Philosophy of Language Senior Course Paper Essay

Philosophy of Language Senior Course Paper - Essay Example When a mathematician is presented with the equation, 38 + 16, instinctively, the mathematician would respond by adding the two terms while computing for its sum. Thus, the mathematician would reply, claiming that the sum of 38 and 16 is equal to 54. Given this example, what does ‘+’ mean? Does the mathematician really know what was meant by ‘+’ in the equation? Does it pertain to the computational procedure for adding two values, or does it pertain to something else? How can one tell what the mathematician meant? This paper will attempt to formulate a sufficient theory of meaning with regards to the use of ‘+.’ In doing so, I will argue that an intensional framework must be taken into account as opposed to a purely extensional framework. From a general perspective, the issue revolves around the relation between two fundamental concepts, truth and meaning. Truth, from a logical point of view, has traditionally been thought of as extensional. So t he truth of a given expression is associated with it’s meaning in terms of logical structure, reference, and truth-value. This move of neglecting meaning in relation to that of the sense of a given expression is what this paper shall argue against by using ‘+’ as its test case throughout the paper. For herein, to say that 36 + 16 = 54 could mean two things: ‘36 plus 16,’ and ‘36 quus 16,’ with both referring to 54. It is in this regard that a theory of intensions must be taken into account. For, if a person is presented with an equation involving ‘+’, how can one know as to whether that person meant ‘+’ as plus or ‘+’ as quus? What makes the interlocutor assume what is being referred to by the use of ‘+’? Herein is where the problem of rule following comes into light, for if what we are after is semantics, then it seems paradoxical that we refer to general rules from which a class parti cipates in. Rule following applies in the level of syntax, for verifying what the individual knows privately is not required in such cases. Indeed, the problem with ‘+’, as explicated by Kripke is that ‘+’ is understood to represent a semantic rule rather than a syntactical rule, and a semantic rule following leads to several problems with regards to the meaning and truth of ‘+’ statements. Thus, Kripke argues that â€Å"it is possible to construct an unlimited range of related but non-equivalent semantic rules, incorporating the potential truth conditions C1, C2, †¦ Cn respectively, such that there are simply no facts at all about the speaker’s use of ‘+’ that determines which, if any, of these possible rules the speaker has actually adopted† (Wilson, 2006, p.155). Therefore, this points towards the problem of indeterminacy, since according to Kripke, discovering the truth conditions of the speaker’s use of + is not possible, since there is no specific semantic rule that underlies one’s use of ‘+’, regardless of its truth function. However, this creates a problem with regards to the use of ‘+’ in language, for if ‘+’ could mean several things at the same time and in the same respect, then that would lead to the ambiguity of ‘+’ which cannot be, for it is used in disciplines such as mathematics and logic. It is a common thing