In lieu of an abstract, here is a brief excerpt of the content:Titles, Labels, and Names:A House of MirrorsGreg Petersen (bio)An EducationAmong the harshest critiques ever received during my doctoral coursework came from a professor who was noticeably perturbed that I had researched and written a paper on an artwork without considering the title in the interpretation and analysis of the work. The professor insisted that the title is necessary to understand the piece. As a diligent student, the lesson (...) was learned, and the following semester I wrote a different paper for a different professor including the title as part of the interpretation and analysis. The professor's response asserted that the sections of the paper discussing the title should be deleted to improve the paper because a title is a name only—a linguistic referent to speak and write about the work that has no other relationship to the work. The discussions that followed with the two professors evolved into a permanent interest in the relationship between appellations and the works they represent. The debate of whether titles are or are not important is not a two-sided argument but rather a maze. This article is not a specialized theoretical argument but an explication of this maze of disjointed relationships among images, their appellations, and the theories espoused by various artists, art critics, art historians, and philosophers. Nevertheless, the clearest exits from the maze are found by treating the appellations as literature and applying literary theory to them.Between Text and ImageMuch of the world we live in is visual and linguistic in nature: visual to the extent that seeing is associated with knowing, and linguistic to the extent that we can communicate through the use of words and letters. For thousands [End Page 29] of years there has been a close relationship between images and language. Both are commonly represented through the use of pigments on a two-dimensional surface. While we know of no literary relationships in early paintings, it is extremely rare today to find paintings without a literary appellation attached. Today we study paintings through words, but only on the most elementary levels do we study words through paintings. It appears that literate cultures give dominance to textual symbols over those in paintings, while illiterate cultures reverse these relationships. The problem is that words have culturally agreed upon meanings, often more so than visual images. We read and listen and then write and speak about those things we have read and heard. Historically, it may be that the relationship between language and images has reversed itself, and perhaps even reverses itself in our own educational process as we begin teaching children letters and words through the use of pictures. After all, which came first: image or language?There has been little written on the use of word associations with iconographic images during the Middle Ages. Nevertheless, it is clear that identification characteristics other than linguistic ones existed. Hazard Adams is one of the few to raise this issue in his essay on titles: "Before I turn to literary titles it might be well to ask whether... I am correct in assuming that there has never been a nonverbal title of a literary work or of anything else for that matter, the word-objects relation of a title being irreversible. There are certainly nonverbal labels like coats of arms and crowns that imply title in a related sense."1 It may be true that titles are typically thought of as word associations identifying objects, but it may also be possible that medieval imagery was at least as communicatively accurate as our present textual system. For example, a man with arrows fixed in his flesh would still be recognized by a medieval illiterate as St. Sebastian, yet most of the depictions of this Catholic saint are simply titled St. Sebastian. Would hanging the text St. Sebastian next to these depictions have created more meaning or a deeper understanding to a medieval Catholic? Often sacred personages and other important visual images have their own identifying characteristics that make a correlative text unnecessary. These identifying characteristics, to those familiar with them, remain very effective nonverbal symbols that conjure the stories they represent.Furthermore, during the medieval... (shrink)

The growing literature on philosophical thought experiments has so far focused almost exclusively on the role of thought experiments in confirming or refuting philosophical hypotheses or theories. In this paper we draw attention to an additional and largely ignored role that thought experiments frequently play in our philosophical practice: some thought experiments do not merely serve as means for testing various philosophical hypotheses or theories, but also serve as facilitators for conceiving and articulating new ones. As we will put it, (...) they serve as ‘heuristics for theory discovery’. Our purpose in the paper is two-fold: to make a case that this additional role of thought experiments deserves the attention of philosophers interested in the methodology of philosophy; to sketch a tentative taxonomy of a number of distinct ways in which philosophical thought experiments can aid theory discovery, which can guide future research on this role of thought experiments. (shrink)

