We study the modal logic M L r of the countable random frame, which is contained in and `approximates' the modal logic of almost sure frame validity, i.e. the logic of those modal principles which are valid with asymptotic probability 1 in a randomly chosen finite frame. We give a sound and complete axiomatization of M L r and show that it is not finitely axiomatizable. Then we describe the finite frames of that logic and (...) show that it has the finite frame property and its satisfiability problem is in EXPTIME. All these results easily extend to temporal and other multi-modal logics. Finally, we show that there are modal formulas which are almost surely valid in the finite, yet fail in the countable random frame, and hence do not follow from the extension axioms. Therefore the analog of Fagin's transfer theorem for almost sure validity in first-order logic fails for modal logic. (shrink)

We consider random processes more general than those considered by Erdös and Rényi for generating the countable random graph. It is proved that, in the category sense, almost all random processes we consider generate the countable random graph with probability 1. Under a weak boundedness assumption we give a criterion for the random processes which generate the countable random graph almost surely. We also consider further questions asked by Jackson regarding the (...) outcome graphs when the process fails to produce the countable random graph. (shrink)

De Finetti would claim that we can make sense of a draw in which each positive integer has equal probability of winning. This requires a uniform probability distribution over the natural numbers, violating countable additivity. Countable additivity thus appears not to be a fundamental constraint on subjective probability. It does, however, seem mandated by Dutch Book arguments similar to those that support the other axioms of the probability calculus as compulsory for subjective interpretations. These two lines of reasoning (...) can be reconciled through a slight generalization of the Dutch Book framework. Countable additivity may indeed be abandoned for de Finetti's lottery, but this poses no serious threat to its adoption in most applications of subjective probability. Introduction The de Finetti lottery Two objections to equiprobability 3.1 The ‘No random mechanism’ argument 3.2 The Dutch Book argument Equiprobability and relative betting quotients The re-labelling paradox 5.1 The paradox 5.2 Resolution: from symmetry to relative probability Beyond the de Finetti lottery. (shrink)

Every Berman’s variety \ which is the subvariety of Ockham algebras defined by the equation \ and \) determines a finitary substitution invariant consequence relation \. A sequent system \ is introduced as an axiomatization of the consequence relation \. The system \ is characterized by a single finite frame \ under the frame semantics given for the formal language. By the duality between frames and algebras, \ can be viewed as a \-valued logic as it is characterized (...) by a distributive lattice of \ elements with a unary operator. Moreover, a structural-rule-free, cut-free and terminating sequent system \ is established for \. The Craig interpolation property of \ is shown proof-theoretically utilizing \. (shrink)

It is true in the Cohen, Solovay-random, dominaning, and Sacks generic extension, that every countable ordinal-definable set of reals belongs to the ground universe. It is true in the Solovay collapse model that every non-empty OD countable set of sets of reals consists of \ elements.

A set $B\subseteq\mathbb{N}$ is called low for Martin-Löf random if every Martin-Löf random set is also Martin-Löf random relative to B . We show that a $\Delta^0_2$ set B is low for Martin-Löf random if and only if the class of oracles which compress less efficiently than B , namely, the class $\mathcal{C}^B=\{A\ |\ \forall n\ K^B(n)\leq^+ K^A(n)\}$ is countable (where K denotes the prefix-free complexity and $\leq^+$ denotes inequality modulo a constant. It follows that (...) $\Delta^0_2$ is the largest arithmetical class with this property and if $\mathcal{C}^B$ is uncountable, it contains a perfect $\Pi^0_1$ set of reals. The proof introduces a new method for constructing nontrivial reals below a $\Delta^0_2$ set which is not low for Martin-Löf random. (shrink)

The idea of this paper is to explore the existence of canonical countably saturated models for different classes of structures. It is well-known that, under CH, there exists a unique countably saturated linear order of cardinality \. We provide some examples of pairwise non-isomorphic countably saturated linear orders of cardinality \, under different set-theoretic assumptions. We give a new proof of the old theorem of Harzheim, that the class of countably saturated linear orders has a uniquely determined one-element basis. From (...) our proof it follows that this minimal linear order is a Fraïssé limit of certain Fraïssé class. In particular, it is homogeneous with respect to countable subsets. Next we prove the existence and uniqueness of the uncountable version of the random graph. This graph is isomorphic to \,\in \cup \ni )\), where \\) is the set of hereditarily countable sets, and two sets are connected if one of them is an element of the other. In the last section, an example of a prime countably saturated Boolean algebra is presented. (shrink)

