22 March: Alessandro Torza (UNAM) – “Ideology in a Desert Landscape”
Sala Seminari, Via Festa del Perdono 7, h. 11.00-13.00.
Abstract: The fascination for desert landscapes has been a recurring theme in contemporary ontology and metaphysics. In his Writing the Book of the World, Ted Sider has defended a new incarnation of that ideal. The view turns on a broadly Quinean principle of ideological commitment: a term is joint-carving (structural) iff it is indispensable in the formulation of our best total theory. Accordingly, the class of fundamental notions should include all first-order logical constants, as well as the set-theoretic membership relation and a few terms from fundamental physics. One consequence of this view is that there exists some first-order quantifier – presumably the one used in the ontology room – which is joint-carving. On the other hand, run-of-the-mill modal notions (metaphysical, nomic, epistemic, deontic etc.) are ruled out, since they fail to occur in our best theory. The resulting picture seems to entail a twofold condition: (i) some quantifier is joint-carving; (ii) no modal operator is joint-carving.
However, this view clashes with a logical result due to Arnold Koslow who proved that, given a structuralist characterization of modality – one sufficiently general to cover all well-known systems of modal logic –, the first-order quantifier counts as a modal. Although a number of strategies can be put forward for blocking Koslow’s characterization, none of them is ultimately convincing. It must be concluded that modality is not a good indicator of non-fundamentality. Therefore, the best option available to the friend of desert landscapes is to provide an alternative demarcation between the fundamental and the non-fundamental.
Some passages from Sider suggests that what he has in mind might instead go thus: (i) some quantifier is joint-carving; (ii*) no intensional operator is joint-carving. Nevertheless, another logical result also due to Koslow entails that the first-order quantifier is an intensional operator. If the result is sound, the second proposal for making sense of the fundamental vs. non-fundamental distinction is doomed as well. However, I will analyze and criticize Koslow’s second result by showing that the notion of extensionality should be understood in a slightly different way. Koslow defines an operator O as intensional just in case it satisfies the condition
Ext. (Px ↔ Qx) ⇒ (OPx ↔ OQx)
It can be shown, however, that when ‘⇒’ is understood model-theoretically (rather than structurally, as does Koslow), Ext gives inconsistent results. That gives us reasons to believe that Ext does not correctly captures the notion of extensionality. I submit a revision of the definition of extensionality as per the condition
Ext’. ∀x(Px ↔ Qx) ⇒ ∀x(OPx ↔ OQx)
As it turns out, Ext’ does not give inconsistent model-theoretic results and, most importantly, makes the quantifier extensional as desired, when ‘⇒’ is understood in Koslow’s structuralist fashion. I conclude that the alleged proof of the intensionality of the quantifier rests on a mistake.
The moral of the discussion is that the conjunction of (i) and (ii*) appears to be the most promising characterization of the demarcation between fundamental and non-fundamental in the context of Sider’s metaphysics. Nevertheless, it is worth remarking that (ii*) is incompatible with Sider’s view that the predicate ‘being joint-carving’ is itself joint-carving, since that predicate is intensional. I will argue that there are reasons to uphold (ii*), while rejecting the thesis that ‘being joint-carving’ is a joint-carving predicate.
References
[1] Koslow, A. 1992. A Structuralist Theory of Logic. CUP.
[2] Koslow, A. 2014. The Modality and Non-Extensionality of the Quanti- fiers. Synthese.
[3] Sider, T. 2012. Writing the Book of the World. OUP.
Co-organized with OntoForMat.