Present progress in mind science is racing away in the direction of denying the existence of human freewill and animal and human sentience. This brief paper attempts to summarise a few brief reasons why areas of present work by prominent authors have departed from fact to the realms of folk psychology and summarises some of the ways in which present work can be put right. An experiment is described and carried out in an attempt to breach a little more of (...) the present gap between experimental fact and the outmoded theory which others have tried to apply blindly.<br>. (shrink)

John Ellis McTaggart defended an idealistic view of time in the tradition of Hegel and Bradley. His famous paper makes two independent claims (McTaggart1908): First, time is a complex conception with two different logical roots. Second, time is unreal. To reject the second claim seems to commit to the first one, i.e., to a pluralistic account of time. We compare McTaggarts views to the most important concepts of time investigated in physics, neurobiology, and philosophical phenomenology. They indicate that (...) a unique, reductionist account of time is far from being plausible, even though too many conceptions of time may seem unsatisfactory from an ontological point of view. (shrink)

In this paper, I study one aspect of the philosophical encounter between Spinoza and Hegel: the question of the reality of time. The precise reconstruction of the debate will require a close examination of Spinoza's concept of tempus (time) and duratio (duration), and Hegel's understanding of these notions. Following a presentation of Hegel's perception of Spinoza as a modern Eleatic, who denies the reality of time, change and plurality, I turn, in the second part, to look closely at Spinoza's text (...) and show that Hegel was wrong in reading Spinoza as denying the reality of duration and change. Ironically, Hegel's misreading of Spinoza as denying the reality of duration and change has been compensated for by a reading of Hegel as denying the reality of time by one of Hegel's most prominent followers, John Ellis McTaggart. I discuss McTaggart's reading of Hegel's Logic in the final part of the paper. (shrink)

This paper argues that 'duality' accounts of time, as exemplified by Henri Bergson's, Edmund Husserl's, and John McTaggart's ideas, parallel the decomposition of temporal experience in depressive psychosis into objective and subjective dimensions of time. The paper also proposes to comprehend the full-fledged depressive temporal delusion, in which the subjective flow of time comes to a standstill, via the idea of a double orientation to reality characteristic of schizophrenic delusions. In the depressive temporal delusion a person claims that (...) time is not moving while simultaneously her cognitive orientation in temporal surroundings remains largely unaffected, hence the double orientation. The juxtaposition of temporal experience in depression with the temporal disorientation in dementia enables us to situate the depressive delusion regarding the flow of time in the middle of a proposed scale of the disintegration of normal temporal experience. (shrink)

We find the claim that time is not real in both western and eastern philosophical traditions. In what follows I will call the view that time does not exist temporal error theory. Temporal error theory was made famous in western analytic philosophy in the early 1900s by John McTaggart (1908) and, in much the same tradition, temporal error theory was subsequently defended by Gödel (1949). The idea that time is not real, however, stretches back much further than that. (...) It is common to hear it said that according to Buddhist philosophy (as though that were a monolithic view) time is illusory. While it is not true that, in general, either contemporary or ancient Buddhist scholars have thought time to be illusory, there are certainly some schools of Buddhist thought, such as that of traditional Dzogchen practitioners, according to which there is no time. This paper is an attempt to set out a taxonomy of different views about what it takes for there to be time and, alongside that, a taxonomy of views about whether there is time or not, and if there is time what it is like. (shrink)

In this paper, I try to make sense of the growing block view using Kit Fine’s three-fold classification of A-theoretic views of time. I begin by motivating the endeavor of making sense of the growing block view by examining John Earman’s project in ‘Reassessing the prospects for a growing block model of the universe’. Next, I review Fine’s reconstruction of McTaggart’s argument and its accompanying three-fold classification of A-theoretic views. I then consider three interpretations of Earman’s growing block (...) model: the hybrid growing block, the purely tensed growing block, and Michael Tooley’s growing block. I argue for three claims. First, Finean ‘standard’ versions of these views are less congenial to the growing blocker than ‘non-standard’ ones. Second, the hybrid view is problematic on either version. And third, ‘non-standard’ versions are not fully intelligible. I provide further support for the first and third of these claims and explain why I take them to support a minimal account of passage as succession, which undercuts some of the motivation for Earman’s project. Lastly, I answer three objections. (shrink)