We show that for any real number, the class of real numbers less random than it, in the sense of rK-reducibility, forms a countable real closed subfield of the real ordered field. This generalizes the well-known fact that the computable reals form a real closed field. With the same technique we show that the class of differences of computably enumerable reals (d.c.e. reals) and the class of computably approximable reals (c.a. reals) form real closed fields. The d.c.e. result (...) was also proved nearly simultaneously and independently by Ng (Keng Meng Ng. Master's Thesis. National University of Singapore, in preparation). Lastly, we show that the class of d.c.e. reals is properly contained in the class or reals less random than Ω (the halting probability), which in turn is properly contained in the class of c.a. reals, and that neither the first nor last class is a randomness class (as captured by rK-reducibility). (shrink)

This paper proves that certain supertasks constitute counterexamples to countable additivity even in the frame of an objective (not subjective, à la de Finetti) conception of probability. The argument requires taking conditional probability as a primitive notion.

This paper investigates aspects of measure and randomness in the context of locale theory . We prove that every measure μ, on the σ-frame of opens of a fitted σ-locale X, extends to a measure on the lattice of all σ-sublocales of X . Furthermore, when μ is a finite measure with μ=M, the σ-locale X has a smallest σ-sublocale of measure M . In particular, when μ is a probability measure, X has a smallest σ-sublocale of measure 1. (...) All σ prefixes can be dropped from these statements whenever X is a strongly Lindelöf locale, as is the case in the following applications. When μ is the Lebesgue measure on the Euclidean space Rn, Theorem 1 produces an isometry-invariant measure that, via the inclusion of the powerset P in the lattice of sublocales, assigns a weight to every subset of Rn. When μ is the uniform probability measure on Cantor space {0,1}ω, the smallest measure-1 sublocale, given by Theorem 2, provides a canonical locale of random sequences, where randomness means that all probabilistic laws are satisfied. (shrink)

A mass problem is a set of Turing oracles. If P and Q are mass problems, we say that P is weakly reducible to Q if every member of Q Turing computes a member of P. We say that P is strongly reducible to Q if every member of Q Turing computes a member of P via a fixed Turing functional. The weak degrees and strong degrees are the equivalence classes of mass problems under weak and strong reducibility, respectively. We (...) focus on the countable distributive lattices P w and P s of weak and strong degrees of mass problems given by nonempty Π 1 0 subsets of 2 ω . Using an abstract Gödel/Rosser incompleteness property, we characterize the Π 1 0 subsets of 2 ω whose associated mass problems are of top degree in P w and P s , respectively. Let R be the set of Turing oracles which are random in the sense of Martin-Löf, and let r be the weak degree of R. We show that r is a natural intermediate degree within P w . Namely, we characterize r as the unique largest weak degree of a Π 1 0 subset of 2 ω of positive measure. Within P w we show that r is meet irreducible, does not join to 1, and is incomparable with all weak degrees of nonempty thin perfect Π 1 0 subsets of 2 ω . In addition, we present other natural examples of intermediate degrees in P w . We relate these examples to reverse mathematics, computational complexity, and Gentzen-style proof theory. (shrink)

Let ≤r and ≤sbe two binary relations on 2ℕ which are meant as reducibilities. Let both relations be closed under finite variation and consider the uniform distribution on 2ℕ, which is obtained by choosing elements of 2ℕ by independent tosses of a fair coin.Then we might ask for the probability that the lower ≤r-cone of a randomly chosen set X, that is, the class of all sets A with A ≤rX, differs from the lower ≤s-cone of X. By c osure (...) under finite variation, the Kolmogorov 0-1 aw yields immediately that this probability is either 0 or 1; in case it is 1, the relations are said to be separable by random oracles.Again by closure under finite variation, for every given set A, the probability that a randomly chosen set X is in the upper ≤r-cone of A is either 0 or 1; let Almostr be the class of sets for which the upper ≤r-cone has measure 1. In the following, results about separations by random oracles and about Almost classes are obtained in the context of generalized reducibilities, that is, for binary relations on 2ℕ which can be defined by a countable set of total continuous functionals on 2ℕ in the same way as the usual resource-bounded reducibilities are defined by an enumeration of appropriate oracle Turing machines. The concept of generalized reducibility comprises a natura resource-bounded reducibilities, but is more general; in particular, it does not involve any kind of specific machine model or even effectivity. The results on generalized reducibilities yield corollaries about specific resource-bounded reducibilities, including several results which have been shown previously in the setting of time or space bounded Turing machine computations. (shrink)

