Issue Two

Quoc Thai
 University of Houston

Discourse on the Raven paradox

Since Carl Hempel proposed Raven paradox in his “Studies in the Logic of Confirmation” in 1945, the “infamous” raven paradox is a recurring problem in philosophy of science. The paradox raised the inconsistency between our intuition and the logical system, especially the law of logical equivalent and the principal of confirmation.  The paradox contains two questions, an easy one and a harder one. In this paper, I will try to answer both questions: the advance question and the basic question of the Raven paradox.

Before we raise questions, we need to look at the paradox first, the Raven paradox contain an inconsistency between the system of logic and our intuition, and from that further questionable aspect arise. The quote below from Jerrold L. Aronson’s “the Bayesians and the Raven Paradox” explains in a nutshell the raven paradox.

We are all familiar with the traditional genesis of the raven paradox. The law that all ravens are black is logically equivalent to all non-black things are non-ravens. By Nicod’s criterion, where (Fa & Ga )is a positive instance of (x) (FxD Gx)), a white shoe ends up serving as evidence for ‘All ravens are black. (Aronson 221)

But for this paper, further analysis and explanation are necessary. I will take the liberty of explaining the paradox in my own words, not quoting Carl Hempel. The classic example situation for Raven paradox is the situation where we raise the following question: Is a non-black, non-raven thing such as a white dove qualifies as evidence to confirm the general statement “All ravens are black”. We have two particular statements that we should assume to be true for the sake of this paper: Poe is a black raven and John is a white dove. We also have two universal statements: “All ravens are black” and “Everything that is not black is not a raven”. The problem appears when we ask the question “is white dove an evidence that confirms the universal statement ‘All ravens are black’ or not?” While it nearly seems to us that John, the white dove, is evidence for “Everything that is not black is not a raven” but John seems not to be evidence for “All ravens are black”. However, apply logical rule, the result should be different, in which a white dove is a confirmation evidence of “All ravens are black”.

The law of logical equivalent stated that if two statements are logical equivalents, no matter if the two statements are identical or not, then any statement that is evidence for one must be evidence for the other. “All ravens are black” and “Everything that is not black is not a raven” is logically equivalent. For two statements to be logically equivalent, a statement cannot be true when the other is false. The requirement of logically equivalent leaves only statements that express the same thing in reality logically equivalent with each other. While their “aboutness” is differences, they both express the same meaning in reality. If “All ravens are black” it true, then there will be no non-black raven. No non-black raven results in “All non-black is non-raven”. The two general claims are no doubt logically equivalent with each other and if there is any fact supporting one statement, then that fact must also support the other as well.

There is a rule in logic called the “principle of confirmation”. In inductive logic, if any instance of a general statement is true then it must be an evidence for that general statement. For example, a four legged dog is an instance of “All dogs are four legged”, and if we saw a four-legged dog anywhere, we can take that fact as evidence to confirm the general statement “All dogs are four-legged”. Apply the same basic structure of reasoning into the Raven case, if Poe is black and it is true that Poe is a raven, and then Poe is an instance of “All ravens are black”, thus Poe is evidence for the general statement “All ravens are black”. John is a white dove is a confirmation evidence for the statement “Everything that is not black is not a raven”, for John is an instance of both non-black and non-raven.

At this point, everything went without any problem and it does not clash with intuition at any place. Intuition is the ability to understand something immediately, without the need for conscious reasoning. In other words, intuition is when one knows or considers likely from instinctive feeling rather than conscious reasoning. I have an intuition that “All ravens are black” and the same with “All non-black is non-raven”. I have an intuition that Poe, a black raven, is evidence for me to believe that all ravens are black. But if we apply the law of logically equivalent, then if Poe is a confirmation of “All ravens are black” then he must also be evidence for “Everything that is not black is not a raven”. At this point, the problem has appeared when my intuition for Poe is evidence for “Everything that is not black is not a raven” is weaker than before with the case of “All ravens are black”. Any philosopher who defends intuition will point out that there is no problem since black and non-black in Poe and “Everything that is not black is not a raven” are related by the sense of positive and negative concept. One can say non-black and black gives us a little sense of relevant, and a little sense of aboutness. But if we apply that same step to John, the white dove, we cannot apply the above argument about relevant and aboutness anymore. John is an instance of “Everything that is not black is not a raven” for a dove is not a raven and white is a non-black color. If John is evidence for “Everything that is not black is not a raven” then it must be evidence for “All ravens are black” according to the law of logically equivalent. Now I do not have an intuition of a white Dove that confirms that all ravens are black. We stepped into the paradoxical conclusion.