I present a new problem for the tense realist concerning the evaluation of cross-temporal claims, such as ‘John is now taller than Michael was in 1984’. Time can play two different roles in the evaluation of an utterance of a sentence: either as an element that completes the content expressed by the utterance (the completion role), or as part of the circumstances against which the content is evaluated (the evaluation role). It is this latter role that time plays in (...) the realist view of tenses. I argue that if the content of a cross-temporal sentence is taken at face value (as an ascription of a crosstemporally instantiated relation), time does not play the evaluation role. Therefore, the world of the tense realist seems to leave no room for cross-temporality. (shrink)

According to factive accounts of the norm of belief and decision-making, you should not believe or base decisions on a falsehood. Even when the evidence misleadingly suggests that a false proposition is true, you should not believe it or base decisions on it. Critics claim that factive accounts are counterintuitive and badly mischaracterize our ordinary practice of evaluating beliefs and decisions. This paper reports four experiments that rigorously test the critic’s accusations and the viability of factive accounts. The results undermine (...) the accusations and provide the best evidence yet of factive norms of belief and decision-making. The results also help discriminate between two leading candidates for a factive norm: truth and knowledge. Knowledge is the superior candidate. (shrink)

We present Backward Clock, an original counterexample to Robert Nozick’s truth-tracking analysis of propositional knowledge, which works differently from other putative counterexamples and avoids objections to which they are vulnerable. We then argue that four ways of analysing knowledge in terms of safety, including Duncan Pritchard’s, cannot withstand Backward Clock either.

A collaborative article by the Editorial Collective of Social Imaginaries. Investigations into social imaginaries have burgeoned in recent years. From ‘the capitalist imaginary’ to the ‘democratic imaginary’, from the ‘ecological imaginary’ to ‘the global imaginary’ – and beyond – the social imaginaries field has expanded across disciplines and beyond the academy. The recent debates on social imaginaries and potential new imaginaries reveal a recognisable field and paradigm-in-the-making. We argue that Castoriadis, Ricoeur, and Taylor have articulated the most important theoretical frameworks (...) for understanding social imaginaries, although the field as a whole remains heterogeneous. We further argue that the notion of social imaginaries draws on the modern understanding of the imagination as authentically creative. We contend that an elaboration of social imaginaries involves a significant, qualitative shift in the understanding of societies as collectively and politically-instituted formations that are irreducible to inter-subjectivity or systemic logics. After marking out the contours of the field and recounting a philosophical history of the imagination, the essay turns to debates on social imaginaries in more concrete contexts, specifically political-economic imaginaries, the ecological imaginary, multiple modernities and their inter-civilisational encounters. The social imaginaries field imparts powerful messages for the human sciences and wider publics. In particular, social imaginaries hold significant implications for ontological, phenomenological and philosophical anthropological questions; for the cultural, social, and political horizons of contemporary worlds; and for ecological and economic phenomena. The essay concludes with the argument that social imaginaries as a paradigm-in-the-making offers valuable means by which movements towards social change can be elucidated as well providing an open horizon for the critiques of existing social practices. (shrink)

Recent work has shown that knowledge attributions affect how people think others should behave, more so than belief attributions do. This paper reports two experiments providing evidence that knowledge attributions also affect behavioral predictions more strongly than belief attributions do, and knowledge attributions facilitate faster behavioral predictions than belief attributions do. Thus, knowledge attributions play multiple critical roles in social cognition, guiding judgments about how people should and will behave.

In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...) by means of a formal deduction in the system. Review of the system makes the first point obvious. The purpose of the present article is to prove the second. Strong completeness is demonstrated for the Aristotelian system. (shrink)

Cognitivism in respect to the arts refers to a constellation of positions that share in common the idea that artworks often bear, in addition to aesthetic value, a significant kind of cognitive value. In this paper I concentrate on three things: (i) the challenge of understanding exactly what one must do if one wishes to defend a cognitivist view of the arts; (ii) common anti-cognitivist arguments; and (iii) promising recent attempts to defend cognitivism.