Countable homogeneous relational structures have been studied by many people. One area of focus is the Ramsey theory of such structures. After a review of background material, a partition theorem of Laflamme, Sauer, and Vuksanovic for countable homogeneous binary relational structures is discussed with a focus on the size of the set of unavoidable colors.

Let $\Gamma$ be the random bipartite graph, a countable graph with two infinite sides, edges randomly distributed between the sides, but no edges within a side. In this paper, we investigate the reducts of $\Gamma$ that preserve sides. We classify the closed permutation subgroups containing the group $\operatorname {Aut}(\Gamma)^{\ast}$ , where $\operatorname {Aut}(\Gamma)^{\ast}$ is the group of all isomorphisms and anti-isomorphisms of $\Gamma$ preserving the two sides. Our results rely on a combinatorial theorem of Nešetřil and Rödl and (...) a strong finite submodel property for $\Gamma$. (shrink)

We consider the following problem for various infinite-time machines. If a real is computable relative to a large set of oracles such as a set of full measure or just of positive measure, a comeager set, or a nonmeager Borel set, is it already computable? We show that the answer is independent of ZFC for ordinal Turing machines with and without ordinal parameters and give a positive answer for most other machines. For instance, we consider infinite-time Turing machines, unresetting and (...) resetting infinite-time register machines, and α-Turing machines for countable admissible ordinals α. (shrink)

Let us consider multimodal logics and. We assume that is characterised by a class of connected frames, and there exists an -frame with a so-called -starting point. Similarly, the logic is characterised by a class of connected frames, and there exists an -frame with a -starting point. Using isomorphic copies of the frames and, we construct a connected frame which characterises the fusion. The frame thus obtained has some useful properties. Among others, is countable if (...) both and are countable, and there is a special world of the frame such that any formula is valid in the frame if and only if it is valid at the point. We also describe a similar construction where we assume the existence of two classes consisting of rooted frames only. Using those classes and frames with so-called -roots, we construct a rooted frame adequate for the fusion of modal logics characterised by the classes under consideration. Both constructions can be used interchangeably. The selection of the construction depends on... (shrink)

The way research is, and should be, funded by the public sphere is the subject of renewed interest for sociology, economics, management sciences, and more recently, for the philosophy of science. In this contribution, I propose a qualitative, epistemological criticism of the funding by lottery model, which is advocated by a growing number of scholars as an alternative to peer-review. This lottery scheme draws on the lack of efficiency and of robustness of the peer-review based evaluation to argue that the (...) majority of public resources for basic science should be allocated randomly. I first differentiate between two distinct arguments used to defend this alternative funding scheme based on considerations about the logic of scientific research. To assess their epistemological limits, I then present and develop a conceptual frame, grounded on the notion of “system of practice”, which can be used to understand what precisely it means, for a research project, to be interesting or significant. I use this epistemological analysis to show that the lottery model is not theoretically optimal, since it underestimates the integration of all scientific projects in densely interconnected systems of conceptual, experimental, or technical practices which confer their proper interest to them. I also apply these arguments in order to criticize the classical peer-review process. I finally suggest, as a discussion, that some recently proposed models that bring to the fore a principle of decentralization of the evaluation and selection process may constitute a better alternative, if the practical conditions of their implementation are adequately settled. (shrink)

