Friedrich Ludwig Gottlob Frege, a German philosopher, was one of the founder fathers of establishing a systematic and analytical approach to the philosophy of language. He instituted the idea of logically proving the quantified statements. In Frege's philosophy of language he found two puzzles, of which one related to the identity of statements. Frege says
Now if we were to regard equality as a relation between that which the names 'a' and 'b' designate, it would seem that a = b could not differ from a = a (i.e. provided a = b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing (Bencivenga E, 1993).
Here, he observed that mere representation of names and descriptions does not convey the information content of a statement or a sentence in terms of logic and meaning. He further probed and found that a minimum of two relations are required for significant understanding of the language. In the subsequent paragraphs we will discuss the Frege's Puzzle of identity statements in detail and reasonably justify the solution of the puzzle as suggested by Frege himself.
Identity statements are the expressions that equate the objects on both sides of the identity sign (Geach, O. and Black, Max, 1960). For example, "(2+3) = 5", "Clint is Eastwood" and "John is Peter's father". All these statements essentially belong to the same clan of kind " a= b". The statement "a = b" can only hold true when "a" and "b" both represent the same object or an individual. Now, consider a statement of kind "a = a". This statement also requires the same truth condition as required for the statement of kind "a = b". For both the cases, object or the individual is same and also, the denotations represent the same individual or the object. However, the meaning conveyed in the two cases is different. This appears to be a paradoxical situation as the representations of a unique object or an individual have a difference while being true at the same time. The Frege's puzzle states that when the difference in the representations, that is, "a" or "b" is not established by the two cases under consideration, then how we can find the difference in meaning or cognitive significance between the two true identity statements (Fiengo, Robert and May, Robert, 2006).
Cognitive Significance of the Difference of Identity Statements
To resolve the issue of difference, we first understand cognitive significance of a name or a statement. Cognitive significance of a statement, as brought out by Frege, can only be described by two important aspects of the statement, namely, 'sense' and 'reference' (Zalta, Edward N, 2005). Here, the 'sense' of the statement conveys more information then its interpretation by mere visual inspection (Schirn, M, 1976). Moreover, 'sense' is the integral part of the name and different names are associated with different 'sense' (Zalta, Edward N, 2005). A group of two or more statements may indicate or refer to a singular object but each statement has a unique sense of its own.
Next, we obtain the distinction between the