The A-theory and the B-theory advance competing claims about how time is grounded. The A-theory says that A-facts are more fundamental in grounding time than are B-facts, and the B-theory says the reverse. We argue that whichever theory is true of the actual world is also true of all possible worlds containing time. We do this by arguing that time is uniquely groundable: however time is actually grounded, it is necessarily grounded in that way. It follows that if either the (...) A-theory or the B-theory is actually false, then it is necessarily false. (shrink)

For each positive n , two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are definitionally equivalent [or synonymous in the sense of deBouvere]. It (...) is further shown that each member of one class is synonymous with each member of the other class; thus that all of the theories are definitionally equivalent with each other and with Peano arithmetic. Categoricity of Peano arithmetic then implies categoricity of each of the above theories. (shrink)

The journal of Cognitive Computation is defined in part by the notion that biologically inspired computational accounts are at the heart of cognitive processes in both natural and artificial systems. Many studies of various important aspects of cognition (memory, observational learning, decision making, reward prediction learning, attention control, etc.) have been made by modelling the various experimental results using ever-more sophisticated computer programs. In this manner progressive inroads have been made into gaining a better understanding of the many components of (...) cognition. Concomitantly in both science and science fiction the hope is periodically re-ignited that a manmade system can be engineered to be fully cognitive and conscious purely in virtue of its execution of an appropriate computer program. However, whilst the usefulness of the computational metaphor in many areas of psychology and neuroscience is clear, it has not gone unchallenged and in this article I will review a group of philosophical arguments that suggest either such unequivocal optimism in computationalism is misplaced—computation is neither necessary nor sufficient for cognition—or panpsychism (the belief that the physical universe is fundamentally composed of elements each of which is conscious) is true. I conclude by highlighting an alternative metaphor for cognitive processes based on communication and interaction. (shrink)

Argumentations are at the heart of the deductive and the hypothetico-deductive methods, which are involved in attempts to reduce currently open problems to problems already solved. These two methods span the entire spectrum of problem-oriented reasoning from the simplest and most practical to the most complex and most theoretical, thereby uniting all objective thought whether ancient or contemporary, whether humanistic or scientific, whether normative or descriptive, whether concrete or abstract. Analysis, synthesis, evaluation, and function of argumentations are described. Perennial philosophic (...) problems, epistemic and ontic, related to argumentations are put in perspective. So much of what has been regarded as logic is seen to be involved in the study of argumentations that logic may be usefully defined as the systematic study of argumentations, which is virtually identical to the quest of objective understanding of objectivity. (shrink)

After a short preface, the first of the three sections of this paper is devoted to historical and philosophic aspects of categoricity. The second section is a self-contained exposition, including detailed definitions, of a proof that every mathematical system whose domain is the closure of its set of distinguished individuals under its distinguished functions is categorically characterized by its induction principle together with its true atoms (atomic sentences and negations of atomic sentences). The third section deals with applications especially those (...) involving the distinction between characterizing a system and axiomatizing the truths of a system. (shrink)

This article argues that the word ψυχαγωγία and its cognates which are found in the writings of Philodemus retain a semantic connection to the domain of magic and are best translated in terms of ‘enchantment’ rather than the more generic sense of ‘entertainment’.

The paper explores the handling of singular analogy in quantitative inductive logics. It concentrates on two analogical patterns coextensive with the traditional argument from analogy: perfect and imperfect analogy. Each is examined within Carnap’s λ-continuum, Carnap’s and Stegmüller’s λ-η continuum, Carnap’s Basic System, Hintikka’s α-λ continuum, and Hintikka’s and Niiniluoto’s K-dimensional system. Itis argued that these logics handle perfect analogies with ease, and that imperfect analogies, while unmanageable in some logics, are quite manageable in others. The paper concludes with a (...) modification of the K-dimensional system that synthesizes independent proposals by Kuipers and Niiniluoto. (shrink)

