Logic is about reasoning, or so the story goes. This thesis looks at the concept of logic, what it is, and what claims of correctness of logics amount to. The concept of logic is not a settled matter, and has not been throughout the history of it as a notion. Tools from conceptual analysis aid in this historical venture. Once the unsettledness of logic is established we see the repercussions in current debates in the philosophy of logic. Much of the (...) battle over the ‘one true logic’ is conceptually talking past each other. The theory of logics-as-formalizations is presented as a conceptually open theory of logic which is Carnapian in flavour and grounding. Rudolf Carnap’s notions surrounding ‘external’ and ‘pseudo-questions’ about linguistic frameworks apply to formalizations, thus logics, as well. An account of what formalizations are, a more structured sub-set of modelling, is given to ground the claim that logics are formalizations. Finally, a novel account of correctness, the COFE framework, is developed which allows the notions of logical monism, pluralism and nihilism to be more precisely formulated than they currently are in the discourse. (shrink)

I. Prelude -- About this Book -- II. School Mathematics and Its Consequences -- The Foundations of Mathematical Thinking -- Compression, Connection and Blending of Mathematical Ideas -- Set-befores, Met-befores and Long-term Learning -- Mathematics and the Emotions -- The Three Worlds of Mathematics -- Journeys through Embodiment and Symbolism -- Problem-Solving and Proof -- III. Interlude -- The Historical Evolution of Mathematics -- IV. University Mathematics and Beyond -- The Transition to Formal Knowledge -- Blending Knowledge Structures in the (...) Calculus -- Expert Thinking and Structure Theorems -- Contemplating the Infinitely Large and the Infinitely Small -- Expanding the Frontiers through Mathematical Research -- Reflections -- Appendix: Where the Ideas Came From. (shrink)

The consistency of a second-order version of Morley’s Theorem on the number of countable models was proved in [EHMT23] with the aid of large cardinals. We here dispense with them.

Keywords: Elementary Submodel; Real Line; Order-Isomorphic.

The Dirac δ function has solid roots in nineteenth century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac’s discovery by over a century, and illuminating the nature of Cauchy’s infinitesimals and his infinitesimal definition of δ.

The Foundations of Mathematics (Stewart and Tall) is a horse of a different color. The writing is excellent and there is actually some useful mathematics. I definitely like this book."--The Bulletin of Mathematics Books.

By utilizing the topological concept of pseudocompactness, we simplify and improve a proof of Caicedo, Dueñez, and Iovino concerning Terence Tao's metastability. We also pinpoint the exact relationship between the Omitting Types Theorem and the Baire Category Theorem by developing a machine that turns topological spaces into abstract logics.

Given a space in an elementary submodel M of H, define XM to be X∩M with the topology generated by . It is established, using anti-large-cardinals assumptions, that if XM is compact and its regular open algebra is isomorphic to that of a continuous image of some power of the two-point discrete space, then X=XM. Assuming in addition, the result holds for any compact XM satisfying the countable chain condition.

A cardinal κ is tall if for every ordinal θ there is an embedding j: V → M with critical point κ such that j > θ and Mκ ⊆ M. Every strong cardinal is tall and every strongly compact cardinal is tall, but measurable cardinals are not necessarily tall. It is relatively consistent, however, that the least measurable cardinal is tall. Nevertheless, the existence of a tall cardinal is equiconsistent with the existence of (...) a strong cardinal. Any tall cardinal κ can be made indestructible by a variety of forcing notions, including forcing that pumps up the value of 2κ as high as desired. (shrink)

Tall tales presents a sweeping survey of common myths about the mind and brain. In a lighthearted and accessible style, it exposes the truth behind these beliefs, how they are perpetuated, why people believe them, and why they might even exist in the first place.

Oestrogen treatment for girls, to prevent psychosocial problems due to extreme tallness, has been available for almost 50 years but uncertainty about its position prevails. The ethical problems of this treatment are focused on in this paper. After a brief overview on historical and medical aspects, ethical issues such as the general justification of oestrogen treatment, evaluation of its success and ethical concerns related to research in this subject are dealt with in detail.

