Carl the Logic of Confirmation,” introduces a
Carl Hempel’s “Paradox of the Ravens,”proposed in 1965 through his “Studies in the Logic of Confirmation,” introducesa problem where inductive reasoning disagrees with own intuition in response toNicod’s Criterion of Confirmation. Hempel states that a law where A calls for Bis validated if a recording of B corresponds with A, and that same law isinvalidated if A does not correspond with B. In other words, a hypothesis isconfirmed by observation and disproven where it is observed either to beincorrect or incorrectly.
Seemingly simple to understand, yet this idea comeswith several pieces of baggage, one being the Paradox of the Ravens. Hempel introduces this paradoxthrough two hypotheses: A, whereas all ravens are black, and B, whereas allnon-black things are non-ravens. These two hypotheses are logical and equal, asthey are different versions of the same hypothesis, arguing the same content.According to Nicod’s initial criterion, observing a black raven confirms A, allravens are black, but is neutral to B, all non-black things are non-ravens.Very similar to as the observation of a non-black non-raven would confirm B butbe neutral to A, this violates the equivalence condition – as whatever confirmsor disconfirms one of two equivalent hypotheses also must confirm or disconfirmthe other. This brings the Paradox of the Ravens into light, as observationsupporting one hypothesis cannot be used to support another hypothesis that istechnically logically equivalent to the first. Different philosophers haveattempted to understand and solve this paradox, with the most successful beingthe Bayesian confirmation theory being used hand-in-hand with Hempel’s originalcriterion.
Quine and Foster try to solve theparadox through the deemed “projectability” of a hypothesis. Projectablehypothesis are confirmations generalized by their occasions according to Nicod’scriterion of confirmation, more or less hypotheses made up of predicatescommonly used in projections. The Foster-Quine argument says although allravens are black is a projectable statement, all non-black things arenon-ravens is not projectable because “non-black” is a projectable predicate.
Allnon-black things being non-ravens is not projectable, and the observation ofnon-black non-ravens is not confirming, so therefore the observation of anon-black non-raven does not confirm B either. Likewise, the observation of ablack raven does actually confirm both A and B on account of the projectabilityof A that all ravens are black. According to the Foster-Quine argument, theequivalency condition should not be denied after the difference in projectabilityis taken into account. This account, however, is not conclusive, as theparadox itself comes out of the idea that non-black non-ravens do not confirmA, but the solution of the paradox claims the observations of black ravens isused to support B. Therefore, the Foster-Quine argument takes away from thisidea’s persuasiveness, but can be explained through projectability.
However,the Foster-Quine argument creates another paradox in itself, stating that ablack raven can confirm that “all non-black things are non-ravens,” but anon-black non-raven cannot do so. Goodman and Schleffer point out that theFoster-Quine argument misinterprets the general idea of projectability, as itis not the nature of the predicate that is the determining factor whether ahypothesis is projectable or not, but it is always still projectable as long asno conflicting hypotheses are present. Therefore, the Foster-Quine argumentdoes not show B to be projectable and this argument loses foundation. Goodman and Schleffer argue that Adoes logically differ from B, as A has an excluded contrary that all ravens arenot black while B has the excluded contrary that all non-black things areravens. As these two contraries conflict, the observation of a non-blacknon-raven does not support A, that all ravens are black, as according toGoodman and Schleffer, the two hypotheses are not logically equivalent. Theobservation of a non-black non-raven does not support B as it also invalidatesthe contrary. Also, an observation of a black raven supports A but does notsupport B, as it satisfies its contrary that all non-black things are ravens,in the way where it does not invalidate it. This introduces the idea ofselective confirmation, whereas that an observation that supports a conditionalhypothesis must also not invalidate its contrary.
The observation of anon-black non-raven does not confirm A, that all ravens are black, any more orany less than it confirms that all ravens are not black. Hempel himself tried to solve theparadox by arguing that it wasn’t a paradox at all, and that it was 100%logical for the observation of a non-black, non-raven to confirm in some waythat all ravens are black. Hempel argued that A, all ravens are black, suggestthat everything in the universe is either not a raven or is black, so observinganything with both conditions satisfies is a confirmation to the paradox initself.
With this being said, observing a non-black non-raven confirms A as itsatisfies these conditions, just as seeing a black raven or a yellow bananadoes. This is known as Hempel’s Satisfaction Criterion of Confirmation, whichcorresponds with the Bayesian Confirmation Theory. The Bayesian Confirmation Theory isbased on mathematical probabilities, starting with the assumption that a personcan have different degrees of certainty about a belief. These degrees aredescribed with any number between 0 and 1, with values closer to 1 denoting acertainty about a belief. The conditional probability of A given B is P(A/B) =P(A and B)/P(B). If a piece 35to equal the probability of E, written P(H/E),equaling P(H and E)/P(E).
So, the Bayesian confirmation theory attempts tosolve the paradox of the ravens by arguing the observation of a non-blacknon-raven does support the hypothesis that all ravens are black, to anegligible extent. So, according to the Bayesiantheory, observing a black raven will double the belief of the Hypothesis, P(H),the conditional probability given for HG to double is that of the initialprobability. For the Bayesian Theory to work it must be possible for a singleobservation to have an effect on each of the subjunctive probabilities.
Witheither the Foster-Quine theory of confirmation or the Selective ConfirmationModel the Bayesian Theorem would not hold. Ido believe it is plausible to believe observing every non-black thing in theworld and discovering that none of them are ravens would have strong supportfor the idea that all ravens are black, if one could observe that. Both piecesof evidence account for many intuitions in terms of confirmation, like how eachsuccessful confirming observation of seeing a black raven will cause P(H) toincrease by a lesser amount than the increase from a previous observation.
Bayesian theory does not suggest that it would be logical to base a hypothesissuch as all ravens are black on an observation of a non-black non-raven as suchan observation will cause the P(H) to increase by such a miniscule amount thatno difference is made. Only the observation of an actual black raven canincrease P(H) enough for a different hypothesis to be able to be entertained.By reading into the Bayesian theorem, and Hempel’s initial satisfactioncriterion, the Paradox of the Ravens is able to be solved