Science is not a great way to make money, or these days, even a job. But there are great riches in it, and in this book too. Tim Bradford, 'New Scientist'.

A boolean algebra is shown to be completely representable if and only if it is atomic, whereas it is shown that neither the class of completely representable relation algebras nor the class of completely representable cylindric algebras of any fixed dimension (at least 3) are elementary.

We confirm a conjecture, about neat embeddings of cylindric algebras, made in 1969 by J. D. Monk, and a later conjecture by Maddux about relation algebras obtained from cylindric algebras. These results in algebraic logic have the following consequence for predicate logic: for every finite cardinal α ≥ 3 there is a logically valid sentence X, in a first-order language L with equality and exactly one nonlogical binary relation symbol E, such that X contains only 3 variables (each of which (...) may occur arbitrarily many times), X has a proof containing exactly α + 1 variables, but X has no proof containing only α variables. This solves a problem posed by Tarski and Givant in 1987. (shrink)

We consider the problem of finding and classifying representations in algebraic logic. This is approached by letting two players build a representation using a game. Homogeneous and universal representations are characterized according to the outcome of certain games. The Lyndon conditions defining representable relation algebras (for the finite case) and a similar schema for cylindric algebras are derived. Finite relation algebras with homogeneous representations are characterized by first order formulas. Equivalence games are defined, and are used to establish whether an (...) algebra is ω-categorical. We have a simple proof that the perfect extension of a representable relation algebra is completely representable. An important open problem from algebraic logic is addressed by devising another two-player game, and using it to derive equational axiomatisations for the classes of all representable relation algebras and representable cylindric algebras. Other instances of this approach are looked at, and include the step by step method. (shrink)

For every finite n ≥ 4 there is a logically valid sentence φ n with the following properties: φ n contains only 3 variables (each of which occurs many times); φ n contains exactly one nonlogical binary relation symbol (no function symbols, no constants, and no equality symbol): φ n has a proof in first-order logic with equality that contains exactly n variables, but no proof containing only n - 1 variables. This result was first proved using the machinery of (...) algebraic logic developed in several research monographs and papers. Here we replicate the result and its proof entirely within the realm of (elementary) first-order binary predicate logic with equality. We need the usual syntax, axioms, and rules of inference to show that φ n has a proof with only n variables. To show that φ n has no proof with only n - 1 variables we use alternative semantics in place of the usual, standard, set-theoretical semantics of first-order logic. (shrink)

We study relation algebras with n-dimensional relational bases in the sense of Maddux. Fix n with 3nω. Write Bn for the class of non-associative algebras with an n-dimensional relational basis, and RAn for the variety generated by Bn. We define a notion of relativised representation for algebras in RAn, and use it to give an explicit equational axiomatisation of RAn, and to reprove Maddux's result that RAn is canonical. We show that the algebras in Bn are precisely those that have (...) a complete relativised representation of this type. Then we prove that whenever 4nshrink)

We prove, for each 4⩽ n ω , that S Ra CA n+1 cannot be defined, using only finitely many first-order axioms, relative to S Ra CA n . The construction also shows that for 5⩽n S Ra CA n is not finitely axiomatisable over RA n , and that for 3⩽m S Nr m CA n+1 is not finitely axiomatisable over S Nr m CA n . In consequence, for a certain standard n -variable first-order proof system ⊢ m (...) , n of m -variable formulas, there is no finite set of m -variable schemata whose m -variable instances, when added to ⊢ m , n as axioms, yield ⊢ m , n +1. (shrink)

Let S be a signature of operations and relations definable in relation algebra, let R be the class of all S-structures isomorphic to concrete algebras of binary relations with concrete interpretations for symbols in S, and let F be the class of S-structures isomorphic to concrete algebras of binary relations over a finite base. To prove that membership of R or F for finite S-structures is undecidable, we reduce from a known undecidable problem—here we use the tiling problem, the partial (...) group embedding problem and the partial group finite embedding problem to prove undecidability of finite membership of R or F for various signatures S. It follows that the equational theory of R is undecidable whenever S includes the boolean operators and composition. We give an exposition of the reduction from the tiling problem and the reduction from the group embedding problem, and summarize what we know about the undecidability of finite membership of R and of F for different signatures S. (shrink)

We characterise the class S Ra CA n of subalgebras of relation algebra reducts of n -dimensional cylindric algebras by the notion of a ‘hyperbasis’, analogous to the cylindric basis of Maddux, and by representations. We outline a game–theoretic approximation to the existence of a representation, and how to use it to obtain a recursive axiomatisation of S Ra CA n.

