly does not adequately describe the function of neurochemicals in the brain, habituation, long term potentiation / depression, Hebbian learning or synaptic drift. These are gradual and continual processes better described using an alternative language to logic such as continuous equations.

Nor is logic useful in describing the higher functions of the brain such as temporal sequence learning, arbitration between exploration / exploitation, pattern matching, competition, memory etc.
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22-08-2014, 06:18 AM
RE: What is a proof?
And Mathilda has a new bitch...

Hate the belief, love the believer.
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22-08-2014, 06:41 AM
RE: What is a proof?
(22-08-2014 04:28 AM)Muslim Wrote:  
(21-08-2014 06:27 AM)Hafnof Wrote:  In mathematics we define logical systems in terms of a set of starting axioms. A proof within a logical system is based on the axioms of that system and shows using those axioms as a starting point that a particular proposition is true or is false within that logical system. A different set of axioms will result in a different set of true and false propositions. Propositions that are true or false in a given logical system may or may not correspond to true or false propositions in the real world depending on how consistent those axioms are with our reality. A logical system itself can be shown to be incoherent if a proof can be made that true is equal to false.

That is to say, mathematical proofs cannot be said to prove something in the real world unless we can also show that the axioms used match the real world - or how well they do so.
Now we are into something, this is absolutely true Thumbsup
It is called "Direct Proof"

No. I cover all forms of mathematical proof in the above section. You define a mathematical system and you work within that mathematical system to more fully describe it. I think there is no mathematical proof that falls outside this definition. Would you care to present one?

(22-08-2014 04:28 AM)Muslim Wrote:  
Quote:In order to apply mathematical thinking to the real world we need to use a scientific approach. That is,
1. Come up with ideas about the real world
2. Identify ideas that make testable predictions about the real world. Label ideas that make testable predictions "hypotheses", and discard other ideas as unfalsifiable - ie outside the scope of science to be able to verify.
3. Identify predictions between hypotheses that are mutually exclusive
4. Perform experiments to identify which (if any) of a given set of mutually exclusive predictions are inerrantly reliable. Discard of modify all hypotheses that fail to make inerrant predictions.
5. Identify the simplest hypotheses that have so far stood up to substantial experimentation that have the smallest burden of assumption built into them and have so far proven inerrant as our "scientific knowledge"
6. Continue to include our scientific knowledge in steps 3-5 to continually refine that knowledge and increase our ability to make unerringly accurate predictions about the real world in new contexts, with greater accuracy, and with greater precision over time.
True, but this is only one type of scientific proofs (proof by induction)

No, this is scientific verification of hypotheses. This is the scientific method. It is not proof by induction.

Proof by induction is a mathematical proof:
* You prove that a property holds for the first element of a sequence
* You prove that if a property holds for a given element in the sequence it must necessarily hold the next element in the sequence
* By induction, you can conclude that the property holds for all elements of the sequence

The scientific method has some connection to inductive reasoning but it is not an inductive proof or any kind of mathematical proof. For every hypothesis there is an infinite number of alternative hypotheses that make the same set of verified predictions: Assume you have a hypothesis that perfectly predicts all available results of experiments capable of falsifying its predictions. Take that hypothesis and add two unknown opposing but perfectly balanced forces. Now you have a new hypothesis that makes the same inerrant predictions. That is why we choose the hypothesis with the least burden of unfounded assumption to include in our scientific knowledge. If we accepted any claim that makes inerrant predictions we would have to believe many contradictory claims.

(22-08-2014 04:28 AM)Muslim Wrote:  
Quote:... or do you intend to propose a more reliable path to truth and knowledge than mathematical proof and scientific knowledge? If so, please do describe it.
there are other types (methods) of proofs:
deduction
Proof by countraposition
Contradictions
Perfect induction (exhaustion)
Construction
Statistical

No. All of these are mathematical proofs that fall under my description above. You define a mathematical system and you prove that a certain property holds or does not hold for that system.

