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Gottlob Frege’s Puzzle of Identity Essay

There has been much philosophical debate over a solution to this complex language we use everyday. Gottlob Frege, a German mathematician, logician and philosopher, developed a puzzle about identity and a Descriptive Theory of Reference to address these issues. With the consideration of meaning, cognitive value, sense and reference, Frege attempts to organize a solution to these statements, but due to several problems regarding his theories, I oppose his solution. Consider this example:

1) a=a; ‘morning star=morning star’ 2) a=b; ‘morning star=evening star’ 3) b=a; ‘evening star=morning star’

Frege’s puzzle of identity concerns the identity and semantics of proper names and objects. In 1892 Frege noticed the equation a=a had the same meaning while a=b had the same cognitive value. He believed that, with logic, it is clear that a=a, and with careful examination and calculation that a=b. ‘Morning star=morning star’ is an obvious statement that everyone knows, but no one can know ‘morning star=evening star’ without astronomical investigation. Frege believed that a and b had to be completely identical in order for the statement a=b to be valid. He claims that statements 1 and 2 are “analytic” and “priori” meaning they are guaranteed valid through logic. In statement 2, ‘morning star=evening star’ is true because both names are referring to the same planet, Venus. It’s the same as stating ‘morning star’=’morning star’.

However, according to Frege, if the statement were to switch around to create statement 3, ‘evening star=morning star’, it would be unequal to statement 2. Although a=a is like a=b; a=b does not have the same cognitive value to b=a. According to Frege, there are several reasons why statements 2 and 3 are unequal. Statement 2 is informative and an astronomical discovery to us. Statement 3 is a trivial fact and can be known without work. Frege’s statements are special because while a=a is referring to one thing, a=b is referring to two things. In the same sense, however, they are both referring to the same thing. As confusing as that seems, with these arguments Frege is able to conclude that each singular term has different meanings above their reference.

In Frege’s solution, Descriptive Theory of Reference, he attempts to divide each singular term by two distinct semantic aspects: sense and reference. According to Frege, sense is linguistic meaning that presents representation for an object through a singular term. Reference is the object that is represented by that singular term. For example, ‘morning star’ and ‘evening star’ are different senses for the same reference, Venus. Since the two expressions have the same sense, they also have the same referent.

His two aspects explain why the statements ‘morning star=morning star’ and ‘morning star=evening star’ differ in cognitive value. Statement 1 designates the same object through the same mode of presentation while statement 2 designates the same object through different modes of presentation. Frege’s solution proves that the true meaning of an object lies within its reference and not it’s sense. ‘Morning star’ may not equal ‘evening star’, but ‘Venus’ will always equal ‘Venus’. However, with these two semantic aspects Frege, unsuccessfully addresses the complex language.

Although I agree to some of his claims, I oppose to Frege’s solution because I believe there are many problems facing it. Firstly, when referring to a proper name, there can be false references. For example, a possible sense for referring to Nina can be ‘Michael’s daughter and Mimi’s older sister’. If Nina is not Michael’s daughter and Mimi’s older sister, and instead Lina (Nina’s older sister) is Michael’s daughter and Mimi’s older sister then, according to Frege, Lina is therefore Nina. Whether or not she is Michael’s daughter and Mimi’s older sister or not, Nina is still Nina and Lina cannot replace her. This proves that objects with a similar sense can obtain the same reference as another object. Another example can be mistaking identity with different senses provided. For example, if Vivian is talking about Alex and describes him as ‘a soccer player with nice hair’ while another friend describes him as ‘a rude boy in my Philosophy class’, the listener would be confused on whom the speakers are referring to. To some people Alex is just ‘a soccer player with nice hair’ and to others he is ‘a rude boy in my Philosophy class’. In this case Alex’s senses are not the same, in fact they hold no similarities.

Thus, sense is not an accurate representation in differing objects and their cognitive value. As previously stated, Frege believes that statements 1 and 2 are known through logic and do not require examination to be learned. Since statement 2 is informative (‘morning star=evening star’), then it does not make sense to know this information by logic alone. You cannot simply know that ‘morning star’ and ‘evening star’ is the same planet without astronomical examination. Here, Frege is false in stating that they are “analytic” and “a priori”, as previously mentioned. This is also seen in many mathematic statements.

In the equation 1+2=3 we know this statement is informing us, but aside from knowing by logic alone, it can also be evaluated through mathematics as well. Not everything is known through logic. Sometimes it is explained my science or history. Also some may believe that Frege’s theories prove correct in simpler terms, in more complex scenarios they are unsound. With these flaws it is safe to conclude that Frege’s theories and assumptions are invalid. When put in simpler terms his statements may be true, but once replaced with real life scenarios his solution doesn’t make sense. Instead of viewing language in simpler terms, Frege should have considered the more complex scenarios. While considering meaning, cognitive value, sense and reference, Frege did create a well-structured solution, but he should have expanded his theory so that it would apply to flexible situations.


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