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both (...) students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading. (shrink)

We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalisation of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points. Different logics are modeled by varying the kinds of collections used: they can be sets, multisets, lists or trees. We show that collection frames on trees are sound and complete for (...) the basic positive distributive substructural logic $\mathsf {B}^+$, that collection frames on multisets are sound and complete for $\mathsf {RW}^+$ (the relevant logic $\mathsf {R}^+$, without contraction, or equivalently, positive multiplicative and additive linear logic with distribution for the additive connectives), and that collection frames on sets are sound for the positive relevant logic $\mathsf {R}^+$. The completeness of set frames for $\mathsf {R}^+$ is, currently, an open question. (shrink)

Beall and Restall’s Logical Pluralism (2006) characterises pluralism about logical consequence in terms of the different ways cases can be selected in the analysis of logical consequence as preservation of truth over a class of cases. This is not the only way to understand or to motivate pluralism about logical consequence. Here, I will examine pluralism about logical consequence in terms of different standards of proof. We will focus on sequent derivations for classical logic, imposing two different restrictions on classical (...) derivations to produce derivations for intuitionistic logic and for dual intuitionistic logic. The result is another way to understand the manner in which we can have different consequence relations in the same language. Furthermore, the proof-theoretic perspective gives us a different explanation of how the one concept of negation can have three different truth conditions, those in classical, intuitionistic and dual-intuitionistic models. (shrink)

The two-dimensional modal logic of Davies and Humberstone [3] is an important aid to our understanding the relationship between actuality, necessity and a priori knowability. I show how a cut-free hypersequent calculus for 2D modal logic not only captures the logic precisely, but may be used to address issues in the epistemology and metaphysics of our modal concepts. I will explain how the use of our concepts motivates the inference rules of the sequent calculus, and then show that the completeness (...) of the calculus for Davies–Humberstone models explains why those concepts have the structure described by those models. The result is yet another application of the completeness theorem. (shrink)

In this paper I introduce a sequent system for the propositional modal logic S5. Derivations of valid sequents in the system are shown to correspond to proofs in a novel natural deduction system of circuit proofs (reminiscient of proofnets in linear logic, or multiple-conclusion calculi for classical logic). -/- The sequent derivations and proofnets are both simple extensions of sequents and proofnets for classical propositional logic, in which the new machinery—to take account of the modal vocabulary—is directly motivated in terms (...) of the simple, universal Kripke semantics for S5. The sequent system is cut-free and the circuit proofs are normalising. (shrink)

I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.

Different natural deduction proof systems for intuitionistic and classical logic —and related logical systems—differ in fundamental properties while sharing significant family resemblances. These differences become quite stark when it comes to the structural rules of contraction and weakening. In this paper, I show how Gentzen and Jaśkowski’s natural deduction systems differ in fine structure. I also motivate directed proof nets as another natural deduction system which shares some of the design features of Genzen and Jaśkowski’s systems, but which differs again (...) in its treatment of the structural rules, and has a range of virtues absent from traditional natural deduction systems. (shrink)

An text for introducing both formal and philosophical logic.

Once the Kripke semantics for normal modal logics were introduced, a whole family of modal logics other than the Lewis systems S1 to S5 were discovered. These logics were obtained by changing the semantics in natural ways. The same can be said of the Kripke-style semantics for relevant logics: a whole range of logics other than the standard systems R, E and T were unearthed once a semantics was given (cf. Priest and Sylvan [6], Restall [7], and Routley et al. (...) [8]). In a similar way, weakening the structural rules of the Gentzen formulation of classical logic gives rise to other ‘substructural’ logics such as linear logic (as in Girard [4]). This process of ‘strategic weakening’ is becoming popular today, with the discovery of applications of these logics to areas such as linguistics and the theory of computation (cf. van Benthem [1]). Until now no-one has (to my knowledge) examined what the process of weakening does to the Kripke-style semantics of intuitionistic logic. This paper remedies the deficiency, introducing the family of subintuitionistic logics. These systems have some appealing features. Unlike other substructural logics such as linear logic (which lack distribution of extensional disjunction over conjunction) they have a very natural Kripke-style worlds semantics. Also, the difficulties with regard to modelling quantification in these systems may be able to shed some light on the difficulties in naturally modelling quantification in relevant logics, as it must be admitted that the semantics currently available for quantified relevant logics are rather baroque (cf. Fine [3]). But most importantly, delving in the undergrowth of logics such as intuitionistic logic gives us a ‘feel’ for how such systems are put together, and what job is being done by each aspect of the modelling conditions in.. (shrink)

Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives. It is a mildly bilateralist, single-conclusion natural deduction proof system in which the connective rules are unmodi_ed from the usual Prawitz introduction and elimination rules — the extension is purely structural. This framework is general: it can be used for (1) classical logic, (2) relevant logic without distribution, (3) affine logic, and (4) linear logic, keeping the connective rules fixed, and varying purely (...) structural rules. The key result of this paper is that the two principles that introduce kinds of irrelevance to natural deduction proofs: (a) the rule of explosion (from a contradiction, anything follows); and (b) the structural rule of vacuous discharge; are shown to be two sides of a single coin, in the same way that they correspond to the structural rule of weakening in the sequent calculus. The paper also includes a discussion of assumption classes, and how they can play a role in treating additive connectives in substructural natural deduction. (shrink)

Propositional logic -- Propositions and arguments -- Connectives and argument forms -- Truth tables -- Trees -- Vagueness and bivalence -- Conditionality -- Natural deduction -- Predicate logic -- Predicates, names, and quantifiers -- Models for predicate logic -- Trees for predicate logic -- Identity and functions -- Definite descriptions -- Some things do not exist -- What is a predicate? -- What is logic?

This unique collection of essays not only explores the complexity of ancient Greek thought, but also reveals Popper's engagement with Presocratic philosophy and the enlightenment he experienced in reading Parmenides. It includes writings on Greek science, philosophy and history, and demonstrates Popper's lifelong fascination and admiration of the Presocratic philosophers, in particular Parmenides, Xenophanes and Heraclitus.

In this paper we introduce a new natural deduction system for the logic of lattices, and a number of extensions of lattice logic with different negation connectives. We provide the class of natural deduction proofs with both a standard inductive definition and a global graph-theoretical criterion for correctness, and we show how normalisation in this system corresponds to cut elimination in the sequent calculus for lattice logic. This natural deduction system is inspired both by Shoesmith and Smiley's multiple conclusion systems (...) for classical logic and Girard's proofnets for linear logic. (shrink)

This paper concerns a key point of decision in Donald Davidson's early work in philosophy of language — a fateful decision that set him and the discourse in the area on the path of truth-theoretic semantics. The decision of moment is the one Davidson makes when, in the face of a certain barrier, he gives up on the idea of constructing an explicit meaning theory that would parallel Tarski's recursive way with truth theory. For Davidson there was little choice: he (...) tells us he does not see how to deal with the difficulty except in the radical way he proposes. But there is a way to give such a meaning theory — a meaning theory proper which, using classical logic only, meets a meaning-theoretic analogue of Convention T, satisfies Davidson’s three key desiderata for a theory of meaning, reflects linguistic competence, and avoids quantifying over meanings. The meaning theory sketched here uses Tarskian strategies, as Davidson proposed, but differs from Davidson's approach in not going by way of a truth theory for the target language. (shrink)

