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I am trying to understand logic and I came across a set of actions that I describe below that I can't get my head around.

Suppose you have a bag of multiple colored balls.

Situation 1.  
Argument: There are no red balls in the bag. 
Action: Pick up balls at random until you find a red one.

Situation 2. 
Action: Pickup a random ball from the bag. 
Argument: All the balls in the bag are of same color as the ball you picked up.

I have some questions.

  1. What is the correct conclusion in each situation?
  2. Are these situation logic related?
  3. Can one be converted to another?
  4. Which is correct and which is flawed?
  5. What are the names for the logic contained in these situations?
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    What logic? I can't get my head around it either. What are the premise? What is the conclusion?
    – Seamus
    Feb 14 '12 at 14:59
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    I don't really understand how this question is posed, least of all the "situations". Could you elaborate on these? (Normally, arguments consist of premises and conclusions)
    – stoicfury
    Feb 14 '12 at 16:01
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    Is there any chance I might be able to persuade you to clarify the headline here a bit? (They should ideally encapsulate or at least reflect some of the specific content of the question)
    – Joseph Weissman
    Feb 14 '12 at 16:25
  • @seamus , stoucfury I am sorry. I know there has to be a conclusion but I don't know what followed them and didn't want to post nonsense. May be I'll add it as another question.
    – Dirt
    Feb 14 '12 at 20:16
  • @Joseph whether this is flawed was the main question and others were for better understanding, so I posted it that way. I didn't know how to frame a question that reflected what it described.
    – Dirt
    Feb 14 '12 at 20:20
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The first situation is an exhaustive disproof of existence, and is (if I understand what you have written) sound in its logic. The second is perhaps reasonable, and (again if I understand your writing) is called inductive reasoning, it is however not logical- not a valid deduction, as was explosively pointed out by Hume in An Enquiry Concerning Human Understanding. As such, in 'the finite case' they are profoundly different, one being logically valid, the other not.

When the bag of balls becomes infinitely large, however, the situations become nearly identical in practice, as in finite time one can never check every ball to see that it is not red, and so some inductive reasoning is necessary in both cases.

In the latter case, however, they are not entirely the same- for the first situation is still slightly better than the second. In the first situation, we make a hypothesis 'there are no red balls in the bag' that we subsequently test in a way that could falsify it: in the second, since we do not repeat the experiment after we make our hypothesis, our hypothesis is not fallible (this is important for reasons articulated by Karl Popper amongst others).

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  • In your final comment, you said "our hypothesis is not fallible." Did you mean to say that "our hypothesis is fallible?" I do not understand the former.
    – commando
    Feb 14 '12 at 12:16
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    I did indeed mean not fallible! The reasoning is somewhat subtle- or at least the stuff of a mid sized essay- but fallibility is a very useful property for a proposition about the world to have- in fact it is the criterion by which a good scientific hypothesis can be judged. Read the link 'for reasons articulated...' and that should explain it to some extent. Feb 14 '12 at 12:29
  • I should probably add a caveat that the second situation is not in principle unfalsifiable, but by the design of our methodology is unfalsifiable in practice. Feb 14 '12 at 12:32
  • Ah, I understand now, thank you. I hadn't thought of it that way.
    – commando
    Feb 14 '12 at 13:45

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