The history of science and the philosophy of science have a long and tangled relationship. On the one hand, philosophical reflection on science can be guided, shaped, and challenged by historical scholarship—a process begun by Thomas Kuhn and continued by successive generations of ‘post-positivist’ historians and philosophers of science. On the other hand, the activity of writing the history of science raises methodological questions concerning, for instance, progress in science, realism and antirealism, and the semantics of scientific theories, questions which (...) are the subject of continued debate in philosophy. Clearly the history and the philosophy of science will continue to challenge each other's research agendas and guiding assumptions. (shrink)

A cylindric algebra atom structure is said to be strongly representable if all atomic cylindric algebras with that atom structure are representable. This is equivalent to saying that the full complex algebra of the atom structure is a representable cylindric algebra. We show that for any finite n >3, the class of all strongly representable n-dimensional cylindric algebra atom structures is not closed under ultraproducts and is therefore not elementary. Our proof is based on the following construction. From an arbitrary (...) undirected, loop-free graph Γ, we construct an n-dimensional atom structure E(Γ), and prove, for infinite Γ, that E(Γ) is a strongly representable cylindric algebra atom structure if and only if the chromatic number of Γ is infinite. A construction of Erdős shows that there are graphs (k < ω)with infinite chromatic number, but having a non-principal ultraproduct $\prod _D\Gamma _k $ whose chromatic number is just two. It follows that $E(\Gamma _k )$ is strongly representable (each k < ω) but $\Pi _D E(\Gamma _k)$ is not. (shrink)

For as long as history has been with us, religion has been a feature of human life. There is no known culture for which we have an ethnographic or an archaeological record that does not have some form of religion. Even in the secular societies that have become more common in the past few centuries, there are people who consider themselves religious and aspire to practise the rituals of their religion. These religions vary in form, style and size from small (...) cults numbering a few hundred people centred around a charismatic leader to worldwide organizations numbering tens, or even hundreds, of millions of adherents with representations in every country. Some, like Buddhism, take an individualistic stance (your salvation is entirely in your own hands), some like the older Abrahamic religions view salvation as more of a collective activity through the performance of appropriate rituals, and a few (Judaism is one) have no formal concept of an afterlife. Some like Christianity and Islam believe in a single all- powerful God. (shrink)

We outline a simple approach to axiomatising the class of representable relation algebras, using games. We discuss generalisations of the method to cylindric algebras, homogeneous and complete representations, and atom structures of relation algebras.

It is known that for all finite n ≥ 5, there are relation algebras with n-dimensional relational bases but no weak representations. We prove that conversely, there are finite weakly representable relation algebras with no n-dimensional relational bases. In symbols: neither of the classes RA n and wRRA contains the other.

Formalised knowledge systems, including universities and research institutes, are important for contemporary societies. They are, however, also arguably failing humanity when their impact is measured against the level of progress being made in stimulating the societal changes needed to address challenges like climate change. In this research we used a novel futures-oriented and participatory approach that asked what future envisioned knowledge systems might need to look like and how we might get there. Findings suggest that envisioned future systems will need (...) to be much more collaborative, open, diverse, egalitarian, and able to work with values and systemic issues. They will also need to go beyond producing knowledge about our world to generating wisdom about how to act within it. To get to envisioned systems we will need to rapidly scale methodological innovations, connect innovators, and creatively accelerate learning about working with intractable challenges. We will also need to create new funding schemes, a global knowledge commons, and challenge deeply held assumptions. To genuinely be a creative force in supporting longevity of human and non-human life on our planet, the shift in knowledge systems will probably need to be at the scale of the enlightenment and speed of the scientific and technological revolution accompanying the second World War. This will require bold and strategic action from governments, scientists, civic society and sustained transformational intent. (shrink)

Reply to Ian Johnston Content Type Journal Article Pages 1-2 DOI 10.1007/s11712-012-9274-1 Authors Dan Robins, School of Arts and Humanities, The Richard Stockton College of New Jersey, 101 Vera King Farris Drive, Galloway, NJ 08205, USA Journal Dao Online ISSN 1569-7274 Print ISSN 1540-3009.

There are two issues I want to very briefly raise in response to Robin McKenna’s paper, “Epistemic Contextualism, Epistemic Relativism, and Disagreement.” First, I want to question whether or not the disagreement problem faced by indexical contextualism is truly a problem. Secondly, I want to consider whether or not McKenna’s solution is really in keeping with indexical contextualism.