In the debate over testimony to miracles, a common Humean move is to emphasize the prior improbability of miracles as the most important epistemic factor. Robert Fogelin uses the example of Henry, who tells multiple tall tales about meeting celebrities, to argue that low prior probabilities alone can render testimony unbelievable, with obvious implications for testimony to miracles. A detailed Bayesian analysis of Henry’s stories shows instead that the fact that Henry tells multiple stories about events that occurred independently (...) if they occurred at all is crucial to his loss of credibility. The epistemic structure is similar to that of a case of multiple lottery wins by the same person. Each of Henry’s stories can confirm only one event, but all the stories confirm the hypothesis that Henry is a liar. This structure does not apply to testimony to just one event, however antecedently improbable. Such examples therefore do nothing to undermine a standard Bayesian analysis involving both priors and likelihoods in evaluating testimony to an improbable event. (shrink)

In Insensitive Semantics (2004), we argue for two theses – Semantic Minimalism and Speech Act Pluralism. In this paper, we outline our defense against two objections often raised against Semantic Minimalism. To get to that defense, we first need some stage setting. To that end, we begin with five stage setting sections. These lead to the first objection, viz., that it might follow from our view that comparative adjectives are context insensitive. We defend our view against that objection (not, as (...) you might expect, by denying that implication, but by endorsing it). Having done so, we address a second objection, viz., that Semantic Minimalism makes it difficult to see what role semantic content plays in communicative exchanges. We respond and end with a reversal, i.e., we argue that even though the second objection fails against us, it works against those who raise the objection. In particular, we show that Recanati ends up with a notion of communicated content that fails various tests for psychological reality. (shrink)

This paper investigates the semantics of implicit comparatives (Alice is tall compared to Bob) and its connections to the semantics of explicit comparatives (Alice is taller than Bob) and sentences with adjectives in plain positive form (Alice is tall). We consider evidence from two experiments that tested judgments about these three kinds of sentence, and provide a semantics for implicit comparatives from the perspective of degree semantics.

New Zealand has an unspoken commandment: ‘thou shalt not be a tall poppy’. A tall poppy is someone who stands out from the crowd, usually by excelling at one or more pursuits. Sadly, many New Zealanders are all too familiar with this phrase as they have been ‘cut down’ by those around them, taunted for their success and discouraged from celebrating their achievements. This social phenomenon of cutting down tall poppies is called Tall Poppy Syndrome and (...) is present in many areas of New Zealand culture, such as sport, academic achievement, and entrepreneurship. Consequently, the church is not immune to this phenomenon. Tall Poppy Syndrome, whether within or outside the church, discourages excellence and prevents flourishing. This article engages Moral Foundations Theory to understand why Tall Poppy Syndrome exists in New Zealand, and then proposes Christian humility as a remedy for Tall Poppy Syndrome within the church. When humility and excellence can co-exist, then Tall Poppy Syndrome will no longer exist; thus the church could have an important role in enabling New Zealand to be a place where tall poppies can freely flourish. (shrink)

We construct two models containing exactly one supercompact cardinal in which all non-supercompact measurable cardinals are strictly taller than they are either strongly compact or supercompact. In the first of these models, level by level equivalence between strong compactness and supercompactness holds. In the other, level by level inequivalence between strong compactness and supercompactness holds. Each universe has only one strongly compact cardinal and contains relatively few large cardinals.

In this paper I argue that metalinguistic negotiations are not as common as David Plunkett and Timothy Sundell assume. They make two related controversial claims: the claim that speakers don’t know what they say and the claim that they directly communicate metalinguistic contents. These two claims generate two challenges that the metalinguistic-negotiation view should meet. Firstly, it should clarify why speakers are oblivious to what they are saying and communicating, and secondly, it should explain the mechanism that transforms what seems (...) like a typical object-language disagreement into a metalinguistic dispute. I argue that the way in which Plunkett and Sundell meet these challenges is unsatisfactory. Regarding their answer to the first challenge, I’ll argue that the theoretical cost of postulating massive semantic and pragmatic blindness in otherwise competent speakers is too high. Regarding what they say in relation to the second challenge, I’ll claim that metalinguistic contents can only be conveyed when speakers uttering apparently contradicting claims know that they are using terms with different meanings. If my arguments are correct, then metalinguistic negotiations are certainly not ubiquitous. (shrink)

In Insensitive Semantics (2004), we argue for two theses – Semantic Minimalism and Speech Act Pluralism. In this paper, we outline our defense against two objections often raised against Semantic Minimalism. We begin with five stage-setting sections. These lead to the first objection, viz., that it might follow from our view that comparative adjectives are context insensitive. We defend our view against that objection (not, as you might expect, by denying that implication, but by endorsing it). Having done so, we (...) address a second objection, viz., that Semantic Minimalism makes it difficult to see what role semantic content plays in communicative exchanges. We respond and end with a reversal, i.e., we argue that even though the second objection fails against us, it works against those who raise the objection. In particular, we show that our critics, especially, Carston (2002) and Recanati (2004), end up with a notion of communicated content that fails various tests for psychological reality. (shrink)

We provide a defense of our insensitive semantics: that is, the combination of semantic minimalism and speech act pluralism argued for at more length in our book Insensitive Semantics.