The basic question require us to point out which parts out of the three (law of logical equivalent, principle of confirmation, and intuition), which is incorrect. The reason why we need to answer the basic question is because clearly, the three cannot be true at the same time. There is an inconsistency of at least two sides, especially the laws of logic and intuition. The paradox is a tricky question because no matter which angle you try to answer the basic question; there will not be an easy and non-controversial follow up answer for the advance question. Simply deny one claim out of those three (the principle of confirmation, the logical equivalent rule, intuition) will answer the basic question but the real problem is with the advance questions. I wrote questions because there is not one but at least two advance questions, depend on which side we denied in the basic question. If you denied the logical system, you need to come up with the alternative logical system and make sure that system will not make the same mistake the first system did (whatever mistake you pointed out to deny the logical system in the first place). If you deny the intuition, that means you agreed that non-black, non-raven thing did confirm “All ravens are black”. If you agreed on that claim, you need to explain why we do not think it a good scientific method to actively looking for any non-black, non-raven to be evidence for “All ravens are black”. A solution for this paradox need to be deeply analyze in the advance question.

One solution to the paradox, which is popular among Popperian is the argument of the impossible of induction (confirmation). Though a series of proofs and examples, Karl Popper and David Miller argue that induction is impossible (Popper, and Miller 687). But it is next to impossible to completely deny the logical system without sounding like a skeptic. I cannot give any alternative system of logic that guarantee we will not run into the raven paradox again. Even if the new logical system guarantee that we will not to run into the raven paradox again, it still no guarantee that any other paradox out there will be solve using the new logical system. Even if we able to find a system of logic that fit to solve all the paradox that exist, we still cannot guarantee that no new paradox will be raise base on the new logical system. We do not want the advance question any harder than we can handle. For that reason, even though deny the system of logic might be a possible method; it is not practical in this paradox and in any other paradox.

Without denying the system of logic, we can only deny our intuition. Just like what I said above, denying our intuition will lead to the problem of why we do not think it a good method to actively looking for any non-black, non-raven to be evidence for “All ravens are black” when we agreed that non-black, non-raven thing did confirm “All ravens are black”. To be able to solve the raven paradox once and for all, I need to support the following claim: even though non-black, non-raven is evidence to support “All ravens are black”, it is impractical for us to actively looking for any non-black, non-raven thing to be evidence for “All ravens are black.”

I do not have an intuition that a non-black, non-raven thing is not an evidence to confirm the statement “All ravens are black”. At this point, after working with the paradox for a certain period of time, I even have an intuition that any non-black, non-raven thing is evidence to confirm “All ravens are black”. But many other will have a complete opposite intuition, I do respect that intuition and I do not think that there is anything wrong with intuition that different than mine. The majority of people intuition will have intuition that non-black, non-raven things are not evidence for “All ravens are black”, while I am one of the few who think different. The reason that I have a different intuition than the rest of people will be talk later on in this paper. First, we need to go through intuition of the majority first.

When I look at Poe, a black raven, I picked up an immediate awareness that Poe is an instance of “All ravens are black” since Poe has both feature of blackness and ravenness. When I look at John, a white dove, normally I will immediately aware that John is an instance of “All doves are white”, since John has both feature of whiteness and doveness. Without someone bringing the concept of non-blackness, non-ravenness into the conversation, I cannot see a white dove as non-black, non-raven thing. It will not only me who have that kind of intuition, ask normal people who heard nothing about our discussion on the raven paradox, who recently have no-exposed to the concept of non-black, non-raven, they will normally say the same: the John is a white dove. It is rare to have any person who have the intuition John is a non-black, non-raven.

