quote:

Originally posted by shaolin_Z Did you accidentaly misphrase the question or did you accidentaly put the opposite explanation next to 'Yes' and 'No' ...

Neither...

Inductive logic = logic of probabilities
i.e. Aliens exist because the universe is too big to not have aliens.

Deductive logic = logic of definitive fact
i.e. Aliens don't exist because we've never scientifically proven they do.

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quote:

Originally posted by Krypton Kinda like... Are we the only life in the universe? Yes = Inductive; the universe is too big for there not to be life. No = Deductive; there is no proven evidence for extraterrestrial existence. My point is...wisdom can be attained by both deductive and inductive reasoning.

Well, you need to incorperate both to have any sense of balance in your reasoning... so that's true in a sense, but rationalist supposedly stick to deductive reasoning... I'm guessing most of them don't even understand what the fuck it is lol

___________________
"The Greatest enemy of knowledge is not ignorance, it is the illusion of knowledge." -Stephen Hawking
"First they came for the communists, and I did not speak out— because I was not a communist;
Then they came for the socialists, and I did not speak out— because I was not a socialist;
Then they came for the trade unionists, and I did not speak out— because I was not a trade unionist;
Then they came for the Jews, and I did not speak out— because I was not a Jew;
Then they came for me— and there was no one left to speak out for me." -Martin Niemöller

quote:

Originally posted by Krypton Neither... Inductive logic = logic of probabilities i.e. Aliens exist because the universe is too big to not have aliens. Deductive logic = logic of definitive fact i.e. Aliens don't exist because we've never scientifically proven they do.

sort of - your descriptions were right: deductive logic requires that the truth of the evidence guarantees the accuracy of the conclusion. on the other hand, in an inductive argument the truth of the evidence makes it highly probable that the conclusion is accurate.

your examples, however, were off the mark. the first example is slightly weak because the size of the universe is less relevant than many other factors. the deductive example is off the mark. the fact that we have never scientifically proven that aliens exist does not make it impossible for aliens to actually exist.

quote:

Originally posted by jerZ07002 sort of - your descriptions were right: deductive logic requires that the truth of the evidence guarantees the accuracy of the conclusion. on the other hand, in an inductive argument the truth of the evidence makes it highly probable that the conclusion is accurate. your examples, however, were off the mark. the first example is slightly weak because the size of the universe is less relevant than many other factors. the deductive example is off the mark. the fact that we have never scientifically proven that aliens exist does not make it impossible for aliens to actually exist.

That's one thing that's driving me nuts. When you boil down logic all you're left with is a set of axioms or assumption that have no proof eigther... I've never gotton around this for a good 4 yrs now maybe?

___________________
"The Greatest enemy of knowledge is not ignorance, it is the illusion of knowledge." -Stephen Hawking
"First they came for the communists, and I did not speak out— because I was not a communist;
Then they came for the socialists, and I did not speak out— because I was not a socialist;
Then they came for the trade unionists, and I did not speak out— because I was not a trade unionist;
Then they came for the Jews, and I did not speak out— because I was not a Jew;
Then they came for me— and there was no one left to speak out for me." -Martin Niemöller

quote:

Originally posted by shaolin_Z That's one thing that's driving me nuts. When you boil down logic all you're left with is a set of axioms or assumption that have no proof eigther... I've never gotton around this for a good 4 yrs now maybe?

that's true for inductive logic, but not deductive logic. In deductive logic the conclusion is not assumed true based on the truth of the premises, rather, the conclusion is guaranteed if the premises are true. on the other hand, in inductive logic the conclusion is assumed true because it is highly probable if the premises hold true.

i hear what you are saying though, it's tricky. you should just step back for a minute look at the big picture.

quote:

Originally posted by jerZ07002 that's true for inductive logic, but not deductive logic. In deductive logic the conclusion is not assumed true based on the truth of the premises, rather, the conclusion is guaranteed if the premises are true. on the other hand, in inductive logic the conclusion is assumed true because it is highly probable if the premises hold true. i hear what you are saying though, it's tricky. you should just step back for a minute look at the big picture.

