Logical form, conditionals, pseudo-conditionals (Q6559164)

This article deals with the issue of finding the correct formalisation of certain kinds of natural-language sentences which superficially resemble genuine conditionals, yet exhibit distinctive logical features. In particular, the author focuses on three cases, respectively dubbed ``whether-or-not'' sentences, ``biscuit conditionals'', and ``concessive conditionals''.\N\NSection 2 is devoted to the analysis of ``whether-or-not sentences'', which are exemplified by the sentence ``Whether or not you like it, my plan is to go out tonight''. It is suggested that such sentences should be better formalised as \((\alpha > \beta) \And (\neg\alpha > \beta)\), where \(>\) is assumed to adequately formalise standard conditionals and \(\alpha\) and \(\beta\) represent the whether-or-not clause (``Whether or not you like it'', in the example) and the main clause (``my plan is to go out tonight''), respectively.\N\N``Biscuit conditionals'' owe their name to the following example, due to Austin: ``There are biscuits on the sideboard if you want them''. In Section 3, the author proposes to formalise this and similar examples by a formula logically equivalent to the main clause (``There are biscuits on the sideboard'').\N\NFinally, in Section 4, the author examine ``concessive conditionals'', which are exemplified by the sentence ``Even if you do not like it, my plan is to go out tonight''. The suggested formalisation is the formula \((\alpha > \beta) \And (\neg\alpha \triangleright \beta)\), where \(\beta\), as in the whether-or-not case, represent the main clause and \(\triangleright\) is a new symbol assumed to adequately formalise concessive conditionals. The author refers to [\textit{V. Crupi} and \textit{A. Iacona}, J. Philos. Log. 51, No. 3, 633--651 (2022; Zbl 07535475)], for a definition of the symbol of concessive conditional \(\triangleright\) in terms of the evidential account of conditionals introduced by the two authors.\N\NThe common structure to the analyses done in Sections 2--4 is the following: First, a natural-language sentence exemplifying one case of ``pseudo-conditional'' is presented. Secondly, some observations regarding what distinguishes these kind of sentences to ``real conditionals'' are put in the forefront. Thirdly, a possible formalisation of these sentences is suggested providing some argument to sustain that it fits well the intuitive observations.\N\NAs the author warns the reader, the intuitive observations about each case of ``pseudo-conditional'' which are discussed ``only concern the logical profile [of pseudo-conditionals] -- their truth conditions -- so they are not intended to provide a complete characterization'' (pp. 151 and 153). Under this respect, the author's thesis is that in all three cases we are facing examples of ``pseudo-conditionals'', rather than real conditionals, and that to find the correct way of formalising these sentences we need to take in account not only their syntactic structure and their linguistic meaning but also the content, possibly context-dependent, they express.\N\NThe latter claim links this study on the formalisation of pseudo-conditionals to the more general thesis that ``in the sense of `logical form' that matters to logic, logical form is determined by truth conditions'' (p. 145). This thesis -- in short the \emph{truth-conditional view} -- lies at the core of the book [\textit{A. Iacona}, Logical form. Between logic and natural language. Cham: Springer (2018; Zbl 1380.03001)] previously published by the same author. This fact makes the article apt to serve two purposes. On the one hand, it helps the reader interested in the truth conditional view of logical form to go deeper in the theses illustrated in the book by means of further case-studies; on the other hand, the analysis, conducted in the light of this view, of three well-known borderline cases, adds important ideas to the debate about the correct logical interpretation of the conditionals and the pseudo-conditionals.