Freges Puzzle of Identity Statements - Essay Example

Running head: FREGE'S PUZZLE OF IDENTITY MENTS Frege's Puzzle of Identity ments Namita Sharma This paper will critically examine the Frege's puzzle of identity statements and provide a solution based on the works of G. Frege. The emphasis will be on resolution of the cognitive significance of difference between the identity statements based on the famous work of philosophy - "On sense and reference" by G. Frege. Major issues like defining the puzzle, significance of sense and reference in identities and establishing distinction between sense and reference will be covered in detail. The paper will also discuss Metalinguistic solution to the puzzle and attempt to highlight its shortcomings, thereby establishing the superiority of 'sense and reference' approach. Frege's Puzzle of Identity Statements Introduction 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. Defining Frege's Puzzle of Identity Statements 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 two aspects of 'sense' and 'reference' of a statement. The statement or the name refers to an object. The object stimulates the mind which gives rise to an idea about the object. Thus, the stimulation provided by the object resulting in origin of an idea which is subjective and will vary for the same statement, depending on the personal experience and knowledge (Geach, O. and Black, Max, 1960). Therefore, such ideas should not be mistaken for 'sense' of the statement. 'Sense' is the common thought conveyed by a statement and is unique for a statement. For example, the statement "The Morning Star" conveys the 'sense' of 'star seen in the morning'. The responsive idea may be of the colour and shade of the star or its beauty. Thus, 'sense' lies in between the 'reference' and the idea, assuming that the statement has a definite 'reference'. There are instances, where the statements do not have any 'reference' but possess a unique 'sense'. For example, the statement "The Largest Integer" does not have any 'reference' as the largest integer runs into an infinite value integer which can not be determined. For such statements, the 'sense' is enough. If that be the case, then how do we justify our quest for 'reference' of the statement 'Reference' is queried, if and only if, the truthfulness of the statement is to be established. Therefore, 'reference' is indicative of the truth value of the statement (Geach, O. and Black, Max, 1960). Let's illustrate the distinction of 'sense' and 'reference' with the help of an example. Consider the following statements:- "The Morning Star" (1) "The Evening Star" (2) It is a well known fact that the star seen during sunrise and sunset is the planet Venus, as has been proved in astronomical studies. Both the statements above are referring to the same object, that is, planet Venus. Therefore, 'reference' aspect of both the statements is same. However, the 'sense' conveyed by the statements differs. "The Morning Star" conveys the 'sense' of the star during morning and "The Evening Star" conveys the 'sense' of the star during evening, morning and evening being entirely different times of the day. Therefore, we conclude that statements with same 'reference' do not convey the same 'sense' or information. Having established the distinction between 'sense' and 'reference', we revert back to the basic Frege's puzzle. Assuming "a" represents statement (1) and "b" represents statement (2) as given above, we can rewrite the two identity statements of Frege's puzzle as "a = a" and "a = b", both the statements being true. The statements "a = a" and "a = b" are the compound statements, composed by constituent statements (1) and (2) with identity relation. By the principle of compositionality, if the 'sense' of constituent statements differs, the resulting 'sense' of the compound statements will also differ (Zalta, Edward N, 2005). To ascertain the cognitive significance of the difference between the two compound statements, we examine the sense conveyed by them. The statement "a = a" is less informative as the 'reference' and 'sense' conveyed by the flanking constituent statements of the identity are the same. However, the statements "a = b" is more informative wherein the 'reference' of the flanking constituent statements of the identity is the same while the 'sense' conveyed by them is not. Thus the cognitive significance of the difference between the two compound statements can be arrived at on account of difference 'sense' conveyed by "a = a" and "a = b". Metalinguistic Solution to Identity Statements As per Metalinguistic Solution, there cannot be any restriction on usage of sign for representing any object or event, that is, two statements referring to the same object or different objects can be arbitrarily selected (Ramachandran, M, 1994). The identity statement 'a = b' stands for two arbitrary linguistic entities conveying only the mode of denoting or representing an object without any knowledge of the object. Apparently, it may convey to resolve the information content lent actually, if fails to do so. The identity statement 'a = a' stands for a single linguistic entity. The constituent statements only co-refer to the object without revealing anything about it. Let us consider the following identity statement to illustrate:- "Venus is the morning star". This statement means that 'Venus' and 'the morning star' co-refer. implies that, 'Venus' refers to the same object as 'the morning star'. that is, The Referent of the 'Venus' is the Referent of 'the morning star'. which conveys that "The Referent of 'Venus'" and "The Referent of 'the morning star'" co - refer. This results in infinite regression, losing information content in the process. Conclusion The Frege's puzzle for identity statements can be explained on the basis of two aspects of 'sense' and 'reference' which account for information content and truth value of the statements, respectively. The cognitive significance of the difference of identity statements can be attributed to the different 'sense' conveyed by them. Earlier solutions, involving Metalinguistic approach are not recommended as these are only apparent solutions to the Frege's puzzle and suffer from the disadvantage of infinite regression. References Bencivenga, E. (1993). A Specious Puzzle. Erkenntnis, 38, 131-133. Fiengo, Robert and May, Robert. (2006, October). De Lingua Belief. Cambridge: Bradford Books. Geach, O. and Black, Max. (1960). Translations from Philosophical Writings of G. Frege, Oxford: Basil Blackwell. Ramachandran, M. (1994). Frege's Objection to the Metalinguistic View. Retrieved February 9, 2007 from the World Wide Web: http://www.sussex.ac.uk/Users/muralir/pubs/fregmeta.htm Schirn, M. (1976). Study on Frege: Logic and Philosophy of Language, Stuttgart: Bad Cannstat. Zalta, Edward N. (2005, 25 May). Gottlob Frege. Retrieved February 9, 2007 from the World Wide Web: http://plato.stanford.edu/entries/frege.htm Read More