El papel de las variables

Por • 29 abr, 2022 • Sección: Educacion

Kit Fine

It is generally supposed – by logicians and philosophers alike – that we now possess a perfectly good understanding of how variables work in the symbolism of logic and mathematics. Once Frege had provided a clear syntactic account of variables and once Tarski had supplemented this with a rigorous semantic account, it would appear that there was nothing more of significance to be said. It seems to me, however, that this common view is mistaken. There are deep problems concerning the role of variables that have never been properly recognized, let alone solved, and once we attempt to solve them we see that they have profound implications not only for our understanding of variables but also for our understanding of other forms of expression and for the general nature of semantics.

It is my aim in the present lecture to explain what these problems are and how they are to be solved. I begin with an antimony concerning the role of variables which I believe any satisfactory account of our understanding of them should solve (§1). I then argue that the three main semantical schemes currently on the market – the Tarskian, the instantial and the algebraic – are unsuccessful in solving the puzzle (§2-3) or in providing a satisfactory semantics for first order logic (§4-5). Finally, I offer an alternative scheme that it is capable of solving the antimony (§6) and of providing a more satisfactory semantics for first-order logic (§7). It is based upon a new approach to representational semantics, which I call semantic relationism; and in the remaining three lectures, I will discuss the implications of this approach for the semantics of names and belief-reports.

“The Role of Variables, (PDF)” Journal of Philosophy, vol. 50, no. 12, 605–631, 2003, reprinted in the Philosophers’ Annual (2003).

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