A paradox of evidence #2

[The idea]

Suppose there is a particular shelf of books somewhere.

Hypothesis: for every sentence in any of these books, if the sentence contains the word "impropriety" then it doesn't contain the word sequence "Nastasya Filippovna."

I notice several novels by Dostoyevsky in the shelf, but I ignore them. (Maybe it's a very long shelf and those books are far from me.) I take a book about ethical and legal issues that arise in securities trading. I find some sentences in that book that contain the word "impropriety." In each of these sentences, I confirm that the word sequence "Nastasya Filippovna" doesn't occur.

Have I reinforced your belief in the hypothesis?

Now imagine that you can see and compare words as sequences of symbols, but you cannot understand them and they mean nothing to you. In your state of ignorance, you might take the results of my investigation as evidence in support of the hypothesis.

 

[The idea]

Related thread:

http://www.randi.org/vbulletin/showthread.php?s=&threadid=54944

 

[Stimpson J. Cat]

The idea,

Have I reinforced your belief in the hypothesis?

Of course not, since at this point I would not hold any such belief.

In order for me to believe that the hypothesis is likely to be true, you would have to first look through the majority of the books, repeatedly showing that the hypothesis is true for them. In addition, you would have to provide some reasonable argument for why I should think that probabilities of finding those words together should be consistent across all of the books, otherwise I could not reasonably infer anything about the books we haven't looked at from the ones we have looked at.

Now imagine that you can see and compare words as sequences of symbols, but you cannot understand them and they mean nothing to you. In your state of ignorance, you might take the results of my investigation as evidence in support of the hypothesis.

I might, if I did not understand how basic scientific epistemology works, and more importantly, why it works. If I understand this, then I know that I require some sort of justification for assuming that I can infer probabilistic information about books I haven't seen from those I have. I cannot just blindly make this assumption. Not if I want to actually be able to logically draw conclusions from the results of my observations.


Dr. Stupid

 

[The idea]

In addition, you would have to provide some reasonable argument for why I should think that probabilities of finding those words together should be consistent across all of the books, otherwise I could not reasonably infer anything about the books we haven't looked at from the ones we have looked at.

Isn't there a similar issue that arises in the other thread? Given that an entity near your computer (a coffee mug) satisfies the property "if it's non-black, then it's a non-raven", is there any reason to infer anything about entities in the many regions of the world that are far from your computer?

 

[ReFLeX]

Hypothesis: for every sentence in any of these books, if the sentence contains the word "impropriety" then it doesn't contain the word sequence "Nastasya Filippovna."

In the bookshelf you have a reasonable expectation of covering every sentence that contains "impropriety". You will be going about the wrong way for proving the hypothesis, for obvious reasons. But is conceivable that since the bookshelf contains a finite number of sentences, you will be able to prove: If the sentence contains "impropriety" then it does not contain "Nastasya Filippovna". Only now, once you have proved that, do you have proper justification for asserting the converse, that any sentence with "Nastasya Filippovna" does not have "impropriety".

 

[Art Vandelay]

if original= "If the sentence contains "impropriety" then it does not contain "Nastasya Filippovna". "
contrapositive= "any sentence with "Nastasya Filippovna" does not have "impropriety". "
converse = "If the sentence does not contain "Nastasya Filippovna", then it contains "impropriety". "

Note that while the contrapositive is logically equivalent, then converse is not (and in fact is almost certainly false; it would require that every sentence contain one of the phrases).

 

[Stimpson J. Cat]

The idea,

In addition, you would have to provide some reasonable argument for why I should think that probabilities of finding those words together should be consistent across all of the books, otherwise I could not reasonably infer anything about the books we haven't looked at from the ones we have looked at.

Isn't there a similar issue that arises in the other thread? Given that an entity near your computer (a coffee mug) satisfies the property "if it's non-black, then it's a non-raven", is there any reason to infer anything about entities in the many regions of the world that are far from your computer?

Yes. I already addressed this issue in the other thread, although in a somewhat different way. The fundamental issue is that viewing the coffee mug near your computer simply does not provide you with any new information which is pertinent to the hypothesis. In this case, it fails to provide any such information for two reasons:

1) There is no real logical connection between the existence of the non-black coffee mug here, and the existence of non-black ravens elsewhere.

and

2) We already know that coffee mugs are not ravens, so even if there was some logical connection, we would already possess the information that knowledge provides. Our observation would tell us nothing new.

As I stated in the other thread, the apparent paradox stems from the misconception that any observation which is consistent with a theory should be equally considered to be supporting evidence for the theory. What makes an observation supporting evidence for a theory is not that it is consistent with the theory, but that the information which that observation provides us with increases our confidence that the theory is true. In order for it to do this, there must be a logical connection between the observation and the theory. There must be some established reason for thinking that information relevant to the theory can actually be inferred from the observation. The simple fact that the observation is consistent with the theory, while certainly necessary, is not sufficient for this.


Dr. Stupid