Formal systems seem to come in two general kinds: useful and useless. This is painting things starkly, but the point is important. Formal structures can either be used in interesting and important ways, or they can languish unused and irrelevant. Lewis' modal logics are good examples. The systems S4 and S5 are useful in many different ways. They map out structures that are relevant to a number of different applications. S1, S2 and S3 however, are not so lucky. They are (...) little studied, and used even less. It has become dear that the structures described by S4 and S5 are important in different ways, while the structures described by S1 to S3 are not so important. In this paper, we will see another formal system with a number of different uses. We will examine a substructural logic which is important in a number of different ways. The logic of Peirce monoids, inspired by the logic of relations, is useful in the independent areas of linguistic types and information flow.In what follows I will describe the logic of Peirce monoids in its various guises, sketch out its main properties, and indicate why it is important. As proofs of theorems are readily available elsewhere in the literature, I simply sketch the relevant proofs here, and point the interested reader to where complete proofs can be found. (shrink)

Alfred Tarski (1944) wrote that "the condition of the 'essential richness' of the metalanguage proves to be, not only necessary, but also sufficient for the construction of a satisfactory definition of truth." But it has remained unclear what Tarski meant by an 'essentially richer' metalanguage. Moreover, DeVidi and Solomon (1999) have argued in this Journal that there is nothing that Tarski could have meant by that phrase which would make his pronouncement true. We develop an answer to the historical question (...) of what Tarski meant by 'essentially richer' and pinpoint the general result that stands behind his essential richness claim. In defense of Tarski, we then show that each of the several arguments of DeVidi and Solomon are either moot or mistaken. One of the fruits of our investigation is the reclamation of what Tarski took to be his central result on truth. This is a reclamation since: (i) if one does not understand 'essential richness', one does not know what that result is, and (ii) we must unearth a heretofore unrecognized change that occurs in Tarski's view - an alteration of his main thesis in light of a failing he discovered in it. (shrink)

Here is a puzzle, which I learned from Terence Parsons in his “True Contradictions” [8]. First Degree Entailment is a logic which allows for truth value gaps as well as truth value gluts. If you are agnostic between assigning paradoxical sentences gaps and gluts, then this looks no different, in effect, from assigning them a gap value? After all, on both views you end up with a theory that doesn’t commit you to the paradoxical sentence or its negation. How is (...) the fde theory any different from the theory with gaps alone? In this paper, I will present a clear answer to this puzzle – an answer that explains how being agnostic between gaps and gluts is a genuinely different position than admitting gaps alone, by using the formal notion of a bi-theory, and showing that while such positions might agree on what is to be accepted, they differ on what is to be rejected. (shrink)

According to one tradition in realist philosophy, 'truthmaking' amounts to necessitation. That is, an object x is a truthmaker for the claim A if x exists, and the existence of x necessitates the truth of A. I argued in my paper "Truthmakers, Entailment and Necessity" [14], that if we wish to use this account of truthmaking, we ought understand the entailment connective "=>" in such a claim as a relevant entailment, in the tradition of Anderson and Belnap and their co-workers (...) [1, 2, 8, 11]. Furthermore, I proposed a number of theses about truthmaking as necessitation. The most controversial of these is the disjunction thesis: x makes a disjunction A v B true if and only if it makes one of the disjuncts (A or B) true. That paper left one important task unfinished. I did not explain how the theses about truthmaking could be true together. In this paper I give a consistency proof, by providing a model for the theses of truthmaking in my earlier paper. This result does two things. First, it shows that the theses of truthmaking are jointly consistent. Second, it provides an independently philosophically motivated formal model for relevant logics in the 'possible worlds' tradition of Routley and Meyer [8, 16, 17]. (shrink)

The paradoxes of self reference have to be dealt with by anyone seeking to give a satisfactory account of the logic of truth, of properties, and even of sets of numbers. Unfortunately, there is no widespread agreement as to how to deal with these paradoxes. Some approaches block the paradoxical inferences by rejecting as invalid a move that classical logic counts as valid. In the recent literature, this deviant logic analysis of the paradoxes has been called into question.This disagreement motivates (...) a re-examination of the philosophy of formal logic and the status of logical truths and rules. In this paper I do some of this work, and I show that this gives us the means to defend the deviant approaches against such criticisms. As a result I hope to show that these analyses of the paradoxes are worthy of more serious consideration than they have so far received. (shrink)

