Paradox of Confirmation Term Paper

Download this Term Paper in word format (.doc)

Note: Sample below may appear distorted but all corresponding word document files contain proper formatting

Excerpt from Term Paper:

Paradox of Confirmation

Paradoxes seem to form the essence of irrationality and to continuously prove that rationality has a limit and that rationally inducing a fact may in fact prove the fact wrong. What is in fact a paradox? If we follow one definition, a paradox is "a parody on proof. It begins with realistic premises, but the conclusion falsifies these premises." More so, however, a paradox "arises when a set of apparently incontrovertible premises gives unacceptable or contradictory results." (Blackburn 1996, p. 276).

Before starting to analyze one of the most well-known paradoxes in philosophy, let us first have a look at three of the more important concepts of evidence, the classificatory concept, the comparative and the quantitative concept. Classificatory concepts are "those which serve for the classification of things or cases into two or a few mutually exclusive kinds." This concept helps divide a larger set into a series of smaller subsets with the obvious advantage that it is much easier to analyze the characteristics of a set with fewer elements. In our case, related to the ravens paradox, such a concept would be represented by classifying all objects into ravens or non-ravens, as well as into black and non-black objects.

The quantitative concepts serve to "characterize things or events or certain of their features by the ascription of numerical values." Indeed, several things, especially physical characteristics, can be described by using numerical value. Things like height or weight can easily have a number associated to them. In our case, we can relate for example the number of ravens in the world. Using this quantitative concept when discussing the paradox will help in the end make probabilistic assumptions about the statement "all ravens are black."

Comparative concepts, on the other hand, "serve for the formulation of the result of a comparison in the form of a more-less-statement without the use of numerical values." Seeing the discussion of our paradox, such a concept can be applied in finally stating that it is more or less probable that our statement is true given a certain fact.

Some preliminary approaches to paradoxes: Nicod's Criterion of Confirmation and The Equivalence Condition

Nicod's criterion of confirmation is one of the most important evidences around which the raven paradox will revolve. The criterion basically proposes the following statements:

For every x if x is a P. then it follows that x is a Q.

A a) A confirming instance would be, x is P. And x is Q (Px & Qx) b) A disconfirming instance would be, x is P. And x is not Q (Px & ~Qx).

A c) A neutral or irrelevant instance would be, x is not P (~Px).

Now to turn to the equivalence condition. Humberstone argues that such a condition is reasonable because "whether or not a hypothesis is confirmed by an observation should depend on the content of the hypothesis and not on the way that it happens to be formulated." Hence, "logically equivalent formulas have the same content." Other wise put, the equivalence condition states that if we have two hypotheses H. And H', logically equivalent and a proposition E. that confirms H, than it will confirm H'. Applied to the ravens paradox that will be discussed below, the observation of a purple cow will confirm statement H' that says that "all non-black objects are not ravens," hence it will also confirm its logical equivalent "all ravens are black."

Now, as we see from the lines above, the equivalence condition and Nicod's criterion lead to a paradox situation by themselves. If observations that confirm a hypothesis confirm anything logically equivalent, then this contradicts Nicod's statement that a non-As non-Bs are irrelevant.

The Paradox of the Ravens

Carl Hempel was the first to publish the paradox of the ravens in Theoria, a Swedish periodical, in 1937, and ever since, the paradox has been a source of numerous controversies. In his paper, Hempel concludes that the generalization of a simple statement, such as "all ravens are black" can be confirmed by another simple observation, such as that of a purple cow. The observation of a purple cow would, in Hempel's opinion, increase, even slightly, the probability that all ravens are black. Briefly summarizing his paradox, professor Hempel notes that the statement "all ravens are black" is logically equivalent to the statement that "all non-black objects are not ravens" (this is a true logical equivalence). Therefore, finding a purple cow weakly confirms the statement that all ravens are black, because it confirms its logical equivalent that all non-black objects are not ravens. As Hempel states, observing a non-black object will confirm his statement that all ravens are black to "an infinitesimal degree." The more observations of non-black objects, the stronger the statement will be confirmed. The catch of Hempel's paradox would be that the observation of a purple cow also confirms the statement that "all ravens are white," following the same logical discussion ("all non-white objects are not ravens, hence a purple cow will confirm this statement and its logical equivalent that all ravens are white). How can a purple cow then confirm two opposite statements that "all ravens are white" and "all ravens are black"?

This was but a brief description of the paradox. Let us now dig in further and discover some probabilistic and logical assumptions about this statement. The paradox itself is constituted of three propositions:

1) Observations of black ravens confirm 'All ravens are black'.

2) Observations of purple cows, white swans, etc., are neutral to (i.e. do not confirm) 'All ravens are black'.

3) If observations confirm one formulation of a hypothesis they confirm any logically equivalent formulation

The three propositions are themselves incompatible with one another. For example, an observation of a purple cow will confirm "all non-black objects are not ravens" (A), hence also "all ravens are black" (B) (deductible from proposition number 3: observation that confirms A true implies B. true). However, the same observation denies the neutrality derived from 2. It can thus be concluded that proposition 3 cannot be denied (it is a logically proven fact), hence, the paradox could be solved by denying either 1 or 2. As we have seen in the brief presentation of the paradox, professor Hempel denies proposition 2 and concludes that any observation of non- black objects will infinitesimally prove the statement.