Give me your argument in the form of a published paper, and then we can start to talk.
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22-08-2014, 09:19 AM
RE: What is a proof?
(22-08-2014 04:58 AM)Bucky Ball Wrote:  
(22-08-2014 04:28 AM)Muslim Wrote:  True, but this is only one type of scientific proofs (proof by induction)

Wrong, L'll Muzzy Wuzzy.
When you get all big and go to school, teacher will explain that "Proof by induction" is an example of logical reasoning. It's not even considered "proof" formally.
Inductive reasoning (as opposed to deductive reasoning) is reasoning in which the premises seek to supply strong evidence for (not absolute proof of) the truth of the conclusion.
http://en.wikipedia.org/wiki/Inductive_reasoning

It's not "scientific". At All. Clearly you know nothing about science. Science is a method. The word "proof" does not appear in the steps of the method.

So.
Now that you've demonstrated you haven't a clue what you're pretending you know enough about to say anything about, maybe, slink back to your hole, and try to come up with Plan B.
If we need "preparing" for anything, you patronizing ass hole, we'll be sure and let you know.

One clarification for the audience.

Muzzy Wuzzy may be confusing inductive reasoning with mathematical induction.

Mathematical induction is one form of direct proof in mathematics, mostly used for proofs about natural numbers and infinite series.

One proves a statement about a number i then proves that it must be true for i+1. It is therefore true for all natural numbers.

Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
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22-08-2014, 09:25 AM
RE: What is a proof?
I think the name Muzzy Wuzzy is going to stick now.
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22-08-2014, 10:49 AM
RE: What is a proof?
(22-08-2014 09:25 AM)Mathilda Wrote:  I think the name Muzzy Wuzzy is going to stick now.

Muzzy Wuzzy was a bear. Muzzy Wuzzy had no hair. ....
Wait .... Consider

Insufferable know-it-all.Einstein God has a plan for us. Please stop screwing it up with your prayers.
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22-08-2014, 11:10 AM
RE: What is a proof?
(22-08-2014 10:49 AM)Bucky Ball Wrote:  
(22-08-2014 09:25 AM)Mathilda Wrote:  I think the name Muzzy Wuzzy is going to stick now.

Muzzy Wuzzy was a bear. Muzzy Wuzzy had no hair. ....
Wait .... Consider

No Muzzy Wuzzy was a bore.

(31-07-2014 04:37 PM)Luminon Wrote:  America is full of guns, but they're useless, because nobody has the courage to shoot an IRS agent in self-defense
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22-08-2014, 11:16 AM
RE: What is a proof?
(22-08-2014 11:10 AM)Revenant77x Wrote:  
(22-08-2014 10:49 AM)Bucky Ball Wrote:  Muzzy Wuzzy was a bear. Muzzy Wuzzy had no hair. ....
Wait .... Consider

No Muzzy Wuzzy was a bore.

...and his logic had a flaw!
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23-08-2014, 07:36 AM
RE: What is a proof?
(22-08-2014 04:38 AM)Mathilda Wrote:  And that is precisely my point. If logic were 'absolute' and existed as part of the fabric of reality then you would not be able to have logical paradoxes.

The fact that even a single logical paradox exists demonstrates this.
I'm not sure what do you mean, but a logical paradox doesn't exist
You can prove the non-existence of something if it is leading to a logical paradox
It will be your method to refute my proof, to prove that my claim is paradoxing, if not I can claim anything contradicting, then you cannot refute it!

Quote:Logic is a representation of reality. We can also use language for this. We can use logic to create paradoxes in much the same way that we can use words to create non sequiturs.
(formal) Logic is how are brains work, they are just a few very simple rules

Quote:Neither logic nor words underlie reality (despite people believing that God spoke the universe into existence).
?


Quote:The proof also only works if people accept that the proposed mapping between the real world and the logical representation of the real world is both complete and accurate.
Yes, but just for the premises of the proof

Quote:For example, Lord Kelvin published mathematical calculations that the age of the Earth was between 20 million and 400 million years. For some of his followers this was mathematical proof but not all scientists were convinced because it did not match all the evidence that had been collected.
it is called a scientific theory using mathematics, but not a mathematical proof!

Quote:What you are failing to recognize is that logic is just a single step within an iterative cycle rather than the final step. It cannot prove anything by itself because it is dependent upon how much evidence has been gathered. All logic can do is create hypotheses or to disprove hypotheses.
Yes, Logic is a just a mean to use it on observations
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