Stephen Neale presents, in Facing Facts (Oxford: Clarendon Press, 2001), one convenient package containing his reasoned complaints against theories of facts and non-extensional connectives. The slingshot is a powerful argument (or better, it is a powerful family of arguments) which constrains theories of facts, propositions and non-extensional connectives by showing that some of these theories are rendered trivial. This book is the best place to find the state of the art on the slingshot and its implications for logic, language and (...) metaphysics. It provides a useful starting point for anyone who has wondered what all of the fuss about the slingshot amounts to. Neale shows that the fuss does amount to something, and that theories of facts must “face facts” and present an adequate response to the slingshot. However, Neale’s evaluation of the state of play for theories of facts is too pessimistic. As the book draws near to a close, Neale writes: As I have stressed, Russell’s Theory of Facts, according to which facts have properties as components, is safe. It is certainly tempting to draw the moral that if one wants non-collapsing facts one needs properties as components of facts. I have not attempted to prove this here, but I suspect it will be proved in due course. (page 210) Neale concludes that while theories which take facts to be structured entities are safe from slingshot arguments, and he suspects that this is the only kind of fact theory safe from slingshot-style collapse. If this were the case, then theories such as situation theories or accounts of truthmakers may well be threatened. However, Neale’s suspicion is ill-founded, as I shall soon show. Not only do Russellian theories of facts survive the slingshot unscathed, but so can theories of facts which take them to be unstructured entities. Furthermore, the way that this may be not only argued for, but proved can provide a new weapon in the armoury of the theorist investigating fact theories. (shrink)

This paper proposes a retributive argument against punishment, where punishment is understood as going beyond condemnation or censure, and requiring hard treatment. The argument sets out to show that punishment cannot be justified. The argument does not target any particular attempts to justify punishment, retributive or otherwise. Clearly, however, if it succeeds, all such attempts fail. No argument for punishment is immune from the argument against punishment proposed here. The argument does not purport to be an argument only against retributive (...) justifications of punishment, and so leave open the possibility of a sound non-retributive justification of punishment. Punishment cannot be justified, the paper argues, because it cannot be demonstrated that any punishment, no matter how minimal, is not a disproportionate retributive response to criminal wrongdoing. If we are to hold onto proportionality—that is, proportionality as setting a limit to morally permissible punishment—then punishment is morally impermissible. The argument is a retributive argument against punishment insofar as a just retributive response to wrongdoing must be proportionate to the wrongdoing. The argument, that is, is concerned with proportionality as a retributive requirement. The argument against punishment is set out on the basis of a familiar version of the ‘anchoring problem’, according to which it is the problem of determining the most severe punishment to anchor or ground the punishment scale. To meet the possible criticism that we have chosen a version of the anchoring problem particularly favourable to our argument, various alternative statements of the anchoring problem are considered. Considering such statements also provides a more rounded view of the anchoring problem. One such alternative holds that the punishment scale must be anchored not just in the most severe punishment, but in the least severe punishment as well. Other alternatives hold that it is necessary and sufficient to anchor the punishment scale in any two punishments, neither of which needs to be the most or least severe punishment. A further suggestion is that one anchoring point anywhere along the punishment scale is sufficient, because it is possible to ‘project’ from such a point, so as to determine the correlative punishments for all other crimes, and so derive a complete punishment scale. Finally, the suggestion is considered that one can approach the issue of a punishment scale ‘holistically’, denying any distinction between anchoring and derived (or ‘projected’) punishments. (shrink)