Intuitively, we can state that proposition 2 is more likely to be rejected than proposition 2. This is because the most obvious proof of the statement "all ravens are black" would be observations of black ravens. Hence, if we are to reject proposition 2, then Hempel's solution to the paradox is right in this context and Nicod's definition can be rejected as well.

It is time to introduce a further dilemmatic element: we can add the information that there are far more non-black things than ravens. If we regard this additional information, we can still deny proposition 2, regarding neutrality, but we can now affirm that observing non-black non-ravens, such as a purple cow, is not as good a proof of the statement as observing black ravens. This does not reject Hempel's assumption (that rejects proposition number 2), but somewhat limits the context in which it is placed.

We may assume that from the three propositions mentioned above, we can accept proposition 3 as a logical axiom, as well as proposition 1, and reject proposition 2. However, it is notable to make a brief reference to Professor Watkin's view, in which he accepts both propositions 1 and 2. The statement we are dealing with includes two elements: ravens and black. Let us assume one of these fixed (that is, we will be assuming that we are observing an object, which we KNOW is black), hence, the outcome of the observation can either be that it is a raven or that it is not a raven. Thus, the observation will either confirm the hypothesis or it will not (in the sense that if the outcome is the other way, it does not confirm). The fact that two different observations cannot both confirm our hypothesis means that if we observe an object that we know is a raven and it turns out to be black, this confirms out hypothesis, but if we inspect a black object and it turns put to be a raven, this does not.

We have entered an area of ambiguous hypothesis and conclusions, that is why I would like to restate the paradox and follow up a different approach to it. However, the observations made here above still stand as assumptions and discussions around the paradox.

The paradox itself seems to revolve around two elements: the first that the observation of a purple cow really has nothing to do with the generalization of the statement "all ravens are black" and the second that such an observation also proves that "all ravens are white." Let us have a look at the first paradox. Solving it would either mean contradicting Hempel in…[continue]

Cite This Term Paper:

"Paradox Of Confirmation" (2004, February 25) Retrieved December 2, 2016, from

"Paradox Of Confirmation" 25 February 2004. Web.2 December. 2016. <>

"Paradox Of Confirmation", 25 February 2004, Accessed.2 December. 2016,

Other Documents Pertaining To This Topic

  • Can Bayesians Give an Adequate Explanation of Confirmation of Scientific...

    Bayes Probability Can Bayes Confirmation Theory Give an Adequate Explanation for Confirmation of Scientific Theories? Theorizing in science is a complex and time-consuming undertaking. The theorist uses collected evidence from some means of scientific inquiry to project a generalized case. However, there is a difficulty with this process. There is some amount of probability that the theory will be wrong. Even if this is not a harmful outcome, it is difficult for

  • Reading Comprehension

    Augustine, Anselm and Aquinas Question #1 from "Augustine Confessions 2nd edition. Translated by F.J Sheed: Please explain Augustine's theory that evil is the privation of good, and argue for its relevance to at least one other main theme in the confessions. Rather than subscribe to the prevailing theory that evil represented the polar opposite of good -- acting as a necessary counterbalance within the realm of human morality -- Augustine proposes

  • Interventionism From the Perspective of Realism vs

    interventionism from the perspective of realism vs. idealism. Realism is defined in relationship to states' national interests whereas idealism is defined in relation to the UN's Responsibility to Protect doctrine -- a doctrine heavily influenced by Western rhetoric over the past decade. By addressing the question of interventionism from this standpoint, by way of a case study of Libya and Syria, a picture of the realistic implications of "humanitarian

  • Effect of Forgiveness on Health

    forgiveness on human health. In its simplest form, the purpose of the study is to evaluate human psychological stress that might constitute a risk factor for heart disease. Further, the study will also evaluate the impact of forgiveness on heart disease. However, such a simple dissertation clearly demands further definition. What, exactly, do we signify when we speak of heart disease? What is properly considered as forgiveness? What impact

  • Salvador Minuchin

    Salvador Minuchin and his structural method of family therapy. We will discuss a brief history of Minuchin's life, his peers and influences. The discussion will include a clear description of this particular type of therapy, including the five basic concepts of the therapy and the different strategies used. We will also discuss the strengths and weaknesses of this modality. Finally examples of a family session will be provided. Salvador Minuchin

  • Sartre on Freedom and Existentialism

    E. The lack of attachment to other people and things) is beneficial from an individual perspective, but damaging for society as a whole because it hinders advancement. In reality however, in order to maintain such a belief in our own self-sufficiency and freedom of choice, we would have to rewrite the laws of human nature. As this is highly improbable, we are likely to continue in our flight from freedom for

  • Female Elements in Their Eyes

    This renunciation, depending on one's perspective, represents either a willful act of sacrifice or a selfish act of disobedience. Sandra Pouchet Paquet, however, frames this problematic deed in neutral terms in her analysis of the text, which focuses on its ambivalence toward the role of ancestral knowledge in identity formation. Paquet (2009) asserts that Janie "repudiates the values of her surrogate parents in her conscious quest for selfhood" (p.501).

Read Full Term Paper
Copyright 2016 . All Rights Reserved