Humans are causing global climate change (GCC), and such climate change causes harms. Robin Attfield explained how individuals should be understood to be culpable for these harms. In this paper, I use a critical analysis of Attfield’s explanatory framework to explore further difficulties in accounting for corporate responsibility for these harms. I begin by arguing that there are some problems with his framework as it is applied to individuals that emit greenhouse gases (GHGs). I then show that it will be (...) very difficult to extend this framework to corporations. This is not a criticism of Attfield’s work (as he does not discuss corporate responsibility for those harms associated with GCC), but it will serve to show the difficulty in philosophically explaining corporations’ moral culpability when it comes to these harms. In fact, one positive conclusion of this paper is that it highlights a new area of concern that has been ignored in discussions of corporate responsibilities—that of mediated responsibilities—which is how Attfield understands our responsibilities regarding GCC. The discussion of this concern will draw attention to another positive conclusion of this paper: the harms associated with CO2 are very unlike the harms associated with other airborne-emitted substances, which will indicate that we will need new ways of understanding how individuals and corporations are philosophically responsible for these harms. The final positive conclusion of this paper will be a discussion of what the constraints should be on new approaches to explaining our culpability. (shrink)

I offer a working analysis of the concept of 'epistemic corruption', then explain how it can help us to understand the relations between epistemic vices and social oppression, and use this to motivate a style of vice epistemology, inspired by the work of Robin Dillon, that I call critical character epistemology.

I discuss the relationship of epistemic corruption to non-ideal epistemology. A symposium on Robin McKenna's book "Non-Ideal Epistemology".

It is natural to think of remembering in terms of causation: I can recall a recent dinner with a friend because I experienced that dinner. Some fifty years ago, Martin and Deutscher (1966) turned this basic thought into a full-fledged theory of memory, a theory that came to dominate the landscape in the philosophy of memory. Remembering, Martin and Deutscher argue, requires the existence of a specific sort of causal connection between the rememberer's original experience of an event and his (...) later representation of that event: a causal connection sustained by a memory trace. In recent years, it has become apparent that this reference to memory traces may be out of step with memory science. Contemporary proponents of the causal theory are thus confronted with the question: is it possible to develop an empirically adequate version of the theory, or is it time to move beyond it? This chapter traces the recent history of the causal theory, showing how increased awareness of the theory’s problems has led to the development of modified version of the causal theory and ultimately to the emergence of postcausal theories. (shrink)

The study of the neural basis of memory has advanced over the past decade. A key contributor to this memory “renaissance” has been new tools. On its face, this matches what might be described as a neuroscientific revolution stemming from the development of tools, where this revolution is largely independent of theory. In this paper, we challenge this tool revolution account by focusing on a problem that arises in applying it to this “renaissance”: it is centered around memory, but the (...) tools were not developed for solving problems in memory science. To resolve this problem, we introduce an account that distinguishes tool development and tool uptake, and we argue that while theoretical considerations may not inform development, they do inform uptake. Acknowledging the distance between these stages of tool use draws our attention to the questions of why and how tool uptake occurs in the domains that it does. (shrink)

This article presents a theoretical model of the self processes involved in autobiographical memories and proposes competing hypotheses for the role of visual perspective in autobiographical memory retrieval. Autobiographical memories can be retrieved from either the 1st person perspective, in which individuals see the event through their own eyes, or from the 3rd person perspective, in which individuals see themselves and the event from the perspective of an external observer. A growing body of research suggests that the visual perspective from (...) which a memory is retrieved has important implications for a person’s thoughts, feelings, and goals, and is integrally related to a host of self-evaluative processes. We review the relevant research literature, present our theoretical model, and outline directions for future research. (shrink)

In days past, epistemologists expended a good deal of effort trying to analyze the basing relation—the relation between a belief and its basis. No satisfying account was offered, and the project was largely abandoned. Younger epistemologists, however, have begun to yearn for an adequate theory of basing. I aim to deliver one. After establishing some data and arguing that traditional accounts of basing are unsatisfying, I introduce a novel theory of the basing relation: the dispositional theory. It begins with the (...) pedestrian observation that beliefs stand or fall with their bases. The theory I offer is an elucidation and refinement of this thought. (shrink)

Introduction -- Evidence from children -- Evidence form infants and non-human animals -- Evidence from neuroimaging and neuropsychology -- Evidence from adults -- The cognitive basis of mindreading -- Elaborating and applying the theory.

Classical logic has been attacked by adherents of rival, anti-realist logical systems: Ian Rumfitt comes to its defence. He considers the nature of logic, and how to arbitrate between different logics. He argues that classical logic may dispense with the principle of bivalence, and may thus be liberated from the dead hand of classical semantics.