Epidemics, the medical historian Charles Rosenberg argued, typically have four Acts, as in a play. In Act I, which he termed ‘Progressive revelation’, ‘merchants’, ‘municipal authorities’ and ‘the complacency of ordinary men and women’, alike are reluctant to acknowledge an epidemic because of its threat to their ‘economic and institutional interests’ and to ‘their accustomed way of doing things’: gradually however, ‘inexorably accumulating deaths and sicknesses’ bring ‘ultimate, if unwilling, recognition’. In Act II, ‘Managing randomness’, ‘collective agreement’ is sought on (...) an ‘explanatory framework’ to manage the epidemic’s ‘dismaying arbitrariness’. Such frameworks, in previous centuries mainly religious, are now more ‘secular and mechanistic’, but again also moral and social: explanation for example of the ‘differential susceptibility of particular individuals’ is sought in terms of ‘risk-enhancing behaviour’ and ‘style of life’, but also of environmental and social factors, such as ‘residence and occupation’, providing ‘a vehicle for social criticism as well as a rationale for social control’. In Act III, ‘Negotiating public response’, pressure is generated for ‘decisive and visible community response’, often taking the form of ‘collective rites integrating cognitive and emotional elements’. Such rites, including not only ‘the imposition of a quarantine’ and ‘procedures to cleanse and disinfect’, but also religious, or now more often moral or social rituals, afford ‘the reassurance of familiar frames of explanation and logically consequent policies that provide both meaning and the promise of efficacy’. Finally, In Act IV, ‘Subsidence and retrospection’, ‘incidence of the disease gradually declines’, and questions are raised ‘for retrospective moral judgement’ about ‘what “lasting impact” particular incidents have had and what “lessons” have been learnt. Have the dead died in vain? Has a heedless society reverted to its accustomed ways of doing things as soon as denial became once more a …. (shrink)

For each k 1, let Γk be the countable universal homogeneous k-hypergraph. In this paper, we shall classify the closed permutation groups G such that Aut G Sym. In particular, we shall show that there exist only finitely many such groups G for each k 1. We shall also show that each of the associated reducts of Γk is homogeneous with respect to a finite relational language.

We show that for each computable ordinal $\alpha > 0$ it is possible to find in each Martin-Löf random ${\rm{\Delta }}_2^0 $ degree a sequence R of Cantor-Bendixson rank α, while ensuring that the sequences that inductively witness R’s rank are all Martin-Löf random with respect to a single countably supported and computable measure. This is a strengthening for random degrees of a recent result of Downey, Wu, and Yang, and can be understood as a randomized version (...) of it. (shrink)

We investigate the relation between intermediate predicate logics based on countable linear Kripke frames with constant domains and Gödel logics. We show that for any such Kripke frame there is a Gödel logic which coincides with the logic defined by this Kripke frame on constant domains and vice versa. This allows us to transfer several recent results on Gödel logics to logics based on countable linear Kripke frames with constant domains: We obtain a complete characterisation of (...) axiomatisability of logics based on countable linear Kripke frames with constant domains. Furthermore, we obtain that the total number of logics defined by countable linear Kripke frames on constant domains is countable. (shrink)

We prove that the conjugacy problem for the automorphism group of the random graph is Borel complete, and discuss the analogous problem for some other countably categorical structures.

ABSTRACT This article brings together Toni Morrison, Jane Jacobs, and Howard Hodgkin to consider the stress they each place on “contact,” albeit through their distinctive media of literature, urban planning, and oil paint, respectively. The article begins with Morrison's account of the stranger as not foreign or unusual but “random.” Morrison views literature as a means of bringing readers into controlled contact with others and especially with those others one might fear, avoid, or overlook. Morrison sets the stage for (...) thinking about contact in relation to the concept of randomness. Part 2 turns to Jacobs, who investigates city sidewalks as sites of interpersonal contact that affect the safety, health, solidarity, responsibility, and freedoms of those living in urban environments. Part 3 turns to Hodgkin and his obsession with the frame as an invitation to touch. The figures brought together in this article serve as touchstones for how to create, foster, or enlarge sites for contact. Together they might help us to expand the parameters of what contact might mean, how it might occur, and where it can happen. (shrink)

Given a countable graph, we say a set A of its vertices is universal if it contains every countable graph as an induced subgraph, and A is weakly universal if it contains every finite graph as an induced subgraph. We show that, for almost every graph on, (1) every set of positive upper density is universal, and (2) every set with divergent reciprocal sums is weakly universal. We show that the second result is sharp (i.e., a random (...) graph on will almost surely contain non‐universal sets with divergent reciprocal sums) and, more generally, that neither of these two results holds for a large class of partition regular families. (shrink)