Thirteen meanings of 'implication' are described and compared. Among them are relations that have been called: logical implication, material implication,deductive implication, formal implication, enthymemic implication, and factual implication. In a given context, implication is the homogeneous two-place relation expressed by the relation verb 'implies'. For heuristic and expository reasons this article skirts many crucial issues including use-mention, the nature of the entities that imply and are implied, and the processes by which knowledge of these relations are achieved. This paper is (...) better thought of as an early stage of a dialogue than as a definitive treatise. (shrink)

One innovation in this paper is its identification, analysis, and description of a troubling ambiguity in the word ‘argument’. In one sense ‘argument’ denotes a premise-conclusion argument: a two-part system composed of a set of sentences—the premises—and a single sentence—the conclusion. In another sense it denotes a premise-conclusion-mediation argument—later called an argumentation: a three-part system composed of a set of sentences—the premises—a single sentence—the conclusion—and complex of sentences—the mediation. The latter is often intended to show that the conclusion follows from (...) the premises. The complementarity and interrelation of premise-conclusion arguments and premise-conclusion-mediation arguments resonate throughout the rest of the paper which articulates the conceptual structure found in logic from Aristotle to Tarski. This 1972 paper can be seen as anticipating Corcoran’s signature work: the more widely read 1989 paper, Argumentations and Logic, Argumentation 3, 17–43. MR91b:03006. The 1972 paper was translated into Portuguese. The 1989 paper was translated into Spanish, Portuguese, and Persian. (shrink)

As a topic in the philosophy of psychology, dreaming is a fascinating, diverse, and severely underdeveloped area of study. The topic excites intense public interest in its own right, while also challenging our confidence that we know what the words “conscious” and “consciousness” mean. So dreaming should be at the forefront of our interdisciplinary investigations: theories of mind which fail to address the topic are incomplete. This chapter illustrates the tight links between conceptual and empirical issues by highlighting surprisingly deep (...) disagreements among leading dream scientists over what might seem basic aspects of their topic. (shrink)

The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this paper (...) is to demonstrate that ordinary English properly used has the resources for intricate and philosophically sound investigation of rather deep issues in logic and philosophy of language. No mathematical, logical, or linguistic symbols are used. Meanings need to be identified and clarified before being expressed in symbols. We hope to establish that clarity is served by deferring the extensive use of formalized or logically perfect languages until a solid “informal” foundation has been established. Questions of “ontological status”—e.g., whether propositions or sentences, or for that matter characters, numbers, truth-values, or instants, are “real entities”, are “idealizations”, or are “theoretical constructs”—plays no role in this paper. As is suggested by the title, this paper is written to be read aloud. -/- I hope that reading this aloud in groups will unite people in the enjoyment of the humanistic spirit of analytic philosophy. (shrink)

This study concerns logical systems considered as theories. By searching for the problems which the traditionally given systems may reasonably be intended to solve, we clarify the rationales for the adequacy criteria commonly applied to logical systems. From this point of view there appear to be three basic types of logical systems: those concerned with logical truth; those concerned with logical truth and with logical consequence; and those concerned with deduction per se as well as with logical truth and logical (...) consequence. Adequacy criteria for systems of the first two types include: effectiveness, soundness, completeness, Post completeness, "strong soundness" and strong completeness. Consideration of a logical system as a theory of deduction leads us to attempt to formulate two adequacy criteria for systems of proofs. The first deals with the concept of rigor or "gaplessness" in proofs. The second is a completeness condition for a system of proofs. An historical note at the end of the paper suggests a remarkable parallel between the above hierarchy of systems and the actual historical development of this area of logic. (shrink)

A philosophical analysis of different kinds of memory used in the film Memento.