The pressures that led to the evolution of episodic memory have recently seen much discussion, but a fully satisfactory account of them is still lacking. We seek to make progress in this debate by taking a step backward, identifying four possible ways that episodic memory could evolve in relation to simulationist future planning—a similar and seemingly related ability. After distinguishing each of these possibilities, the paper critically discusses existing accounts of the evolution of episodic memory. It then presents a novel (...) argument in favor of the view that episodic memory is a by-product of the evolution of simulationist future planning. The paper ends by showing that this position allows for the maintenance of the traditional view that episodic memory operates on stored memory traces, as well as explaining a number of key features of episodic memory: its being subject to frequent and systematic errors, its neural co-location with the capacity for simulationist future planning, and the potential existence of non-human episodic memory. (shrink)

The Archival and Constructive views of memory offer contrasting characterizations of remembering and its relation to memory errors. I evaluate the descriptive adequacy of each by offering a close analysis of one of the most prominent experimental techniques by which memory errors are elicited—the Deese-Roediger-McDermott paradigm. Explaining the DRM effect requires appreciating it as a distinct form of memory error, which I refer to as misremembering. Misremembering is a memory error that relies on successful retention of the targeted event. It (...) differs from both successful remembering and from confabulation errors, where the representation produced is wholly inaccurate. As I show, neither the Archival nor the Constructive View can account for the DRM effect because they are insensitive to misremembering’s unique explanatory demands. Fortunately, the explanatory limitations of the Archival and Constructive Views are complementary. This suggests a way.. (shrink)

The more interest philosophers take in memory, the less agreement there is that memory exists—or more precisely, that remembering is a distinct psychological kind or mental state. Concerns about memory’s distinctiveness are triggered by observations of its similarity to imagination. The ensuing debate is cast as one between discontinuism and continuism. The landscape of debate is set such that any extensive engagement with empirical research into episodic memory places one on the side of continuism. Discontinuists concerns are portrayed as almost (...) exclusively conceptual and a priori. As philosophers of memory become increasingly interested in memory science, this pushes continuism into an apparent lead. The aim of this paper is to challenge this characterization of the continuism debate—namely, that a naturalistic approach to the philosophy of mind and memory favors continuism. My response has two components. First, I argue for weakening the alignment between naturalism and continuism. Second, I defend a naturalistically oriented, empirically-informed discontinuism between memory and imagination. I do so by introducing seeming to remember, which I argue is distinct from other mental attitudes—most importantly, from imagining. (shrink)

According to the Causal Theory of Memory, remembering a particular past event requires a causal connection between that event and its subsequent representation in memory, specifically, a connection sustained by a memory trace. The CTM is the default view of memory in contemporary philosophy, but debates persist over what the involved memory traces must be like. Martin and Deutscher argued that the CTM required memory traces to be structural analogues of past events. Bernecker and Michaelian, contemporary CTM proponents, reject structural (...) analogues in favor of memory traces as distributed patterns of event features. The proposals are understood as distinct accounts of how memory traces represent past events. But there are two distinct questions one could ask about a trace’s representational features. One might ask how memory traces, qua mental representations, have their semantic properties. Or, what makes memory traces, qua mental representations of memories, distinct from other mental representations. Proponents of the CTM, both past and present, have failed to keep these two questions distinct. The result is a serious but unnoticed problem for the CTM in its current form. Distributed memory traces are incompatible with the CTM. Such traces do not provide a way to track the causal history of individual memories, as the CTM requires. If memory traces are distributed patterns of event features, as Bernecker and Michaelian each claim, then the CTM cannot be right. (shrink)

Confabulation is a symptom central to many psychiatric diagnoses and can be severely debilitating to those who exhibit the symptom. Theorists, scientists, and clinicians have an understandable interest in the nature of confabulation—pursuing ways to define, identify, treat, and perhaps even prevent this memory disorder. Appeals to confabulation as a clinical symptom rely on an account of memory’s function from which cases like the above can be contrasted. Accounting for confabulation is thus an important desideratum for any candidate theory of (...) memory. Many contemporary memory theorists now endorse Constructivism, where memory is understood as a capacity for constructing plausible representations of past events. Constructivism’s aim is to account for and normalize the prevalence of memory errors in everyday life. Errors are plausible constructions that, on a particular occasion have led to error. They are not, however, evidence of malfunction in the memory system. While Constructivism offers an uplifting repackaging of the memory errors to which we are all susceptible, it has troubling implications for appeals to confabulation in psychiatric diagnosis. By accommodating memory errors within our understanding of memory’s function, Constructivism runs the risk of being unable to explain how confabulation errors are evidence of malfunction. After reviewing the literature on confabulation and Constructivism, respectively, I identify the tension between them and explore how different versions of Constructivism may respond. The paper concludes with a proposal for distinguishing between kinds of false memory—specifically, between misremembering and confabulation—that may provide a route to their reconciliation. (shrink)