Let V be a finite relational vocabulary in which no symbol has arity greater than 2. Let be countable V‐structure which is homogeneous, simple and 1‐based. The first main result says that if is, in addition, primitive, then it is strongly interpretable in a random structure. The second main result, which generalizes the first, implies (without the assumption on primitivity) that if is “coordinatized” by a set with SU‐rank 1 and there is no definable (without parameters) nontrivial equivalence (...) relation on M with only finite classes, then is strongly interpretable in a random structure. (shrink)

In the paper Randomizations of Scattered Sentences, Keisler showed that if Martin’s axiom for aleph one holds, then every scattered sentence has few separable randomizations, and asked whether the conclusion could be proved in ZFC alone. We show here that the answer is “yes”. It follows that the absolute Vaught conjecture holds if and only if every \-sentence with few separable randomizations has countably many countable models.

Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, each (...) non-inertial coordinate frame has its own vacuum state. In particular, there is a distinction between the “Minkowski vacuum” for a box at rest in an inertial frame and a “Rindler vacuum” for an accelerating box which has fixed spatial coordinates in an (accelerating) Rindler frame. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. The behavior of classical zero-point radiation in a noninertial frame is found by tensor transformations and still depends only upon the geodesic separations, now expressed in the non-inertial coordinates. It makes no difference whether a box of classical zero-point radiation is gradually or suddenly set into uniform acceleration; the radiation in the interior retains the same correlation function except for small end-point (Casimir) corrections. Thus in classical theory where zero-point radiation is defined in terms of geodesic separations, there is nothing physically comparable to the quantum distinction between the Minkowski and Rindler vacuum states. It is also noted that relativistic classical systems with internal potential energy must be spatially extended and can not be point systems. The classical analysis gives no grounds for the “heating effects of acceleration through the vacuum” which appear in the literature of quantum field theory. Thus this distinction provides (in principle) an experimental test to distinguish the two theories. (shrink)

The essays that constitute this dissertation explore three strategies for understanding the role of modality in philosophical accounts of propensities, randomness, and causation. In Chapter 1, I discuss how the following essays are to be considered as illuminating the prospects for these strategies, which I call reductive essentialism, subjectivism and pragmatism. The discussion is framed within a survey of approaches to modality more broadly construed. ;In Chapter 2, I argue that any broadly dispositional analysis of probability as a physical property (...) will either fail to give an adequate explication of probability, or else will fail to provide an explication that can be gainfully employed elsewhere . The diversity and number of arguments suggests that there is little prospect of any successful analysis along these lines. ;The concept of randomness has been unjustly neglected in recent philosophical literature, and when philosophers have thought about it, they have usually acquiesced in views about the concept that are fundamentally flawed. In Chapter 3 I try to redress this. After indicating the ways in which the existing accounts are flawed, I propose that randomness is to be understood as a special case of the epistemic concept of the unpredictability of a process. This proposal arguably captures the intuitive desiderata for the concept of randomness; at least it should suggest that the commonly accepted accounts cannot be the whole story and more philosophical attention needs to be paid. ;Russell famously argued that causation should be dispensed with. He gave two explicit arguments for this conclusion, which can be defused if we loosen the ties between causation and determinism. In Chapter 4, I define a concept of causation which meets Russell's conditions but does not reduce to triviality. Unfortunately, a further serious problem is implicit beneath the details of Russell's arguments, which I call the causal exclusion problem. Meeting this problem involves deploying a pragmatic account of the nature and function of modal concepts. Russell's scruples about causation can be accommodated, even as we partially legitimise the pervasiveness of causal explanations in folk and scientific practice. (shrink)

We tested the plausibility of a cognitive-emotional model to understand the effects of messages framed in terms of gain, non-loss, non-gain, and loss, and related to the health consequences of red/processed meat consumption. A total of 544 Italian participants reported their attitude toward reduced red/processed meat consumption and intention to eat red/processed meat. One week later, participants were randomly assigned to four different message conditions: gain messages focused on the positive health outcomes associated with low meat consumption; non-loss messages focused (...) on the avoided negative health outcomes associated with low meat consumption; non-gain messages focused on the missed positive health outcomes associated with high meat consumption; loss messages focused on the negative health outcomes associated with high meat consumption. After reading the messages, participants answered a series of questions regarding their emotional and cognitive reactions to the messages, their evaluation of the messages, and again their attitude and intention toward red/processed meat consumption. Comparing different multivariate linear models under the Bayesian approach, we selected the model with the highest plausibility conditioned to observed data. In this model, message-induced fear influenced systematic processing, which in turn positively influenced message evaluation and attitude, leading to reduced intention to consume red/processed meat. Vice versa, message-induced anger reduced systematic processing, which in turn negatively influenced message evaluation, and led to no effect on attitude and intention. The comparison among message conditions showed that gain and non-loss messages activated integrated emotional and cognitive processing of the health recommendation, while loss and non-gain messages mainly activated emotional shortcuts toward attitude and intention. Overall, these results advance our comprehension of the effects of message framing on receivers' attitudes and intentions. (shrink)