In this short paper, I compare and contrast the kind of symmetric treatment of negation favoured in different ways by Huw Price (in “Why ‘Not’?”) and by me (in “Multiple Conclusions”) with Robert Brandom’s analysis of scorekeeping in terms of commitment, entitlement and incompatibility. Both kinds of account are what Brandom calls a normative pragmatics. They are both semantic anti-realist accounts of meaning in the significance of vocabulary is explained in terms of our rule-governed (normative) practice (pragmatics). These accounts differ (...) from intuitionist semantic anti-realism by providing a way to distinguish the inferential significance of “A” and “A is warranted.” Although proof plays a central role, in neither accont is verification the primary bearer of meaning. Our accounts make these distinctions in terms of a subtle analysis of our practices. On the one hand according to Price and me, we assert as well as deny; on the other, Brandom distingushes downstream commitments from upstream entitlements and the notion of incompatibility definable in terms of these. In this paper I will examine a number connections between these different approaches, and end with a discussion of the kind of account of proof that might emerge from these considerations. (shrink)

Graham Priest defends the use of a nonmonotonic logic, LPm, in his analysis of reasoning in the face of true contradictions, such as those arising from the paradoxes of self-reference. In the course of defending this choice of logic in the face of the criticism that this logic is not truth preserving, Priest argued that requirement is too much to ask: since LPm is a nonmonotonic logic, it necessarily fails to preserve truth. In this article, I show that this assumption (...) is incorrect, and I explain why nonmonotonic logics can nonetheless be truth preserving. Finally, I diagnose Priest's error, to explain when nonmonotonic logics do indeed fail to preserve truth. (shrink)

Famously, Saul Kripke proposes that there are contingent a priori truths, and has offered a number of examples to illustrate his claim. The most well-known example involves the standard meter bar in Paris. Purportedly, a certain agent knows a priori that the bar is one meter long. However, in response to a long-standing objection to such examples - the "existential complaint" - generally only modified examples having a conditional form are now considered candidates for the contingent a priori. Gareth Evans (...) argues that these conditionals must be understood free-logically, and on this basis argues against Keith Donnellan's analysis of the contingent a priori. I show Evans' argument mistaken. I also take issue with the existential complaint, and suggest a way of understanding Kripke's original examples that is not subject to it. My approach focuses the debate in its right place, and allows us to take Kripke's original examples seriously. (shrink)

Proponents of “truth-value glut” responses to the paradoxes of self-reference, such as Priest [6, 7] argue that “truth-value gap” analyses of the paradoxes fall foul of the strengthened liar paradox: “this sentence is not true.” If we pay attention to the role of assertion and denial and the behaviour of negation in both “gap” and “glut” analyses, we see that the situation with these approaches has a pleasing symmetry: gap approaches take some denials to fail to be expressible by negation, (...) and glut approaches take some negations to not express denials. But in the light of this symmetry, considerations against a gap view point to parallel considerations against a glut view. Those who find some reason to prefer one view over another (and this is almost everyone) must find some reason to break this symmetry. (shrink)

Alasdair Urquhart’s work on models for relevant logics is distinctive in a number of different ways. One key theme, present in both his undecidability proof for the relevant logic R and his proof of the failure of interpolation in R, is the use of techniques from geometry. In this paper, inspired by Urquhart’s work, I explore ways to generate natural models of R+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document} from geometries, and different constraints that an accessibility relation (...) in such a model might satisfy. I end by showing that a set of natural conditions on an accessibility relation, motivated by geometric considerations, is jointly unsatisfiable. (shrink)

This note explains an error in Restall’s ‘Simplified Semantics for Relevant Logics (and some of their rivals)’ (Restall, J Philos Logic 22(5):481–511, 1993 ) concerning the modelling conditions for the axioms of assertion A → (( A → B ) → B ) (there called c 6) and permutation ( A → ( B → C )) → ( B → ( A → C )) (there called c 7). We show that the modelling conditions for assertion and permutation proposed (...) in ‘Simplified Semantics’ overgenerate. In fact, they overgenerate so badly that the proposed semantics for the relevant logic R validate the rule of disjunctive syllogism. The semantics provides for no models of R in which the “base point” is inconsistent. This problem is not restricted to ‘Simplified Semantics.’ The techniques of that paper are used in Graham Priest’s textbook An Introduction to Non-Classical Logic (Priest, 2001 ), which is in wide circulation: it is important to find a solution. In this article, we explain this result, diagnose the mistake in ‘Simplified Semantics’ and propose two different corrections. (shrink)