Because non-blackness and non-ravenness is not picking up by our intuition, we cannot agree that looking any non-black, non-raven things to be evidence for “All ravens are black” is a scientific method. To be able to understand the relationship between non-black, non-raven things and the statement “All ravens are black”, we need conscious reasoning, which consume more time than just immediate identification. While we may come up with evidence for “All ravens are black” when we look at a white dove, it is much more effective and easier to look in to a black raven and try to find evidence.

“Any non-black is non-raven” is a combination of a lot of sentences with a similar structure but about many things that included in the categories non-black and non-raven. While black and raven are natural properties. Non-black means blue, red, yellow, etc.; non-raven means table, pencil, cup, etc. Non-black and non-raven is not a natural property, or more accuracy, a bundle of natural properties. Property is a predicable logical variable. Property is single attribute that we can replace any predicate in symbolic logic such as Poe is a black raven can be express by (Bp & Rp) in which (B)lack and (R)aven is property of Poe. John is a non-black, non-raven can be express by (~Bj & ~ Rj). Negative concept is not natural property, it is a denial of a property, leaving the object with potentially any other property other than the negated property in their area (color, shape, solidity, etc.). Just expressing potential properties and not real property of an object mean that the negative property do not express reality, thus it do not exist in nature. So we simply cannot look for a non-black or non-raven property in things. When we try to find non-black, our mind will set it to find any color other than black. Our mind will simple process within the conscious reasoning and confirm which object is non-black. For example, when we see John, a white dove, it is natural that we perceive John as a white object; we do not perceive John as a non-black object. Through a process of conscious reasoning, we translate white into non-black. While I find it is not possible for my intuition to pick up immediately the relation between white and non-black in normal condition, in this case, because we talking about this relations, my intuition seem to temporary pick up the relation and aware of that relation for the short period of time so we can process information more quickly.

For the above claim to work, we need to be clear about natural property and its concept. So what is this natural property? Natural property is an attribute inside an object that can be found in nature and not subject to and effect by any other object. According to Chris Swoyer and Francesco Orilia, property are “those entities that can be predicated of things or, in other words, attributed to them. For example, if we say that that thing over there is an apple and is red, we are presumably attributing the properties red and apple to it. Thus, properties can be characterized as predicables.” (Swoyer, and Orilia 1). For example, a raven has natural properties of blackness and ravenness. While blackness describe the color of the object raven, ravenness is the sum of many properties that have biological characteristic that distinguishes raven from other living being and scientist used those characteristic to identify raven. Ravenness and blackness can be understood by itself and need not to have any other property support for it to be understood. So what make a creature a raven? All the properties of a raven make it a raven (raven in general, not biological subspecies). Blackness is an observed property of raven; in fact, all property must be perceptible and tied to object by the mean of perception. Property that can be perceived in nature by the mean of intuition (immediate identification) is natural property, in contrast with unnatural property, which cannot be observed in nature by the mean of intuition. Unnatural property must be outside of an object, which means it exists independently from an object. Because natural property can be observe and independent property (unnatural properties) exists outside of an object, it must come from other object regard to the original object not by the mean of observation. The unnatural property must acquire by the mean of reasoning.

Looking at the red apple, we can say that the one of the property of that apple is redness. The unnatural property of the same apple in color should be non-greenness, which express the potential of the apple is everything other than green, not express the reality of an apple, which is red. We are intuitively aware or immediately identify the natural property of the apple as soon as we saw the apple, we are not intuitively aware that the apple is non-red. One potential argument against my explanation is if there is a possible world, where every fruit divided in green and non-green for green is safe to eat and non-green is non-safe to eat. People in that world were trained to quickly aware that the red apple is non-green rather than quickly aware them as non-green. If that is the case, is non-green is a natural property in that possible world?

While that is a valid concern, I do not think in that case, non-green is a natural property nor natural property is depending on the observation. We can say that the perceptions that we have on natural property are process to our mind by intuition. We can immediately aware that the apple bear redness as its property, we do not immediately aware the apple bear non-greenness as its property. If by some reason, we do immediately aware non-greenness in a red apple, it is not because non-greenness is natural property but rather we had trained ourselves to put the relation between redness and non-greenness into our intuition range. The process of training to aware the non-greenness immediately is because of the important of identification of non-green in nature. In the possible world counter example, people trained to aware the non-greenness immediately because they are unable to eat anything non-green. The non-greenness property of the apple can be acquired by perceived the redness inside the apple, then translate into non-greenness by some process in our mind. So when someone look into any object and their intuition tell them that object property is negative property, it is because their brain had trained to translate the relation between positive property and negative property so fast that they have that kind of intuition, not because the negative property is natural intuition.