Prior research in judgment and decision making (JDM) has investigated the effect of problem framing on human preferences. Furthermore, research in JDM documented the absence of such reversal of preferences when making decisions from experience. However, little is known about the effect of context on preferences under the combined influence of problem framing and problem format. Also, little is known about how cognitive models would account for human choices in different problem frames and types (general/specific) in the experience format. One (...) of the primary objectives of this research is to investigate the presence of preference reversals under the influence of problem framing (gain/loss), problem format (experience/description), and problem type (general/specific). Another objective of this research is to develop cognitive models to account for human choices across different problem frames and types in the experience format. A total of 320 participants from India were randomly assigned to one of eight between-subjects conditions that differed in problem frame, format, and type. Results revealed preference reversals in the description condition; however, they were absent in the experience condition. Moreover, preference reversals were less pronounced in the general problem framing compared to the specific problem framing. Furthermore, specific problems influenced risk-seeking behavior among participants. We developed cognitive and heuristics models using instance-based learning theory and natural mean heuristic. Results reveal models’ dependency on recent and frequent observations during information sampling. These experience-based cognitive models could help build artificial intelligence models with fewer preference reversals. (shrink)

What is everything made of? -- Do I have free will? -- Can I know the world? -- Does God exist? -- How shall I live? -- What are my rights? -- How can I be saved? -- Appendix: Letters on philosophical topics.

The 1968 My Lai Massacre in South Vietnam and shocking events at Abu Graibh prison in Iraq in 2003 show that the behaviour of some in the American military has descended into barbarism. How strong is the military's commitment to avoiding misconduct and atrocity? This timely and compelling book asks critical questions and raises sobering issues the Australian Army can't ignore. Leading military personnel, aid workers, commentators and scholars discuss the Australian Army's commitment to behaving ethically and the challenges associated (...) with contemporary warfare. With chapters on social media and inciting violence, cyberweapons, and special operations and humanitarian deployments, 'Ethics Under Fire' offers a rare insight into the key issues facing the modern army, from technology and tactics to terrorism"--Back cover. (shrink)

The Kuznetsov-Index of a modal logic is the least cardinal such that any consistent formula has a Kripke-model of size if it has a Kripke-model at all. The Kuznetsov-Spectrum is the set of all Kuznetsov-Indices of modal logics with countably many operators. It has been shown by Thomason that there are tense logics with Kuznetsov-Index . Futhermore, Chagrov has constructed an extension of K4 with Kuznetsov-Index . We will show here that for each countable ordinal there are logics with (...) Kuznetsov-Index . Furthermore, we show that the Kuznetsov-Spectrum is identical to the spectrum of indices for -theories which is likewise defined. A particular consequence is the following. If inaccessible (weakly compact, measurable) cardinals exist, then the least inaccessible (weakly compact, measurable) cardinal is also a Kuznetsov-Index. (shrink)

John Frame gives us an accessible introduction to "triperspectival" study-where theological issues are fruitfully viewed from multiple perspectives without compromise to their unity and truth. Book jacket.

A History of Western Philosophy and Theology is the fruit of John Frame's forty-five years of teaching philosophical subjects. No other survey of the history of Western thought offers the same invigorating blend of expositional clarity, critical insight, and biblical wisdom. The supplemental study questions, bibliographies, links to audio lectures, quotes from influential thinkers, twenty appendices, and indexed glossary make this an excellent main textbook choice for seminary- and college-level courses and for personal study. Book jacket.

Charles Darwin found much in Australia to challenge and inform his thinking. This book explores the impact that Darwin’s short visit to Australia in 1836 had on the man himself and on the emerging nation. Now, more than 170 years later, Darwin continues to influence Australian attitudes to life and living.