A plausible thought about vagueness is that it involves semantic incompleteness. To say that a predicate is vague is to say (at the very least) that its extension is incompletely specified. Where there is incomplete specification of extension there is indeterminacy, an indeterminacy between various ways in which the specification of the predicate might be completed or sharpened. In this paper we show that this idea is bound to founder by presenting an argument to the effect that there are vague (...) predicates which cannot be sharpened in such a way as to meet certain basic constraints (of penumbral connection and public accessibility) that must be imposed on the very notion of a sharpening. (shrink)

Worrall argued that structural realism provides a ‘synthesis’ of the main pro-realist argument – the ‘No Miracles Argument’, and the main anti-realist argument – the ‘Pessimistic Induction’. More recently, however, it has been claimed that each of these arguments is an instance of the same probabilistic fallacy – sometimes called the ‘base-rate fallacy’. If correct, this clearly seems to undermine structural realism and Magnus and Callender have indeed claimed that both arguments are fallacious and ‘without [them] we lose the rationale (...) for … structural realism ’. I here argue that what have been shown to be fallacious are simply misguided formalisations of ‘the’ arguments and that when they are properly construed they continue to provide powerful motivation for favouring structural realism. (shrink)

That in Gettier's alleged counterexamples to the traditional analysis of knowledge as justified true belief the belief condition is satisfied has rarely been questioned. Yet there is reason to doubt that a rational person would come to believe what Gettier's protagonists are said to believe in the way they are said to have come to believe it. If they would not, the examples are not counter-examples to the traditional analysis. I go on to discuss a number of examples inspired by (...) Gettier's and argue that they, too, fail to be counter-examples either for reasons similar to those I have urged or because it is not clear that their subject does not know. (shrink)

An encyclopedic article on epistemic supervenience in Blackwell companion to epistemology, 2 ed.

Climate negotiations under the United Nations Framework Convention on Climate Change have so far failed to achieve a robust international agreement to reduce greenhouse gas emissions. Game theory has been used to investigate possible climate negotiation solutions and strategies for accomplishing them. Negotiations have been primarily modelled as public goods games such as the Prisoner’s Dilemma, though coordination games or games of conflict have also been used. Many of these models have solutions, in the form of equilibria, corresponding to possible (...) positive outcomes—that is, agreements with the requisite emissions reduction commitments. Other work on large-scale social dilemmas suggests that it should be possible to resolve the climate problem. It therefore seems that equilibrium selection may be a barrier to successful negotiations. Here we use an N-player bargaining game in an agent-based model with learning dynamics to examine the past failures of and future prospects for a robust international climate agreement. The model suggests reasons why the desirable solutions identified in previous game-theoretic models have not yet been accomplished in practice and what mechanisms might be used to achieve these solutions. (shrink)

I objected that the defeasibility theory of knowledge prohibits you from knowing that you know that p if your knowledge that p is a posteriori. Rodrigo Borges claims that Peter Klein has already satisfactorily answered a version of my objection. He attempts to defend Klein’s reply and argues that my objection fails because a principle on which it is based is false.I will show that my objection is not a version of the old one that Klein attempts (unsuccessfully) to address, (...) that Borges’ defence of Klein’s reply fails and that his argument against my new objection leaves it untouched. (shrink)

This essay consists of two parts. Part I offers an explanation of Berkeley's understanding of the relationship between materialism and evil. Berkeley regards materialism as the chief instrumental cause of evil in the world. It is the belief in matter that encourages us to believe that God is not immediately, intimately present in every aspect of our life. Immaterialism, by contrast, makes God's immediate presence vivid and thereby serves to undermine the motivation to vice. Part II locates Berkeley's view on (...) matter and evil within the Christian Neoplatonic tradition. I compare Plotinus' minimalist approach to matter and his identification of matter with evil to Berkeley's eliminitivism about matter and his corresponding identification of materialism as the chief source of evil. (shrink)

K.L. Reinhold advocates a theory of free will as the capacity to choose for or against the moral law. Reinhold’s theory has often been accused of being psychologistic due to its alleged appeal to empirical facts of consciousness. This paper argues that instead of merely positing free will as a fact of consciousness, Reinhold provides an argument for free will as a necessary condition for moral responsibility. This sheds new light on the development of the concept of will in the (...) wake of Kant’s practical philosophy. (shrink)

A core feature of Kant’s Critical account of moral motivation is that pure reason can be practical by itself. I argue that Kant developed this view in the 1770s concerning the principium diiudicationis and principium executionis. These principles indicate the normative and performative aspects of moral motivation. I demonstrate that cognition of the normative principle effects the moral incentive. So, the hallmark of Kant’s Critical account of motivation was contained in his pre-Critical view. This interpretation resolves a controversy about Kant’s (...) apparent eudaimonism in the first Critique and shows that he developed his account of moral autonomy in the 1770s. (shrink)

