We note that a plural version of logicism about arithmetic is suggested by the standard reading of Hume's Principle in terms of `the number of Fs/Gs'. We lay out the resources needed to prove a version of Frege's principle in plural, rather than second-order, logic. We sketch a proof of the theorem and comment philosophically on the result, which sits well with a metaphysics of natural numbers as plural properties.
There has been very little discussion of the appropriate principles to govern a modal logic of plurals. What debate there has been has accepted a principle I call (Necinc); informally if this is one of those then, necessarily: this is one of those. On this basis Williamson has criticised the Boolosian plural interpretation of monadic second-order logic. I argue against (Necinc), noting that it isn't a theorem of any logic resulting from adding modal axioms to the plural logic PFO+, and (...) showing that the most obvious formal argument in its favour is question begging. I go on to discuss the behaviour of natural language plurals, motivating a case against (Necinc) by developing a case that natural language plural terms are not de jure rigid designators. The paper concludes by developing a model theory for modal PFO-f which does not validate (Necinc). An Appendix discusses (Necinc) in relation to counterpart theory. Of course, it would be a mistake to think that the rules for "multiple pointing" follow automatically from the rules for pointing proper. Max Black—The Elusiveness of Sets In some influential articles during the 1980s George Boolos proposed an interpretation of monadic second-order logic in terms of plural quantification [4, 5]. One objection to this proposal, pressed by Williamson [22, 456-7], focuses on the modal behaviour of plural variables, arguing that the proposed interpretation yields the wrong results in respect of the modal status of atomic predications. In the present paper I will present this objection and argue against it. In the course of developing the argument, I will have cause to consider the under-investigated question of how a logic for plurals should be extended to incorporate modal operators. (shrink)
This paper raises the question under what circumstances a plurality forms a set, parallel to the Special Composition Question for mereology. The range of answers that have been proposed in the literature are surveyed and criticised. I argue that there is good reason to reject both the view that pluralities never form sets and the view that pluralities always form sets. Instead, we need to affirm restricted set formation. Casting doubt on the availability of any informative principle which will settle (...) which pluralities form sets, the paper concludes by affirming a naturalistic approach to the philosophy of set theory. (shrink)
This paper develops a formal system, consisting of a language and semantics, called serial logic ( SL ). In rough outline, SL permits quantification over, and reference to, some finite number of things in an order , in an ordinary everyday sense of the word “order,” and superplural quantification over things thus ordered. Before we discuss SL itself, some mention should be made of an issue in philosophical logic which provides the background to the development of SL , and with (...) respect to which I wish to contend that the system permits progress. (shrink)
There is no interesting entailment either way between theism and various forms of realism. Taking its cue from Dummett's characterisation of realism and his discussion of it with respect to theistic belief, this paper argues both that theism does not follow from realism, and that God cannot be appealed to in order to secure bivalence for an otherwise indeterminate subject matter. In both cases, significant appeal is made to the position that God is not a language user, which in turn (...) is motivated by an account of understanding as aptitude possession. The resulting picture sits comfortably with the apophatism common within living religious traditions and with the view that the philosophy of religion ought to reorientate itself away from metaphysics towards more practical questions. (shrink)
A version of Frege's theorem can be proved in a plural logic with pair abstraction. We talk through this and discuss the philosophical implications of the result.
This paper transforms a development of an argument against pantheism into an objection to the usual account of God within contemporary analytic philosophy. A standard criticism of pantheism has it that pantheists cannot offer a satisfactory account of God as personal. My paper will develop this criticism along two lines: first, that personhood requires contentful mental states, which in turn necessitate the membership of a linguistic community, and second that personhood requires limitation within a wider context constitutive of the ’setting’ (...) of the agent’s life. Pantheism can, I argue, satisfy neither criterion of personhood. At this point the tables are turned on the Swinburnian theist. If the pantheist cannot defend herself against the personhood-based attacks, neither can the Swinburnian, and for instructively parallel reasons: for neither doctrine is God in the material world; in the pantheist case God is identical with the world, in the Swinburnian case God transcends it. Either way both the pantheist and the Swinburnian are left with a dilemma: abandon divine personhood or modify the doctrine of God so as to block the move to personhood. (shrink)
We can introduce singular terms for ordered pairs by means of an abstraction principle. Doing so proves useful for a number of projects in the philosophy of mathematics. However there is a question whether we can appeal to the abstraction principle in good faith, since a version of the Caesar Problem can be generated, posing the worry that abstraction fails to introduce expressions which refer determinately to the requisite sort of object. In this short paper I will pose the difficulty, (...) and then propose a solution. (shrink)
Permissivist metaontology proposes answering customary existence questions in the affirmative. Many of the existence questions addressed by ontologists concern the existence of theoretical entities which admit precise formal specification. This causes trouble for the permissivist, since individually consistent formal theories can make pairwise inconsistent demands on the cardinality of the universe. We deploy a result of Gabriel Uzquiano’s to show that this possibility is realised in the case of two prominent existence debates and propose rejecting permissivism in favour of substantive (...) ontology conducted on a cost–benefit basis. (shrink)
It is argued that Gabriel Uzquiano's approach to set-theoretic indefinite extensibility is a version of in rebus structuralism, and therefore suffers from a vacuity problem.
