A study of the making of George Peacock's highly influential, yet disturbingly split, 1830 account of algebra as an entanglement of two separate undertakings: arithmetical and symbolical or formal.

A family of familiar linguistic tests purport to help identify when a term is ambiguous. These tests are philosophically important: a familiar philosophical strategy is to claim that some phenomenon is disunified and its accompanying term is ambiguous. The tests have been used to evaluate disunification proposals about causation, pain, and knowledge, among others. -/- These ambiguity tests, however, have come under fire. It has been alleged that the tests fail for polysemy, a common type of ambiguity, and one that (...) is at issue in philosophically interesting cases. Furthermore, the objection that the tests fail for polysemy is often taken to be an undeniable bit of linguistic data. -/- We argue that this is mistaken. The objection implicitly relies on controversial assumptions about how to account for copredicational sentences, in which a single argument is ascribed prima facie incompatible properties. Furthermore, on several viable theories of copredication, the objection fails. However, our discussion also reveals that even if ambiguity tests are preserved, they may be significantly harder to execute than previously thought. (shrink)

Robert Brandom's "The Pragmatist Enlightenment" describes the advent of American pragmatism as signaling a sea-change in our understanding of human reason away from the top-down Euclidian models of reasoning, warrant and knowledge inspired by the physical sciences, toward the far more bottom-up, narrative, inherently fallible and dialogical forms of reasoning of the life and human sciences. It is against this backdrop that Talmudic Judaism emerges not only as an early anticipation of the pragmatist enlightenment, but as going a substantial and (...) radical step beyond it, that in the context of religious commitment and reasoning, is unprecedented. (shrink)

Babbage wrote two relatively detailed, yet significantly incongruous, autobiographical accounts of his pre-Cambridge and Cambridge days. He published one in 1864 and in it advertised the existence of the other, which he carefully retained in manuscript form. The aim of this paper is to chart in some detail for the first time the discrepancies between the two accounts, to compare and assess their relative credibility, and to explain their author's possible reasons for knowingly fabricating the less credible of the two.

Essay review of Y. Gingras, Science and Religion: An Impossible Dialogue, Polity Press, 2017.

This article introduces the confrontational theology of the rabbinic literature of late antiquity by means of a well-known, yet ill-understood legend. It goes on to argue that Talmudic confrontationalism comes coupled with an insistent dialogism that, unlike any other major human undertaking, displays a profound awareness of the indispensable role of external normative critique in the process of changing one’s mind.

The problems divulged, analyzed and allegedly solved in Science, Order & Creativity are not scientific problems. They attest to a fundamental failure of science but not to scientific failure per se. Bohm and Peat's meta-scientific undertaking cannot afford, therefore, to remain negative. However, neither science itself nor current professional philosophy are capable of the radical positive rethinking required, in their view, in order to restore and ensure scientific creativity.

In a recent paper, Breckenridge and Magidor argue for an interesting and counterintuitive account of instantial reasoning. According to this account, in arguments such as one beginning with 'There is some x such that x is mortal. Let O be such an x. ...', the 'O' refers to a particular object, although we cannot know which. I give and defend a simple counterexample involving the notion of an unreferred-to object.

Review of: Menachem Fisch; Simon Schaffer (Editors). William Whewell: A Composite Portrait. xiv + 403 pp., bibl., index. Oxford: Clarendon Press of Oxford University Press, 1991. $98.

What is the relation between meaning and use? This chapter first defends a non-reductionist understanding of Wittgenstein’s suggestion that ‘the meaning of a word is its use in the language’; facts about meaning cannot be reduced to, or explained in terms of, facts about use, characterized non-semantically. Nonetheless, it is contended, facts about meaning do supervene on non-semantic facts about use. That supervenience thesis is suggested by comments of Wittgenstein’s and is consistent with his view of meaning and rule-following. Semantic (...) supervenience is then defended against two criticisms: first, John McDowell’s suggestion that the supervenience thesis falsifies the epistemology of meaning and fails to accommodate common-sense truths about meaning; second, a series of counter-examples proposed by Stephen Kearns and Ofra Magidor, who argue that worlds may differ semantically without differing non-semantically. It is argued that neither criticism is convincing: we should accept the thesis that semantic facts supervene on non-semantic facts. (shrink)

Strict finitism is the position that only those natural numbers exist that we can represent in practice. Michael Dummett, in a paper called Wang’s Paradox, famously tried to show that strict finitism is an incoherent position. By using the Sorites paradox, he claimed that certain predicates the strict finitist is committed to are incoherent. More recently, Ofra Magidor objected to Dummett’s claims, arguing that Dummett fails to show the incoherence of strict finitism. In this paper, I shall investigate whether (...) Magidor is successful in preventing Dummett from proving the incoherence of strict finitism. Though not all the counterarguments Magidor presents are successful, she does in the end manages to corner Dummett. There remains a small opportunity for Dummett to insist on the incoherence of strict finitism, but this is a very small opening. The final conclusion of this paper is that Dummett cannot logically prove the incoherence of strict finitism, even though not all hope is lost. (shrink)

This paper responds to commentaries by Kaiserman and Magidor, and Hawthorne. The case of the infinite clowns can teach us several things.

