Observation A Non Black Non Raven example essay topic

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 in case 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. OrI f E = (Fa & Ga) and T = All Fs are Gs, then E confirms T. (2.) If E confirms T, and T is logically equivalent to S, then E confirms S. At first glance these two simple statements of logic seem to be uncontentious, but they can easily be shown to generate a puzzle, as follows. (L) All ravens are black. (M) All non-black things are non-ravens. Notice that these two statements are logically equivalent. Now, take our evidence being the observation that: (I) That white thing over there is a shoe.

Since (I) is an instance of a non-black thing being a non-raven, then assumption (1.) tells us that (I) confirms (M). Add this to the fact that (M) is logically equivalent to (L), then assumption (2.) tells us that (I) also confirms (L). So, it follows that the observation of a white shoe confirms the claim that all ravens are black. This obviously is absurd and runs counter to intuition and therein lies the paradox. The first thing that springs to mind is that one or both of the original assumptions is wrong, but it's hard to see where.

Assumption (2) - logically equivalent propositions make exactly the same claims about the world, so how can a piece of evidence support one without supporting the other, it makes sense. And assumption (1) seems beyond reproach that if generalizations can be confirmed by anything then they are confirmed by their instances. One method of solving this paradox is to try and quantify our initial confirmation theory, one such method of doing this is Bayesian confirmation theory. Developed by and after Tomas Bayes (1702-61), this theory uses the notion of subjective probability to explicate the relation of confirmation.

The initial assumption made by Bayesian confirmation theory is that our attitudes towards theories are measured by the subjective probability we attach to them. So if we fully believe a theory we attach a subjective probability of 1; whereas as if we regard it as a more spurious argument we attach a subjective probability closer to 0. They then say that a piece of evidence E confirms theory T only if learning E increases a persons subjective probability that they have attached to T. To further develop this theory we need to show the notion of conditional probability. The conditional probability of A given B, (written 'Prob (A / B) ') is defined as the quotient Prob (A and B) / Prob B, or can be said as the probability-of-A-on-the-assumption-that-B-is-true.

This quotient gives us a measure of the likelihood of A happening given that B has happened. Now applying this to our confirmation. Prob (T / E) is the probability of T, on the assumption that E is true. Bayesians therefore argue that when you learn E you should increase your subjective probability for T equal to this number.

So E will confirm T if and only if Prob (T / E) is greater than Prob (T). Now Bayesians will look at the paradox of the ravens and will concede both assumptions (1.) and (2.) to be true and with them their apparently absurd conclusion that a white shoe does in fact confirm the theory that all ravens are black. But then Bayesians will explain this by saying that the observation of a white shoe only confirms the theory that all ravens are black a tiny bit, so small in fact as to render it almost trivial. They can illustrate this using simple figures. Suppose you imagine that 1/5 of the universes' physical objects are black, and that 1/10 of them are ravens. Then your subjective probability for the next object you see being a black raven should be 1/50, and for it being a non-black non-raven should be 36/50.

Now consider the conditional probability of a black raven and a non-black non-raven on the assumption (T) that all ravens are black. This assumption will increase your subjective probability for both of these observations, simply because it decreases your subjective probability for seeing a non-black raven from 4/50 to 0. Suppose now that your subjective probability for seeing a black raven given (T) is 2/50, and a non-black non-raven 38/50. Now applying Bayes's theorem we see that the initial subjective probability of seeing a black raven is 1/50, but the subjective probability of seeing a black raven given (T) is 2/50.

So the observation of a black raven given (T) will double our subjective probability, therefore it lends a lot of confirmation to (T). Whereas our initial subjective probability for seeing a non-black non-raven is 36/50, and the subjective probability given (T) is 38/50. So the observation of a white shoe only increases our subjective probability by 2/36 ths. The point being that the theory that all ravens are black makes the observation of a black raven significantly less surprising than we might otherwise think. While the observation a non-black non-raven was never very surprising to begin with and becomes only marginally less so on the hypothesis that all ravens are black. So black ravens confirm the theory that all ravens are black a lot, white shoes confirm it barely at all (indeed using realistic figures we would see that a white shoe confirms the theory such an infinitesimal amount that it seems pointless saying it).

In this theory I think that the Bayesians make sense of the paradox of the ravens quite nicely and provide a very satisfactory conclusion.