The meaning of an utterance is often enriched by the pragmatic context in which it is uttered. This is because in ordinary conversations we routinely and uncontroversially compress what we say, safe in the knowledge that those interpreting us will ‘add in’ the content we intend to communicate. Does the same thing hold true in the case of legal utterances like ‘This constitution protects the personal rights of the citizen’ or ‘the parliament shall have the power to lay and collect (...) taxes’? This article addresses this question from the perspective of the constitutional originalist—the person who holds that the meaning of a constitutional text is fixed at some historical moment. In doing so, it advances four theses. First, it argues that every originalist theory is committed to some degree of pragmatic enrichment, the debate is about how much. Second, that in determining which content gets ‘added in’, originalists typically hold to a common knowledge standard for enrichment, protestations... (shrink)

In Social Imaginaries, vol. 1, nr. 1 (Spring 2015) due out in May 2015.

This is an encyclopedia article about epistemic closure principles. The article explains what they are, their various philosophical uses, how they are argued for or against, and provides an overview of the related literature.

This issue of the Kybernetes journal is concerned with the philosophical question- Can a Machine Think? Famously, in his 1950 paper `Computing Machinery andIntelligence' [9], the British mathematician Alan Turing suggested replacing this question - which he found \too meaningless to deserve discussion" - with a simple -behavioural - test based on an imagined `Victorianesque' pastime he entitled the`imitation game'. In this special issue of Kybernetes a selection of authors with a special interest in Turing's work (including those who participated (...) in the 2008 AISB Turing Symposium) have been invited to explore and clarify issues arising from Turing's 1950 paper on the Imitation Game; now more widely known as the Turing test. (shrink)

Fifty years ago this year a legal practitioner turned military intelligencer turned philosopher, Herbert Hart, published The Concept of Law, still deservedly best-seller in thought about law. It presents law, especially common law and constitutionally ordered systems such as ours, as a social reality which results from the sharing of ideas and making of decisions that, for good or evil, establish rules of law which are what they are, whether just or unjust. But right at its centre is a chapter (...) on justice, informed by Hart’s professional knowledge of Plato and Aristotle and the tradition of civilized thought about justice, thought which he sums up like this: “the general principle latent in [the] diverse applications of the idea of justice is that individuals are entitled in respect of each other to a certain relative position of equality or inequality.” “Hence”, he goes on, “[the] leading precept [of justice] is often formulated as ‘Treat like cases alike’; though we need to add … ‘and treat different cases differently’”. This article will say something about three aspects of this vast topic: (i) about the factual basis and normative grounds of equality; (ii) about the proposed principle of equal concern; and (iii) about laws and social policies that pursue equality by selective prohibition of direct and indirect discrimination, and of harassment or vilification, victimisation and offence. (shrink)

Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the last: the (...) parallel postulate. -/- Euclid’s axioms are general principles of magnitude: they concern geometric magnitudes and magnitudes of other kinds as well even numbers. The first is often translated “Things that equal the same thing equal one another”. -/- There are other differences that are or might become important. -/- Aristotle [fl. 350 BCE] meticulously separated his basic principles [archai, singular archê] according to subject matter: geometrical, arithmetic, astronomical, etc. However, he made no distinction that can be assimilated to Euclid’s postulate/axiom distinction. -/- Today we divide basic principles into non-logical [topic-specific] and logical [topic-neutral] but this too is not the same as Euclid’s. In this regard it is important to be cognizant of the difference between equality and identity—a distinction often crudely ignored by modern logicians. Tarski is a rare exception. The four angles of a rectangle are equal to—not identical to—one another; the size of one angle of a rectangle is identical to the size of any other of its angles. No two angles are identical to each other. -/- The sentence ‘Things that equal the same thing equal one another’ contains no occurrence of the word ‘magnitude’. This paper considers the problem of formalizing the proposition Euclid intended as a principle of magnitudes while being faithful to the logical form and to its information content. (shrink)