Recursive rules are rules that can beĪpplied repeatedly. On this view, language is a formal object that consists of a finite interpreted lexicon and a finite set of recursive rules for combining lexical items. Syntax concerns the rules for combining expressions into well-formed sentences within the language while semantics gives us a theory of the meanings of words and sentences. The new logic, thus, distinguishes the formal features of language from meaning, laying the groundwork for the tripartite distinction between syntax, semantics, and pragmatics. "Horses are mammals" can be written in a special concept-script ( Begriffsschrift ) that displays the different roles that the constituent words play in the sentence, "(x)(Hx → Mx)." This is done in a way that abstracts from the meaning of any particular sentence. Just as "x y z" expresses the form of all instances of addition through the use of variables (x, y, z) and a special sign for the addition function (), so language can be modeled. Frege's key insight was to see that formal arithmetic modeling can be used to display the structure of language. Gottlob Frege (1848 –1925) revolutionized our conception of logic and its relation to thought and language. Logic was seen as the study of thought itself. Well into the nineteenth century, Aristotelian logic dominated. This great shift began with Gottlob Frege's foundational work in mathematical logic. In the twentieth century, Anglo-American philosophy took "the linguistic turn." Instead of seeking solutions to problems of knowledge and thought in an examination of the nature of our ideas, philosophers looked to the nature of language. Founders of the Twentieth-Century " Linguistic Turn" The solution to the problem of general words would follow from this. The important problem concerned the nature of abstract ideas. Three major positions emerged: (1) realism or Platonism, the view that general terms name real abstract objects (horsiness) (2) conceptualism, the view that terms stand for abstract ideas or concepts (the concept of horsiness) and (3) nominalism, the view that a term is general if it denotes more than one particular object. There was great controversy over what general terms, like "horse," denote. Proper names, like "Silver," denote particular objects. The meanings of words are their denotations, the objects that the words stand for or denote, or the ideas of particular objects. A simple denotational theory of meaning predominated. Language was seen as the public conventional medium for communicating private thought. To solve this problem of knowledge, philosophers had to account for how we grasp generalities (and not just particulars) and how we determine which of our ideas represent the world truly. How is it possible for human beings to have knowledge of the world? The solution for both rationalists and empiricists was to be found in the nature of mind since, as was universally held, all we can know directly are the ideas of our own minds. The fundamental concern was the problem of knowledge. Although discussions of language in seventeenth-and eighteenth-century philosophy foreshadowed many issues that came to full bloom in the twentieth century, before the twentieth century language was thought to have a secondary role in understanding the special place human beings have in the world.
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