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Carefully Reherse The Reasoning That Leads To The Paradox Of The Raven

Carefully rehearse the reasoning that leads to the Paradox of the Ravens.   Is there a satisfactory conclusion?

Throughout the scientific history of the world there have been many changes in the way we think, in the way we perceive the world to work.   Indeed theories that were held as unshakably true in the past now seem laughable, for example the theory that the universe revolved around the Earth was deemed true by all of the scholarly community of the time, until Galileo came along and proved otherwise.   Such changes in thought have lead people to be a little more cautious before giving commitment to certain scientific theories incase ten or fifteen years on the are proven to be wrong.   In at least some areas of science evidence is often fragmentary and inconclusive, therefore it would of benefit to be able to say more about the degree to which a given piece of evidence supports a given theory.   In short to develop a quantitative account of the relationship between evidence and theory.   Philosophy has sought to do this under the heading ‘confirmation theory'.   They have tried understanding to what extent various bodies of evidence ‘confirm' different theories.   They do this so that if we know a piece of evidence highly confirms a theory then we are relatively safe in believing it to be true; but should there only be a small degree of confirmation then we can moderate our trust accordingly.   However, finding this intuitive notion of confirmation is not as straightforward as it may seem and one of the problems that stems from this is the Paradox of the Ravens.

Starting with the assumption that there is a relationship of confirmation and that sometimes E confirms T, where E is some body of evidence and T is some theory.   Then it seems logical to make the following two assumptions about confirmation:

(1.)   That generalizations are confirmed by their instances.
Or
If E = (Fa & Ga) and T= All Fs are Gs, then E confirms T.

(2.)   If E confirms T, and T is...