No, it's true for all forms of reasoning. Formal logic is strictly deductive, although inductive principles are used but somehow are magically deductive which is what is still driving me nuts ... and I'm taking a look at my philosophy / logic text books right now... unfortunately I don't have my discrete mathematics text books anymore so I can't reference those. Take a biconditional or conditional "thing" for lack of a better term for example, they're axioms and can't have any proofs... plus they rely on being well defined. Predicate on the other hand require an antecent to exist. And when you "recurse" back to your base antecedents all you're left with is assumption that have no proof... in any form of reasoning... so science and religion are logically equally valid and full of shit

EDIT: I meant "recurse"

___________________
"The Greatest enemy of knowledge is not ignorance, it is the illusion of knowledge." -Stephen Hawking
"First they came for the communists, and I did not speak out— because I was not a communist;
Then they came for the socialists, and I did not speak out— because I was not a socialist;
Then they came for the trade unionists, and I did not speak out— because I was not a trade unionist;
Then they came for the Jews, and I did not speak out— because I was not a Jew;
Then they came for me— and there was no one left to speak out for me." -Martin Niemöller

Last edited by shaolin_Z on Jun-03-2008 at 22:44

Fuck, I've taken my own thread on a completely different tangent! Thanks a bunch Krypton ... although this is interesting too

___________________
"The Greatest enemy of knowledge is not ignorance, it is the illusion of knowledge." -Stephen Hawking
"First they came for the communists, and I did not speak out— because I was not a communist;
Then they came for the socialists, and I did not speak out— because I was not a socialist;
Then they came for the trade unionists, and I did not speak out— because I was not a trade unionist;
Then they came for the Jews, and I did not speak out— because I was not a Jew;
Then they came for me— and there was no one left to speak out for me." -Martin Niemöller

quote:

Originally posted by shaolin_Z No, it's true for all forms of reasoning. Formal logic is strictly deductive, although inductive principles are used but somehow are magically deductive which is what is still driving me nuts ... and I'm taking a look at my philosophy / logic text books right now... unfortunately I don't have my discrete mathematics text books anymore so I can't reference those. Take a biconditional or conditional "thing" for lack of a better term for example, they're axioms and can't have any proofs... plus they rely on being well defined. Predicate on the other hand require an antecent to exist. And when you "resurse" back to your base antecedents all you're left with is assumption that have no proof... in any form of reasoning... so science and religion are logically equally valid and full of shit

i'm pretty far removed from school right now, so i'm just running on memory. if you are viewing logic strictly in the abstract you are probably correct. logical theories, however, can be proven. for example: humans can't survive without breathing gaseous oxygen -> water does not contain gaseous oxygen -> humans can't survive underwater in a natural state. that deductively reasoned conclusions can be proven by holding someone underwater. that conclusion is not an axiom.

that's a shaky example, but i think you should get my point.

quote:

Originally posted by jerZ07002 i'm pretty far removed from school right now, so i'm just running on memory. if you are viewing logic strictly in the abstract you are probably correct. logical theories, however, can be proven. for example: humans can't survive without breathing gaseous oxygen -> water does not contain gaseous oxygen -> humans can't survive underwater in a natural state. that deductively reasoned conclusions can be proven by holding someone underwater. that conclusion is not an axiom.

That's true. The conlucison is not an axim and neigther are any of the predicates above . Don't worry, I took logic / philosphy / discrete mathematics / number theory / probability et all ages ago myself and took time off school... only to come back recently to finish up my goddamn degree... and I only have 3 CS electives left and 2 required courses... and I'm thinking of switching majors now lol. Anyways, that aside... when you take a look at predicate logic, which is sort of the foundation for logic... and all the principles and axioms it based on or formal logic period is based on... you're left with assumptions . There's a really funny argument by James Randi. The example goes as follows:

If you take 100 raindeers to the top of a tall building, and drop them one of the time to see if they can fly. At the end of the experiment, unless one or more actually took off and flew away, all you have definitively proven is that those 100 raindeers could not fly, or chose not to.

I know it's sounds fucking ridiculous by it's logicaly sound lol.

