<p>A hundred years ago, Ramsey (<i>Aristotelian Society Supplementary</i> 7(1):153-170, 1927) devised a new system of notation to more perspicuously represent the idea that ‘<i>p</i>’ and ‘<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lnot \lnot p\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>¬</mo> <mo>¬</mo> <mi>p</mi> </mrow> </math></EquationSource> </InlineEquation>’ express the same fact. Recently, Monroy Pérez (<i>Mind</i> 131(524):1083–1107, 2022) has argued that we can apply Ramsey’s insight to solve a recalcitrant problem for logical elitism—the thesis, most famously defended by Sider (<i>Writing the Book of the World</i>, Oxford University Press), that the world’s fundamental metaphysical structure includes logical structure. Here, I discuss the general role of language in the framing of logical elitism and present four arguments that show that the Ramseyan strategy for defending logical elitism fails. First, it does not eliminate all arbitrariness even for zeroth-order classical logic (§<InternalRef RefID="Sec3">3</InternalRef>). Second, it is a case of a more general strategy that exploits the fact that classical negation is an <i>involution</i>; then, choosing the Ramseyan proposal among the other cases is arbitrary (§<InternalRef RefID="Sec4">4</InternalRef>). Third, there are proposals to solve the riddle that are <i>simpler</i> than every case of the involutory strategy (§<InternalRef RefID="Sec5">5</InternalRef>). The discussion has consequences for logical elitism at large: in my fourth argument I contend, contrary to a fairly favoured opinion, that logical elitism should not be thought of as a thesis about <i>languages</i>, but as a thesis about <i>joints</i> in metaphysical structure (§<InternalRef RefID="Sec6">6</InternalRef>).</p>

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Notation, Redundancy and Fundamental Logical Structure

  • Carlos Romero

摘要

A hundred years ago, Ramsey (Aristotelian Society Supplementary 7(1):153-170, 1927) devised a new system of notation to more perspicuously represent the idea that ‘p’ and ‘ \(\lnot \lnot p\) ¬ ¬ p ’ express the same fact. Recently, Monroy Pérez (Mind 131(524):1083–1107, 2022) has argued that we can apply Ramsey’s insight to solve a recalcitrant problem for logical elitism—the thesis, most famously defended by Sider (Writing the Book of the World, Oxford University Press), that the world’s fundamental metaphysical structure includes logical structure. Here, I discuss the general role of language in the framing of logical elitism and present four arguments that show that the Ramseyan strategy for defending logical elitism fails. First, it does not eliminate all arbitrariness even for zeroth-order classical logic (§3). Second, it is a case of a more general strategy that exploits the fact that classical negation is an involution; then, choosing the Ramseyan proposal among the other cases is arbitrary (§4). Third, there are proposals to solve the riddle that are simpler than every case of the involutory strategy (§5). The discussion has consequences for logical elitism at large: in my fourth argument I contend, contrary to a fairly favoured opinion, that logical elitism should not be thought of as a thesis about languages, but as a thesis about joints in metaphysical structure (§6).