In this paper, I ask whether mishpat ivri (Jewish Law) is appropriately conceived as a “legal system”. I review Menachem Elon’s use of a “Sources” Theory of Law (based on Salmond) in his account of Mishpat Ivri; the status of religious law from the viewpoint of jurisprudence itself (Bentham, Austin and Kelsen); then the use of sources (and the approach to “dogmatic error”) by halakhic authorities in discussing the problems of the agunah (“chained wife”), which I suggest points to (...) a theory more radical than the “sources” theory of law, one more akin to the ultimate phase of the thought of Kelsen (the “non-logical” Kelsen) or indeed to some form of Legal Realism (with which that phase of Kelsen’s thought has indeed been compared)? I finally juxtapose an account based on internal theological resources (a “Jurisprudence of Revelation”). Downloadable at at http://www.biu.ac.il/JS/JSIJ/jsij1.html. (shrink)

We think and speak in figures. This is key to our creativity. We re-imagine one thing as another, pretend ourself to be another, do one thing in order to achieve another, or say one thing to mean another. This comes easily because of our abilities both to work out meaning in context and re-purpose words. Figures of speech are tools for this re-purposing. Whether we use metaphor, simile, irony, hyperbole, and litotes individually, or as compound figures, the uses are all (...) rooted in literal meanings. These uses invite us to explore the context to find new meanings, new purposes, beyond the literal. -/- This special issue of Philosophical Studies brings together eight papers on various aspects and applications of figurative speech including: David Hills, Mitch Green, Liz Camp, Ofra Magidor, Larry Horn, Ken Walton, Stephen Barker, and Mihaela Popa-Wyatt. (shrink)

We motivate the idea that presupposition is a transparent attitude. We then explain why epistemic opacity is not a serious problem for Robert Stalnaker's theory of content and conversation. We conclude with critical remarks about John Hawthorne and Ofra Magidor's alternative theory.

It is common belief that semantic properties supervene on non-semantic properties: no two possible worlds can be non-semantic duplicates and fail to be semantic duplicates. The view enjoys somewhat of an orthodoxy status in contemporary philosophy of language and metaphysics, and is often assumed without argument. Yet, work by Stephen Kearns and Ofra Magidor has claimed that it is vulnerable to a variant of the classical arguments against the supervenience of the phenomenal on the physical. This paper does three (...) things: it clarifies what semantic supervenience is about, it responds to the objections that have been leveled against it, and provides a new battery of arguments in its favor. I argue that the thesis of semantic supervenience is safe from classical anti-supervenience arguments, and show that its rejection generates unwelcome consequences. I conclude that there are substantial reasons to embrace the received wisdom: semantic properties supervene. (shrink)

Existential instantiation is a rule of inference that allows us infer, from the proposition that there are some p things, the proposition that a is a p thing. What role does 'a' play here? According to one account, recently defended by Breckenridge and Magidor, we use 'a' to refer to a p thing. I argue that this cannot be right. I propose an alternative account, according to which we use 'a' to refer to a supposedly p thing.

This paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences from infinite sets of premises. The semantics is formulated in terms of selection functions and is a generalization of the preferential semantics of Shoham (1987), (1988), Kraus, Lehman, and Magidor (1990) and Makinson (1989), (1993). A selection function picks out from a given set of possible states (worlds, situations, models) a subset consisting of those states that are, in some sense, the most preferred ones. (...) A proposition α is a nonmonotonic consequence of a set of propositions Γ iff α holds in all the most preferred Γ-states. In the literature on revealed preference theory, there are a number of well-known theorems concerning the representability of selection functions, satisfying certain properties, in terms of underlying preference relations. Such theorems are utilized here to give corresponding representation theorems for nonmonotonic inference operations. At the end of the paper, the connection between nonmonotonic inference and belief revision, in the sense of Alchourrón, Gärdenfors, and Makinson, is explored. In this connection, infinitary belief revision operations that allow for the revision of a theory with a possibly infinite set of propositions are introduced and characterized axiomatically. (shrink)