Entire libraries can be filled with volumes exploring the cultures, politics and geographies of the largely horizontal mobilities and transportation infrastructures that are intrinsic to urban modernity. And yet the recent ‘mobilities turn’ has almost completely neglected the cultural geographies and politics of vertical transportation within and between the buildings of vertically-structured cityscapes. Attempting to rectify this neglect, this article seeks, first, to bring elevator travel centrally into discussions about the cultural politics of urban space and, second, to connect elevator (...) urbanism to the even more neglected worlds of elevator-based descent in ultra-deep mining. The article addresses, in turn: the historical emergence of elevator urbanism; the cultural significance of the elevator as spectacle; the global ‘race’ in elevator speed; shifts towards the ‘splintering’ of elevator experiences; experiments with new mobility systems which blend elevators and automobiles; problems of vertical abandonment; and, finally, the neglected vertical politics of elevator-based ‘ultra-deep’ mining. (shrink)

We prove the following version of Hechler's classical theorem: For each partially ordered set (Q, ≤) with the property that every countable subset of Q has a strict upper bound in Q, there is a ccc forcing notion such that in the generic extension for each tall analytic P-ideal J (coded in the ground model) a cofinal subset of (J, ⊆*) is order isomorphic to (Q, ≤).

Starting from a model “κ is supercompact” + “No cardinal is supercompact up to a measurable cardinal”, we force and construct a model such that “κ is supercompact” + “No cardinal is supercompact up to a measurable cardinal” + “δ is measurable iff δ is tall” in which level by level equivalence between strong compactness and supercompactness holds. This extends and generalizes both [, Theorem 1] and the results of.

We present an investigation of the ways in which speakers' subjective perspectives are likely to affect the meaning of gradable adjectives like tall or heavy. We present the results of a study showing that people tend to use themselves as a yardstick when ascribing these adjectives to human figures of varied measurements: subjects' height and weight requirements for applying tall and heavy are found to be positively correlated with their personal measurements. We draw more general lessons regarding the (...) definition of subjectivity and the ways in which a standard of comparison and a significant deviation from that standard are specified. (shrink)

Given a family${\cal C}$of infinite subsets of${\Bbb N}$, we study when there is a Borel function$S:2^{\Bbb N} \to 2^{\Bbb N} $such that for every infinite$x \in 2^{\Bbb N} $,$S\left \in {\Cal C}$and$S\left \subseteq x$. We show that the family of homogeneous sets as given by the Nash-Williams’ theorem admits such a Borel selector. However, we also show that the analogous result for Galvin’s lemma is not true by proving that there is an$F_\sigma $tall ideal on${\Bbb N}$without a Borel selector. (...) The proof is not constructive since it is based on complexity considerations. We construct a${\bf{\Pi }}_2^1 $tall ideal on${\Bbb N}$without a tall closed subset. (shrink)

Die aramäischen Texte aus Tall Šēḫ Ḥamad/Dūr-Katlimmu/Magdalu. By Wolfgang Röllig. Berichte der Ausgrabung Tall Šēḫ Ḥamad/Dūr-Katlimmu, vol. 17. Wiesbaden: Harrassowitz Verlag, 2014. Pp. lxiv + 284, illus. €84.

Die mittelassyrischen Personen- und Rationlisten aus Tall Šēḫ Ḥamad/Dūr-Katlimmu. By Saqer Salah. Berichte der Ausgrabung Tall Šēḫ Ḥamad/Dūr- Katlimmu, vol. 18. Wiesbaden: Harrassowitz Verlag, 2014. Pp. lxxiv + 454, plates. €118.

New empirical evidence on the long-term effects of oestrogen treatment for tall adolescent girls has shown that the intended psychosocial benefit of the treatment may not have been realised. This paper describes recent trends in the prevalence of the treatment and the results of a large Australian cohort study evaluating girls assessed between 1959 and 1993 for excessive growth. The paper concludes that oestrogen treatment to prevent extreme tallness should belong to the past, not to the future.