THE RAVEN PARADOX 

In a 1965 work, “Studies in the Logic of Confirmation,” German Philosopher Carl G. Hempel revealed a key paradox in the scientific method as it is generally accepted. He demonstrated the inadequacies in these time-honoured procedures in a stunning and eloquent dissertation. His Raven Paradox challenged the accepted methods of generalisation, falsifiability, and inductive reasoning.

Introduction

Take into account the following to demonstrate what the Paradox of the Ravens is:

(H1) All ravens are black

(H2) All non-black things are not ravens

H2 is the logically equivalent hypothesis to H1, which holds that all non-black items are not ravens. H1 is the claim that all ravens are black. According to conventional first-predicate logic, this is represented as follows:

Since  (1) and (2) are logically similar, any observation or piece of data that supports either hypothesis must also (equally) support the other. But while it does seem reasonable that observing black ravens should confirm H1, observing a white ball, a red sofa, a yellow shirt, or any non-black non-raven, all of which do confirm H2, also confirm the logically equivalent hypothesis H1 (that “all ravens are black”), which does not seem reasonable.

Two intuitive inductive reasoning principles cause the paradox:

 (i) Logically identical assertions can be used interchangeably, and 

(ii) Specific examples support the corresponding universal generalisation.

The Origin of the Paradox

Even though the two types of conceptions are very different ontologically, the so-called Paradox of the Ravens results from the erroneous representation of both ontological and logical notions by predicates in conventional first-order predicate logic (FOPL).

A logical representation that treated logical and ontological notions equally, i.e., by considering them as predicates in first-order logic, was the sole cause of the seeming paradox in the so-called Paradox of the Ravens.