___________________
"The Greatest enemy of knowledge is not ignorance, it is the illusion of knowledge." -Stephen Hawking
"First they came for the communists, and I did not speak out— because I was not a communist;
Then they came for the socialists, and I did not speak out— because I was not a socialist;
Then they came for the trade unionists, and I did not speak out— because I was not a trade unionist;
Then they came for the Jews, and I did not speak out— because I was not a Jew;
Then they came for me— and there was no one left to speak out for me." -Martin Niemöller

quote:

Originally posted by shaolin_Z That's true. The conlucison is not an axim and neigther are any of the predicates above . Don't worry, I took logic / philosphy / discrete mathematics / number theory / probability et all ages ago myself and took time off school... only to come back recently to finish up my goddamn degree... and I only have 3 CS electives left and 2 required courses... and I'm thinking of switching majors now lol. Anyways, that aside... when you take a look at predicate logic, which is sort of the foundation for logic... and all the principles and axioms it based on or formal logic period is based on... you're left with assumptions . There's a really funny argument by James Randi. The example goes as follows: If you take 100 raindeers to the top of a tall building, and drop them one of the time to see if they can fly. At the end of the experiment, unless one or more actually took off and flew away, all you have definitively proven is that those 100 raindeers could not fly, or chose not to. I know it's sounds fucking ridiculous by it's logicaly sound lol.

i was actually thinking something like that when i was writing the example above. the premise is actually an assumption - that humans breathe oxygen. no matter how much we think something is guaranteed, it is only guaranteed based on our limited knowledge. we know we breathe oxygen because of the data we have gathered - not because it is what we breathe. there could be some undetectable unknown element that attaches itself to oxygen that is actually sustaining us, however, because we can't detect the element we attribute it to oxygen. i totally understand what you are saying.

Ok, stupid me for not looking at wikipedia on the proof of validity for mathematical induction.

http://en.wikipedia.org/wiki/Mathematical_induction <--- scroll down to Proof or reformulation of mathematical induction and then the Generalization part.

Quick question, or clarification rather. Unforutnately I'm obsessing over induction at the moment (and have been since I made the first post refering to mathematical induction, and it not being "inductive" but rather deductive in nature)... and am stuck on the transfinite induction step if anyone care to help out with it... I've gotton this far working it out all over again...

Peano's Axiom
There is a relational system <Nat, 0, s>, which satisfies the following axioms:

1. There is a special element of Nat denoted by 0.
   
2. s is the successor function from Nat to Nat
   
3. s is one-one
   
4. ~ (∀ k ∈ Nat : s(k) == 0)
   
5. The Induction Axiom
   Let S be any subset of Nat,
   IF: (i ) (0 ∈ S) and (ii) (∀ k ∈ Nat) ∧ (∃ k ∈ S) ⇒ (s(k) ∈ S)
   THEN: S == Nat
   

These three "assumptions"

1. Nat is well-ordered.
   
2. ∀ k, n ∈ Nat: (k == 0) ∨ (k == n +1)
   
3. ∀ n ∈ Nat: (n << n +1)
   

Now the proof goes:

• We have a proposition P(n) defined on Nat where n is any natural number.
  
• ∃ m ∈ Nat: m < n
  
• S ⊆ Nat: (k ∈ Nat ∧ k < m)
  
• P(base case) is shown to be true.
  
• P(k) is shown to be true. (or that P is true for S)
  
• P(m) is shown to be true.
  

Now the last step left is to show that P(n) is true via 'Transfinite induction.' That's the step in the proof that not making any sense at the moment.

Notation:

• ∃ <-- existential quantifier
  
• ∀ <-- universal quantifier
  
• ~ <-- negation
  
• ∧ <-- conjunction
  
• ∨ <-- disjunction
  
• ⇒ <-- implication
  
• ⇔ <-- material equivalence
  
• == <-- (mathematicaly) equality
  
• != <-- not equal
  
• <, > <-- less than, greater than
  
• ≤, ≥ <-- less than or equal, greater than or equal
  
• ∈ <-- is a member
  
• ⊆ <-- is a subset
  
• ø <-- empty set
  
• Nat <-- the set of natural numbers
  

EDIT: Oh, do not bother explaining it in words as language is a very poor medium for expressing complex concepts. Formal proofs only, or at least psuedo-formal.

___________________
"The Greatest enemy of knowledge is not ignorance, it is the illusion of knowledge." -Stephen Hawking
"First they came for the communists, and I did not speak out— because I was not a communist;
Then they came for the socialists, and I did not speak out— because I was not a socialist;
Then they came for the trade unionists, and I did not speak out— because I was not a trade unionist;
Then they came for the Jews, and I did not speak out— because I was not a Jew;
Then they came for me— and there was no one left to speak out for me." -Martin Niemöller

quote:

Originally posted by shaolin_Z Fuck, I've taken my own thread on a completely different tangent! Thanks a bunch Krypton ... although this is interesting too

We're talking about wisdom aren't we? Reasoning is very important in attaining wisdom.

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