Stephen Read (2002, 2006) has recently discussed Bradwardine's theory of truth and defended it as an appropriate way to treat paradoxes such as the liar. In this paper, I discuss Read's formalisation of Bradwardine's theory of truth and provide a class of models for this theory. The models facilitate comparison of Bradwardine's theory with contemporary theories of truth.

This paper explores models for arithmetic in substructural logics. In the existing literature on substructural arithmetic, frame semantics for substructural logics are absent. We will start to fill in the picture in this paper by examining frame semantics for the substructural logics C (linear logic plus distribution), R (relevant logic) and CK (C plus weakening). The eventual goal is to find negation complete models for arithmetic in R.

I offer an interpretation of a familiar, but poorly understood portion of Tarskis work on truth – bringing to light a number of unnoticed aspects of Tarskis work. A serious misreading of this part of Tarski to be found in Scott Soames Understanding Truth is treated in detail. Soamesreading vies with the textual evidence, and would make Tarskis position inconsistent in an unsubtle way. I show that Soames does not finally have a coherent interpretation of Tarski. This is unfortunate, since (...) Soames ultimately arrogates to himself a key position that he has denied to Tarski and which is rightfully Tarskis own. (shrink)

summary of work in relevant in the Anderson– tradition.]; Mares Troestra, Anne, 1992, Lectures on , CSLI Publications [A quick, easy-to.

Consider this situation: Here are two envelopes. You have one of them. Each envelope contains some quantity of money, which can be of any positive real magnitude. One contains twice the amount of money that the other contains, but you do not know which one. You can keep the money in your envelope, whose numerical value you do not know at this stage, or you can exchange envelopes and have the money in the other. You wish to maximise your money. (...) What should you do?1 Here are three forms of reasoning about this situation, which we shall call.. (shrink)

In his 1993 Nicod Lectures (The Elm & the Expert), Jerry Fodor proposed a solution to a certain version of the problem of 'inscrutability of reference', which problem poses a challenge to a certain naturalistic, computational approach to cognition which Fodor has favored. The problem is that a purely informational account of an agent's mental contents cannot discriminate meanings finely enough. Fodor proposes a strategy of solution which appeals to the inferential dispositions of agents to discriminate contents more finely. After (...) a brief exposition of the problem and Fodor's bid for solution, I employ three counterexamples to argue that Fodor's proposal cannot succeed. (shrink)

The problem with model-theoretic modal semantics is that it provides only the formal beginnings of an account of the semantics of modal languages. In the case of non-modal language, we bridge the gap between semantics and mere model theory, by claiming that a sentence is true just in case it is true in an intended model. Truth in a model is given by the model theory, and an intended model is a model which has as domain the actual objects of (...) discourse, and which relates these objects in an appropriate manner. However, the same strategy applied to the modal case seems to require an intended modal model whose domain includes mere possibilia. Building on recent work by Christopher Menzel (Synthese 85 (1990)), I give an account of model-theoretic semantics for modal languages which does not require mere possibilia or intensional entities of any kind. Menzel has offered a representational account of model-theoretic modal semantics that accords with actualist scruples, since it does not require possibilia. However, Menzel's view is in the company of other actualists who seek to eliminate possible worlds, but whose accounts tolerate other sorts of abstract, intensional entities, such as possible states of affairs. Menzel's account crucially depends on the existence of properties and relations in intension. I offer a purely extensional, representational account and prove that it does all the work that Menzel's account does. The result of this endeavor is an account of model theoretic semantics for modal languages requiring nothing but pure sets and the actual objects of discourse. Since ontologically beyond what is prima facie presupposed by the model theory itself. Thus, the result is truly an ontology-free model-theoretic semantics for modal languages. That is to say, getting genuine modal semantics out of the model theory is ontologically cost-free. Since my extensional account is demonstrably no less adequate, and yet is at the same time more ontologically frugal, it is certainly to be preferred. (shrink)

