What does the Slingshot need to shoot?
An investigation of term forming operators as a essential feature of Slingshots Arguments
Slingshot arguments; Term forming operators; Plural Logic
The family of arguments called "Slingshot Arguments" receives this name in the work by Jon Barwise and John Perry (see Barwise & Perry, 1981 "Semantic innocense and uncompromising situations") due to the minimal machinery used to prove its cogent consequence. Usually seen as a kind of collapsing argument, the slingshot consists in proving that, once you suppose that there are some items that are references of sentences (as facts or situations, for example), these items collapse into just two items: The True and The False. In "The impossibility of certain Higher-order Non-classical Logics with Extensionality" (J. Michael Dunn, 1989) Dunn argued that the argument makes use of three devices: (i) Indiscernibility of identicals, (ii) a certain notion of Replacement and (iii) a term forming operator. In this dissertation we're going to focus in one specific machinery, i.e, we're going to analyze the notion of term forming operator as a essential ingredient for the slingshot to prove its conclusion. Further, considering the new developments on the field of Plural Logics in the book "Plural Logic" (Oliver & Smiley, 2013) we shall investigate two possible critics to Oliver and Smiley work. One, if the Slingshot argument can also be recovered in a context of plural logic when we change the concept of terms to plural terms. This would be undesirable to Oliver and Smiley since, although they accept singular terms as proper names as Frege does, they do not agree in considering sentences as proper names as well. In this case a Slingshot would appear as an argument to force them to put sentences "under the same umbrella" of proper names. Two, since Oliver and Smiley's book starts by defending that there is such a thing as a 'Plural Phenomena' in the language, we shall contrast this view with Ben-Yami's "Plural Quantification Logic: A critical Appraisal" (Ben-Yami, 2009), where Ben-Yami argues that there is no clear distinction between singular and plural quantification in Natural Language that justifies the need to creat a Plural Logic.