John, the white dove, has unnatural properties: non-blackness and non-ravenness. Because that reason, it is not reasonable to look for non-black, non-raven object to find evidence for “All ravens are black”. Here is my standing on what is natural property and what is not: In Universal as Attributes, D, M. Armstrong denied the existence of unnatural property such as disjunctive universal and negative universal property (non-blackness, non-ravenness). He thinks that for any object to share any universal property, that property must bring a similarity into two objects. Any object that share the universal property redness must have something in common and that common must be related to redness.

The whole point of a universal, however, is that it should be identical in its different instances. (Armstrong 201)

Armstrong does not think that disjunctive and negative properties bring any similarity in instances. “C or M” is a disjunctive universal, one object, in which, C is present but not M and one other object, in which it carried M but not C supposed to be identical if the disjunctive universal exist. But if M brings mass to object and C brings charge in object, one object in which has mass but no charge and another object in which have charge but have no mass cannot be identical. For the similar reason, negative universal do not exist because it do not brings any similarity into instances, to quote Armstrong on the matter:

Is there really something in common, something identical, in everything that lacks charge C? Of course, there might be some universal property that just happened to be co-existensive with lacking C. But the lack itself does not seem to be a factor found in each thing that lack charge C (Armstrong 201)

W. V. Quine in his natural kind also has a similar idea with Armstrong. He thinks that universal property can only found in objects that have the same natural kinds. Natural kind is an assemble of things that are similar to each other more than other object outside of the kinds.

Similarity is immediately definable in terms of a kind; for, things are similar when they are two of a kind. The very words for “kind” and “similar” tend to run in etymologically cognate pairs. Cognate with “kind” we have “akin” and “kindred.”… Suggesting a gathering into kinds (Quine 234)

According to Armstrong and Quine, non-blackness is not natural property since it does not express the similarities among the non-black set of kind. Blackness is natural properties since a kind black thing have a similarity among themselves, which is blackness. Similar reason can be said about ravenness and non-ravenness, and why ravenness is natural property and non-ravenness is unnatural property. With the concept of natural kind and unnatural property, we can say that there are no set of non-black thing, at least naturally speaking. While whiteness and redness are both non-blackness, the lack of similarity between whiteness and redness prevent it to be a kind, in which it will represent non-blackness. Blackness in any two objects can be a kind since it is similar to each other.

With that reason, It is not effective for us to looking for evidence for “All ravens are black” by actively look into non-black, non-raven thing. The paradox now had been solved completely, both easy and advance questions. We now know that while non-black, non-raven thing does confirmed “All ravens are black”, it is not practical and efficiency to take them as effective evidence for scientific use.

Work Cited

Aronson, Jerrold. “The Bayesians and the Raven Paradox.” Noûs. 23.2 (1989): 221-240. Print.

Armstrong, David. “Universals as Attributes.” Edited by. Kim Jaegwon and Earnest Sosa.

Metaphysics: An Anthology. Malden, MA: Blackwell Publishing, 1999. 198-208. Print.

Hempel, Carl. “Studies in the Logic of Confirmation.” Mind, New Series, Vol. 54, No. 213.

(Jan., 1945), pp. 1-26. Print.

Popper, Karl, and David Miller. “A Proof of the Impossibility of Inductive Probability.” Letters

to Nature. 302.21 (1983): 687-688. Print.

Quine, William. “Natural Kinds.” Edited by. Kim Jaegwon and Earnest Sosa. Metaphysics: An

Anthology. Malden, MA: Blackwell Publishing, 1999. 233-242. Print.

Swoyer, Chris and Orilia, Francesco, “Properties”, The Stanford Encyclopedia of

Philosophy (Winter 2011 Edition), Edward N. Zalta (ed.), URL <;.



~ by texasphilosophical on May 31, 2012.

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