Combining non-classical (or sub-classical) logics is not easy, but it is very interesting. In this paper, we combine nonclassical logics of negation and possibility (in the presence of conjunction and disjunction), and then we combine the resulting systems with intuitionistic logic. We will find that Kracht's results on the undecidability of classical modal logics generalise to a non-classical setting. We will also see conditions under which intuitionistic logic can be combined with a non-intuitionistic negation without corrupting the intuitionistic fragment of (...) the logic. (shrink)

Together, these stories and images convey a sense of reverence for the landscape and the playful joy felt by those who paddle north.

Reading Nietzsche, now available in English for the first time, is a group of essays that grew out of this monumental work.

I sketch an application of a semantically anti-realist understanding of the classical sequent calculus to the topic of mathematics. The result is a semantically anti-realist defence of a kind of mathematical realism. In the paper, I begin the development of the view and compare it to orthodox positions in the philosophy of mathematics.

We present an integrative review of research and theory on major factors involved in the early development of attentional biases to faces. Research utilizing behavioral, eye-tracking, and neuroscience measures with infant participants as well as comparative research with animal subjects are reviewed. We begin with coverage of research demonstrating the presence of an attentional bias for faces shortly after birth, such as newborn infants’ visual preference for face-like over non-face stimuli. The role of experience and the process of perceptual narrowing (...) in face processing are examined as infants begin to demonstrate enhanced behavioral and neural responsiveness to mother over stranger, female over male, own- over other-race, and native over non-native faces. Next, we cover research on developmental change in infants’ neural responsiveness to faces in multimodal contexts, such as audiovisual speech. We also explore the potential influence of arousal and attention on early perceptual preferences for faces. Lastly, the potential influence of the development of attention systems in the brain on social-cognitive processing is discussed. In conclusion, we interpret the findings under the framework of Developmental Systems Theory, emphasizing the combined and distributed influence of several factors, both internal (e.g., arousal, neural development) and external (e.g., early social experience) to the developing child, in the emergence of attentional biases that lead to enhanced responsiveness and processing of faces commonly encountered in the native environment. (shrink)

In his 1993 Nicod Lectures, Jerry Fodor proposed a solution to a certain version of the problem of‘inscrutability of reference’, which problem poses a challenge to a certain naturalistic, computational approach to cognition which Fodor has favoured. The problem is that purely informational accounts of an agent's mental contents cannot discriminate meanings finely enough. Fodor proposes a strategy of solution which appeals to the inferential dispositions of agents to discriminate contents more finely. After a brief exposition of the problem and (...) Fodor's bid for solution, I employ three counterexamples to argue that Fodor's proposal cannot succeed. (shrink)

According to Nancy Cartwright, a causal law holds just when a certain probabilistic condition obtains in all test situations which in turn satisfy a set of background conditions. These background conditions are shown to be inconsistent and, on separate account, logically incoherent. I offer a corrective reformulation which also incorporates a strategy for problems like Hesslow's thrombosis case. I also show that Cartwright's recent argument for modifying the condition to appeal to singular causes fails.Proposed modifications of the theory's probabilistic condition (...) to handle effects with extreme probabilities (0 or 1) are found unsatisfactory. I propose a unified solution which also handles extreme causes. Undefined conditional probabilities give rise to three good, but non-equivalent, ways of formulating the theory. Various formulations appear in the literature. I give arguments to eliminate all but one candidate. Finally, I argue for a crucial new condition clause, and show how to extend the results beyond a simple probabilistic framework. (shrink)