On the face of it Aquinas stands in the mainstream of Western mystical theology, and in particular is a noteworthy proponent of negative theology. This view, however, is challenged within anglophone philosophical theology. The clearest attack on the view that Aquinas is an apophatic theologian is to be found in Eleonore Stump's Aquinas. This paper lays out Stump's reasons for reading Aquinas as non-apophatic, and shows that they are not convincing. Aquinas, it concludes, meant what he said when he claimed (...) that we do not know what God is. (shrink)
ABSTRACTThe doctrine of the Real Presence of Christ in the Eucharist presents a particular challenge to its defenders: how is it so much as intelligible? This paper explores Dummett’s response to this question, centred on the notion of deeming. Whilst instructive, Dummett’s position is unsustainable as it stands, since it fails to secure the meaningfulness of the doctrine. Once deeming is brought together with an account of bodiliness and an appreciation of the nature of the Eucharist as a meal, however, (...) the way is open to demonstrating the intelligibility of the doctrine. This is a prerequisite even for its rejection as false. (shrink)
It is common for contemporary ontologists to claim that they are not concerned with what exists simpliciter, but rather with what exists ’fundamentally’, or what ’really’ exists. I argue that positions of this sort cannot satisfy reasonable constraints concerning the acquisition of language. I assess and dismiss possible responses to this complaint before commenting on the prospects for a metaphysics without bespoke existence claims.
Herbert McCabe was, by widespread acclaim, one of the greatest Catholic thinkers in the English speaking world during the final quarter of the last century. He was also deeply committed to radical left‐wing politics. What is the relationship between these two facts? I lay out what I take to be the key themes in McCabe's politics before arguing that, in contrast to significant strands in present day political theology, he had a keen sense of the respective roles of faith and (...) reason in guiding political action. This allowed him to commit himself to a politics which was more radical than much of what has followed him, whilst having a clear sense of how Christian faith ought to be allowed to condition political engagement. The article concludes by drawing out lessons from McCabe for thinking about faith and politics. Not least of these is that we ought to avoid the lure, often articulated in terms of the ‘unifying’ role of the Church, to eschew conflict. (shrink)
An important trend in contemporary metaphysics denies that the structure of natural language is an important datum for investigating fundamental structure. Ted Sider proceeds on this basis to propose a metaphysical semantics for natural language. Within this framework he argues that natural language and a fundamental, ‘jointcarving’, language could be subject to distinct logics. Developing an argument of Hartry Field’s, I show that Sider’s preferred option of fundamental classicality combined with non-fundamental non-classicality trivialises within the framework of Siderian metaphysical semantics. (...) The position can be saved only by revising key claims about truth and metaphysical semantics. This has serious implications for methdology in the metaphysics of logic. (shrink)
Michael Dummett offered a semantic characterisation of a variety of realism-antirealism debates. This approach has fallen out of fashion. This has been to the detriment of metaphysics. This paper offers an accurate characterisation of Dummett’s view, often lacking in the literature, and then defends it against a range of attacks. This understanding of realism debates is resilient, and if we take it seriously the philosophical terrain looks importantly different. In particular, the philosophy of language has a foundational role with respect (...) to metaphysics. (shrink)
There is no interesting entailment either way between theism and various forms of realism. Taking its cue from Dummett’s characterisation of realism and his discussion of it with respect to theistic belief, this paper argues both that theism does not follow from realism, and that God cannot be appealed to in order to secure bivalence for an otherwise indeterminate subject matter. In both cases, significant appeal is made to the position that God is not a language user, which in turn (...) is motivated by an account of understanding as aptitude possession. The resulting picture sits comfortably with the apophatism common within living religious traditions and with the view that the philosophy of religion ought to reorientate itself away from metaphysics towards more practical questions. (shrink)
It is often assumed that pluralities are rigid, in the sense of having all and only their actual members necessarily. This assumption is operative in standard approaches to modal plural logic. I argue that a sceptical approach towards the assumption is warranted.
